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Number Sense
May 25, 2014 8:00 PM   Subscribe

Five reasons not to share that Common Core worksheet on Facebook

Context: Only tangentially related bonus: Math Class Needs a Makeover
posted by eviemath (202 comments total) 41 users marked this as a favorite

 
We parents absolutely should share that Common Core worksheet on Facebook. We just need to have different goals when we share it. Instead of pointing at it and saying "What is this shit?!?!", we should be sharing it with the intention of trying to understand it.

We can't realistically expect the teachers to teach us what each new method is doing/ how it works. And the materials, as far as I can tell, are written just for the kids, and there's not a lot to help the parents understand what's going on. So the parents need to help each other out.

In that spirit, this is what I wrote on Facebook when I saw this:
Parents hoping to help their kids with their math homework might be surprised to see that their kids are learning things differently. I encourage people to keep an open mind about the new approaches being taught, for a couple reasons.

First, you may need to actually help your kid with it, and it's hard to learn something if you're too busy rejecting it.

Second, the new methods are often not considered to be "the" way to solve a problem, but each as one tool in a box of varied methods. Any given problem might be easier to solve with one or another tool. Even if a particular method seems inefficient for some or even most possible combinations of numbers, it's worth learning if it works well in a common enough case, or more importantly teaches you something new about how numbers connect or relate.

Think for a moment about how you drive from an address in one city to an address in another city. Ultimately you'd like to use a freeway, but chances are, you have to take a couple smaller roads to get to an on ramp first. So you go from whatever out-of-the-way road you're on to progressively larger and faster roads; then, after you've made it to the city you need to get to, you end up exiting the freeway and going on smaller and slower roads until you get to the exact place you were interested in.

Anyway, if you're thinking along those lines, this "new" approach to subtraction will make sense. Starting from the subtrahend, you add upward to get to progressively rounder numbers, where the work is fast and easy, and then take an exit to the specific neighborhood you need to get to.
posted by Jpfed at 8:19 PM on May 25 [73 favorites]


I favorited Jpfed's comment, not just because I basically agree with it, but because he used the word "subtrahend."
posted by escabeche at 8:22 PM on May 25 [15 favorites]


i don't know what's worse - the baroque methods being used to teach simple math these days or the pretense that 99% of the students aren't going to grow up, say fuck it, and use a calculator
posted by pyramid termite at 8:26 PM on May 25 [8 favorites]


When I saw that "Frustrated Parent" letter on my Facebook feed I had to sit on my hands.

The disdain for teachers is just amazing - and to be honest, I can't help but wonder how much of it is due to the devaluing of professions that are female-dominated.

On the other hand, I feel a lot of what I think is justified bitterness towards the system, having entered college needing to take remedial math courses due to the extremely poor quality of instruction that I received. The teachers probably weren't responsible for most of the decisions that made the instruction poor, but they were - as that blog post points out - the public face of it. Actually, I had everything going for me: I was good at math, I was from a stable, financially comfortable family that valued school performance. I did well in the classes they put me in in high school, but when I got to college, I found nothing had stuck. The way I was taught was just too incoherent.

But that was the old system. The one that didn't work.

As a personal side note, I know one brilliant, passionate math educator who just quit due to how awful the working conditions are. We really are sabotaging our kids when we drive people like that away.
posted by Kutsuwamushi at 8:32 PM on May 25 [12 favorites]


I love how people seem to be able to simultaneously up in arms about how teaching methods have changed (as if you should not want things to change/improve over time), and yet the vast majority of them probably can no longer do anything more advanced than everyday adding/subtraction (and maybe not even that -- I can hand someone $22.50 when my bill is $12.50 and they look at me like I'm the idiot). Attempting to mock these worksheets, especially out of context, just makes the mocker look stupid.
posted by axiom at 8:37 PM on May 25 [3 favorites]


I just refer people to Tom Lehrer's "New Math".
posted by Tell Me No Lies at 8:38 PM on May 25 [15 favorites]


I don't think there's a disdain for teachers. The teachers are just doing their jobs per state curriculum, right? (Personally, I think these number lines are ridiculous, and would teach my kid the "real" way to subtract at home.)
posted by roomthreeseventeen at 8:39 PM on May 25 [1 favorite]


The use of "algorithm" in the first linked article was slightly odd to my ear. Is it common in math pedagogy to refer to problem-solving processes that way?
posted by clockzero at 8:41 PM on May 25


Subtrahend? Stick a feather in it and call it macaroni...

I had many instances in school of "getting it" in my head, but not via the method that was taught. Many more for having the correct answer, but not "showing my work." I recall trying once to explain to a teacher that I could "see" the answer, but not being able to explicate how I arrived at that answer...FAIL.

At university, I was marked down for using recursion in a CS assignment, because "we haven't covered that in the class yet...."

Gist: Students should be encouraged to work things out other than the standardized/taught official methods. This fixed, common-core (stick a feather in that one too) rigidity is stifling.
posted by CrowGoat at 8:41 PM on May 25 [5 favorites]


Roomthreeseventeen, that's all well and good once your kid understands how subtraction works in the first place, but there's a lot to be said for explaining the concept before explaining the shortcut that happens to work. Turns out that education definitely isn't a "one size fits all" process; if you were one of the ones it did fit at the time, it's easy not to notice or realize this.
posted by DoctorFedora at 8:42 PM on May 25 [9 favorites]


Parents complaining about not being able to help their kids with their homework is precisely the reason we need these higher standards.
posted by inturnaround at 8:43 PM on May 25 [6 favorites]


For people who think number lines are ridiculous: when you do mental math, how do you do it? I do the mental equivalent of number lines, and I don't think I'm unusual.

Yes, you also need to learn the standard method, but I use a number line concept far, far more often in daily life.
posted by jeather at 8:44 PM on May 25 [22 favorites]


A sixth reason: Angry idiots will be afraid you're turning kids gay.
posted by kafziel at 8:44 PM on May 25 [1 favorite]


Ok, so I majored in math, but not at first. I started out college absolutely terrified of math because it wasn't taught with any consistency or passion in high school, but when I became more acquainted with the notion of "math as muscle", it started to become more appealing and accessible.

Math defines our lives, and we need to make the easy stuff digestible for the youngins so that they lose their fear.
posted by oceanjesse at 8:48 PM on May 25 [3 favorites]


Jeather said what I was going to say. There's little point in teaching your kid to "do it the real way", when, actually, the new way is the real way and the old way is a polite fiction we cling to out of a sense of tradition.
posted by Sara C. at 8:51 PM on May 25 [7 favorites]


Hmm. So, I'm curious. China, Korea, and Japan all seem to do better in math -- at least as reported on most published rankings -- than the US does. So, for that matter, do Canada and the UK. What do they do? Is it number lines? Rote drill? Can we copy their success?
posted by tyllwin at 8:52 PM on May 25 [3 favorites]


4. Anecdotal evidence is not research data.

But it is a significant starting point. I would just love if I went to the cops to tell them I was mugged and they said, "Sorry, lady, that's anecdotal evidence."

That is bad logic that is quite manipulative -- just as anecdotal evidence needs to be investigated because it can be truthful and helpful, so does "research data" because studies can be flawed or fraudulent, too.

It is that kind of dismissive thinking that makes me very uneasy. If that many parents are profoundly unhappy with what's going on, then yes, let's take a closer look at the smoke to see if there is a fire...
posted by Alexandra Kitty at 8:52 PM on May 25 [8 favorites]


Jeather said what I was going to say. There's little point in teaching your kid to "do it the real way", when, actually, the new way is the real way and the old way is a polite fiction we cling to out of a sense of tradition.

I don't think so. (And I was an education major.) I, honestly, do math in my head. And yes, clearly the way I learned worked for me, and that was lucky, but there are going to be some kids who don't need or want this way, too.
posted by roomthreeseventeen at 8:53 PM on May 25 [2 favorites]


A sixth reason: Angry idiots will be afraid you're turning kids gay.

Well that was a new one. The thing that baffles me is that none of the CC opponents seem to realize that it's voluntary.
posted by MikeMc at 8:56 PM on May 25 [1 favorite]


i don't know what's worse - the baroque methods being used to teach simple math these days or the pretense that 99% of the students aren't going to grow up, say fuck it, and use a calculator

Here's the thing, though.

It's not just about being able to perform simple math, but to understand it and to be comfortable with it. Mathematical competence is a lot more than being able to apply an algorithm by rote.

It's true that most people won't go on to use much more than simple arithmetic in their daily lives. However, some of them will go on to become actuaries, engineers, physicists, social scientists, architects, chemists, and so on. If we just declare that mathematical competence is useless because 90% of them will find it irrelevant, we're hobbling the 10% who would go on to use it, if only we gave them the chance.

(Personally, I think these number lines are ridiculous, and would teach my kid the "real" way to subtract at home.)

You've probably missed the point of the assignment then.

I would also teach my kids the "real" way to subtract at home - although I might not have to, because that's already required by the common core, as pointed out in the article. I would show them alternative ways to think about basic arithmetic too, because illustrating a concept in different ways can be very beneficial when trying to build conceptual understanding. I wouldn't want my kids to have a list of algorithms memorized for particular situations. I would want them to have strong mathematical reasoning skills, which involves having a strong conceptual understanding and the ability to be flexible (which are closely related).
posted by Kutsuwamushi at 8:56 PM on May 25 [41 favorites]


You, like, carry the one and such, in your head?

Good for you, I suppose.
posted by Sara C. at 8:57 PM on May 25 [3 favorites]


There is no profession in the United States more prone to armchair quarterbacking than the teaching profession. Because everyone went to school at one point and everyone had at least one really bad teacher, that makes everyone an expert on education.

On the other hand, some of us actually studied education and know the nuances of assessment, instruction, and testing, and that that posting your outrage about this stuff betrays a certain ignorance of material that is completely without context. I can't speak for elementary math techniques (I'm in secondary language arts), but if a student is being assessed in this strange way*, then that student must have been taught that strange way previously. If that original instruction was never done, then that would be the problem, not necessarily an alternative method.

*Yes, it's strange to me, too. Why? Because no one has taught me that technique before. If a teacher had, then it wouldn't be strange.
posted by zardoz at 9:02 PM on May 25 [17 favorites]


Ok, so I majored in math, but not at first. I started out college absolutely terrified of math

I had a similar experience. I started out college needing remedial math, and ended up majoring in it. I wasn't terrified of it, but I easily could have been! I think about all of the kids in my situation who just gave up on math and therefore didn't have the same range of opportunities I did.
posted by Kutsuwamushi at 9:02 PM on May 25 [2 favorites]


Can I think that number lines look reasonable while still thinking the "write a letter" problem shown was pretty silly?
posted by markr at 9:03 PM on May 25 [6 favorites]


The thing that baffles me is that none of the CC opponents seem to realize that it's voluntary.

Just like so many things in life are "voluntary".

If you don't like your metadata being used and sold, just don't give it to the people using it and selling it, right?

Somehow I'm guessing that if you don't volunteer for CC there are pushback methods for not agreeing.
posted by rough ashlar at 9:04 PM on May 25 [1 favorite]


"Somehow I'm guessing that if you don't volunteer for CC there are pushback methods for not agreeing."

If there are I'm not aware of what they are. AFAIK CC hasn't been adopted by all 50 states and one that did (Indiana) has since dropped it.
posted by MikeMc at 9:08 PM on May 25


All I know is that homework is the bane of my existence as a parent. It's pointless and a waste of time.
posted by KokuRyu at 9:09 PM on May 25 [6 favorites]


The number lines are not how I was taught to solve a subtraction problem with pencil and paper, no. But c'mon, that's how you do subtraction in your head once you've mastered subtraction. Teaching them is a good thing, because it helps kids visualize subtraction in a way that translates directly to how mental subtraction is done.
posted by kafziel at 9:13 PM on May 25 [3 favorites]


I also have no problem with Jack's algorithm as mental arithmetic, but I still think the worksheet in the blog post is ridiculous. The "number line" is way more confusing than just writing out the sequence of operations:

427 - 300 = 127
127 - ..10 = 117
117 - ....6 = 111

(or 427 - 100 - 100 - 100 = 127 to match the algorithm exactly)

The exercise itself does a terrible job of teaching a trivial lesson ("don't forget the tens, if there are tens"). I suppose it would make sense as an example done orally in class, or on the blackboard. As a homework exercise it's contrived, as if the teacher were teaching their training rather than applying it. Problem-solving somebody's mental arithmetic is getting lost in the details.
posted by ormon nekas at 9:16 PM on May 25 [10 favorites]


Surely we can agree that teachers are simultaneously caring, selfless people and bad at their jobs. They're the complete opposite of Goldman Sachs executives -- embrace it!
posted by michaelh at 9:17 PM on May 25 [4 favorites]


Well, you get better teachers if you give the teaching profession enough respect and resources. There's only so much any one caring, selfless person can do.
posted by ormon nekas at 9:26 PM on May 25 [12 favorites]


Actually I would have found this approach a lot more useful when I was little than what I was actually taught. I found that to be completely mystifying. It seemed to assume a lot of a priori knowledge and reasoning that I completely lacked. In 7th or 8th grade when we did formal logic I had a tutor who just explained it using logic instead of expecting me to memorize a bunch of stuff that didn't make sense and suddenly my whole mind opened up. I was pretty pissed off that I had been failing at this one thing my whole life for no real reason.
posted by bleep at 9:30 PM on May 25 [5 favorites]


Clock zero, yes that's the standard word now. It's the correct way to describe it and also hopefully gets kids comfortable with the word/concept.
posted by chaz at 9:34 PM on May 25 [1 favorite]


I'm not sure if I've said this before here, but I repeat it ad nauseum: I pretty much taught myself how to do a lot of math in my head as a child, and the way the Common Core worksheets everybody is terrified of do the math is exactly the way my brain has always done it. I don't even like math very much and I have always been considered "good at math". All that skipping around by tens and hundreds and whatnot, once you're used to it, is very fast. Carrying and borrowing ones is not.

And yes, eventually, kids will generally use calculators for most things, but you should not need to have a calculator on hand for every single situation where you could possibly be doing double- or triple-digit addition and subtraction. Often in those cases, the point isn't so much that you need a precise dollar figure, it's that you need to know that you had $780-something in the bank before you went to the grocery, and that grocery trip has rung up to be $112. Quick, are you going to have enough money to not bounce your rent check after you leave the store, when you've got three days before payday, or do you need to put something back and make a whole new trip to the grocery store in three days? Oh, and your phone lost charge two hours ago. There are a lot of little ways it helps to be comfortable with those numbers.
posted by Sequence at 9:35 PM on May 25 [20 favorites]


I know I'm supposed to feel compassion for math teachers as a result of this post, but I feel nothing but numb horror that this is what basic elementary school math has become. Story problems can be useful things to test on, and considering alternate ways of approaching a problem is great and all, but those are really testing para-mathematics skills, not basic skills. IMHO.
posted by deathpanels at 9:38 PM on May 25


The "number line" is way more confusing than just writing out the sequence of operations:

427 - 300 = 127
127 - ..10 = 117
117 - ....6 = 111


But then what happens when you have:

407 - 300 = 107
107 - ..10 = 1(-1)7
???

Like yes obviously 107 - 10 is still 97. But how do you teach that? A number line is a good way to do so.
posted by Lemurrhea at 9:47 PM on May 25 [9 favorites]


If common core can teach kids to approach math in a more logical way and be less scary, then that is great. However, if you send home a worksheet that makes no sense at all to parents, then you should expect this sort of shit to happen. Kids these days do a lot of homework and parents are their teachers at home. If you wouldn't leave a sub with lesson plans they can't comprehend, then don't leave parents hanging either. Perhaps the answer is a school-sponsored webpage. Perhaps the answer is save common core for the classroom.
posted by Foam Pants at 9:48 PM on May 25 [6 favorites]


This entire discussion reminds me that choosing not to become a math teacher (after completing student teaching) was probably one of the smarter things I've done.

Software has its problems, but there's probably an order of magnitude fewer people who are sure you're not doing your job right.
posted by weston at 9:53 PM on May 25 [7 favorites]


escabeche wrote: I favorited Jpfed's comment, not just because I basically agree with it, but because he used the word "subtrahend."

Escabeche, do not read below this line:
--------------------------------------------

Folks, are you intimidated by maths? Are you fazed by fractions, scared of surds, confused by calculi? Well, it turns out that mathematicians are just like us - but opposite. They are impressed by words! So next time you're talking to a maths-using-person, just drop these terms and you'll immediately see them respond with awe:

A multiplicand multiplied by a multiplier gives you their product.
A dividend divided by a divisor gives you their quotient.
A subtrahend minus a minuend gives you their difference.
Two or more addends added together gives you their sum.

BEFORE
Regular person: The tip should be twenty percent of the bill minus sales tax.
Mathematician: (yawn) I have to get up early tomorrow to do maths things.

AFTER
Regular person WHO KNOWS MATHS WORDS: Let x represent the value of the bill. Let r be the the sales tax rate of 8.875%. The tip should equal the quotient of the quotient of x divided by the sum of 1 and r, divided by five.
Mathematician person WHO IS NOW IN LOVE: Wouldn't it be simpler to approximate the tip by multiplying x by 32/72?
Regular person: Uh, yeah, if you want to approximate. So, coffee at my place?
posted by Joe in Australia at 10:03 PM on May 25 [37 favorites]


I was another one terrified of math because of a precalculus class taught by a guy whose method of explaining when you didn't understand something was to say exactly the same thing he'd just said, but slower and louder in a really exasperated tone, the way American tourists talk to people who don't speak English. I was a B/C student in math, never great but okay, and that class was one of my few earned Fs...initially, until it turned out that every kid in the class was failing and we mustered up a student and parent revolt that was eventually resolved in our favor. So I was pretty convinced I was bad at math and kind of hated it.

So I was less than thrilled when my placement tests put me in basically 8th grade math. I am being rebuilt from the foundation up...and I can't even remember what I was so afraid of. I got a 99 in my first class and am on course for a 99 or so in my second. I wouldn't say I'm wild about it, but whatever that cloak of terror was is gone. It's just weird how one bad teacher can screw things up so wildly and influence your entire self image so far down the road.

That said, I totally recognize the number line thing, it's how they're teaching it now. I remember enough of The Old Ways to do it that way, but apparently it's the way it's being taught, at least at my community college. I don't get the number line thing either but it seems to work for some people.

And the easiest way to calculate a tip, math person, is slide the decimal over one place to get 10%, then double that.
posted by Ghostride The Whip at 10:36 PM on May 25 [4 favorites]


Ok, what I really don't get is...this whole argument is predicated on the idea that parents who don't know CC would be stymied by this homework, and thus be unable to explain it to their kids. It's not about "this is different" but "this is so different that adults don't get it". But the only example I'm seeing is the number line thing, which...is really goddamn easy. I've never seen it used before, but looking at it for about 5 seconds was enough to make me able to answer a kid's question about it.

tyllwin: "So, I'm curious. China, Korea, and Japan all seem to do better in math -- at least as reported on most published rankings -- than the US does. So, for that matter, do Canada and the UK. What do they do? Is it number lines? Rote drill?"

For Japan, at least, it's a mix of all of it. I don't remember number lines for my son (though I wouldn't have been surprised if he used them), but I remember adding up numbers bigger than ten by using "cherries". For example, given "9 + 4 = ?", as this picture shows, you draw a little picture where the 4 is turned into two cherries, "1" and "3", and use the "9" and the "1" to make "10", then adding the "3". Which is a pretty similar idea to the number line.

So kids start with the cherries, then when they get faster/better, they stop using the cherries, like you start riding a bike with training wheels and then get rid of them. They do lots of homework and drills, but the actual instruction, from what I've seen, has been far more CC-like than the "Here are the mechanical operations to get the answer. Do them. There is no need for understanding" vibe I get from American parents on the internet.

I'm not really versed in education, so take the following as a personal speculation and not gospel in any way: the feeling I get about math education in Japan is that it moves way faster than in the US. I don't know if it's that there is less time spent on each new concept, or if it's just that there are more hours spent each week on math, so you get further in the same number of months.
posted by Bugbread at 10:37 PM on May 25 [11 favorites]


The real question here is not whether today's math curriculum sucks, but why a 7 year old has homework in the first place.
posted by madajb at 10:37 PM on May 25 [19 favorites]


["This guy I know pees in the sink" derail deleted. Come on. ]
posted by taz at 10:38 PM on May 25 [5 favorites]


madajb: "The real question here is not whether today's math curriculum sucks, but why a 7 year old has homework in the first place."

...Because he's a school kid? The real question here is why your real question is why a 7 year old has homework. Am I missing something?
posted by Bugbread at 10:40 PM on May 25 [1 favorite]


If you wouldn't leave a sub with lesson plans they can't comprehend, then don't leave parents hanging either.

Mostly I agree with this. The point where I stop, though, is that the curriculum has always assumed that you have parents at home who can help you with this and who'll be able to handle it. And now that parents are upset they can't handle it, they're blaming the curriculum, not the lack of support for students whose parents don't know the material. There have always been huge numbers of kids who didn't have those parents, even at the elementary level, but especially once you hit about grade 5, and why wasn't anybody screaming about this back then? Oh, but now it also impacts middle-class white people, and isn't just a problem for the children of immigrants and kids growing up in poverty and kids without stable family situations.

I am all about the complaint that we are expecting too much of parents to support a public education system that is supposed to be there for all children, but I feel like most of the people who get upset about Common Core's math do not care about the kids who were already struggling with this before Common Core came along. Not all! But most.
posted by Sequence at 10:43 PM on May 25 [13 favorites]


Ok, to be a bit less flippant and more straightforward (sorry):

"The real question here is not whether today's math curriculum sucks, but why a 7 year old has homework in the first place."

To practice what he/she has learned in school, helping ideas sink in better and move from short-term memory to longer-term memory, allowing classroom time to be spent on teaching instead of review.
posted by Bugbread at 10:44 PM on May 25 [9 favorites]


... I feel nothing but numb horror that this is what basic elementary school math has become.

Based on one problem on one worksheet? Did you read the article, in which the author states quite clearly that this is merely one of many techniques taught to create conceptual understanding? I'd go on, but it's, you know, in the linked article.

Your objection has the flavor of being part of the problem.
posted by under_petticoat_rule at 10:51 PM on May 25 [9 favorites]


You, like, carry the one and such, in your head?

People can't do that? Usually it's faster to just know that 13-9 is 4 or whatever, but you still have to keep track of the places.

Honestly, the number line seems like the innumerate way to do super basic calculations. The only occasion I have done number line style calculations in my head was the time I had to build a house using plans where all the dimensions had been converted from inches to metric. So it was constantly 141cm plus 223 minus half of 45, all day long, with a side dose of all the materials being sized in inches so bonus conversions for that along the way. That was not fun and I did number line kinds of things to keep magnitudes straight in my head.

Outside of that, I can't imagine using it for any daily math. I'll do easy stuff in my head and switch to paper or calculator if it's hard. Both of my grandfathers knew a bunch of mental tricks for doing complex math in their heads, but my father didn't need to learn that (he had a sliderule instead) and I never learned any of the neat head math tricks. I can remember my grandfathers being unimpressed with the basic calculations that I couldn't do in my head, compared to how they learned it.
posted by Dip Flash at 10:58 PM on May 25


but those are really testing para-mathematics skills, not basic skills.

I think the point is that decades of research and experience have clearly shown that starting with, and advancing from, para-mathematics skills leads to children more quickly and firmly grasping "basic skills", whatever that phrase means (notwithstanding the insecurities of parents who feel dumb when faced with unfamiliar handouts and an excess of soapboxes).
posted by fatbird at 11:00 PM on May 25 [7 favorites]


Yay. Shitting on teachers again! Teacher here -

The method of math does not really matter in the long run as long as a logical process is being followed that results in a correct answer. The standard old-school algorithm is fine for pretty much everyone.

The point that is not being made here that needs to be in regards to all of these arguments:

Hurr. they'll just use a calculator.
Why do they have homework? They're little.
Why are you doing it that way?

Is this: Doing math problems strengthens logical processing skills. The earlier the better. 100 minutes a day, 5-6 days a week is a bare minimum. You need to get their brains making those connections as a foundation for logical processing later on in life. Using a calculator does not do this, sorry.

If you want, i can dig up some of the studies and research on this.
posted by Fuka at 11:03 PM on May 25 [21 favorites]


The only occasion I have done number line style calculations in my head was the time I had to build a house using plans

Your brain on housebuilding duty works differently than a six year old being introduced to foreign concepts.

Since so many are confidently sharing their horror at how teachers do their jobs, I'll share my horror at parents who seem unable to grasp that educating their children might be different in form than their own experience, or how they would do it if they home-schooled, which they totally could.
posted by fatbird at 11:03 PM on May 25 [7 favorites]


To expand on a detail from the linked article that seems to be of interest to folks in this discussion:

Understanding number lines and their relationship to arithmetic is a key pre-algebra concept, since in algebra we start thinking of and using numbers and basic arithmetic operations a little differently than they were used before. We start thinking of numbers as points, and generalize from points on a line to points in a plane or points in space (or even higher dimensions). We also start thinking of subtraction as merely the inverse operation to addition rather than two separate operations; with negative numbers being not just any old other numbers, but paired with positive numbers as their additive inverses. Students not making key conceptual shifts like this at key stages like algebra and calculus is also a major contributor to math anxiety and to students ceasing to take further math courses. Also, the number line sets the stage for students to learn about the concepts of magnitude and direction, which are pretty key for calculus and derivatives, and linear algebra and vectors. The number line has been a part of pre-algebra classes for a long time; this subtraction example in the linked article just introduces this concept a bit earlier, giving students more time to become comfortable and familiar with it before that becomes really critical for their mathematical progress.

Another important advantage of the subtraction method demonstrated in the link and in many of the anti-common core facebook and internet posts I've seen is that it gets students to practice estimation. I've been told that research shows that one major difference between people (adults and youth) who are successful with math and those who aren't is this thing called "number sense". One example: someone who is successful at math will tend to look at a number like 1,234,567,891 and, depending on context, think, "oh, that's about 1 billion" or "oh, that's about 1,234 million" or "oh, that's about 1,234,567 thousand". That is, they will immediately contextualize the number as being of some approximate magnitude. This makes it much easier to compare and reason with numbers than the lack of number sense case, where folks are so focused on the exact individual digits that they don't reason about the number as a whole, or get too caught up in the exact details of arithmetic calculations to reason on a broader level. It might seem paradoxical, but looking at a number as a random collection of individual digits - lacking number sense - seems to make even the precise, technical arithmetic computations like the traditional multi-digit addition and subtraction algorithms, where you do need to use all of those specific digits, harder for people. That is, even if your end goal is rote proficiency with the traditional multi-digit arithmetic algorithms, exercises like the number line one shown in the linked article help students develop number sense, which (through a number of intermediate cognitive steps no doubt) helps most people in developing rote proficiency with the traditional multi-digit arithmetic algorithms. (In other words, Dip Flash, early math education should absolutely allow for folks like yourself, but statistically you are an outlier.)
posted by eviemath at 11:04 PM on May 25 [30 favorites]


Dip Flash: "People can't do that? Usually it's faster to just know that 13-9 is 4 or whatever, but you still have to keep track of the places. "

I highly doubt that people here would do things like "13-9" using a number line (or something like it), but working out stuff like "4976-2143"? Totally.
posted by Bugbread at 11:09 PM on May 25 [2 favorites]


In other words, Dip Flash, early math education should absolutely allow for folks like yourself, but statistically you are an outlier.

I don't remember much of my early math education, but I'm sure it was typical for the time. Lots of rote stuff, like times tables, along with exercises with blocks and coins. I'm sure it wasn't great, because my math skills now are pretty haphazard, and for all I know number lines may have featured, though I don't remember them.

In other words, I am not at all down on the idea of this as a pedagogical tool, just my reading (or misreading) of comments that suggested it was a common tool for doing math later in life. Eg:

I highly doubt that people here would do things like "13-9" using a number line (or something like it), but working out stuff like "4976-2143"? Totally.
posted by Dip Flash at 11:18 PM on May 25


There absolutely is cultural disdain for teachers and teaching in the U.S., and it's widespread. Teaching is not generally regarded as something that requires its own expertise, it is seen as a lesser form of actually doing ("those who can't do, teach"). The parent's assumption, as pointed out in the post, is that the ability to perform higher maths well is superior to (and therefore inclusive of) the ability to teach mathematics well. That is of course incorrect.

I see it in my field all the time, the assumption that those who teach music are the ones not good enough to make it as, e.g., performers. There really is very little awareness, generally speaking, that teaching requires talent, skill, acumen, expertise all its own--why else is so much educational reform determined by non-teachers? In what other professional field are the opinions of expert practitioners so widely questioned? So many people assume, because they've been students, that they know what's involved effective teaching--which is crazy. I mean, I don't suddenly think I know better than the medical community just because I've gone to the doctor a bunch. But people do, just like this parent. I encounter it all. the. time.
posted by LooseFilter at 11:23 PM on May 25 [14 favorites]


Eviemath: One example: someone who is successful at math will tend to look at a number like 1,234,567,891 and, depending on context, think, "oh, that's about 1 billion" or "oh, that's about 1,234 million" or "oh, that's about 1,234,567 thousand".

So, like reading, do math skills rely on "chunking" numbers together into a um, I guess a "number word"?
posted by Annika Cicada at 11:29 PM on May 25 [2 favorites]


All I know is that homework is the bane of my existence as a parent.

You're not supposed to do the homework yourself.
posted by MartinWisse at 11:39 PM on May 25 [5 favorites]


Honestly, the number line seems like the innumerate way to do super basic calculations.

Your comment comes across as pretty condescending toward people who do things differently than you. Using the standard algorithm is just one way to do sums; using a number line is another. Neither one is more mathematically true or advanced than the other - although it's worth pointing out that number lines are all over the place in advanced mathematics.

If you want to use the standard algorithm in your head, that's great. But I like my number line and I'm far from innumerate.
posted by Kutsuwamushi at 11:53 PM on May 25 [15 favorites]


The parent's assumption, as pointed out in the post, is that the ability to perform higher maths well is superior to (and therefore inclusive of) the ability to teach mathematics well. That is of course incorrect.
I think there's also an assumption, rightly or wrongly, that the parent is also required to teach it. Then they look at something like this and go "WTF?" Because they haven't been a part of the conversation that led to this.

I know that was the case in my house growing up (my mom having to do a lot of teaching when it came to homework time, because I, an otherwise A student, had no clue how to proceed) and it didn't work very well because she wasn't a teacher. I was a tutor for first and second grade kids when I was in high school and I felt responsible for teaching them everything from reading to math because we had to get these worksheets done and they truly had no idea what to do, malingering aside.
posted by bleep at 12:26 AM on May 26


If you want to use the standard algorithm in your head, that's great. But I like my number line and I'm far from innumerate.

Do you write it down as in the link?
Not trying to be condescending at all, but I've never seen a "number line"* as in the example above.

It seems like writing it out would be far slower than what I think of as "regular" subtraction, that is:

4354
- 532
------
3822

* To me, a "number line" is:
-5 -4 -3 -2 -1 0 1 2 3 4 5

posted by madajb at 1:13 AM on May 26


...Because he's a school kid?

A 7 year old kid, a second grader.
posted by madajb at 1:16 AM on May 26 [1 favorite]


madajb: "A 7 year old kid, a second grader."

Yes, that's been established. Like I said, the non-flippant answer to your question is "to practice what he/she has learned in school, helping ideas sink in better and move from short-term memory to longer-term memory, allowing classroom time to be spent on teaching instead of review".

And I reiterate my question: Why are you asking why a 7 year old second-grader has homework? I mean, I understand it's a rhetorical statement meant not as a question but to mean "I don't think 7 year olds should have homework", but my question is, why don't you think they should have homework?
posted by Bugbread at 2:01 AM on May 26 [4 favorites]


Do you write it down as in the link?

We were talking about mental computation, not pen-and-paper computation. The link is to a homework problem that seems to be focused on teaching concepts; it's not practice doing subtraction by algorithm.

But putting that aside, I'm not sure how to answer. The homework problem is set up in a particular way, so of course if I were to do some arithmetic using a number line, it wouldn't be the same. On the other hand, it's not conceptually any different, so it is the same.

If I'm doing pen-and-paper I probably do it the same way you do.
posted by Kutsuwamushi at 2:19 AM on May 26 [3 favorites]


My group of kids hangs out with me, sometimes after they should have gone home, and we go for walks.

We talk about the world, what it means, what we should do.

During the walks, I teach them magic.

"Here's how to multiply 85 times 85. Take the 8. Multiply by one more. So you multiply 8 X 9, which is 72. Stick 25 after that." They learn that quickly. "85 X 85 = 7225. This always works."

"Here's some more magic," I say. "Every number divided by 7 has a predictable decimal expansion." For example, 1/7 is .142857142857... and if you double that, you just shift the decimal place a little, so 2/7 = .2857142857..."

And I teach them how to kill, because mental arithmetic isn't enough to keep them alive. So I show them pressure points. There's one in your neck, just to the left of the Adam's apple. And if you curl your finger and punch it just so, you'll kill your aggressor.

It's not enough, mental arithmetic and killing, so I teach them about art and philosophy and religion. How complementary colors can be computed in hexadecimal, the way cyan is 00FFFF and red is FF0000, and how they should learn to balance these subtleties when considering interior design. I try to teach them that balance is more than sensation, that it includes a relationship between "I" and "Other".

During our walks, sometimes I point out small creatures and ask the children to think about what they are seeing. "Why do spiders have 8 legs? Why do we have 2 legs?"

There's no way I can ever teach them what I know. More precisely, there's no way I can ever teach them how much I don't know, or how much I know no one will ever know.

Worth trying though.
posted by twoleftfeet at 2:59 AM on May 26 [44 favorites]


... but my question is, why don't you think they should have homework?

First and foremost, because they are children.
Children who are going to spend a sizeable portion of their lives doing schoolwork and shouldn't be asked to more of it once the schoolday is over.
They should, quite frankly, be doing kid things.

From a less philosophical point of view, it is my understanding that educational studies are divided as to the effectiveness of homework at the elementary school level, with studies showing a negligible effect of homework on the achievement levels of young children especially.
Even the studies that suggest homework has a positive effect on achievement recommend 10-15 minutes a night, not the hour-plus referenced in the link.

Finally, I believe that the reliance on homework to "practice what he/she has learned in school, helping ideas sink in better and move from short-term memory to longer-term memory, allowing classroom time to be spent on teaching instead of review" represents a failure of an educational model.
If self-directed practice is important to educational attainment, then it should be built into the school day, where it can be monitored by professionals familiar with the curriculum, not outsourced onto parents who are not familiar with or trained in pedagogical techniques.
posted by madajb at 3:09 AM on May 26 [25 favorites]


But putting that aside, I'm not sure how to answer.

I'm just curious as to how the "number line" idea is used, never having encountered it before.

That is to say, when presented with a non-trivial subtraction problem, are kids being taught to actually write down a number line with the "arcs", etc, as we were taught to 'show our work' when I was a kid.

Or is it just being taught as a visualization of a mental process a lot of people (at least in this thread) seem to use already?
posted by madajb at 3:17 AM on May 26 [1 favorite]


madajb: "Children who are going to spend a sizeable portion of their lives doing schoolwork and shouldn't be asked to more of it once the schoolday is over."

The length of the schoolday is fairly arbitrary, though, right? If you having 5 hours of classes is acceptable, then why is 4 hours and 45 minutes of class, and 15 minutes of homework, not acceptable? You can do exactly as many kid things. Plus, even if that 15 minutes is separate from your "optimal school time", it's only 15 minutes. It does not severely impact how much time is left to do "kid stuff".

madajb: "Even the studies that suggest homework has a positive effect on achievement recommend 10-15 minutes a night, not the hour-plus referenced in the link."

Ah, well that's a problem with homework volume, and we're in agreement there. The rule of thumb I heard from an educator here is "10 minutes per grade", which seems reasonable. A 1st grader would be doing 10 minutes a night, a 12th grader 2 hours a night.

madajb: "If self-directed practice is important to educational attainment, then it should be built into the school day, where it can be monitored by professionals familiar with the curriculum"

Ok, that makes sense. So you'd find, for example, a 10 to 15 minute study-hall period at the end of the day, where kids do homework and get help if needed, to be acceptable? Because that would make sense to me, too.

madajb: "Or is it just being taught as a visualization of a mental process a lot of people (at least in this thread) seem to use already?"

I'm not an educator, let alone a US educator, let alone a CC US educator. But, that said: My own experience in the US schools as a child, and as the parent of a child in Japanese school, is that at the first/second/third grade level there is a lot of mathematical visualization that later on is deprecated, and for a little kid, with sometimes short attention spans, it is easier to visualize something by actually writing it down and looking at it than being told to just imagine it. I would be very surprised if the kids were told to mentally visualize a number line and conceptualize number arcs. That's hard. It would be much easier to put them on paper, where you don't have to juggle everything in your head. With reference to the cherry addition I mentioned earlier, in first grade my son was taught that method to add numbers over 10. He would physically write it down. Once the kids got the idea, and got good, and got fast, they became able to do it without drawing it. It turned from a physical, written thing into a purely conceptual one.
posted by Bugbread at 3:32 AM on May 26 [4 favorites]


The number line is a concept, not an algorithm for solving problems. There are many different ways to use it.

I'm not a math educator, but I doubt that kids are being taught to use a number line to do subtraction except in problems like the one in the link that are about the concepts. It's cumbersome, as you said. But it's an extremely useful concept that you can use to visualize simple arithmetic operations.

Here's an example: If I want to estimate how much 7/9 of something is, one way I can do that is to picture a line segment from 0 to 9, with 7 of the intervals colored in. Is there an algorithm I was taught? No. There's a concept. It's not just a visualization tool, but it can be used that way. eviemath has an explanation earlier in the thread about why the concept's important.
posted by Kutsuwamushi at 3:50 AM on May 26 [5 favorites]


Dan Meyers completely changed the way I taught math.

I teach remedial math to teenagers who have fairly substantial gaps in learning and I will say that teaching math used to suck majorly to these kids until I scrapped the textbook and began pulling lessons from Dan Meyer's dy/dan >> 3acts website and another real-world math site, YummyMath.

I've got teenagers who are mathphobic. Practicing algorithms has them shut down immediately. Seeing a worksheet with multiple iterations of similar concepts can make them scream.

These are the kids who ask, "When will I use this outside of math?" and they need a real answer.

So they do real math. They figure out how to maximize meatballs for a pot of sauce, how long it will take to fill up a fish tank; how many miles the Olympic torch took around the world; math that has some genuine connection to things they will be doing in their lives.

Once I've got their buy in that the lesson is going to be interesting, then we talk about different ways to solve problems and algorithms.

But we don't ever start with a worksheet or a dumbass number line because who cares.

*oh, and to this line of discussion: why not put study time into the school day instead of homework, the short answer is: we can't.

We already cut Physical Education and Art and Music and foreign language because we don't have time and our kids have to pass state assessments (I do not mean to open THAT can of worms but come on, please don't suggest we add something to the school day. As is, we're cutting important things from the day.) Also, states mandate an increasing amount of "time on learning;" study halls are not considered time on learning. I don't give my kids homework because I can't make them do it and they don't so it sets them up to fail, but my own kids had shittons of homework and they did it and it seemed to help them, speaking anecdotally.

**and this: 'I'm not a teacher but here's how I would improve schools ..if you want to drive educators insane, then say that.

Unless you teach, you really don't know how schools work from an educator's perspective.

We know you mean well, but...please don't.
posted by kinetic at 4:01 AM on May 26 [10 favorites]


The number line is a concept, not an algorithm for solving problems. There are many different ways to use it.

It's not a pedagogical construct. It's not a thing somebody made up to teach kids about arithmetic.

You have to use the number line when you think about lengths. For example, if you make a square and you measure the diagonal of the square, you have to measure a length which isn't a counting number (like 1, 2, 3,...) or even a fraction made out of counting numbers (like 1/2 or 2/3).

So the number line is something a person uses to distinguish simple distances between things, much as an animal would use simple distances when capturing prey.

The pedagogical need for an understanding of the number line among humans can only be questioned if one posits a role for humans similar to that of any being oblivious to such an understanding, such as a plant or a rock.
posted by twoleftfeet at 4:15 AM on May 26


kinetic: "I do not mean to open THAT can of worms but come on, please don't suggest we add something to the school day."

Sorry, I thought that the conversation started with CC but had gone onto talking about how to teach kids math, etc. in general, not just how to teach kids in the US. If this is a US-only discussion, let me know and I'll bow out.
posted by Bugbread at 4:25 AM on May 26 [1 favorite]


Bugbread, I just meant that I don't want to personally derail into NCLB and assessments by talking about dealing with homework by extending the school day or adding study to the school day.
posted by kinetic at 4:32 AM on May 26


It's not a pedagogical construct. It's not a thing somebody made up to teach kids about arithmetic.

I agree with you completely, and that's exactly why it's hard to answer a question about how it's "used" to do basic arithmetic. Asking how you use the number line is kind of like asking how you use numbers - there are too many answers at too many different levels.
posted by Kutsuwamushi at 4:33 AM on May 26 [2 favorites]


Children who are going to spend a sizeable portion of their lives doing schoolwork and shouldn't be asked to more of it once the schoolday is over.
They should, quite frankly, be doing kid things.


Kid things like practicing newly acquired knowledge so as to become more comfortable with it? Kid things like learning how to perform tasks outside of the immediate environment and conditions in which the tasks were learned? Kid things like learning that they really can figure things out on their own, given the instruction and examples a few hours previously?

Hell, I'd even throw in that one of the kid things they need to learn is that you do your work before you play, but I'm basically a fascist.
posted by Etrigan at 5:08 AM on May 26 [9 favorites]


I was helping my 10 yo nephew with his math homework, multiplying large numbers, and he was struggling. So I took an example, here multiply these two units together and carry the 1 and that's when he wailed, you're doing it all wrong!

Okay, so there is a new method for learning math, fine, and I wasn't there at the beginning as a parent would be, but what I really wanted at that moment was a nice simple low-tech stand-in-front-of-the blackboard and demonstrate-the-problem video posted on Youtube by that particular teacher, so I could pick up the new technique.
posted by TWinbrook8 at 5:40 AM on May 26 [4 favorites]


Common core worksheets have destroyed my child's love of math. Math is now this boring and tedious thing where she is forced to do busy work. She now thinks she is terrible at math.
posted by humanfont at 5:45 AM on May 26 [1 favorite]


Common core worksheets have destroyed my child's love of math. Math is now this boring and tedious thing where she is forced to do busy work. She now thinks she is terrible at math.

But do you think this is more likely to happen in 2014 than it would have been in 2010, or 2000, or 1970? I see no reason to think so.
posted by escabeche at 6:01 AM on May 26 [4 favorites]


Did she enjoy non-common core math worksheets before? Because "boring and tedious" describes the math worksheets I did back in the 80s, before common core. And while I never thought math itself was boring and tedious, just the worksheets, my dad found both the subject and the homework to be boring, tedious, and difficult, when he was a kid back in the 50s. I'm thinking "boring and tedious" are more a trait of math homework in general than of Common Core.
posted by Bugbread at 6:03 AM on May 26 [10 favorites]


Common Core turned my daughter into a newt!
posted by Brocktoon at 6:09 AM on May 26 [25 favorites]


Maybe "Common core worksheets have destroyed my child's love of math." has more to do with the worksheets part than the common core part? They don't seem like a tremendously useful way to teach anything.

For the median child sure, they'll find it a challenge but hit no dead ends. For a child ahead of the curve it'll be boring busy work, if they're smart they'll learn to do the steps for the best tradeoff of grade vs time spent. When they hit a topic they struggle with they'll have no idea how to attack it. For the child who is currently behind the curve they'll stare at it and learn "I suck at math" (and that sentence alone can ruin your chances for ever). The problem is there is no median child. That means basically everyone is bored or struggling.

Far better to set homework that allows creativity for those that get it and allows partial solutions for those that don't. That means setting homework at a class level, not a national level. The problem is far too granular to achieve a good solution with a set of binary right-or-wrong one-size-fits-all questions on a sheet.

(Can I ask any teachers in the room, why would one ask for a letter style explanation? Is it to cross over with the english language syllabus or does it actually help with learning the mathematical concepts?)
posted by ElliotH at 6:21 AM on May 26 [3 favorites]


Isn't part of the linked article that the number line thing has nothing to do with common core? I mean, I don't know! I haven't read any CC specs or anything, but I suspect most of the folks here haven't either. It just seems like maybe it would be more productive to talk about specific questions or difficulties than it would be to whisper about the shadowy menace of common core.

The number line doesn't make immediate intuitive sense to me, but I'm 33. What does make sense to me is remembering what it was like trying to help my nephew with subtraction a few years ago and how much he struggled with tens, hundreds, and so on. I tried a huge variety of ways to explain what was going on when we wrote down a number as "387", including doing stuff like circling the 3 and having an arrow coming out of it and going to a bubble with three 100s in it. I think his curriculum at some point used the number line thing? Maybe it was helpful for him! In general I'm a fan of "tools in the toolbox" approaches to education.

I'm also mystified that people seem to dislike practice? You don't get good at a thing by doing it once or twice. Everything in the world requires practice, and there's not enough time in the school day to get the requisite practice for everything. Learning is hard, there's no way around it.
posted by kavasa at 6:27 AM on May 26 [4 favorites]


I was helping my 10 yo nephew with his math homework, multiplying large numbers, and he was struggling. So I took an example, here multiply these two units together and carry the 1 and that's when he wailed, you're doing it all wrong!

In elementary schools, kids are taught multiple methods of solving problems and often their homework is to solve multiple problems but they have to use a certain method and the work is considered correct but will be marked down if they use straight multiplication instead of lattice, for instance.

What I've seen over the years, in addition to the massive headache this causes caregivers (which it does), is kids combine various methods, so they'll start with lattices, then switch to old-school multiplication, etc. and they get really confused and they give incorrect answers.

Can I ask any teachers in the room, why would one ask for a letter style explanation? The idea is that students can express their reasoning behind their problem-solving to demonstrate they're thinking mathematically. It's a nice idea.

But really, it's mostly because on high stakes tests students have to explain how they got their answer because just writing out formulas and answers will get lower scores. It's practice for the test.
posted by kinetic at 6:27 AM on May 26


I don't get that Jack problem at all. Any number of things could be wrong with his approach. Too many small humps, too few small humps, inconsistent size of the small humps...
posted by mantecol at 6:33 AM on May 26


> You're not supposed to do the homework yourself.

Homework is one of the many things you can share with your kids. Like baking cookies together. But you can't share if the pedagogical methods popular with educators during this fifteen minute interval make sharing homework tasks with your kids impossible unless you have had special training. Which leaves large numbers of students in isolation from their families during big chunks of the afternoon and evening. Often enough, if they don't understand or can't do something, isolated and in torment.

> If self-directed practice is important to educational attainment, then it should be built into
> the school day, where it can be monitored by professionals

Which leads directly to professionals wanting to keep students in school all day and all year.
posted by jfuller at 6:34 AM on May 26 [2 favorites]


mantecol: "Any number of things could be wrong with his approach."

The question is "427 - 316". He subtracts 100, then 100, then 100, then 20, then 10, then 10, then 10, then 10, then 10.

That's not subtracting 316, it's subtracting 370.

He should have subtracted 100, then 100, then 100, then 10, then 1, then 1, then 1, then 1, then 1, then 1.

Saying "it could have been any number of things, too many small humps, too few small humps, inconsistent size of the small humps" is like looking at:
  2
  27
  x3
------
  71
...and saying "it could have been any number of things. The carried two could have been written on the bottom, or next to the three, or you could have carried a nine".
posted by Bugbread at 6:42 AM on May 26 [3 favorites]


Just anecdata from the 70s and 80s. I hated rote math due to the double bind of "slow down, I can't read your writing" and "do twenty of them in 10 minutes to get an A." When I was reintroduced to the number line via algebra and linear equations, I fell in love all over again.
posted by CBrachyrhynchos at 6:45 AM on May 26 [2 favorites]


You do mean 27x3=81, right?
posted by Dip Flash at 6:47 AM on May 26


jfuller: "you can't share if the pedagogical methods popular with educators during this fifteen minute interval make sharing homework tasks with your kids impossible unless you have had special training"

Ok, non-snarkily, can we get some more examples of these difficult questions? We've only got one here, and I don't get why it's being seen as difficult, but MeFites are generally smart folk and we've got people saying the questions are hard for parents, so maybe the questions are hard and for some reason this one was just easy for me. Maybe with some more examples people's complaints would make more sense.
posted by Bugbread at 6:48 AM on May 26 [2 favorites]


Is there a reason these work sheets don't have short examples of the methods being tested so interested parents can follow along? (Not to mention as a reminder to the confused student)
posted by ElliotH at 6:49 AM on May 26 [1 favorite]


The question is "427 - 316". He subtracts 100, then 100, then 100, then 20, then 10, then 10, then 10, then 10, then 10.

But who says the small humps are actually 10s? I think the parent wrote those numbers on there. Since there are 6 small humps and 16/6 is 2.x, my first thought was that the small humps represented 2s, and he drew 6 of them instead of 8.

Or is it part of the standard that you can only subtract by 10s if there are more than 10 digits left to subtract?
posted by mantecol at 6:52 AM on May 26


I imagine one only subtracts by powers of 10.
posted by ElliotH at 6:56 AM on May 26


I used to tutor for extra cash. Honors kids from upper middle class families who were used to getting straight A's and then hit algebra and suddenly there was this wall where they couldn't figure anything out. They could do rote memorization of their times tables, but they didn't understand what they were doing, and so they spun in circles when math got more conceptual.

Less than a quarter of US seniors take calculus. In Asia, it's 95%. My cousins don't even think of it as "advanced" math, or something that you need to be "good at math" to learn. That's because they had the conceptual scaffolding for it starting in kindergarten. It's dismaying to think that we are freaking out over doing the same thing for algebra.

It really seems to me that for many parents, "new" methods revive their anxiety about how little they understand math, and that is a huge contributor to the backlash. To them I say: don't worry. Your kid will not think you are stupid. And helping kids with their homework doesn't really get them better grades anyway.

posted by snickerdoodle at 7:01 AM on May 26 [9 favorites]


The new ways of doing math seem like they could be really useful for kids, but parents need to have resources available so they can participate; as noted above, a single YouTube video about "This is how we do math in our school" would have headed off a lot of the upset. Like so much education reform stuff, this strikes me as a good idea that no one bothered to sell to the parents, and the result has been disastrous for everyone.

I mean, I don't suddenly think I know better than the medical community just because I've gone to the doctor a bunch. But people do, just like this parent.

On the contrary: Anyone who's dealt with chronic illness has, at some point, had to tell a doctor "You don't know what's going on, and your confidence in your own ability is blinding you to your ignorance." And anyone in the medical profession has had to handle patients who come in with some crazy theory they acquired on the internet. Your expertise is neither a magic wand nor a magic shield.
posted by ThatFuzzyBastard at 7:01 AM on May 26 [5 favorites]


*oh, and to this line of discussion: why not put study time into the school day instead of homework, the short answer is: we can't.

And this is the line I'll call bullshit on. Time is also a number line - and 35 minutes three days a week and 55 minutes two days a week was an amazing amount of time to learn math, maths, mathematics, arithmetic and whatever else you want to call it. Kids that weren't on my same track had additional time with aids one on one for both conceptual assistance and homework assistance. I don't remember when homework started coming home, but it definitely wasn't an every night concept for every subject in second grade. Sure, every night there would be homework, but it was manageable durations of probably 30 minutes or less by third grade, with maybe a little bit extra on the weekend, and likely reading every week. And that was it until pop quizzes, term papers, science projects and mid-terms were brought into play.

The problem is there is no median child. That means basically everyone is bored or struggling.

This. 1000 times this. We are not on a normal distribution of math ability - we are a bimodal distribution that gets skewed further and further downward as the top kids are prevented from learning a challenging concept. Likewise the "dumb" kids that don't get math not only still aren't getting the math, but because the curriculum is designed with a twenty or thirty year old paradigm shift - the kids can't get help at home either. That means, if they don't get it in the classroom - the kid is fucked. As a kid that excelled at math, did engineering and had a minor in math and has read that number line question 5000 times - giving it as much generosity and benefit of the doubt as possible - the dad isn't right, but he isn't totally wrong either.

Looking at Jack's problem, Jack was screwing off in class and didn't get the question - that I get, looking at his answer. I also get the father's perspective that the question can be answered pretty quickly. because duh. I also get the educators angle which is - don't blame me, I'm teaching to the curriculum, and I also get the curriculum's perspective which is we want to teach the concept with numbers the kid would feel comfortable with. The problem is, that if the kid doesn't feel comfortable with the concept, he has only one way to go because the curriculum has isolated both the father and the educator. When you take away a parent's ability to assist in the education of the child - YOU LOOSE YOUR JOB. Want to understand why teachers have the hardest jobs? Because the administration is putting them in the position where they have to teach something that puts them solely responsible for the child's education.

Are number lines useful? Yes. I use math that this will eventually build to every damn day of my life. I also think problem solving and algorithms are important, and I get that people want to gamify education because people seem to really respond to it. But forced methodology that results in isolation is the wrong path.

Moreover, think of every kid in college that you knew that went into early childhood education. Think of every kid in college that you knew that went into school administration. Think of their damn math scores and math ability. These are the folks that are designing your child's curriculum - because you don't go into education when you understand number theory, graph theory, statistics, and calculus - you go get paid. The people in charge have a bit of a clue, because they've read a bit about algorithms and learning and the faster way to an answer and how math breaks down - but dammit - they've grossly misapplied these concepts to wreck 215 minutes weekly of my childhood (3x35+2x55).

So, while this may sound like I have a problem with the educators, I don't. My beef is with the administrators who have pushed this bullshit methodology.
posted by Nanukthedog at 7:02 AM on May 26 [4 favorites]


I imagine one only subtracts by powers of 10.

Knowing that would make make it easier, I guess.

This all reminds me of a random Cosby Show episode I saw when I was a kid, where the daughter learned base 12 (I think) arithmetic in school because it was faster. She was running circles around her family, and they had no idea what she was doing.
posted by mantecol at 7:03 AM on May 26


At first, I was thinking this backlash was just mathphobia, but it occurs to me that it seems largely to be a preference for showing kids familiar or expedient methods for calculating, rather than the deeper underlying relationships in math. And that isn't a math-specific problem.

"Quickfixery" and short-sightedness is all over the place, from corporations optimizing for short-term profit to programmers yanking in frameworks and Stack Overflow code indiscriminately to legislators band-aiding stuff incessantly.
posted by ignignokt at 7:03 AM on May 26 [13 favorites]


We are not on a normal distribution of math ability - we are a bimodal distribution that gets skewed further and further downward as the top kids are prevented from learning a challenging concept.

I don't know if this is true, but I do know that "challenging concept" in math is far less advanced in this country that in others, judging by the number of kids who take calculus. This tells me that bimodal or not, we aren't doing very good job teaching math to everyone.
posted by snickerdoodle at 7:06 AM on May 26 [1 favorite]


My take on this particular worksheet is that it's asking for a particular graphic output. The exercise employs an implicit assumption that everyone will visualize the concept in a rigidly homogeneous fashion, rather than allowing for alternative but still effective visualizations or for non-visual ways of grasping the concept.

Why assume that all students will find it easiest to use this particular visual output rather than, say, imagining or enacting it as a series of physical distances to traverse on foot, or as a water-container problem that might translate to a vertical rather than a horizontal graph, and so forth?

But I also think that Common Core and education in general needs to consider that the parents also have a role, even a *job* to do, and that this will sometimes mean providing the equivalent of job training for "parent-educators" and even assessment to determine which children need additional support due to parental deficiencies. And then you get a big, scary political fight because a lot of people confuse vigorously protecting their kids with vigorously possessing their kids.
posted by kewb at 7:08 AM on May 26


Think of their damn math scores and math ability. These are the folks that are designing your child's curriculum - because you don't go into education when you understand number theory, graph theory, statistics, and calculus - you go get paid.

In the UK there has been a move towards universities providing some input on what they would like out of the 16-18 curriculum. This seems a fairly smart way of treating this problem if continued down the chain.
posted by ElliotH at 7:10 AM on May 26 [1 favorite]


As an oldster who was utterly traumatized as a child, trying and failing to learn the original "New Math" of the 60's (and subsequently developed a life-long fear of math), could a patient MeFite please explain to me what's going on in that example jpfed linked to? Is that an accurate representation of how subtraction is taught today? I stare and stare at it and cannot for the life of me understand the how and why of it. My first thought is "Why one would start by adding 3 to 12?" Where did the 3 come from?
posted by Thorzdad at 7:13 AM on May 26 [1 favorite]


Dip Flash: "You do mean 27x3=81, right?"

Yes, 81's the right answer, and 71 is the wrong answer. That was the point of the example.

mantecol: "But who says the small humps are actually 10s? I think the parent wrote those numbers on there."

Oh, shit, that makes extra sense. And makes me mad. I'd put a good $100 on Bachelor of Science in Electrical Engineering Dad not actually having a degree in anything close to electrical engineering.

mantecol: "Since there are 6 small humps and 16/6 is 2.x, my first thought was that the small humps represented 2s, and he drew 6 of them instead of 8."

No, look at the printed numbers. 427 goes to 327. Science Dad correctly surmised that this was a reduction of 100. Then to 227, another 100. Then 127, another 100. Then six smaller bumps, at which Jack reached 121. Science Dad figured "Okay, so he subtracted six somethings from 127, and reached 121. What could those somethings have been? Could they be 1s? Well, using my Electrical Engineering math, I know it would be silly to think that subtracting six 1s from 127 would bring you to 121. Instead, I'm gonna guess that the first bump is 20. And all the other ones are 10. And I know over there at left it says I'm supposed to reach "121", but, you know what? Fuck it. I say it's "57". And I conclude that this question makes no sense."

Jack's mistake was more straightforward than Science Dad: he subtracted 100, 100, 100, 1, 1, 1, 1, 1, 1. He forgot to subtract the 10.

I'm sorry, realizing that the handwritten stuff was Science Dad's stuff has A) made the question make even more sense to me (and I suspect if the original question, without his misleading mistakes scrawled all over it, were posted here everyone would have figured it out in less than a minute), and B) made me positively fucking livid. If you're a liberal arts dad (like me) and you can't figure out your kid's homework, just say "I've had 12+ years of math/I'm a college grad/I'm (whatever) and I can't figure this out". Don't pretend to have some degree you don't to give your barb more punch. Don't make up statistics to bolster your position. Don't attribute quotes to Einstein or Hawking to give it oomph. Don't lie for fucking Facebook likes from other exasperated parents. If you're going to complain, at least do it honestly.
posted by Bugbread at 7:14 AM on May 26 [7 favorites]


"Why one would start by adding 3 to 12?" Where did the 3 come from?

I don't know why 3, but the idea is that it's easier to add numbers to 12 to get 32 than the reverse. This is a bad example because 32-12 is easy to see.

Imagine 151-67.

How I would do it, more or less, is say 67 + 3 = 70, 70 +80 = 150, 150 + 1 = 151, so 67 + (3+80+1) = 151, or 67 + 84 = 151, or 151 - 67 = 84. (This isn't quite how I do it -- I wouldn't do ones then tens then ones, but it's close enough.)

So in this case they're going to the multiples of 5s first instead of the multiples of 10s (not sure why) but the general idea is to do most of the math with as round a number as possible.
posted by jeather at 7:19 AM on May 26 [2 favorites]


Is that an accurate representation of how subtraction is taught today?

No, it's an accurate representation of one method of teaching subtraction that's deemed appropriate for a particular audience. They learn others at other times.

One of the most obvious failings of these rage-driven critiques of worksheets like this is this isn't the whole of how they're learning this particular thing!
posted by fatbird at 7:20 AM on May 26 [3 favorites]


Thorzdad: "could a patient MeFite please explain to me what's going on in that example jpfed linked to?"

Ok, it's subtracting by figuring how much you would count up from 12 to get to 32. The first step was to take 12 to a more manageable number. I would've added 8 to get to 20, but I guess the teacher picked going up to the nearest 5 or 10.

So, add 3 to 12 and you're at 15.
Take it up to the next convenient number. 15+5=20
Bump it up another notch. 20+10 = 30
Now bump it up to the goal, 32. 30 + 2 = 32
So to get from 12 to 32, you go up by 3, 5, 10, and 2. Altogether, that means you go up by 20.
posted by Bugbread at 7:20 AM on May 26 [2 favorites]


Thorzdad

We start with 12 and we're trying to make it up to 32. We recall that this is the same as a doing 32 - 12.

(1) We do 12 + 3 to get 15.
(2) Using our 15 from (1) we do 15 + 5 to get 20.
(3) Using our 20 from (2) we do 20 + 10 to get 30.
(4) Using our 30 from (3) we do 30 + 2 to get 32.

3 + 5 + 10 + 2 (= 8 + 12) = 20

At each step we're trying to use facts we already know or can do quickly in our head to do the subtraction.
posted by ElliotH at 7:20 AM on May 26 [3 favorites]


I think the reason we go to 15 first is we might not know our sums to make 10 off by heart yet, but we do probably know that 2 + 3 is 5 and we probably know that 15 + 5 is 20.
posted by ElliotH at 7:25 AM on May 26 [3 favorites]


Also, while that method is not taught at my kid's school, my kid came up with this kind of method on his own before they got to subtraction in school. He didn't write it down, but he surprised me once doing a hard subtraction question in his head (I think he told me how much allowance he'd have left after buying something). I asked him how he did it, and it was "well, blah plus 4 is blah, and that plus 40 is blah, and that plus blah is 3, so I'd have 47 yen left."

Important note: my kid is not a math wizard. He's squarely in the middle of his class. So I say this not in the sense of "my kid is cool" but "anecdotally, this approach may actually be fairly easy for kids to understand and work with".
posted by Bugbread at 7:26 AM on May 26 [6 favorites]


Bugbread, for what it's worth, Science Dad (or someone claiming to be him) has posted a letter providing some context.
posted by valrus at 7:27 AM on May 26


I'm sorry, realizing that the handwritten stuff was Science Dad's stuff has A) made the question make even more sense to me (and I suspect if the original question, without his misleading mistakes scrawled all over it, were posted here everyone would have figured it out in less than a minute), and B) made me positively fucking livid.

Yeah, I think you're right. The handwritten numbers make it much harder to figure out than it needs to be. Why would he possibly pick 20 for the first hump, when there is only 16 left to subtract? And why use a mixture of 20s and 10s, when all of the smaller humps are the same size?
posted by mantecol at 7:28 AM on May 26


I think it's worth repeating this part of the linked article every so often in this thread:
There is nothing in the Common Core State Standards that requires students to use number lines to perform multi-digit subtraction
As you were.
posted by yoink at 7:49 AM on May 26 [4 favorites]


valrus: "Bugbread, for what it's worth, Science Dad (or someone claiming to be him) has posted a letter providing some context."

Thanks. I take back the stuff I said about him not being a real engineer (if you're working with a kid with a learning disability, who is also having a wailing-on-the-floor tantrum, I'd be more surprised if you didn't make some strange mistakes). Science Dad, I doubt you're reading this, but if you are, I'm sorry about the assumptions I made about you and the insults based on those assumptions.

In his more reasoned Facebook entry he discusses something I also totally felt upon reading the question, which is the problem of the question being a cross-disciplinary question (or whatever you call questions requiring both math and language skills). In a non-writing question, if you're good at math, the question is easy. If you're bad at math, the question is hard. In this question, to answer correctly you have to be good at both math and writing. If you have a hard time with either one the question is really hard.

Also, I think this kinda answers the "hour worth of homework" question. It was a two page assignment, but his son is autistic and has a learning disorder.
posted by Bugbread at 7:50 AM on May 26


~jesus.
posted by Thorzdad at 7:51 AM on May 26


The thing I hated more than anything in school was being told "show your work" on my math homework or tests. I remember one time in 7th grade the teacher wrote 25x25 on the board and told us to work on it, and I raised my hand in a few seconds and said 625 and she looked at me like I was Rain Man, but I'd just sort of seen that 4 25s would be 100, so you've got 6 groups of those and one 25 left over, boom.

The thing is, the right approach to a given problem might be rote memory, a number line, "the old way" on paper, some mental chunking, etc. Many problems have multiple good approaches and there's no need for a "one true way". Like 427-111, I'd just subtract 1 from each digit. Oh what if it was 427 - 333, that doesn't work! Then use a different approach.

What's awful is this rigid adherence to forcing kids to use specific mental models for specific problems and to actually transcribe the way you're forcing them to think out onto paper. It's a straightjacket, actively discouraging children from thinking for themselves, building their own mental toolkit and learning how to use it intuitively.

It's like forcing someone to clean a toilet with a toothbrush, except in this analogy the person is perfectly able to just concentrate a bit and clean the toilet with their mind, but a federal bureaucrat decided they still need to film a video of "their work" with the toothbrush, because experts.
posted by crayz at 7:59 AM on May 26 [4 favorites]


Another point that might be relevant to this thread. There is a surprising lack of evidence that helping children with their homework (math or otherwise), or, indeed, inquiring sufficiently into their homework to form opinions about its pedagogical value, does them any good whatsoever.
posted by yoink at 8:00 AM on May 26 [4 favorites]


I'd wager that most people complaining about common core haven't a clue as to what math really is, or even what numbers are.

People are fighting over fucking subtraction and multiplication because it's probably all they remember from school. It's such small potatoes. This is just step one to getting kids moving along a path to learning about really important concepts like functions, algorithms, and so on.
posted by empath at 8:04 AM on May 26 [4 favorites]


> Ok, non-snarkily, can we get some more examples of these difficult questions? We've only got one here, and I don't get
> why it's being seen as difficult, but MeFites are generally smart folk and we've got people saying the questions are hard
> for parents, so maybe the questions are hard and for some reason this one was just easy for me.

I won't be much help either, I had a good discussion of the number line in elementary school, with addition demonstrated as moving the end point of your line segment out in the direction of positive infinity and subtraction as moving the endpoint the other way in the direction of negative infinity. And I had the New Math in high school, so this whole controversy is deja vue to me and will certainly fade out as it did previously.

The New Math did, however, provide me with the experience of crying out to my own dad (an architect who had gotten through The Calculus of Stresses and Strains--as architects must whose buildings aren't going to collapse--at Georgia Tech, and was not at all mathematically backward, let alone innumerate) NO DAD, WHAT YOU'RE SHOWING ME ISN'T THE WAY I HAVE TO DO IT! Which is a hideous frustration to both child and parent, and is clearly still a thing.

But it's a general point that does not pertain only to math instruction. Dahlia Lithwick (who is no dummy and has often been linked approvingly on mefi) addresses the general point.
posted by jfuller at 8:06 AM on May 26


The thing I hated more than anything in school was being told "show your work" on my math homework or tests. I remember one time in 7th grade the teacher wrote 25x25 on the board and told us to work on it, and I raised my hand in a few seconds and said 625 and she looked at me like I was Rain Man, but I'd just sort of seen that 4 25s would be 100, so you've got 6 groups of those and one 25 left over, boom.

You realize that you just showed your work, right?

I mean, I had the same reflexive revulsion to showing my work when I was learning algebra ("Well, duh, x^2 - 25 expands to (x-5)(x+5) because it does."), but that's because I hadn't actually learned how to do that calculation as much as I'd learned by rote the usual expansions. Learning the method (which came much later and after my schooling in math) made it tremendously easier, and I wish my teachers had been more rigorous in making me show my work.
posted by Etrigan at 8:06 AM on May 26 [4 favorites]


I suffer from a fairly acute case of dyscalculia, not just struggling with complex math but with numbers as symbols, period. I just can't hold them in my head the way I can other abstract concepts, and no matter how hard I tried I could never learn the rote formulas. But that was not a diagnosis when I was in school, and because I was performing really well in all other academic areas my troubles with numbers got labeled as laziness, like I was so used to coasting on innate abilities that I just didn't know how to put in the WORK and EFFORT needed for real learning. Bull.

Out of sheer frustration with the whole humiliating affair, I eventually came up with my own shortcuts and workarounds just to pass the required courses, and what I came up with looks a lot like those Common Core methods: breaking apart equations into rounder more manageable ones, all kinds of visual representations of concepts. But even then, I was cut off from the academic paths I really wanted to pursue because of the "bad at math" label.

How many people who think they're bad at math were just never taught in a way they could understand? I look at these worksheets, and all I can think is that if they'd been around when I was in school, I might have become a scientist.
posted by Freyja at 8:09 AM on May 26 [12 favorites]


The thing I hated more than anything in school was being told "show your work" on my math homework or tests. I remember one time in 7th grade the teacher wrote 25x25 on the board and told us to work on it, and I raised my hand in a few seconds and said 625 and she looked at me like I was Rain Man, but I'd just sort of seen that 4 25s would be 100, so you've got 6 groups of those and one 25 left over, boom.

You just showed your work very nicely, there.

You ask students to "show their work" to see if they understand the method. Getting the right answer typically doesn't matter all that much in a math class exercise. You're not building a bridge that will stand or collapse depending on the answer you arrive at. The exercise is arbitrary; what is important is learning a technique for dealing with a certain class of problems. Thus, if a student gets the wrong answer, but in viewing their workings you can see that they understood the problem, tackled it in an appropriate way, and merely made a small arithmetical error at some point you know that they've grasped the essential part of the lesson. If they get the right answer but don't show their working then you have no way of knowing if that right answer was just a lucky guess, or if they chose a technique that happens to work on that problem but wouldn't work on a slightly different version of the problem and so forth (think, for example, of cases where you need to use absolute values; you might have a particular problem where the number in question was positive--in such a case forgetting to take the absolute value wouldn't matter, but in a problem where that number was negative, you'd get the wrong answer).

I remember sitting a calculus exam in my first year at university. I was running into time trouble in a big way as I hit the last question so I just wrote out what steps I would take to solve the problem without actually doing any of the actual calculations. I got nearly full marks for the question. The ability to actually crunch the numbers was not what I was being tested on (I had a calculator at my side, after all); being able to "show my work" was.
posted by yoink at 8:11 AM on May 26 [9 favorites]


My son knew the answer in seconds, but because of his learning disability, could not answer the required question and thus failed the assessment.

It surprises me that the father took this homework so seriously. Is this how parents are "supposed" to deal with their kids' homework? (honest question). I thought the point of homework was so a kid could practice, not so he could prove anything?

I can't imagine the kid having a meltdown on the floor and the father sitting down to write a letter to the teacher to explain the mostly-done-but-maybe-not-entirely-correctly-done assignment. That just seems like *way* too much stress and pressure over some daily homework. Is the father making a mountain out of a molehill or is that kind of involvement expected and/or necessary?
posted by rue72 at 8:15 AM on May 26


Whoa. That dad's letter was illuminating. Note that he said his son was worried about failing his math homework. It seems like the issue is NOT that the common core teaches alternate strategies per se, it's that the way it seems to be applied is to require students to master those alternate strategies. That is, you don't get to skip that last question, even if you already know how to do subtraction another way. If the core really was about just learning subtraction (addition, whatever), it should be okay to write down any (valid) way of answering the question. That seems like an important distinction. I wonder if it might help to set expectations about whether the class is teaching math, or integrated skills, or both?

Similarly, I appreciate that many people here find these methods more intuitive, but by making them required (and again, this might vary across curricula/teachers) they have just as much potential to frustrate some kids as the more traditional methods do.
posted by synapse at 8:25 AM on May 26 [1 favorite]


Anyone who's worked a cash register did this for every single transaction that had change.
posted by Benjy at 8:33 AM on May 26 [4 favorites]


The homework just involves counting the humps that Jack made along the number line, and Jack's count is printed below the number line, so it's easy to see where he went wrong -- he still needs to count down by 10 more.

I'm 28 years old and we didn't learn arithmetic all that differently when I was in school, though we used blocks to count instead of number lines drawn on paper, for the most part. Also, I agree with Benjy that this is exactly how cashiers count change back to people. The math doesn't seem as unfamiliar to me as the father's reaction does. Is it the opposite for other people?
posted by rue72 at 8:35 AM on May 26 [1 favorite]


I teach remedial math to teenagers who have fairly substantial gaps in learning

That's not what Common Core Math is about. It's a college preparatory track. It is intended to give kids the skill set they need at the end of their k12 course to begin college level math courses. A high skilled student will do Algebra as a Junior in high school and AP Calc as a senior. Your remedial kids have gaps because somewhere along the lines, they fell out of the track and nobody got them back on the curriculum. Of course there are kids with disabilities who have trouble with the standard curriculum and you may have some of them in your class. But surely the majority of kids who struggle with remedial math, just had poor education in the abstract structures (simple as they are) that would have helped them progress. Teenagers who get way behind, like years behind the curriculum, of course they're going to be frustrated.

I've been there, although late in the k12 curriculum. I still remember my high school algebra course, I was out sick for a week during the lessons on factoring polynomials. I came back and holy crap I have no idea what they're doing, they're a week ahead of me. I had to get a math tutor to catch up, which took a couple of weeks before I got back in sync with the rest of the class. You are out for a week and you're two weeks behind. Many kids (and teachers) will give up at this point.

This worksheet seemed exceptionally simple and obvious to me, but then, I have worked in CC test development for 3 years (although at high school level only). The ranting Frustrated Parent is focused on the answer, not the concepts being taught. It's a lesson in breaking down a number into powers of ten, and learning the abstract ideas about how to manipulate these units. You could teach this lesson on an abacus. But Frustrated Parent thinks they're teaching subtraction. They are not.
posted by charlie don't surf at 8:36 AM on May 26 [7 favorites]


*oh, and to this line of discussion: why not put study time into the school day instead of homework, the short answer is: we can't.

And this is the line I'll call bullshit on. Time is also a number line - and 35 minutes three days a week and 55 minutes two days a week was an amazing amount of time to learn math, maths, mathematics, arithmetic and whatever else you want to call it.


Hey, I'm not saying you're wrong.

I'm saying that because we need to prove to the Department of Education that we have X hours of time on learning, we've already pulled Music, PE, Spanish, French, Art and Latin.

And we've pulled Study from the schedule because we need to prove more time in class being taught by "Highly Qualified Teachers."

There are so many hours in the day, and once we have the kids take Math, Literacy, History, Science and one extra-curricular, there are no more hours in which to put in extra anything, let alone math.

If we could change those laws or add more hours to the school day, I'd do it in a heartbeat.

But it's not bullshit; it's following the law in order to remain certified.
posted by kinetic at 8:49 AM on May 26 [1 favorite]


At first, I was thinking this backlash was just mathphobia, but it occurs to me that it seems largely to be a preference for showing kids familiar or expedient methods for calculating, rather than the deeper underlying relationships in math. And that isn't a math-specific problem.

I'm thinking it's just plain backlash. I'd say argument over educational standards is probably the biggest political sport in the United States, attracting people who are generally resigned to the sorry state of the federal congress and statehouse.
posted by CBrachyrhynchos at 8:50 AM on May 26


The point where I stop, though, is that the curriculum has always assumed that you have parents at home who can help you with this and who'll be able to handle it. And now that parents are upset they can't handle it, they're blaming the curriculum, not the lack of support for students whose parents don't know the material. There have always been huge numbers of kids who didn't have those parents, even at the elementary level, but especially once you hit about grade 5, and why wasn't anybody screaming about this back then?

Yes, this. I was an adult before I ever heard of parents helping kids with their homework. Kind of defeats the purpose, doesn't it? Or, at least that's what I thought when I first heard of it.
posted by The Underpants Monster at 8:55 AM on May 26


It's a lesson in breaking down a number into powers of ten, and learning the abstract ideas about how to manipulate these units. You could teach this lesson on an abacus. But Frustrated Parent thinks they're teaching subtraction. They are not.

I have no problem with teaching numberlines and alternate ways of looking at problems. Give students a toolbox of options to solve problems rather than a "right way" works great, in my university teaching experience.

However, what's the bullshit about "writing a letter" all about? How does that teach math? It comes off as contrived and patronizing to the child to me. That's not a real-world word math problem, that's English composition---or are they getting graded on writing in math class too (serious question btw)?
posted by bonehead at 9:11 AM on May 26


You ask kids to show their work so you know they're not cheating. Also so you can give partial credit to kids who understand the concepts but messed up the arithmatic.

You assign homework because kids *have* to practice math to get good at it. They think they understand something in class when the teacher is showing them how to do it, but they don't understand until they can do it on their own. "Start this in class and finish it for homework" is also a good way to keep all students working through the whole period in school, otherwise the kids who are faster will finsh early and have nothing to do, which would be fine id they could entertain themselves quietly and non-disruptively but a lot of them
can't do that.
posted by subdee at 9:12 AM on May 26 [1 favorite]


I'm thinking it's just plain backlash. I'd say argument over educational standards is probably the biggest political sport in the United States, attracting people who are generally resigned to the sorry state of the federal congress and statehouse.

The SPLC wrote a thing about the Common Core and the far right.
posted by hoyland at 9:15 AM on May 26 [1 favorite]


So yesterday I went to the hardware store and picked out a few 1 x 4 x 6 boards. (For those of you not familiar with lumber, that's 1 inch thick by 4 inches wide by 6 feet long, and actually the real-life measurements of the thickness and width of the boards fall a little short of the theoretical ones, but forget that for a minute, because this is a comment about estimation).

It's a little local hardware store, so not everything in the shop has tags with bar codes, and these boards didn't. When I got to the register, the cashier, a young lady who looked to be about 18 - 20, said, "So you got some 1 x 2 x 8s there, then?"

"No," I said, "These boards are 1 x 4 x 6."

"Oh," she said. "1 x 4 x 8 then. Okay."

"No," I said, "These are six foot boards."

"Got it," she replied. And rang me up for the eight foot boards.

"Look," I said, "These are really six foot boards." And I pulled a board out of the cart and stood it up vertically, beside me,* for comparison. "See?"

She stared, wide-eyed, uncomprehending, as the line behind me grew. "Are you sure you read the sign right?" she asked. "I can only find 8 foot boards in the computer. So clearly they must be eight feet."

"But . . ." I said.

The cashier went to get another, more senior cashier. "This customer says these boards are six feet long. But the computer says they're eight feet. What do I do?"

"They're six foot boards," I said to the senior cashier. "From a whole display of six foot boards. See? This one I'm holding up? That is only a few inches taller than me?"

The senior cashier stared at me equally uncomprehendingly, then looked at the long line of customers behind me, who were beginning to grumble. Then she sighed, entered a manager's code to authorize a discount, and said, "Just give it to her for whatever price she said she saw on the sign."

*Counter to the hardware store employees' unfortunate misimpression that I am a giantess, I am 5'7" tall.



If two people who spend their entire day counting money and stocking shelves AT A HARDWARE STORE cannot understand that the average human woman is not nearly eight feet tall, I think it's pretty clear that math education has utterly failed an entire generation of Americans. We need to try SOMETHING different. Some approach to help people gain real-life basic number sense. I have issues with the way Common Core is being implemented-- I think it's being rushed in many districts without enough training for teachers; I think a lot of new math teaching methods that really were meant to be used with high quality texts, interactive activities and hands-on math manipulatives are being poorly translated to shitty worksheets by districts that can't afford or don't want to deal with buying and learning to use new materials; I think the emphasis on testing using tests made by private for-profit companies is more of the same stuff that already didn't work with No Child Left Behind-- but let's not throw the baby out with the bathwater here. We desperately need to improve the way we teach American kids about the basics of HOW NUMBERS WORK. I think giving kids a strong, intuitive number sense is what a lot of these new methods are trying to get at, and I think that's a good thing.
posted by BlueJae at 9:25 AM on May 26 [15 favorites]


Here are some questions for Science Parent: What Common Core standard(s) does this worksheet attempt to teach? Why is it not important for those standards to be taught if your child already knows how to do subtraction another way? What are some of the specific standards that are wasting classroom time?

I'll get back to that first question in a minute. I want to preface my answer with some other thoughts.

I have never, ever, ever heard a single parent complain about a single, specific Common Core standard. The grievance in this case seems to be "my child should not be taught this because he can already do this thing in a different way". It is not practical to revise certain components of the curriculum for an entire classroom on the basis of what one child can or cannot easily master. Every child learns different concepts at different speeds; this reality is not adequately addressed by rejecting concepts that are difficult for one child to learn.

The parent complains that the plethora of methods taught by common core obscures the teaching of basic math operations. The parent also complains that even though his child knew the answer in his head immediately, the problem required him to write an answer and use a number line.

If his child has already mastered addition and subtraction, how does this problem rob him of the time and energy required to learn those skills?

If the issue is that expository tasks are unsuitable for a child with the learning disabilities that the parent describes, then the solution is not to reject Common Core. A better solution is to have the child evaluated and, if necessary, placed on an Individual Education Program tailored to his specific needs. A good IEP will specifically address the issues that the parent complains about, and it is required by law to be tailored to the individual student.

Now, on to my initial question: What Common Core standard does this worksheet attempt to teach? The closest standard that I could find was this one:
Relate Addition and Subtraction to Length

CCSS.MATH.CONTENT.2.MD.B.6
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
A number line relates number values to distances and quantities. I think everyone agrees that the ability to add and subtract is of limited use if you cannot relate those skills to distances or quantities. Certainly an engineer must appreciate this — engineering is a discipline that uses math to manipulate numbers corresponding to concepts like distance, mass, and time. This is a great standard!

Pay attention to this language in the standard:
"on a number line diagram with equally spaced points"
And pay attention to this portion of Science Parent's follow-up Facebook post:
"In trying to walk him through the problem, I mistook the line of numbers for an actual number line with consistent scaling like you would see with geometry or coordinates. I assumed too much and struggled making sense of the lack of consistent scale--100's -10's-1's. I was thinking too visually and literally. To make it work then, I associated intervals of 20 & 10 & 1 with the single steps trying to keep it to scale.
Science Parent is absolutely right! The scale on that number line was inconsistent and confusing. It was bonkers. His complaint is, in essence, that the worksheet did not conform to a certain common core standard. And I totally agree with him! It was a lousy worksheet.

The problem with this worksheet is not the big bad federal government and their awful Common Core standards (that states have voluntarily accepted). The problem is with the private business that produced the offending worksheet and the local school board that allowed its purchase.

I encourage every parent with concerns about Common Core to review the actual standards, determine which standards, if any, should not be taught, which standards are missing, and to contact their child's teacher with their concerns. A good teacher will be able to explain what these standards mean, why they are relevant, and the amount of classroom time that is actually devoted to them. Have reasonable expectations. Parents have many different beliefs about what works best in the classroom, and a good teacher will usually not revise the curriculum on the basis of one parent's opinion.
posted by compartment at 9:26 AM on May 26 [8 favorites]


> There is a surprising lack of evidence that helping children with their homework (math or otherwise), or, indeed, inquiring
> sufficiently into their homework to form opinions about its pedagogical value, does them any good whatsoever.

The article actually says

Do our findings suggest that parents are not important for children’s academic success? Our answer is no. We believe that parents are critical for how well children perform in school, just not in the conventional ways that our society has been promoting.

To mention just one way (that will never, ever, ever be examined by any academic studying educational outcomes), your kid is considerably more likely to get screwed over by a teacher or a school administrator if they know they're never going to have to see you or talk to you.
posted by jfuller at 9:31 AM on May 26


twoleftfeet, this is beeautiful
posted by growabrain at 9:49 AM on May 26


>However, what's the bullshit about "writing a letter" all about? ...

You ask kids to show their work so you know they're not cheating. Also so you can give partial credit to kids who understand the concepts but messed up the arithmatic.


You're getting close, but not quite getting the point.

Many schools, even before the CC curriculum, started doing written essays in every class, including math. These students generally have higher performance in writing just because of the constant practice. They also have higher math scores.

But the main point, especially in Math, is something new to the CC curriculum: justification. You're not just showing your work, you must justify its correctness. This is especially important at the higher levels when you're writing proofs. It doesn't matter how much math you know, if you can't communicate your results to other people, and explain why it's correct and appropriate. This places more importance on knowledge of the principles of math, and reasoning, rather than just the results.
posted by charlie don't surf at 10:04 AM on May 26 [7 favorites]


However, what's the bullshit about "writing a letter" all about?

It has the child explain the concept back to the teacher.

This accomplishes two things.

Firstly, being able to explain something in your own words is a great conceptual learning tool, in and of itself.

Secondly, this is a pretty easy way to tell which of the kids are grokking the number line concept. The kids who don't get it will write "I don't know the humps are too small probably", and the kids who get it will say "They miscounted their tens."

You can ask a million computation questions, and a kid can get them right umpteen times, and it'll be impossible to see what's actually going on in her head. By asking the kid to tell you in words why something works or doesn't work, you can see the gears turning and better assess whether the student is understanding the material.
posted by Sara C. at 10:09 AM on May 26 [11 favorites]


Kids that weren't on my same track had additional time with aids one on one for both conceptual assistance and homework assistance.

Here is where I call bullshit on your calling bullshit--you clearly are not aware what a contemporary American classroom is like. Teacher Aids available to teach kids one-on-one??? HAHAHAHAHAHA you're hilarious. Far more likely that the math teacher has 40-45 kids in one class, no additional help, and is buying supplies with her own money so that the kids have something other than a desk, a text, and a notebook to learn from.

There are no classroom aids or tutors or additional teachers available to help students who fall behind. There are no after school tutoring centers on campus for kids to get extra help. There rarely is a study hall one can send a student to during class, simply to have some extra quiet work time.


However, what's the bullshit about "writing a letter" all about?

And here we have a great example of a totally dismissive attitude because of lack of understanding of pedagogy. This is an example of what I was talking about in my earlier comment. A teacher reading about the letter writing part of the assignment would understand immediately the pedagogical (that is, learning) value of this activity--I did, and I do not teach math nor kids, but I am a teacher. But what's the reaction to this piece of proven pedagogical technique? 'I don't understand it, so it's bullshit.' That reaction is a big part of the reason that teaching and teachers are regarded largely with skepticism and contempt in American culture currently.

Combine cultural contempt for the profession with all the practical realities that come from that (shitty facilities, embarrassingly low pay, lack or absence of resources, no professional support, etc. etc.) and the reaction of teachers is not surprising to me:
The statistics for teacher turnover among new teachers are startling. Some 20 percent of all new hires leave the classroom within three years. In urban districts, the numbers are worse. Close to 50 percent of newcomers leave the profession during their first five years of teaching.
Part of my teaching work is training future teachers, and let me tell you: it is not a desirable profession, it is not held in any esteem, and young people--who are otherwise pretty passionate about teaching and learning--are starting to avoid teaching as a profession in large numbers. Especially the brightest ones. It is an urgent problem that few have acknowledged.
posted by LooseFilter at 10:28 AM on May 26 [9 favorites]


What's wrong with "show your steps" or "justify your answer", rather than this farcical window-dressing? I know, even as a grade three student, this would have turned me off. I can see that echoed in my neices and nephews when they deal with similar problem sets today. I get what this is trying to do, I just think this is a horrible example of how to do it.
posted by bonehead at 10:30 AM on May 26


NO DAD, WHAT YOU'RE SHOWING ME ISN'T THE WAY I HAVE TO DO IT! Which is a hideous frustration to both child and parent, and is clearly still a thing.

Yeah, this is a lot of the reason parents hate it, I think. Parent looks at a subtraction problem, finds it absurdly easy. Parent has internalized a (standard) algorithm to solve it. Further, parent feels like they could really teach that algorithm from zero if they had the time. But none of that helps at all. It has to be done by some particular method which the child doesn't understand, and where the parent, like, Thorzdad (and like me) looks at it and goes "WTF?"
posted by tyllwin at 10:50 AM on May 26 [1 favorite]


LooseFilter's comment is interesting. When I took the required Schooling in American Society course, on the first day, the instructor said "Look around you. Five years from now, half of the people you see will not be teachers anymore."

It stuck in my head because I found it so shocking.

I took that course in 1989.
posted by wittgenstein at 10:53 AM on May 26


What's wrong with "show your steps" or "justify your answer", rather than this farcical window-dressing?

That's exactly what they're being asked for. But this isn't a test, so the student is being handed the answer format, told to find the error and explain it. If you say "justify your answer," the student doesn't know what answer he's supposed to justify. The question here is not a subtraction problem, it is to find the error in the process of the answer that was given. This is a lesson in justification, essentially it's finding errors in a proof.

I know, even as a grade three student, this would have turned me off.

Eponysterical.
posted by charlie don't surf at 10:59 AM on May 26 [1 favorite]


And here we have a great example of a totally dismissive attitude because of lack of understanding of pedagogy. This is an example of what I was talking about in my earlier comment. A teacher reading about the letter writing part of the assignment would understand immediately the pedagogical (that is, learning) value of this activity--I did, and I do not teach math nor kids, but I am a teacher.

I get it. I'm trying to learn a language, and at the end of a chapter, the conversations aren't using ONE of the grammar points made in the lesson. The book is using them ALL in combination. I hate it, but I understand it, and even agree with it.

But in this case, the child isn't being given an holistic grade on progress towards a whole group of goals. The child gets a grade in math, and a grade in English. But suppose the child loves and does well in math, but loathes and does poorly in English? Using this approach, the kid fails both. A kid who understands the math perfectly well could get pushed back to remedial math for a language problem. I think it's quite reasonable for parents and children both to see that as frustrating and unfair, even if, in the aggregate, it's beneficial to enough average students in a study to be considered proven.
posted by tyllwin at 11:01 AM on May 26 [2 favorites]


It stuck in my head because I found it so shocking.

I took that course in 1989.


Yep, that's not long after current trends really started. I visit many public school sites in the course of my work, and I'm pretty sure it's been a steady decline on all fronts in education since the 1980s. But lately I feel like a tipping point is finally upon us, the youngest of the baby-boom generation of teachers--who have been propping up the profession as youngsters split--are now retiring, and we're discovering that there are very, very few veteran teachers left to step up.

(Anecdote: in my four county service area, we send out lots of young teachers to student teach every year. I'm not involved in that part of their training, but do consult with our teacher ed dept. to help with placements. Generally, one looks for a teacher with at least 10 years experience and a Master's degree to serve as a supervising teacher for a placement; this past year, most of the student teachers in our discipline were placed with teachers with 4-6 years experience, and no graduate work or post-credential training. Why? There are no veteran teachers in the surrounding four counties who meet the regular qualifications. [We did have one terrific veteran teacher who supervised again this year, but she's now retired.] Most of our student teachers are now being mentored by "veterans" in the profession who are not yet 30 years old. They are effective teachers, but lack so much of what is learned from longer professional experience.)
posted by LooseFilter at 11:17 AM on May 26 [1 favorite]


Math hurts
Math can be difficult, and for those with high levels of mathematics-anxiety (HMAs), math is associated with tension, apprehension, and fear. But what underlies the feelings of dread effected by math anxiety? Are HMAs’ feelings about math merely psychological epiphenomena, or is their anxiety grounded in simulation of a concrete, visceral sensation – such as pain – about which they have every right to feel anxious? We show that, when anticipating an upcoming math-task, the higher one’s math anxiety, the more one increases activity in regions associated with visceral threat detection, and often the experience of pain itself (bilateral dorso-posterior insula). Interestingly, this relation was not seen during math performance, suggesting that it is not that math itself hurts; rather, the anticipation of math is painful. Our data suggest that pain network activation underlies the intuition that simply anticipating a dreaded event can feel painful. These results may also provide a potential neural mechanism to explain why HMAs tend to avoid math and math-related situations, which in turn can bias HMAs away from taking math classes or even entire math-related career paths.
But if math performance itself is not painful, where does all the anxiety come from?

I think there are problems with math teaching methods that go far deeper than anything Common Core can possibly address, and have much more to do with madajb's question of "why a 7 year old has homework in the first place."
posted by jamjam at 11:18 AM on May 26 [2 favorites]


This is a lesson in justification, essentially it's finding errors in a proof.

So make it about that, don't make it about composition.

Look, while we were being taught these level of concepts in school, we were also being taught composition. One of those lessons included "how to write a letter" which included a whole formalized scheme of appropriate address, how many paragraphs a letter should have (openings and closings, etc...), proper salutations and the form a letter should take on a page. We were marked on how we wrote practice letters in grade school. Form and composition were drilled into us.

At the time, I would have confused the two. As a parent, my perception of this would be that, as well as the intent of justifying their thoughts, the students would also be marked on their ability to compose a letter.

If the point of the exercise is to get a student to do a certain thing, then it should be as comprehensible as possible. As it is, I see this as distracting to the students (and the parents), which undermines the exercise's authority and credibility.

If discovery of error and justification of that proof are what's important here, I think that this worksheet could have been done a lot better. I think this really says more about crappy course materials than any merits of a particular teaching curriculum.
posted by bonehead at 11:18 AM on May 26


If the point of the exercise is to get a student to do a certain thing, then it should be as comprehensible as possible. As it is, I see this as distracting to the students (and the parents), which undermines the exercise's authority and credibility.

That's some pretty thorough armchair criticism--do you evaluate your doctor's working methods that confidently? How about your electrician or plumber or lawyer? It is possible, after all, that there may be a whole chunk of this pedagogy that you neither see nor understand. Should the teacher have to explain all of her expertise to you so that you will allow her to proceed with her job uninterrupted? Or should she have to justify her pedagogy, expertise, and methods to every single parent who doesn't get it?

I know of no other profession where qualified, thoroughly trained professionals have to justify everything they do, so often and to so many.

(Edit: maybe coaches.)
posted by LooseFilter at 11:31 AM on May 26 [7 favorites]


bonehead, you're making a lot of assumptions. You're assuming that there's crossover in the school with other learning tasks. You're assuming that that's necessarily bad. You're assuming that it's less confusing to tell a kid to describe the reasoning in a different way. I personally have seen - both in kids and adults - that grounding things in concrete scenarios is often helpful. So it's not "describe what's wrong with this vacuum math" but "tell me what went wrong with Jack". Your bare insistence that "show your steps" is more intuitive doesn't make it so, and in fact it runs directly counter to a lot of my experience. Especially since "show your work" so often results in "well I subtracted that one from the other and this is the answer I got". It's not necessarily wrong, but moving from that to concluding that it's the only valid tack to take is just silly. If you ask me to "justify my answer," are you going to be surprised if I say "it's right."?

I mean, I don't think that your concerns have to be thrown out the window, but I think you're reaching awfully far when you go from "here are my concerns" to "my concerns immediately mark this approach as crappy course materials," especially since it seems clear you've spent 0 seconds attempting to see the strengths of this approach or the possible weaknesses of other approaches. Especially since no approach is going to work for everyone.
posted by kavasa at 11:33 AM on May 26 [7 favorites]


LooseFilter, if we're not allowed armchair opinions on MetaFilter where are we allowed them?
posted by ElliotH at 11:38 AM on May 26 [1 favorite]


I'm not assuming cross-over is bad, but I would wonder, seeing this in a kid's homework if this was a double-barreled exercise to do both. I would further get a kid to fulfill the requirements of both (explanation and letter-writing) on the exercise sheet.

If that isn't what is intended, and I have no way of knowing what is intended but what's on that page, assuming there isn't instruction from the teacher, then we've just wasted time doing a draft letter or two to finalize the student's answer, for something the teacher isn't looking for.

I am very familiar with the problems that "justify your answer" has, at the post-secondary level. PhD students get it wrong too. I am sympathetic with the idea of making exercises concrete, of allowing the student an easy access to a response. I don't think this work sheet does that though, in a way that won't be confused if the intention is just to work on math in this exercise.
posted by bonehead at 11:43 AM on May 26


I despise the whole "just use a calculator" mentality, as someone who became a graphing calculator whiz when I should've been paying attention in Algebra II / Trig, as I learned later in calculus, where we sure as shit didn't allow calculators on exams because yes, you need to understand calculus to know when and why to use it, or to get your brain at least "broken in" to that process of understanding what you're doing, and being able to make reasonable assumptions and estimates without consulting with your cell phone. I think there is a need to form these synaptic connections even if there are always tools available.

Of course we use calculators in practical situations where we aren't trying to learn how to calculate. No, teaching kids to use calculators at an early age does not teach them what they need to know about mathematics, it teaches them to be reliant on a tool and never have any practical grasp on how the numbers relate. It would be absurd to start with "1+1 = 2" on a calculator and where you draw the line and start allowing the calculator is when you need to graph it, or perform calculations in applied mathematics situations where the calculating isn't part of the actual lesson.
posted by aydeejones at 11:44 AM on May 26 [1 favorite]


ElliotH, touché. But my point speaks directly to the FPP, which is about this particular kind of armchair criticism, which I think is pretty pernicious in American culture currently, with widespread deleterious effects.
posted by LooseFilter at 11:45 AM on May 26 [2 favorites]


The path towards Idiocracy lies that way. The movie was problematic but the fundamental point about being frustrated towards and increasingly thoughtless society that mocks thoughtfulness rings true for anyone who was bullied and hassled for being interested in the learning process. I think getting kids to manipulate the mental stack and registers in their brain in these ways is a path towards thoughtfulness and introspection, though all of the basic social skills like kindness and patience and self-awareness are just as important.
posted by aydeejones at 11:48 AM on May 26 [1 favorite]


Their reason number 3 should be reason number one. IT'S NOT COMMON CORE. This drives me nuts, as I have tried to learn exactly what Common Core is I have found lots of people who hate it while simultaneously showing that they don't actually know what Common Core it.
It's not a prescribed teaching method, it's not curriculum. It's more guidelines for what benchmarks kids should be hitting.
posted by MrBobaFett at 11:49 AM on May 26 [4 favorites]


I'm not understanding the problem with the instruction to "write a letter" to Jack to tell him what he did wrong, considering that the math exercise is to figure out what Jack did wrong. That seems like the easiest and clearest way to "show work" possible, considering what the original exercise is about (ie, finding and explaining Jack's mistake).
posted by rue72 at 11:49 AM on May 26 [2 favorites]


Like many others I'm suspicious of the new new math. Especially given how often the children I know reach for the calculator to solve elementary problems, e.g. 7×9. Still, I trust that educators are making these changes thoughtfully.

One thing I think might be getting missed here is how often Common Core is referred to as "Obama's Common Core" (as in, at every commercial break here in Georgia for the last six weeks leading up to the recent primary election) and how closely it's linked with "Agenda 21" in the minds of some people. Not the actual Agenda 21 of course, but the notional idea that it's a secret liberal plan for one world government.

Therefore, I'd take any opposition to it — especially on Facebook — with a grain of salt.
posted by ob1quixote at 11:50 AM on May 26 [2 favorites]


Actually, as much as I disliked the question on first read through, rue72 has a fair point. Also, explaining errors to others is actually something that comes up in the real world fairly often. Being able to teach something is often cited as a good way to learn something. Maybe it would have been better to ask for the answer as part a and then the letter in part b? That way you'd have success early on.
posted by ElliotH at 11:53 AM on May 26 [3 favorites]


What burns my biscuits is hearing parents say "why do they teach Algebra, you never use that..." That was always a cliche when I was in Algebra, and it quickly became apparent in my adult life that it's incredibly useful for deriving things that yes, you can learn as simple rules of thumb, like using reciprocals to solve simple equations without knowing Algebra, but knowing how to find the rules of thumb without remembering them all was the best part. Solving for a single variable in simple equations is something people should understand. They don't have to, but the more you can figure out on your own, the more self-confidence and self-reliance you will develop. It starts small and grows fast. Part of it is personality, in that to me the thought of asking someone "If someone took X from my payment and told me it was 2% of some amount but I only know what X is, what did they originally owe me?" is painful, I'd at least Google it first, and I'm speaking from a nerdy white guy position, but I think much of my privilege was being surrounded by teachers just from K-6th grade alone that really explained the hell out of simple stuff and etched these things into my brain.
posted by aydeejones at 11:54 AM on May 26 [2 favorites]


Someone upthread asked about Canada, and my experience, in an Ontario French public school, is that it seems to be pretty similar to what you are calling Common Core. Math involves a lot of solving strategies that are completely foreign to me and seem extremely convoluted.

When my daughter started in Junior Kindergarten and was bringing work home (DO NOT GET ME STARTED ABOUT HOMEWORK FOR FOUR YEAR OLDS) I was super impressed because she was doing all these things that she thought of as fun games that were clearly math. The approach seemed amazing to me, integrating what were fairly complex (for a four year old) math concepts into other subjects. It gave me a lot of hope!

As she's progressed, I've had mixed feelings. She is EXCELLENT at math, loves it, and has had a good number sense from a really young age. She HATES having to use several algorithms to solve any given problem and doubly hates having to justify which algorithms she used. Some of that is, I suspect, just eleven year old laziness. But also, she just straight up prefers to use the simplest algorithm for the job and resents having to us one that is clearly inappropriate and then explain why it is inappropriate. Which I totally get. (And which, on re-read, I guess is the same thing as laziness.)

The child gets a grade in math, and a grade in English. But suppose the child loves and does well in math, but loathes and does poorly in English?

I think this is something that disproportionately affects boys. I have a friend whose son is a math whiz but had quote delayed language skills. He wasn't a great reader and was a poor writer. Because starting from first grade, the work they did was primarily word problems, he got crappy grades and grew to hate the one subject he really loved.

ANYWAY, when my kid was in second grade, at the first parent-teacher conference of the year, one of the parents asked about the New Grammar because she was trying to help her daughter with her homework and the kid kept saying it was wrong. The teacher parsed a sentence the new way (in French, but still: no subjects! no verbs!) and then just said, "Look: it's way too different from the way you were taught. Your job isn't to teach your children, it's to support them. When they don't understand how to do something, just send them back to me." And that's been my approach to all the homework since then, grammar, math, you name it. I'm not the teacher.
posted by looli at 12:04 PM on May 26 [4 favorites]


Oh and I wanted to say that a lot of the pro-Common Core comments in this thread have been really helpful in helping me understand the pedagogical philosophy about some of the concepts I found dubious (chunking, estimating, that weird substract by adding thing) so thanks for that!
posted by looli at 12:05 PM on May 26 [3 favorites]


So make it about that, don't make it about composition.

Considering the sheer number of people -- in my very humanities oriented field -- who can't write a goddamn work email correctly, I can't see it being a bad thing at all to start kids off having to explain things in writing at an early age.
posted by Sara C. at 12:25 PM on May 26 [4 favorites]


"Look: it's way too different from the way you were taught. Your job isn't to teach your children, it's to support them. When they don't understand how to do something, just send them back to me."

In the half-dozen cases I'm very familiar with, parents and (especially) grandparents have been critical to help kids in grade school achieve their best successes. Critical in that prior to extensive home tutoring they required special education plans in some cases, to going to great academic successes. Worksheets don't have to just communicate with the kids, they have to communicate with parents too. If the parents can't help their kids, because of "a whole chunk of this pedagogy that [they will] neither see nor understand", I think that speaks to real problems with the approach.

This is what I was perhaps clumsily trying to express above. How does this approach help a parent be involved with helping their kids learn? It appears to me to throw up barriers. If this worksheet is representative of that current philosophy then are parents just not supposed to to be able to check homework? Is that the desired outcome of these new methods of teaching?
posted by bonehead at 12:58 PM on May 26 [1 favorite]


If you having 5 hours of classes is acceptable, then why is 4 hours and 45 minutes of class, and 15 minutes of homework, not acceptable? You can do exactly as many kid things.

It's about context.
I firmly believe (and there is research that backs me up) that kids need a chance to be kids, free from the performance expectations of adults and free from formal structure.
For young children, when the school day is over, it should be over.

Ok, that makes sense. So you'd find, for example, a 10 to 15 minute study-hall period at the end of the day, where kids do homework and get help if needed, to be acceptable? Because that would make sense to me, too.

Yes. To me that would be much better than "Send them home and hope they, or their parents, can figure it out".
posted by madajb at 1:29 PM on May 26 [2 favorites]


Should the teacher have to explain all of her expertise to you so that you will allow her to proceed with her job uninterrupted? Or should she have to justify her pedagogy, expertise, and methods to every single parent who doesn't get it?

The problem comes when the students bring this stuff home as homework and the parents (for whom all of this looks like ancient Martian) are expected to somehow help the student. And, if it's coming home as homework, you have to expect the parents to get involved, because "Mom...Can you help? I don't understand this."

So...yeah. You kind of do have to explain the whys and wherefores of what you're trying to accomplish. That, or you explicitly tell parents not to try and help. Good luck with that.
posted by Thorzdad at 1:31 PM on May 26 [1 favorite]


As she's progressed, I've had mixed feelings. She is EXCELLENT at math, loves it, and has had a good number sense from a really young age. She HATES having to use several algorithms to solve any given problem and doubly hates having to justify which algorithms she used. Some of that is, I suspect, just eleven year old laziness. But also, she just straight up prefers to use the simplest algorithm for the job and resents having to us one that is clearly inappropriate and then explain why it is inappropriate. Which I totally get. (And which, on re-read, I guess is the same thing as laziness.)

This seems a case where your daughter is just ahead. She understands a lot of it already and approaching problems from different angles feels like busy work. But the curriculum — all curricula, as has been pointed out above — needs to deal with a large number of kids with a wide range of abilities. I'd wager there are other students in her grade that are getting a lot of value out of the variety of math strategies they're being taught.
posted by wemayfreeze at 1:46 PM on May 26 [2 favorites]


This is what I was perhaps clumsily trying to express above. How does this approach help a parent be involved with helping their kids learn? It appears to me to throw up barriers. If this worksheet is representative of that current philosophy then are parents just not supposed to to be able to check homework? Is that the desired outcome of these new methods of teaching?

The new curriculum needs to be taught to parents as well, so they can help out. That's what I see as the big issue here. It's classic management, really: get buy-in from all stakeholders so everyone feels ownership and can work together to achieve shared goals — smart and happy kiddos.
posted by wemayfreeze at 1:49 PM on May 26 [1 favorite]


I mean, I don't know! I haven't read any CC specs or anything

Not meaning to pick on you, but you stated this thing explicitly and quotably that has come up implicitly in a number of other comments. For everyone's reference: the CC standards, and an explanation around them, are at the first link after the break in the FPP.

Moreover, think of every kid in college that you knew that went into early childhood education. Think of every kid in college that you knew that went into school administration. Think of their damn math scores and math ability. These are the folks that are designing your child's curriculum - because you don't go into education when you understand number theory, graph theory, statistics, and calculus - you go get paid. The people in charge have a bit of a clue, because they've read a bit about algorithms and learning and the faster way to an answer and how math breaks down - but dammit - they've grossly misapplied these concepts to wreck 215 minutes weekly of my childhood (3x35+2x55).

The CC standards were written by teams of educators with graduate degrees in both the subject areas involved and in education. As compartment and others have pointed out, this does not mean that the specific classroom activities that are being used in some districts to attempt to teach to these standards are nearly as well or expertly developed.

The Common Core is something that has been in the process of development for a long time, a step in the history of standards based education reform in the US. Ironically, in light of the right wing backlash to Common Core, as the first link describes,
Standards-based reform first gained momentum in 1983, during the Reagan era, with the federal educational goals and objectives highlighted in "Nation at Risk." This federal interest in reforming education lasted through the Bush ("America 2000") and Clinton eras, and is currently known as "Goals 2000."
(though I suppose it shouldn't be surprising by now that right wingers are opposing Obama policies that are not substantively different from earlier Republican policies, and to be fair, standards-based education reform is more of a progressive cause than a conservative one, ideologically).
posted by eviemath at 1:54 PM on May 26 [2 favorites]


This part of the additional explanation facebook post from the parent who wrote the "Dear Jack" letter,
the rollout of Common Core Standards that introduces a plurality of math methods too early is thus circumventing the learning of those rote, repetitive and yet foundational algorithms necessary as this stage of child growth and development. Common Core philosophy forgets that the "what" and "how" precede the "why" in early childhood education. Once those things that simply must be learned are indeed learned (such as multiplication tables, how to subtract, etc), then into that cultivated soil the introduction of creative, mind-expanding "why" and "what if" questions should be introduced fostering next-level critical thinking.
is really terrible, by the way. Some students may learn better by learning a completely meaningless algorithm for a computation by rote first, and then learning why that algorithm works. Many, perhaps most, students don't. And that's not even getting into a discussion of what the point of education is or should be. Many students learn the rote calculation algorithm better if they also learn the why behind the algorithm first or at the same time. Not all, of course, because there's huge variation in successfully learning strategies for different students, but many.

Ideally, schools are sufficiently funded, with a sufficient number of sufficiently well-trained teachers, and a sufficient supply of exemplary resource materials, so that educators can respond to and work with students' individual talents and needs, presenting topics in the order that will be most useful for each individual student, motivating new ideas with applications that will be engaging for each individual student, allowing each individual student time to work at a pace that is most conducive to their own learning for each topic, yet providing nudges and challenges at just the right time for each student to optimize engagement and learning. Standards-based education or no, most schools in the US (even private ones, but especially public schools) are very far from this ideal; and that, as others have noted above, is a whole huge (though separate) problem.
posted by eviemath at 2:04 PM on May 26 [4 favorites]


Anyone who's worked a cash register did this for every single transaction that had change.

Thank you. I've been trying to rack my brain where I'd done this before. Also making sure the drawer had $100 left in it at the end of the night for the next days shift.
posted by Gygesringtone at 2:07 PM on May 26 [2 favorites]


Yeah, eviemath, that pullquote is so completely backwards. Multiplication tables "must be learned"? And rote, repetitive algorithms = "culitvated soil"? I mean what.
posted by wemayfreeze at 2:09 PM on May 26 [1 favorite]


Addition and multiplication tables, or "math facts", are pretty handy to have in one's quick-recall memory when learning more math, since that's one less step to have to stop and think about, allowing students can focus on new ideas rather than looking up facts needed for each explanatory example. But yeah.
posted by eviemath at 3:02 PM on May 26


Anyone who's worked a cash register did this for every single transaction that had change.

Not anymore they don't. They have cash registers with coin dispensers to deliver the calculated change. Some big-box stores have a display that actually shows pictures of the bills and coins to be dispensed. Counting change is a lost art. And that is too bad, because it's really useful. The other day I bought something for $6.05 and I gave the clerk a ten, a one, and a nickel. He had no idea what I was doing until the register said change=$5. But more importantly, knowing why you are making change that way is important. While working a register, I have caught more than one "shortchange artist" trying to scam me. They depend on you not knowing basic math, and relying on rote procedure. He can make the rote procedure work for him.
posted by charlie don't surf at 3:28 PM on May 26 [1 favorite]


He had no idea what I was doing...

I don't want to derail, but as someone who has actually worked in retail, this sentiment drives me bananas.

No, this did not happen because you are good at math and retail workers are bad at math. It happened because the cashier had eleventy million things on their mind, approximately zero of which was what kind of creative handful of cash you were going to hand over. Seriously, folks, not everything is about you. Cashiers in stores give like a tenth of a teaspoon of a shit whether you get a nice round amount of money back on your piddly little transaction, which is one of about 500 that will be performed in a given day.

Please stop saying this until you've actually worked a retail job.
posted by Sara C. at 3:42 PM on May 26 [3 favorites]


Sara C.: "No, this did not happen because you are good at math and retail workers are bad at math. It happened because the cashier had eleventy million things on their mind, approximately zero of which was what kind of creative handful of cash you were going to hand over."

The only time I've gotten the "what is this bizarre payment amount" reaction has been when I've returned home to the US. I've never seen any consternation or confusion in Japan. You're saying it's not because Japanese generally have better math skills, but because Japanese cashiers don't think about as many things as American cashiers?

(Ok, less flippantly: I suspect it's actually more a customer issue than a cashier issue. Even if you're fucking horrible at math, and the first time a customer tries to pay you $1.05 for something that costs $0.95, you cannot understand what they're trying to do, you will lose this consternation after the fiftieth customer on the same day does the same thing. Even if you can't do all the math in your head, you will grok the trick within your first day at the register. However, if customers don't use this payment approach, you'll never get used to it.)
posted by Bugbread at 3:55 PM on May 26 [1 favorite]


Also, in my experience, the cashiers in the US thinking about a million other things aren't the ones having the change problems. They punch the numbers in the register and give you whatever it shows on screen. All the ones with the change problems have been pretty explicitly the ones who are thinking about the change, pointing out unprompted that $1.00 is enough to pay for a 97 cent thing, and that you don't need to pay $1.02.

(I'm assuming I'm allowed to say this, because I've worked retail)
posted by Bugbread at 4:15 PM on May 26 [1 favorite]


Please stop saying this until you've actually worked a retail job.

You did not even read my comment. It contains relevant details of my working in retail, such as:

While working a register, I have caught more than one "shortchange artist" trying to scam me.

I started running the register and counting cash drawers at closeout when I was about 12. I can't even count the years I spent running a register, either as a primary duty, or a secondary one.

It happened because the cashier had eleventy million things on their mind, approximately zero of which was what kind of creative handful of cash you were going to hand over.

Yeah they have a lot of other things on their mind, like for example, I caught one of the register operators moving pennies and nickels around on the plate on top of the register all day long. That was their little abacus to keep track of how much money they had skimmed while shortchanging customers, and was a running tally of how much money they had to steal from the cash drawer so it balanced at the end of the day. Just to bring this back to relevance, the techniques used in the homework are amazingly similar to this technique of moving pennies around to indicate sums to steal from the till.

So before you fly off the handle in a massive derail and embarrass yourself by demonstrating that you did not even read the comment you objected to, you might consider the possibility that the person making a comment actually knows what the hell he is talking about. I will stop here before I give you my lengthy lecture about the history of the cash register in the 1880s and how some guys from National Cash Register and the Computing-Tabulating-Recording Co. got together with this guy named Herman Hollerith, formed a company called IBM that invented modern computers. And all based on a business idea to keep retail clerks from skimming money out of the till.
posted by charlie don't surf at 4:24 PM on May 26 [4 favorites]


So you just answered your own whine about how dumb retail workers are. The reason cash registers tell people how much change to give is because the retail workflow is optimized to make stealing hard. Not because cashiers literally don't know how math works.
posted by Sara C. at 4:26 PM on May 26 [1 favorite]


The reason cash registers tell people how much change to give is because the retail workflow is optimized to make stealing hard. Not because cashiers literally don't know how math works.

No. Many of them literally do not know how to make change. They never had to. Sometime go to Walmart and buy something with cash. They don't use automatic change dispensers. They have a color display that will show an image of the coins and bills. If you need 74 cents change, it will show a color picture of two quarters, two dimes, and four pennies, all lined up in vertical rows.

I think we have pretty much exhausted your derail.
posted by charlie don't surf at 4:33 PM on May 26 [3 favorites]


And that they can't even correctly identify portobello mushrooms.
posted by Bugbread at 4:35 PM on May 26 [6 favorites]


I've worked a cash register, and it gave me the ability to quickly add up stuff in my head. !****It* *amazes* *my* *friends****!

Anyway, this may be a comment that is only of interest to Bugbread and Charlie Don't Surf due to their Japan sojourns, but 20 years ago, at the tail end of the bubble, when people still had extra cash, it was really uncommon to pay in exact change (something I had always done in Canada) at a restaurant or convenience store. Nobody worried about change, and would happily break a 10 or a 50 or a 100. I don't know what they did with the change, but probably used it for smokes or canned coffee. So it was always really confusing for the conbini clerks when I paid exact change, or paid extra change in order to get a measly 5 yen coin back, instead of a bunch of lousy aluminum slugs.

As for retail cashiers, they will get my sympathy when it is acknowledged that I have a limited amount of money to spend that I work damn hard for and owe to nobody except my wife and kids. I don't mind the indifference I encounter at the Gap or whatever. Customer service is a premium thingy these days.
posted by KokuRyu at 4:38 PM on May 26


Sara C.: "So you just answered your own whine about how dumb retail workers are."

When did charlie don't surf say they were dumb? All I've seen him say is "cashiers nowadays don't count down to make change, they use the change shown on the register screen". Did a comment get deleted or something?

KokuRyu: "So it was always really confusing for the conbini clerks when I paid exact change, or paid extra change in order to get a measly 5 yen coin back, instead of a bunch of lousy aluminum slugs."

Interesting. So that supports the "it's not a matter of the quality of math education, it's a matter of whether or not customers use the change-optimization technique" idea.
posted by Bugbread at 4:47 PM on May 26


[Folks, its up to you whether you want to change this conversation into "Myths about retail workers" but I'd suggest wrapping that one up.]
posted by jessamyn at 4:50 PM on May 26 [2 favorites]


Legend has it that deep in the Everglades lives Father Cashier. His long white beard stretches 100 yards, and he has the cold, flinty eyes of someone who has worked the cash register since before the Civil War. Sometimes, on a hot, muggy night, you can hear his voice rumbling out from somewhere in the swamp, "...Thank you...And have...a nice day."
posted by Bugbread at 4:55 PM on May 26 [4 favorites]


But do you think this is more likely to happen in 2014 than it would have been in 2010, or 2000, or 1970? I see no reason to think so.

One of the promises of this new new math was that it was going to be a better way to teach the subject. It doesn't seem unreasonable for parents to be frustrated that it turned out to be comets bullshit. Also as a secondary datapoint these kids are getting a lot more homework in elementary school than kids did in the 1970s.
posted by humanfont at 5:24 PM on May 26


it turned out to be comets bullshit

Fuckin' comets, man. You just can't trust 'em.
posted by yoink at 5:30 PM on May 26 [4 favorites]


People like that differential equations guy love to poo-poo what's going on in math education nowadays and tout their credentials, but what would be really cool would be to see one of them offer, say, a thousand dollars to any seven year old who could explain that correctly, and encourage the world to share the offer a gazillion times.
posted by alphanerd at 8:50 PM on May 26 [1 favorite]


Number lines are probably a helpful tool as long as you only got one or two sizes of jumps, so single or double digit addition/subtraction. But once you start involving three different sizes of jumps, your scale for the big compared to the small jumps will be so off that any intuitive advantage is lost.
posted by ymgve at 5:19 AM on May 27


"Here's how to multiply 85 times 85. Take the 8. Multiply by one more. So you multiply 8 X 9, which is 72. Stick 25 after that." They learn that quickly. "85 X 85 = 7225. This always works."

Also, what? Did I miss some sarcasm?

54*54 = 2916, with your method it would be 3016.
posted by ymgve at 5:35 AM on May 27 [1 favorite]


It always works for 85 x 85, though :)
posted by empath at 5:51 AM on May 27 [3 favorites]


Yeah, that's not a trick for memorizing AB x AB, it's a trick for memorizing 85 x 85. Here's a handy trick for memorizing 17 x 43: Put the first number at the end, so it becomes 7431, and then remove any even numbers, so it become 731.
posted by Bugbread at 5:56 AM on May 27 [4 favorites]


It's actually a trick for squaring numbers ending in the digit 5. If "x" is the number to be squared, you drop the last digit and consider the remaining digit(s). Let's call that "y". Multiply y by (y+1) and add the digits 2 and 5 at the end of your result to get the answer.

The reason this works is that you're really multiplying x+5 by x-5 and correcting your answer. (x+5) * (x-5) = x^2 -25
which means
x^2 = (x+5) * (x-5) + 25

To do the example above:
85^2 = 80 * 90 + 25
= 7200 + 25
= 7225

So-called "Vedic math" websites are big on marginally-useful things like this.
posted by Joe in Australia at 6:08 AM on May 27 [9 favorites]


What burns my biscuits is hearing parents say "why do they teach Algebra, you never use that..."

Yeah, that always puzzles me, too. I use algebra Every. Single. Day.

Oddly enough, Algebra was the only math course I ever got a perfect score in.
posted by The Underpants Monster at 8:58 AM on May 27 [1 favorite]


So, kids, to review today's lesson:

Every problem in health care is due to ACA.
Every problem in learning is due to Common Core.
Every problem with society is due to liberals.
And every problem in the VA is due to that bastard Ben Ghazi.
posted by Mental Wimp at 10:14 AM on May 27 [6 favorites]


Multiply y by (y+1)...

So squaring is replaced by squaring and then adding one more "times" to the product? Not sure how this makes squaring simpler.
posted by Mental Wimp at 10:17 AM on May 27 [1 favorite]


Instead of multiplying 85 and 85 you're multiplying 8 and 9, which you have memorized as 72.

So, 18 squared is 16 times 20 + 4 which is 324 because 16 * 20 = (18 - 2) (18 + 2) = 18^2 - 4. It's just a mental arithmetic trick that can be useful in a pinch.
posted by Elementary Penguin at 10:26 AM on May 27


Instead of multiplying 85 and 85 you're multiplying 8 and 9, which you have memorized is 72.

6400+2*400+25. I don't see how the algorithm is any easier than this. But I suspect it's just the way my brain works.

As an aside, I almost never have just one way to solve the problem. That way I can check to see if it's one of my "stupid" days.
posted by Mental Wimp at 10:31 AM on May 27 [2 favorites]


I had an intuitive sense for math until factoring, which confounded me and held me back from more advanced classes, after starting in pre-calc my freshman year in high school and ending up in Alg I a couple weeks later. I did well in Trig but got my butt kicked again in Alg II. Something about factoring never made sense, because I wasn't seeing the underlying reason for the way it was done. 20-some years later I'm revisiting algebra and calculus because of personal and professional needs, and it's still challenging, but these days I'm finding it's easier accepting that rules and methods don't have to be fully understood to be practiced. Eventually the reasons will be revealed through putting the methods to work. But learning different methods to conceptualize math might have helped get past a big mental block long ago that I'm still struggling with today.
posted by krinklyfig at 2:47 PM on May 27 [1 favorite]


Mental Wimp: "6400+2*400+25. I don't see how the algorithm is any easier than this."

Well, your algorithm is to separate the two numbers into their tens and their ones, and then multiply it all out. So it's:
80^2 + 2*(80*5) + 5^2
You're squaring one number, multiplying a set of numbers, multiplying that result by two, and squaring another number. I would call that four mathematical steps.
The other algorithm is adding one to a number, multiplying a set of numbers, and adding 25. I'd call that three mathematical steps, and, honestly, "adding one" is so simple I'd actually call it more like 2.1 mathematical steps. To me, at least, it seems far, far faster and easier.
posted by Bugbread at 3:58 PM on May 27


And, on further reflection, with the original trick, you're not so much "adding" 25 as you are "tacking it on the end" (I mean, yes, literally, worked out, what you're doing is adding, but in your head you're just multiplying two single-digit numbers, and tacking 25 after them). With your way, Mental Wimp, you're multiplying two single digits, tacking 00 after them (or multiplying two double digit numbers which are multiples of 10, depending on how you actually mentally do it), then remembering that number while you multiply a two-digit number by a one-digit number, then actually adding the two results (not just tacking one after the other, but regular adding, with remembering to carry digits, etc.) and then tacking 25 to the end.

I mean, if it works faster for you, that's great. But I suspect that's because you've had a ton of practice, not because your method is actually easier.
posted by Bugbread at 5:26 PM on May 27 [1 favorite]


Here's a more generally useful mental arithmetic technique: the Difference of Two Squares. This is very useful in multiplication because you can often use it to convert one pair of numbers into a different pair of numbers that are easier to multiply.

This is the formula: (A+B) * (A–B) = A2 – B2

For instance: 17 * 43 is hard to multiply. But let's add the two numbers together, and halve them, to get their mean: (17+43)/2 = 60/2 = 30. That is, one of our numbers is greater than 30, and one of them is less than 30; their average is 30 and the difference between either number and their average is 13. So let's plug this into our formula:
     17   *   43 
= (30–13) * (30+13)  ⇐ Look! A difference of two squares!
=   302   –   132
I already know that 302 is 900. I happen to know what 132 is (169) but it's not hard to calculate that, either.
17*43 = 302 – 132 
      = 900 – 169 
      = 731
Done.

If your pair of numbers doesn't add to an even number (e.g., 17 * 44) then subtract one from one of the numbers and add the other number at the end:
17*44 = 17 * (43+1) 
      = (17*43) + 17   ⇐ We know (17*43) from before!
      = 731 + 17
      = 748

posted by Joe in Australia at 6:04 PM on May 27 [2 favorites]


Well, that's all the trick we were doing is, though, is a modified difference of two squares. Not universally applicable but useful at times.
posted by Elementary Penguin at 2:37 AM on May 28


Yeah, that always puzzles me, too. I use algebra Every. Single. Day.

Underpants Monster - if I can ask, in what way do you use algebra every day?
posted by zardoz at 11:36 PM on May 28


The new curriculum needs to be taught to parents as well, so they can help out.

I've worked with a few different math curricula and ALL of them have parent worksheets and websites that explain what's being taught and how parents can help.

If parents aren't getting this material, check your kid's overstuffed backpack OR email the teacher.

**IF you are a parent who is inclined to help with math homework, that is.
posted by kinetic at 3:18 AM on May 29


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