Fun math for kids
September 20, 2015 1:39 PM   Subscribe

Unsolved problems with the common core. Computational biologist (and occasional curmudgeon) Lior Pachter pairs unsolved problems in mathematics to common core math standards.
posted by quaking fajita (18 comments total) 30 users marked this as a favorite
 
Interesting, though I suspect most parents would hate this. Mathematicians consider mathematics as a fascinating subject in and of itself. Parents generally want it to be taught as a set of tools to be used in other subjects like accounting, engineering and biology.
posted by monotreme at 2:06 PM on September 20, 2015 [2 favorites]


I like this idea. But I think the authors sense of what a first grade kid is capable of might be a little off?

Relevant common core: “developing understanding of whole number relationships”.

Warm up: Suppose that in a group of people, any pair of individuals are either strangers or acquaintances. Show that among three people there must be at either at least two pairs of strangers or else at least two pairs of acquaintances.

posted by wemayfreeze at 2:18 PM on September 20, 2015 [1 favorite]


What a brilliant idea! I agree that he's a little ambitious in what he thinks a first-grader can understand and focus on (not all of them can reliably color a single shape with a single color) but there are definitely things here you can introduce to kids in the first few years of school, and blow their minds.
posted by Joe in Australia at 2:21 PM on September 20, 2015 [1 favorite]


The mathematics that are taught in K-12 deliberately diverged from the theoretical study of mathematics being taught in universities about 60 years ago, a decision that had the backing of a lot more than a group of concerned parents. (Coincidentally, educational reform typically requires such great buy-in that it needs nearly unanimous support to be implemented. Almost anybody who says "told you so" is lying, or at best being disingenuous.)

There was recently a great podcast episode about this that details just how hackneyed the "new math" backlash has become. We've been having the same exact fight every 20 years for the past 100 years.

The messaging around Common Core could also have been better, and we could have used the backlash as a positive force to improve the initial implementation. At its, erm... core, Common Core is little more than a taxonomy -- a Dewey Decimal System for primary education. Phrase it that way, and suddenly you find far fewer people clamoring to burn the whole thing to the ground, and more people interested in actually having a productive discussion about which topics we should be emphasizing and why.
posted by schmod at 2:25 PM on September 20, 2015 [3 favorites]


The Goldbach Conjecture is definitely a good fit for 4th or 5th graders - for some 4th or 5th graders. It just depends whether they're curious about those kinds of things or not. That doesn't even correlate well to "mathematically talented", like, 'A' students may be getting those A's without the kind of curiosity that finds Goldbach interesting. On the other hand, some kids that don't ordinarily put much effort into math can start obsessively making tables of squares and adding them.
posted by Wolfdog at 2:30 PM on September 20, 2015


Who knows! is my point, I guess.
posted by Wolfdog at 2:34 PM on September 20, 2015


I just tried Goldbach's Conjecture on a bright eight year old. He doesn't really get the idea of a rigorous proof but he's definitely on team Goldbach, if a vote should ever have to be taken.
posted by Joe in Australia at 2:44 PM on September 20, 2015


I'm all in favor of teaching kids early on that there are unanswered questions, and that they can already understand those questions even if they can't find the answers yet. Math (and science) isn't just a body of fact to memorize, it's a set of techniques that we use to explore the unknown.

I like this idea. But I think the authors sense of what a first grade kid is capable of might be a little off?

Among three people, a first-grader could (perhaps with guidance from the teacher) list all the 23=8 ways that people can be acquainted, and notice that there are always "at least two pairs of strangers or else at least two pairs of acquaintances." A rigorous proof for n>3 is beyond them (and so far, everyone else too).
posted by Rangi at 3:12 PM on September 20, 2015 [2 favorites]


İ like this! İ might use it in my high school Geometry class to teach conjectures vs proofs. Right now İ usually use "how many ways can three non-parallel lines intersect" and the four-color theorem as accessible examples of how you can know something is true, but not how to prove it. But of course those two things actually are proven so this might be even better.

İ get the argument that math should be practical and applied for grade school kids, but high school Geometry is the one subject where formal proofs are the whole point so having an easy entry point like this is kinda useful, for those kids who haven't seen these ideas in earlier grades.
posted by subdee at 3:29 PM on September 20, 2015


This is wonderful. (By which I mean, I was intrigued by the puzzles, only a few of which I knew already.)

It won't catch the eye and inspire the obsession of any student exposed to these kinds of examples -- but it will open the eyes of some. And if such things were even briefly discussed (at regular intervals), then all kids will be more aware -- as they should be -- of the limits of human understanding, that "we are always walking right along the precipice of mystery" as Lior says.

There's beauty in that, and excitement, and adventure. All of which are good things that should be encouraged.
posted by brambleboy at 3:31 PM on September 20, 2015 [1 favorite]


From what I know of my kids all they do is ask "why" over and over until I give up.
posted by Annika Cicada at 4:29 PM on September 20, 2015


That's what professional mathematicians do at conferences, too. So it could be a promising sign.
posted by Wolfdog at 4:57 PM on September 20, 2015 [7 favorites]


İ might use it in my high school Geometry class to teach conjectures vs proofs. Right now İ usually use "how many ways can three non-parallel lines intersect" and the four-color theorem as accessible examples of how you can know something is true, but not how to prove it. But of course those two things actually are proven so this might be even better.

Probably not age appropriate, but a possibly good source of inspiration is Lakatos' 'Proof and Refutations,' which uses Euler's 'theorem' that polyhedra satisfy V-E+F=2 as the basis for a discussion of the tension between conjecture, proof, and definitions. And it does it in the form of a kind of play/dialog between a teacher and their students, going through much of the historical development of the problem.
posted by kaibutsu at 6:24 PM on September 20, 2015 [3 favorites]


If a 5th grader proves (or disproves) the Goldbach Conjecture, Faber and Faber better cough up the money even though the kid missed the deadline. It's not fair, they weren't born yet.
posted by axiom at 9:16 PM on September 20, 2015 [1 favorite]


Annika Cicada: "From what I know of my kids all they do is ask "why" over and over until I give up"

This is a suprisingly solveable problem.
posted by Joakim Ziegler at 11:19 PM on September 20, 2015 [1 favorite]


> From what I know of my kids all they do is ask "why" over and over until I give up.

What's worked really well for me has been to ask "Why what?" and answer if they can be more specific. Otherwise you end up really deep in chemistry or physics really fast, and the kids don't actually learn much except that the world is complicated. On the other hand, if they've listened well enough to the previous answer to formulate a question from it, they definitely deserve an answer.
posted by eemeli at 11:42 PM on September 20, 2015 [5 favorites]


I love it! When I first learned graph theory in university I thought they should teach this stuff to kindergarteners!
posted by Joe Chip at 8:03 AM on September 21, 2015 [1 favorite]


Annika Cicada: "From what I know of my kids all they do is ask "why" over and over until I give up"

This is a suprisingly solveable problem.


This happens with my 2.8 year old and I was surprised to find how often the answer series terminated with "entropy."
posted by phearlez at 11:24 AM on September 23, 2015 [1 favorite]


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