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.
There is nothing in the Common Core State Standards that requires students to use number lines to perform multi-digit subtraction
Relate Addition and Subtraction to Length
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.
"on a number line diagram with equally spaced points"
"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.
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.
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.
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."
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.
17 * 43
= (30–13) * (30+13) ⇐ Look! A difference of two squares!
= 302 – 132
17*43 = 302 – 132
= 900 – 169
17*44 = 17 * (43+1)
= (17*43) + 17 ⇐ We know (17*43) from before!
= 731 + 17
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