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Joined: Sep 2007
Posts: 3,299 Likes: 2
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Joined: Sep 2007
Posts: 3,299 Likes: 2 |
There's a piece in today's Times about the Math Wars. The battle over math education is often conceived as a referendum on progressive ideals, with those on the reform side as the clear winners. ... The staunchest supporters of reform math are math teachers and faculty at schools of education. While some of these individuals maintain that the standard algorithms are simply too hard for many students, most take the following, more plausible tack. They insist that the point of math classes should be to get children to reason independently, and in their own styles, about numbers and numerical concepts. The standard algorithms should be avoided because, reformists claim, mastering them is a merely mechanical exercise that threatens individual growth. The idea is that competence with algorithms can be substituted for by the use of calculators, and reformists often call for training students in the use of calculators as early as first or second grade. It isn't clear to me how learning an addition method that works every time threatens growth, nor how using a calculator fosters growth.
Last edited by Val; 06/17/13 02:18 PM.
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Joined: Jun 2012
Posts: 7
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This "progressive" math approach is the one my son's new school uses. He is now, to my mind, behind where he should be in math, after previously being ahead (so, he is where he should be per the standards, but behind where he could be). I'm now looking at summer/school-year supplementation to make up for what he is losing in school. It's ridiculous to teach a kid that the best route to a multiplication result is a process that takes five minutes for two digit multiplication.
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Joined: Feb 2012
Posts: 1,390
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It isn't clear to me how learning an addition method that works every time threatens growth, nor how using a calculator fosters growth. I don't think learning the standard algorithms threatens growth, but I do think that insisting that students master "math facts" before they can learn anything interesting does threaten growth.
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Joined: Sep 2007
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I don't think learning the standard algorithms threatens growth, but I do think that insisting that students master "math facts" before they can learn anything interesting does threaten growth. Oy. I'm with you there 100%.
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Joined: Sep 2010
Posts: 320
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Posts: 320 |
Wasn't it Zen Scanner who said that learning the standard algorithm for long division broke his/her ability to do it all in his/her head? Ah, yes: http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/159629/Zen_Scanner.html#Post159629What I'd like to see is a teaching method that introduces different ways to get to the result, and then let's kids figure out which one works best for them (based on their strengths, be they working memory, processing speed, or whatever) depending on the context. One thing I liked with the latest set of new stuff Dreambox added for the upper elementary grades was a set of little movies with different methods for doing addition/subtraction (including the standard algorithms) made into super heroes and trying to tackle villainous robot operations in the smallest number of steps. Not sure they manage to teach the skill, but showing why it might matter is a start...
Last edited by SiaSL; 06/17/13 03:51 PM.
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Joined: May 2009
Posts: 649
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What I'd like to see is a teaching method that introduces different ways to get to the result, and then let's kids figure out which one works best for them (based on their strengths, be they working memory, processing speed, or whatever) depending on the context. Singapore Math (Primary Mathematics) does this.
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Joined: Sep 2010
Posts: 320
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Add a "widely used" to the above then 
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Joined: Feb 2011
Posts: 5,181
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Joined: Feb 2011
Posts: 5,181 |
What I'd like to see is a teaching method that introduces different ways to get to the result, and then let's kids figure out which one works best for them (based on their strengths, be they working memory, processing speed, or whatever) depending on the context. Singapore Math (Primary Mathematics) does this. I :heart: Singapore's Primary Maths. Love-love-love. I would have to say that my DD, after Primary Mathematics 1a through 3a... COASTED through mathematics through pre-algebra. She seriously didn't really seem to be learning anything new during that two years, which is terribly sad to me. I really thought that even this piece kind of missed the fundamental thing that I object to in progressive math pedagogy-- that there are, in fact, disciplines in which being right actually.. er... MATTERS. The method of getting there that yields the correct answer the greatest percentage of the time for an individual seems to me to be the goal of basic mathematics instruction. I definitely do NOT see that happening in this rigid but strangely stupid approach (as in things like EDM). Students are very definitely NOT encouraged to "explore" for themselves. Nor are they allowed to use more elegant/advanced methodology any more than before. Less, I'd argue.
Schrödinger's cat walks into a bar. And doesn't.
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Joined: Jul 2011
Posts: 312
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Joined: Jul 2011
Posts: 312 |
I think the way I would most like to be taught a new mathematical concept is as follows:
1) Identify the need for a new concept. Show the students why their current abilities are lacking. Task them to answer problems for which the new concept is appropriate before teaching it to them. Often times problems can be solved in a slow, arduous manner relying on previously learned methods. Other times problems are insolvable. Instill in the students a desire to grow their mathematical abilities. Make them a little bit uncomfortable.
2) Discuss the numerous applications of the new concept. Give students a sense of the reasons it's important to learn.
3) Teach the abstract concept.
4) Teach the universal method for solving these types of problems.
5) Practice the universal method.
6) Challenge the students to be creative, and solve problems using methods other than the universal method. Give them problems that are easier to solve with modified techniques based on their number sense. For example: 63x1999. I think we would all calculate that as 63x(2000 - 1) but I know I was never encouraged to do so.
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Joined: Sep 2010
Posts: 320
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Posts: 320 |
All in agreement except... there is no universal method  . The standard algorithm I learned for subtraction as a child (a generation, a continent and an ocean away) is somewhat different from the one my kids are being taught here and now. I happen to think that the "standard" algorithm for subtraction is ugly and clunky, but I might be slightly biased . My poor oldest son, whom my husband and I taught how to subtract and divide "the universal way" before school covered the subject was mightily confused for a while...
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