There's a piece in today's Times about the Math Wars.


It isn't clear to me how learning an addition method that works every time threatens growth, nor how using a calculator fosters growth.

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.

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%.

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#Post159629

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.

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...

Singapore Math (Primary Mathematics) does this.

Add a "widely used" to the above then

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.

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.

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...

SiaSL, when I say universal, I don't mean that it is one method that is taught the same everywhere. I mean that it is one method that can be applied universally to a type of problem, no matter what the specifics of the problem happen to be.

I probably would have found value in the article if they hadn't wrapped it in such inflammatory, nonsensical rhetoric. War on math? Progressive? I feel like I need a shower.

This is why I don't read opinion pieces.

I'm thinking you haven't been following this story? "Math Wars" is a term coined years ago (a decade or more, I think). It arose out of parental frustration with programs like Everyday Mathematics. A large number of mathematician/engineer/scientist types challenged the reform curricula in California and gained high visibility. They lobbied hard for a return to traditional methods. With the publicity came the term math wars. AFAIK, the mathy types didn't make it up (they used the term mathematically correct). Check the Wikipedia entry.

"Progressive" is a term the reform crowd uses (I opened up several chunks of comments and found the term 50 times).

Whether referring to it as a war is a new development or not, it's still language designed to shut down the rational part of the brain.

The commenters are simply using the language they've been presented with. "Progressive" and "progressivist" show up 14 times in the article.

Interesting to note that an article that begins "The Faulty Logic" might as easily be renamed "An Introduction to Logical Fallacy by Example." As in Dude's observation, repeating progressive is a slick ad hominem argument.

One bit in there that gets me is:
"the most efficient — and most elegant and powerful — algorithms for specific operations"
I think that is quite a distortion of the classic algorithms which strike me as foolproof and consistent but neither elegant nor efficient.
My proof:
49,999 + 7 =


I believe the investigations type philosophy is in the right place, but the systems are likely flawed in their execution by being too dogmatic. You can't train creativity or creative problem solving. Forcing a kid to keep guessing at solution approaches until they match the fixed set in the answer guide is a fail.

Reflecting on other threads perhaps in the ideal execution of "reform mathematics" requires both a certain amount of talent in the instructor as well as the learner to realize its intent.

Frame-worthy. That's the problem in a beautifully-put paragraph.

While you can't TRAIN creative-problem solving (or, for that matter, 'critical thinking skills' either, IMO) using any particular method...

you can crush their development in students by stifling exploration. You can encourage and nurture those things and allow room for them to grow.

But that is never going to be possible in a system which has ground itself into a corner of testing-testing-testing and preparation for the same, all in the cheery, (but futile) hope that Every Child Can Master Algebra by Adolescence! which assumes that teaching mathematics requires the same approach as teaching arithmetic.

TBH, I wouldn't mind the testing, testing, testing so much if they DID something with it other than turn it into state / federal offices as a requirement. Testing isn't a bad thing if you use it to actually further the education of the student with feedback and follow up. A GOOD test teaches in the process of analyzing what a student has learned and a good teacher knows how to analyze the tests to improve their own teaching as well as the student's understanding. Unfortunately, that's not what happens with the majority of testing these days and they're not written well enough to teach in the process of testing.

Correct. There is formative assessment (which is what you were referring to, and is what good teachers have always used) and then there are the crazy-making summative assessment practices currently in vogue. "Instant feedback" isn't the same thing as useful feedback, which requires something more than yes/no on a multiple choice assessment or a peek at the solution (which only has about 90% probability of being completely correct in the best of modern texts) in the back of the book.

A lot of the general mathematics pedagogy debate (not here; in general) seems to get framed around and either/or proposition. EITHER you teach algorithms OR you teach concepts. It's possible to teach both. I taught all three of my kids how to do arithmetic, and my lessons were always heavy on concepts.