I just read somewhere the question, "What was wrong with the old way?" That was followed by the statement that "Clearly the old way did not work". This was, I think, based on years of following what was going on with students and math.

I have my own experience from which to draw (my children did not need my help). I learned what subtraction was in my second grade classroom by placing 10 articles on a table, removing 3 of those 10 articles, and counting the 7 articles remaining on the table. 10 take away 3 equals 7. I was able to generalize that experience to cover what I was doing every time subtraction was required by a math problem. I just saw an example of "You paid \$20.00 for a \$3.18 purchase." Then it was said that most people go through some mental exercises to find out the change. What would be wrong with \$20.00 - \$3.18 = \$16.82. My first job, at age 14, was at S. S. Kresge Co. I counted back that change with "\$3.18 (handed 2 pennies) \$3.20 (handed 1 nickel) \$3.25 (handed 3 quarters - 1 at a time) \$3.50, \$3.75, \$4.00 (handed a dollar bill) \$5.00 (handed a five dollar bill) \$10.00 (handed a ten dollar bill) \$20.00.

I have observed that there are few who can count back change that way these days. What happened? If the power fails and the cash register doesn't do the math, they seem to be lost!

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    $\begingroup$ Welcome to the site, Kay! Unfortunately I am not sure what exactly you are asking. Are you asking why educators are attempting to make changes to the way subtraction is taught? $\endgroup$
    – Chris Cunningham
    Oct 15 '14 at 3:28
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    $\begingroup$ This question appears to be off-topic because "what happened" is about history, in the case history of non-academic mathematics, with no articulated connection to contemporary math education. $\endgroup$
    – user173
    Oct 15 '14 at 9:09

There are a lot of sources of information on the history of mathematics education reform, and such sources fill many books. What you may be interested in is knowing that, basically, our understanding of human learning has changed over time. To hugely oversimplify, much of learning that older generations are familiar with is based on ideas of learning linked to behaviorist psychology. A focus on the basics of arithmetic and an idea that practice makes perfect is a very old, traditional approach to math education. Since then we've learned that there are a lot of problems with this approach. Among them, they create a curriculum largely devoid of creativity, problem solving, context, reasoning, etc. But also, they don't reflect the understanding of how students come to adopt new ways of mathematical thinking, and how they make connections to their existing body of knowledge.

There are political wars over this sort of thing. I'm not sure there's a great single treatment of this issue that I can link to, but this one is not too bad:


It describes some of the conflict in mathematics education reform. It's very limited. I only provide it to help you understand that nothing actually happened in the sense I think you mean. But it might be a starting place for you if you're truly interested in understanding how curriculum and instruction in mathematics has had to change.

A better resource is the following, very large, pair of books: A History of School Mathematics. Volumes 1 & 2.

In reality, a lot of things have happened in the policy world. Part of the difficulty for teachers is that so much policy change (as political winds shift) has left them suspicious of any new policy. How long (they must think to themselves) before a new administration comes in and reverses all these directives? Research has marched forward, but politics does not have that sort of cumulative thrust.

  • $\begingroup$ +1 For the nice arguments and references. $\endgroup$ Oct 15 '14 at 19:45

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