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I'd like to able to follow discussions/arguments about maths education, but many of them revolve around the transition to new math.

I was taught in the UK in the early 90s, and none of the examples or explanations look substantially different to how I do it.

What was 'old math' and how was it taught? When an older person says they don't understand all of this 'places' and 'borrowing' nonsense, what are they expecting to see instead?

Is the difference primarily in notation or in the actual algorithm used?

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    $\begingroup$ "Places" and "borrowing" are always part of the standard algorithms for addition, subtraction, etc. I would assert that if an older person says this, they simply don't remember any arithmetic at all. It would be interesting to ask them to write out an addition or subtraction and see if/how they do it. $\endgroup$ – Daniel R. Collins May 1 '16 at 17:15
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New math was introduced in the US in the 1960s. Before it was introduced, math was taught very algorithmically with little emphasis on understanding. Student were taught a method to do an arithmetic problem and drilled until they remembered the process with no understanding of what was being taught.

New math introduced many new topics including boolean logic, other number bases, modular arithmetic, and matrices. Many elementary school teachers were ill prepared for these new topics. Many of these are no longer taught in the standard elementary curriculum.

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    $\begingroup$ And set theory. As a child of this era, one problem I have teaching is to assume that my college students have set-theory concepts from the 2nd grade when that's not the case. $\endgroup$ – Daniel R. Collins May 1 '16 at 17:17
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    $\begingroup$ Remind me youtube.com/watch?v=DfCJgC2zezw $\endgroup$ – user2139 May 1 '16 at 19:13
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    $\begingroup$ Other things have been called New Math since then, I think. And similar problems are arising with the Common Core changes. $\endgroup$ – Sue VanHattum May 1 '16 at 22:43
  • $\begingroup$ @DanielR.Collins If you want to know whether somebody learned set theory properly, ask them to define the real numbers. If they learned it like the utter bedlam I was taught in high school, they'll mumble something about the union of the rational numbers and the "numbers with non-repeating non-terminating decimal expansions". $\endgroup$ – Joe Z. May 17 '16 at 7:21
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Vedic maths techniques which had been used by Aryabhatta can also be described as old Maths. Though, new Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s.

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