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For questions about the mathematical education in the first years in school (ages approx. 5-10).

23 votes

Should we say that fractions "are" or "represent" numbers?

The other answers are good, and/but some of those points are reinforced by a diagnostic that has ever-more been important to me: is intention being communicated? And a different, more linguistic point …
paul garrett's user avatar
  • 14.8k
17 votes

Student: Why not use a calculator?

People who ask why calculators don't resolve the (very low-level) issues well enough are quite accurate in their skepticism, I think, which makes it hard to present an "absolutist" defense of alternat …
paul garrett's user avatar
  • 14.8k
29 votes
Accepted

What was the problem with New Math? Why did it end?

In the first place, the impetus to "reform" math education was motivated by politics, not by any serious observed deficit. By coincidence, there was a "new" style in higher mathematics, reflecting the …
paul garrett's user avatar
  • 14.8k
5 votes

Pi Day Celebration Ideas?

The student AMS chapter here in MN had a pizza party, and (through whatever chain of causality) asked me to give a talk... and I chose to "ramp it up" by talking about "failing to prove the Riemann Hy …
paul garrett's user avatar
  • 14.8k
6 votes

Is there an intuitive explanation for the properties of Pascal's triangle?

How about the fact that $(x+y)^n=(x+y)\cdot (x+y)^{n-1}$, and then equating coefficients? This proves that ${n\choose k}={n-1\choose k-1}+{n-1\choose k}$. ... and... since $(1+1)^n=2^n$, the other ass …
paul garrett's user avatar
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9 votes

The interplay of memory and mathematical performance

Anecdotally, based on self-observation and observation of many faculty and grad students: "if it's not in your head in some form, you can't think about it". A funny point here is that it seems not st …
paul garrett's user avatar
  • 14.8k