7 votes
Accepted

Mathematics and the hermeneutic circle

First, a direct answer: Yes, there is work in mathematics education connected to Gadamer. One soure for such studies is articles by Brent Davis; more generally, google scholar yields such ...
7 votes
Accepted

Funny things students say when learning mathematics

From John Stembridge's web site at http://www.math.lsa.umich.edu/~jrs/plans.html : "Are we going to have to think today, or is it going to be all math?" --a student in Phil Hanlon's Math 115 class
6 votes
Accepted

Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)

I like the idea here, but I agree that it misleads students, and might have the opposite of intended effect. Why not hand out a paragraph to the students, and ask them to critique it. Say that the ...
5 votes

Teaching mathematics and its charms to non-mathematicians

Perhaps (depending on background) give them one of the books by William Dunham, like "Journey through Genius" (Dover, 1990), "The Mathematical Universe" (Wiley, 1997), there are others. He won several ...
  • 12.1k
4 votes

Teaching mathematics and its charms to non-mathematicians

"Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject" is a great book. Lots of fun/interesting problems that are accessible to a wide range of math levels. The ...
  • 41
3 votes

Are there standard notations for 'number talks' / ‘math talks?'

The notation used on the board in math lectures should be the same as that found in any other mathematical writing. That is: Get a good book, read it very carefully, and follow that same notation ...
3 votes

Are there standard notations for 'number talks' / ‘math talks?'

As you realize, this In my brief experience, I’m finding that my written diagrams or notations are not ideal. Admittedly, I will draw operators, numerals, and arrows on-the-fly, and they don’t ...
3 votes

Teaching mathematics and its charms to non-mathematicians

I'm afraid that this might not be of use to you, because it's in Hebrew, but this question reminded me of the really nice Beauty of Mathematics course that Gil Kalai organized at the Hebrew University ...
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3 votes

Funny things students say when learning mathematics

I once had a colleague when I was teaching in Asia who was new to teaching high school, but was a very accomplished Mathematician. In one of his first lessons he was teaching simultaneous equations, ...
3 votes

Mathematics and the hermeneutic circle

This leads me to wonder if it is possible to consider a terrible heresy: Is it possible to imagine mathematics without problems?... What if "conversation" replaced "problem" in the mathematics ...
2 votes

Funny things students say when learning mathematics

From a student learning real analysis: The sequence diverges because the Cauchy criterion is dissatisfied.
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2 votes

Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)

$A\cap B$ is not true or false; but it is true that the intersection of two disjoint sets is the empty set, that is, that $A\cap B = \varnothing$ is true. This comes down to a question about whether A\...
  • 2,038
2 votes

Are there standard notations for 'number talks' / ‘math talks?'

Most elementary school teachers in the USA get their teaching certification by majoring in "elementary education" as an undergraduate. Curriculum for such programs typically includes a sequence of ...
  • 8,043
2 votes

Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)

Another example of this sort of issue: I have often seen students write things like $\frac84$ when they mean $4\mid 8$ (i.e., $4$ divides $8$.) It takes a while (for some) to see that the former has ...
  • 637
1 vote

Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)

I'll go with the common " '$=$' is a key on the calculator" misconception. Many students don't see a problem with and write down things like $$3 \cdot 4 = 12 - 5 = 7$$ when asked to calculate $3\...
  • 2,191
1 vote

Teaching mathematics and its charms to non-mathematicians

People are often keen to develop their knowledge of their current interests so, if you can find out what interests your student (sport, cars, travel, cookery, whatever), you can hang some elegant ...
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