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12 votes

What are some good books on mathematical pedagogy?

In The Teaching Gap, James Stigler and James Hiebert analyze research from the TIMSS studies. Part of their conclusion is that much of our experiences of classroom culture are deeply imprinted in us, ...
Sue VanHattum's user avatar
  • 20.8k
10 votes

Theory-practice order vs practice-theory

A go-to article for me is the following. Short overview article with extensive endnotes to further supporting literature: Clark, Richard, Paul A. Kirschner, and John Sweller. "Putting students on ...
Daniel R. Collins's user avatar
10 votes

What are some good books on mathematical pedagogy?

My favored text that I consider essential for "getting started" as a college math instructor is: Krantz, Steven George. How to teach mathematics. American Mathematical Soc., 1999.
Daniel R. Collins's user avatar
9 votes

What are some good books on mathematical pedagogy?

"Building thinking classrooms" by Liljedahl is a summary of effective teaching practices distilled from Liljedahl's research. TLDR: get students working on questions which require thinking ...
Steven Gubkin's user avatar
7 votes

How did Grigori Perelman , got all the necessary theory and materials to prove the Poincaré conjecture?

Perelman had a conventional academic education through and well past his Ph.D., albeit in Russia. He was exposed to and was a part of the mainstream of research mathematics. He was not a Ramanujan, ...
guest's user avatar
  • 89
5 votes

ADHD superfocus and motivation for mathematics

As often happens: not an answer to the literal question (about references), but just some (substantial?) anecdotal stuff over 50 years of observing mathematicians: I'd agree that being able to focus ...
paul garrett's user avatar
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5 votes

What are some good books on mathematical pedagogy?

This isn't a book, but I recommend (along with looking at the texts suggested here), to read the article by Jaime Escalante. https://files.eric.ed.gov/fulltext/ED345942.pdf This is not to say his ...
guest troll's user avatar
5 votes

Is there a mathematics core assessment rubric?

These assessment rubrics drive me nuts. The Lords of Assessment think that learning can be quantized and put into a grid. Usually they get finicky about verbs and can always find a way to correct you. ...
user52817's user avatar
  • 11k
3 votes

Are some natural languages better for expressing mathematical concepts than others?

This question reminds me of the so-called Hopi time controversy. In 1958, Stuart Chase asserted (see page 3) that a person whose native language is Hopi has less trouble grappling with the "...
user52817's user avatar
  • 11k
3 votes

Are some natural languages better for expressing mathematical concepts than others?

Perhaps taking things to their extreme there are languages which lack simple numbering like the language of the Brazilian Amazonian people the Pirahã which appears to have only words for one and two (...
mdewey's user avatar
  • 301
3 votes

ADHD superfocus and motivation for mathematics

Based on a cursory investigation of the literature, it seems like ADHD can loosely be described as providing an extreme combination of "superfocus" on things that one finds interesting, and &...
Justin Skycak's user avatar
2 votes

Utillizing Lakatos' "Proofs and Refutations" in Secondary Education

Frame-challenge answer: It's better to start with the educational goal you have in mind, and from there decide the best way to achieve it. Starting with a book that you like, and trying to find a way ...
user22788's user avatar
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2 votes

Utillizing Lakatos' "Proofs and Refutations" in Secondary Education

I've used Proofs and Refutations in the classroom (college students in the US), but not in the direct ways you suggested. When leading up to Euler's formula $V-E+F=2$, I try to get the students to see ...
Joseph O'Rourke's user avatar
2 votes
Accepted

Some whiteboard program specialized for "typing" with latex support

Gosh, the very platform where you are asking your question supports MathJax. As you start writing an answer like I am doing now, $\LaTeX$ and math equations $$x^2+x-1=0$$ get rendered in a preview ...
user52817's user avatar
  • 11k
2 votes

What are some good books on mathematical pedagogy?

One of my interests is East Asian mathematics education. A very good book that succinctly describes some of its philosophies is “Principles of Mathematics Education” published by the Association of ...
JRN's user avatar
  • 10.8k
1 vote

Are some natural languages better for expressing mathematical concepts than others?

There is mathematics and then there is mathematics. Languages do presumably affect the speed at which children learn basic number words. It is known that children learn Danish (in general, not ...
Tommi's user avatar
  • 7,203
1 vote

Are some natural languages better for expressing mathematical concepts than others?

Let me give you an example in two languages: English (Dutch), and let's talk about tables (tafels [ˈtafəls]) and tables (tabellen [taˈbɛllən]): A table (tafel) is the piece of furniture at which you ...
Dominique's user avatar
  • 2,119
1 vote

What are some good books on mathematical pedagogy?

I find the MAA's Instructional Practices Guide to be thought-provoking.
Jim Hefferon's user avatar
1 vote

Is there a virtue to learning how to compute by hand?

Let me tell you the story of my father and the number 5.8: My mother had a shop in Belgium, very near to the French border. This happened in the time before the Euro currency was introduced. Normally ...
Dominique's user avatar
  • 2,119

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