December 7

We'll continue discussing visualization and diagrammatic reasoning: And then we'll decompress and reflect on the semester.

November 30

This week, we'll have a brief discussion of Wickelgren, and then move on to talk about Euclidean diagrammatic reasoning. Read any of the following:

November 16

This week, we'll finish the discussion of Schoenfeld, and start discussing Wickelgren's take on problem solving: pdf, pdf, pdf

November 9

This week we will finish up the discussion of Polya; specifically, we'll talk about the excerpt from Patterns of plausible inference (volume II of Mathematics and plausible reasoning).

After that, we will start discussing Schoenfeld, Mathematical problem solving, pdf.

November 2

This week will be devoted to the Polya, and the readings below.

October 26

This week will discuss Arana's paper, and then move on to Polya.

October 19

This week is something of an interlude: we will discuss the draft of

We will focus on sections 4-8.

The week after, we will finish up the discussion of explanation (including Arana's paper), and move on to problem solving. The latter will eventually include Polya, Schoenfeld, and Wickelgren, in particular.

October 12

We will continue with mathematical explanation and proof:

If you are interested in Pick's theorem, see also John Harrison's "A formal proof of Pick's theorem," on the bibliography.

Solomon Feferman's "The logic of mathematical discovery vs. the logical structure of mathematics," a critique of Lakatos' Proofs and Refutations, is also worth reading.

October 5

This week, we will discuss and the paper by Tappenden, and then move on to explanation:

September 28

This week, we will finish the discussion of Wilson, and discuss Husserl.

September 21

Read at least one of these papers by Mark Wilson:

Finally, look at the following study in mathematics education:

September 14

Concepts in general:

Frege on sense and reference (choose readings from among these as you wish):

September 7

Kant's account of mathematics: There are additional links to material on Kant, and concepts, in the bibliography.

August 31