Our main objective is to discuss issues of teaching and learning in the context of combinatorial and algebraic problems – especially those that connect the two- taking particular note of the need for proof.

To that end here are some resources that may help:

- Bogart, K. P. (2004).
*Combinatorics through guided discovery*. *Catalan Number*. Wikipedia.*Combinatorics: High School Math*. Art of Problem Solving.- Gessel, I. M. (2013).
*Rook polynomials*. University of Washington Combinatorics Seminar - Hilton, P., & Pedersen, J. (1991). Catalan numbers, their generalization, and their uses.
*The Mathematical Intelligencer*, 13(2), 64-75. - Hodkinson, J. (2016) Proof by storytelling.
*Chalkdust,*October 3 - Nelsen, R. B. (1993).
*Proofs without words: Exercises in visual thinking*(No. 1). MAA. - Nelsen, R. B. (1994). Proof without words: Geometric series.
*Mathematics magazine*, 67(3), 230. - Richards, I. (1984). Proof without words: Sum of integers.
*Mathematics Magazine*, 57(2), 104-104. *Rook Polymomials*. Wikipedia.- Siu, M. K. (1984). Proof without words: Sum of squares.
*Mathematics Magazine*, 57(2), 92-92.

2017 MATHEMATICS CURRICULUM FRAMEWORK MASSACHUSETTS

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