I really enjoyed reading the Abrahamson & Howison paper. I will be teaching fourth grade math next year, and had determined that I wanted to create a final project that I could actually use in my classroom. In fourth grade, students spend a lot of time learning fractions, and I thought that I would try to make a game to help students intuitively understand probability. I think the idea of the “MIT” is interesting, and it increases the students’ intuition for proportions. Thus, I am planning on building some variant of the MIT to use in my classroom.

The author’s conjecture that some mathematical concepts may be difficult to learn precisely because our everyday experience fails to provide adequate opportunities to develop the requisite body-based imagery underlying those specific concepts resonates strongly with me. I remember learning integrals, and although I could calculate them mathematically, I did not have an intuitive understanding of them until I TAed a probability course at M.I.T. In the course, I had to teach my students about CDFs (cumulative distribution functions) and how to use them to calculate probabilities. Through the exercise of  drawing pictures to communicate how to derive a CDF from a PDF (probability distribution function) something clicked in my head, and integrals became a lot more intuitive to me mathematically. Even now, whenever I need to integrate or derive something, I can’t help but think of going from a PFD to CDF or CDF to PDF, and I think of the functions in terms of probabilities. I think it helps make my math manipulation much stronger. Thus, probability functions were my “body-based imagery” that helped me understand the mathematical concepts of derivatives and integration.

My question for Abrahamson is to learn how he and Howison came up with the idea of the MIT, and how to come up with these tangible, self-discovery, tools for other concepts. Because in trying to come up with ideas for my students, I realized how hard it is to come up with cool tools that can help children learn intuitively. I realized that most of my ideas were just hands-on versions of traditional learning tools, and not necessarily changing the mode of learning.