Jennifer suggests there are three spaces for recursion: reflection, creating/relating, and identifying/problem-solving. She uses the game “Can You Guess Our Mystery Number?” to show readers how she creates these spaces.

While reading this chapter, I kept returning to the idea of “**folding back**.” What did it mean? I needed a deeper understanding, so I did some research and found this: http://www.arvindguptatoys.com/arvindgupta/paperfolding.pdf

This document explains the importance of paper folding in mathematics. It is an interesting read, and it also has many samples for the teacher to try out with the students. Now, I know that this is not exactly what Jennifer meant by “folding back,” but by reading about paper folding I was able to visualize what Jennifer meant by folding back from her chapter. And I discovered that it is like physically folding paper! When we fold paper into a shape, we can unfold it to find out how the shape formed-how many folds did we make, where did we make the folds, what are the shape’s characteristics. This thinking is parallel to Jennifer asking her students to fold back on their chosen number to pick out an image that would be true or characterized that number.

Back to the chapter: Jennifer created three spaces for mathematical recursion by allowing the students to first reflect on their understanding of number, then to create a problem for their peers by relating their thinking, and finally, to identify the correct answer by using their understanding of problem solving. Students had to work together and create clues that would lead their peers to the right answer-not too soon though! They had to think flexibly and work backwards in order to create a set of clues that were logical and could work for other numbers (but every clue needed to be true for the mystery number).

2 takeaways from today:

1- I have a newfound interest in Origami and think it is an excellent way for students to create something beautiful using their math skills (and it teaches patience)

2-Backwords thinking and problem solving needs to be integrated more thoroughly into mathematics curriculum. Being able to think flexibly is an important skill.