The purpose of the following response questions is to support you as you make sense of the assigned readings and synthesize key ideas across them specifically, the connections between multiple representations and conceptual understanding, as well as the role of play and attention to equity in K-12 math classrooms (CLOs 1 & 3). They also provide a space for us to share thoughts, ideas, and wonderings so we can learn with (and from!) one another.

Instructions
After completing the assigned readings for Week 4, choose two of the following response questions. Identify the numbers of the questions you answer in the initial post. Those numbers will be important when it comes to responding to peer posts.

Initial post
Play, and, at that, mathematical play, involves a set of defining characteristics. It is: fun, voluntary, meaningful, follows structure, has freedom within that structure, has exploration, and norms for participating(pp. 49-50). How have you experienced these characteristics in your mathematical journey? What features or characteristics of a mathematics classroom are necessary for mathematical play?
Su notes that mathematical play requires the explorer to change perspective; to probe at an idea from different angles. What do you see as the benefits for engaging with multiple perspectives in inquiry and justification (the two phases of mathematical exploration) for students? for teachers? for human beings in general?
The lecture on multiple mathematical representations introduced 5 different types of mathematical representations. Which of those are you more comfortable with using? Which of those are you least comfortable using? Why? Summarize the benefits and constraints you feel with each representation. What assumptions are you making about what mathematics is and what it looks like to do mathematics?
Last module, we began talking about equity and access in mathematics education. One key point we raised was that it is important for learners to see themselves and their interests in problems they are solving, and that those problems need to be connected to the learners’ worlds. Baron (2015) agrees with this point, as exemplified in the task described in the article. In what ways did this problem prompt the use of multiple mathematical representations? How did the use of multiple mathematical representations build access and more equitable learning opportunities for all students in the classroom? Provide at least 2 examples from the text and analyze them in your own words.
Response post
Respond to two peers who answered at least one question differently than you. For example, if you answered Questions 1&3, you could respond to someone who answered 1&2, 1&4, 2&3, 2&4, or 3&4 ). Remember our guidelines for constructive responses to peers.

reading material: Chapter 4 (pp.48-66), Su, F. (2020). Mathematics for human flourishing. Yale University Press.

other reading attached below