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.

1. Mathematical community is inherently at the heart of learning in the math classroom. Su (2020) points out that often, community consists of hierarchical components (sometimes connected to achievement, sometimes more implicit). What is one hierarchical component of a mathematics classroom that you see or have experienced? Describe how this component functions in a mathematics class and impacts the community of learners. Then, propose two specific alternatives to that hierarchical component and articulate how you see them building a more authentic and inviting community for all learners.

2. Return to the example of two mathematics professors and a group of students solving a Real Analysis problem (Su, 2020, pp. 195-197). In this brief description, we can see multiple ways of engaging in mathematics. Provide at least two separate examples of students or professors developing their strategic competence in this scenario. How did engagement in strategic competence support these math learners in solving the problem? What other strands of mathematical proficiency were grown through their engagement in strategic competence? Make sure to draw upon the NRC (2001) report, Adding It Up, in your response.

3. Keazer & Gerberry (2017) note that in working with future teachers, what it means to make sense of a problem can be interpreted in different ways. If Standard for Mathematical Practice (SMP) 1 is focused on processes of thinking about non-routine, complex problems, how does this shape what teachers and students do across the different phases of doing a math task? Provide at least one example from the article or your experience of a classroom structure, norm, or task feature that you believe supports students to make sense of a problem. Explore how that structure, norm, or task feature can build opportunities for students to engage in strategic competence at the same time as they work on SMP 1. Then, describe how that structure, norm, or task can promote equity and broaden access to high-quality, rigorous mathematics for all students.

4. We have now had the opportunity to explore each of the five strands of mathematical proficiency individually and have started thinking about interrelations across them. While we know that it is imperative that building proficiency happens synchronously across all five strands, we each have constructed a slightly different understanding and organization over this course. Are there certain strands that you see as leading the way or as more interconnected? Briefly share your organization of these strands with your peers. Then, provide a detailed explanation of the relationship you see between a humanized, flourishing, mathematical community and the goal of all students developing
mathematical proficiency. Use examples to contextualize your response.

Just pick two to respond to.

pp. 124 – 129, 133 136, National Research Council. (2001). Adding it up: Helping children learn mathematicsLinks to an external site.. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). book attached below

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