1) What is a take away for you on the development of fluency? a) (required selection) b) In preparing for this interview and thinking about the contents of Chapter Three, I was really drawn to the organization of Bloom’s taxonomy into three levels of mathematical thinking. Higher-order thinking is discussed consistently in the field of education, as is Bloom’s Taxonomy, yet I’ve never seen the two concepts meshed into a singular chart or organizer like that. I enjoyed the chapter’s use of this chart in discussing the idea of fluency because it provided strong support in explaining how procedural knowledge and conceptual understanding work together to achieve deeper learning and result in the development of mathematical fluency. This is a huge takeaway for me on the development of fluency. Especially where the chapter emphasized the historical tendency of our education system to emphasize level one “remembering” procedures over level two and level three procedures, despite being weak in the cognition required. 2) How does the information on worthwhile tasks mesh to what you already know? a) Chapter Three’s information on worthwhile tasks provided more detailed insight as to the goal behind the tasks, how to properly execute such tasks, and flips that can be made to make non-worthwhile tasks worthwhile. The information provided meshes well with what I generally knew from previous courses. Previously, initiating high-level tasks to allow students access to higher-order thinking was a concept often discussed. This aligns incredibly well with the concept of worthwhile tasks, so a new “description” doesn’t conflict with my prior knowledge. It reinforces my understanding that a strong task is one that asks students to justify, explain, and make a choice on how they would like to solve given multiple positions from which they can begin. A little newer to my understanding is the degree to which students should also feel the task is worthwhile. It’s always been important to ensure that tasks are engaging to the student, but I like how this chapter states it: “worthwhile tasks should feel worthwhile to the student.” I’d already known that students should want to engage with the task and feel excited about their learning, but this description in particular makes a good point that I hadn't considered as deeply. More than building engagement, the use of relevant contexts provides a concrete link to more abstract mathematical ideas. b) (required selection) 3) Discuss the Coaching Considerations on p. 50-51. What resonates with you? a) (required option) b) All of the coaching considerations included are of high importance, but the first consideration especially resonated with me. Coaching Consideration #1 regards addressing myths, misinterpretations, and overgeneralizations. This one really stuck out to me because I feel like I rarely see this being discussed in a way that is directed towards teachers. I’ve been consistently informed about student misconceptions and steps that should be taken to catch and correct them, so it was eye-opening to see a list of “mind-traps” that teachers can also fall into. Reading through the list, it was interesting to think about which ones I’ve successfully avoided and which ones I needed to self-reflect on. “1e: hard means cognitively demanding” was a complete “whoa!” moment because this is a trap I commonly fell into through my practicum experiences and I’ve had to work hard to catch myself when this happens. I’ve communicated frequently that I feel like I make things too hard sometimes and that I struggle to find a balance between demanding and still accessible, so it was validating to see that this thinking is more common than I had realized. This misconception mentioned also makes a good point, that “easy” math can still be demanding when we look deeper and think about how we want our students to be thinking. Not just what we want them to, procedurally, do.

Pre-Interview Chapter Thoughts

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