Catwalk problems

Three articles have been published in The Journal of Mathematical Behavior recently that are all related to “the catwalk task”.

1. Steven Case: The catwalk task: Reflections and synthesis: Part 1
Abstract: In this article I recount my experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, I reflect on my own mathematical work on the catwalk task, including my efforts to fit various algebraic models to the data. Second, I reflect on my experiences working with a group of high school students on the catwalk task and my interpretations of their mathematical thinking. Finally, I reflect on the entire experience with the catwalk problem, as a mathematics learner, as a teacher, and as a professional.

2. Emiliano Vega and Shawn Hicks: The catwalk task: Reflections and synthesis: Part 2
Abstract: In this article we recount our experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, we individually reflect on our own mathematical work on the catwalk task. Second, we reflect on our experiences working with a group of community college students on the catwalk task and our interpretations of their mathematical thinking. In so doing we also detail a number of innovative and novel student-generated representations of the catwalk photos. Finally, we each individually reflect on the entire experience with the catwalk problem, as mathematics learners, as teachers, and as professionals.

3. Chris Rasmussen: Multipurpose Professional Growth Sequence: The catwalk problem as a paradigmatic example
Abstract: An important concern in mathematics teacher education is how to create learning opportunities for prospective and practicing teachers that make a difference in their professional growth as educators. The first purpose of this article is to describe one way of working with prospective and practicing teachers in a graduate mathematics education course that holds promise for positively influencing the way teachers think about mathematics, about student learning, and about mathematics teaching. Specifically, I use the “catwalk” task as an example of how a single problem can serve as the basis for a coherent sequence of professional learning experiences. A second purpose of this article is to provide background information that contextualizes the subsequent two articles, each of which details the positive influence of the catwalk task sequence on the authors’ professional growth.

So, you may ask, what is this catwalk problem really about then? The problem is originated in a set of 24 time-lapse photographs of a running cat. The question is simply: How fast is the cat moving at frame 10? Frame 20? (See this pdf for a presentation of the problem!)

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