Case studies in mathematical thinking: extending time for preservice teachers' professional noticing
Date
2022
Authors
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Publisher
University of Delaware
Abstract
This project was a formative intervention (Engestrom, 2011) to (a) discover what preservice teachers (PSTs) and early career teachers listen for, notice, and attend to in order to interpret secondary students’ mathematical understanding, and (b) investigate instructional strategies that support preservice teachers’ and early career teachers’ ability to apply professional noticing skills to interpret secondary students’ mathematical understanding. I was interested in how PSTs’ and early career teachers’ professional noticing forms their ability to interpret secondary students’ mathematical understanding and what instructional strategies, educational philosophies, and ecologies facilitate this ability. Interpreting secondary students’ mathematical understanding is fundamental to the development of mathematical knowledge for teaching (MKT); therefore, understanding how PSTs’ professional noticing evolves can serve to inform teacher preparation regarding the development of MKT. I used classroom-based artifacts during an experimental one-credit university course as my intervention and qualitative methods to analyze data I collected from this intervention. ☐ Results from my preliminary analysis showed that participants’ professional noticing was characterized by an overemphasis on noticing teacher behaviors, a lack of integrating and attending to what they noticed, and a low incidence of interpreting students’ mathematical understanding. As the instructor, this focus created some concern on my part and set the stage for my formative intervention. I had a goal of learning how to create an instructional environment that supported grappling with the meaning behind students’ thinking, namely, interpreting secondary students’ mathematical understanding. The two instructional strategies found to support a higher incidence of interpreting secondary students’ mathematical understanding were the use of directed professional noticing prompts and consensus professional noticing prompts. An instructional planning guide was developed to outline these and important instructional planning decisions for developing cased-based professional noticing opportunities. ☐ A discovery that emerged during my analysis was that there was a shift in my participants’ espoused beliefs regarding the teaching of mathematics, in favor of beliefs about teaching mathematics that are more student-center. This is particularly noteworthy because these new espoused beliefs better align with the National Council of Teachers of Mathematics (NCTM) organizational espoused beliefs and theory of action personifies student-centered teaching. ☐ One reason this project is significant is because it validated several prior claims found in the literature. First, results from my project validated prior researchers’ claims that PSTs must learn to listen for student thinking before they can attend to and interpret students’ mathematical understanding (e.g., Darling-Hammond, 2010). The project also validated the claim that a personal vision of teaching and learning (i.e., the espoused beliefs and theory of action) developed within a professional cultural setting is foundational to what participants listen for when they are teaching a lesson (Louie, 2018). ☐ Based on the findings from the formative intervention I implemented, I am proposing that teacher preparation programs provide PSTs with increased case-based opportunities to practice professional noticing, to interpret student’s mathematical understanding, and to develop their MKT.
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Keywords
Case-based studies, Mathematical knowledge for teaching, Professional noticing, Secondary student thinking, Student-centered teaching