Unpacking First-Year Teachers' Ambitious Mathematics Teaching Practices

• In Event: How Novice Elementary Teachers Learn to Teach Mathematics and Reading/Language Arts in Ambitious Ways

Abstract

Objective. Beginning elementary teachers are increasingly expected to teach mathematics ambitiously from the start. This presents a challenge to prepare new teachers to engage in ambitious practices that foster students’ deep conceptual understanding, problem-solving skills, and application of knowledge to multiple situations (Lampert et al., 2013) and lead students to justify their approaches and clarify their thinking (Franke, Kazemi, & Battey, 2007). Questions remain about how mathematics teacher educators (MTEs) can support preservice teachers’ understanding and ability to engage in ambitious instruction.
Many factors impact how teaching candidates transition from their pre-service experiences into their roles as beginning teachers in classrooms, including student teaching experiences (Peressini, Borko, Romagnano, Knuth, & Willis, 2004), mathematical knowledge for teaching (Desimone, Hochberg, McMaken, 2016), availability of instructional resources (Cohen, Raudenbush, & Ball, 2003), and access to supports, such as formal mentors, teacher colleagues, and instructional coaches (Stanulis & Floden, 2009). Acknowledging these complexities, we examine ambitious mathematics practices that novice teachers are able to enact so that MTEs can provide targeted opportunities and support.
Perspective, Data Sources, and Methods. From a larger study examining features of teacher preparation programs and beginning teachers’ enactment of ambitious instruction, we examined videos of 117 mathematics lessons taught by 43 first-year teachers from four different teacher preparation programs. All videos were scored using the Mathematics Scan (M-Scan) instrument (Berry et al., 2013). Based on the M-Scan elements, we focused on four categories of ambitious teaching: cognitive demand, problem solving, mathematical discourse community, and explanation and justification. We selected a subset of 15 lessons that scored highly in these categories. We double-coded transcripts of these lessons iteratively (Saldaña, 2015) to identify teaching moves related to the categories and we created matrices which we used to generate themes related to teachers’ use of mathematical tasks and turn-level discourse moves.
Findings and Significance. Findings suggest several promising practices that novice teachers used consistently. Across the 15 lessons analyzed, they presented 79 mathematical tasks. Of these, about 70% were focused on procedures with connections to underlying concepts or non-algorithmic, complex thinking. Enacting these tasks, beginning teachers redirected students’ focus toward specific strategies and conceptual connections, and shifted mathematical authority to students to be mathematical thinkers. Additionally, novices supported mathematical discourse communities with about 85% of tasks highlighting teachers frequently soliciting students’ ideas and questions. They also prompted students to clarify and deepen their thinking. Further, some encouraged students to share their own reasoning for why or how particular strategies worked.
Findings also suggest some areas for continued development. Only 15% of the 79 tasks in these lessons were open-ended. Additionally, fewer than 40% of the tasks allowed students to grapple with the mathematics, and in only 30% were students working on mathematics that did not have an already-learned procedure. Based on these findings, we make suggestions for MTEs to focus support for beginning teachers on what it means for a task to be open-ended and the creation of genuine opportunities for students to make quality contributions to lessons through student-to-student talk.

Authors

• Jillian M. Cavanna, University of Hartford

• Holly Henderson Pinter, Western Carolina University