Abstract
Engagement with student thinking involves eliciting and using evidence of student thinking in instruction. This case study explored how three prospective elementary teachers engaged with student thinking in mathematics and used this thinking to guide instruction during their student teaching experiences. The prospective teachers were situated at the same school and same grade level and were supported through team meetings facilitated by a mathematics teacher educator. The prospective teachers then voluntarily sustained a community of practice in which they unpacked the pedagogical and content needs of instructional units focused on fractions. Consideration is given to implementation of similar support structures within teacher preparation programs in order to encourage teachers' engagement with student thinking, especially in mathematics.
TopBackground
The National Council of Teachers of Mathematics (NCTM) focused attention on the characterization of effective mathematics instruction and highlighted what students need to know and do mathematically with a commitment to challenging and supporting students to learn mathematics conceptually (NCTM 1989, 1991, 1995, 2000). NCTM’s (2014)Principles to Actions: Ensuring Mathematical Success for All defined eight effective mathematics teaching practices that align with the reform ideals. These eight practices provide the implementation roadmap for the organization’s vision of effective mathematics teaching. This study moved from those eight practices, and specifically focused on the practice of elicit and use evidence of student thinking (Table 1). In implementing the mathematics teaching practice elicit and use evidence of student thinking, teachers need to know how to elicit student thinking, interpret student understandings and misunderstandings, and respond by adjusting instruction to support and extend learning (Chamberlin, 2005; Jacobs & Empson, 2015; Jacobs et al., 2019; NCTM, 2014). In preparing a PT to engage with student thinking in planning and instruction, attention to this teaching practice needs to be highlighted and thoughtful supports must be in place to help the PT learn to do the work of attending to, interpreting, and using student thinking regularly.
Key Terms in this Chapter
Community Of Practice: Defined as a group of people who share common concerns or passions for something they do, and learn how to do this thing better by interacting ( Wenger, 1998 ; Wenger, McDermott, & Snyder, 2002b ). This study used team meetings as required meeting time for the community of practice participants to unpack reform-based mathematics pedagogies. The voluntary aspect of a community of practice ( Wenger, 1998 ) resulted from the participants’ willingness to meet and extend their collaboration and cooperative learning outside of the required team meetings.
Fraction: Defined as a non-negative rational number that can be written in the form a/b where a and b are both integers and b does not equal zero (Behr, Lesh, Post, & Silver, 1983 AU6: The in-text citation "Behr, Lesh, Post, & Silver, 1983" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ; Charalambous & Pitta-Pantazi, 2005 AU7: The in-text citation "Charalambous & Pitta-Pantazi, 2005" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ; Kieran, 1976 AU8: The in-text citation "Kieran, 1976" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ; Olanoff, Lo, & Tobias, 2014 AU9: The in-text citation "Olanoff, Lo, & Tobias, 2014" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).
Engagement With Student Thinking: Defined as the elicitation and use of evidence of student thinking in instruction ( NCTM, 2014 ). This study’s focus was prospective teachers’ elicitation and use of students’ mathematical ideas and strategies around fractions to inform instruction.
Context: Defined as the real-word situation of the case. When used in this case study, context refers to the situation of the participants’ student teaching experience in both a university teacher preparation program and an elementary school site. The context introduced elements of potential influence that included participants’ prior coursework, interpersonal relationships, and classroom dynamics.