MATHEMATICS TEACHING: LISTENING, PROBING, INTERPRETING AND RESPONDING TO CHILDREN'S THINKING.

Neumann, Maureen D.

The perception of what a teacher says s/he does in the classroom may or may not match the reality of their actual teaching practice. This case study considers one second-grade teacher's instructional methods and pedagogical decisions when teaching number sense and her perception of what informed her teaching practice. This teacher supported students' development of mathematical strategies, valued debriefing time, and students' sharing mathematical strategies. Additionally, she listened to students purposely by probing their thinking. Her experience in a mathematics professional development program helped her be consistent in her beliefs about mathematics learning, her perception of her teaching, and the observed practice. Teaching students so they learn and know mathematics conceptually along with understanding how to move students' mathematical knowledge forward is a complex enterprise (Kazemi & Franke, 2004; Hill, Rowan, & Ball, 2005). However, many elementary school teachers did not learn mathematics or observe mathematics being taught as National Council of Teachers of Mathematics (NCTM) or the Common Core State Standards in Mathematics (CCSS-M) advocate. Most teachers learned mathematics through direct instruction that emphasized fact-based, low-level questions, and rote memorization (Raymond, 1997; Spielman & Lloyd, 2004). Many teachers now use this as their model of how to teach (Stigler & Hiebert, 1999) and therefore struggle to understand what it means to teach mathematics as the NCTM Standards (1989, 1991, 2000) or CCSS-M (2010) envisioned (King, 2011; Murata, Bofferding, Pothen, Taylor, & Wischnia, 2012). All too often, reform in mathematics instruction (i.e., curriculum, teaching, and assessment) is implemented with little or no support for teachers, which leaves them to interpret reform measures on their own (Ball & Cohen, 1996).Teachers then "risk constructing 'lethal mutations' in their classrooms, as they modify practice, or extend it and unintentionally violate rudiments of the reforms theoretical base" (McLaughlin & Mitra, 2001, p. 307). If teachers cannot picture the type of instruction promoted by NCTM because they have never experienced it, then how can we expect teachers to apply this vision effectively? Thus, professional development experiences must inform and transform teachers' beliefs about learning mathematics and instructional practices for teaching mathematics. For this research study, I examined the alignment between one teacher's beliefs on mathematics instruction, her perception of her teaching practice, the observed practice, and the professional development experience that influenced her thinking about teaching mathematics.

MATHEMATICS education; MATHEMATICS students; MATHEMATICAL ability; MATHEMATICS teachers; NONVERBAL ability

Investigations in Mathematics Learning, 2014, Vol 6, Issue 3, p1

1947-7503

Academic Journal

10.1080/24727466.2014.11790333