Abstract
This study examined the extent to which preservice teachers (PSTs) develop their capacity to attend to children’s strategies and interpret and respond on the basis of children’s mathematical understanding in the context of two well-designed assignments: Inquiry into Student Thinking assignment and tutoring assignment. The two assignments were assigned after 6 and 10 weeks of instruction, respectively. The analysis revealed that PSTs attended to children’s strategies and interpreted children’s mathematical understanding but struggled with the component skill of responding to children’s mathematical understanding in the two assignments. Although the nature of tasks selected differed across the two assignments, generally PSTs focused on tasks that would develop children’s mathematical understanding. The findings have theoretical implications for a hypothesized trajectory of professional noticing of children’s mathematical understanding and the design of mathematics methods courses.
Highlights
Teacher educators have argued that lack of a common knowledge base, curriculum, or a common pedagogy in teacher preparation programs has made it challenging to study how content taught in teacher preparation courses supports preservice teachers (PSTs) to acquire the knowledge, practices, and skills required to effectively enact mathematics instruction as beginning teachers [8,9,10,11,12,13]
Using the criteria identified by Ball et al [8], one would argue that PSTs capacity to respond based on children’s mathematical understanding is one of the “high leverage practices” that PSTs should learn as they go through a teacher preparation program because it is a practice that supports work that is central to mathematics
Findings and Results is section presents the results organized in the following subtopics: (a) extent to which PSTs attended to children’s strategies, (b) extent to which PSTs interpreted children’s mathematical understanding, (c) extent to which PSTs responded based on children’s mathematical understanding, (d) outcome of the paired t-test, and (e) the nature of the tasks selected and PSTs’ understanding of tasks that would engage students with high-level thinking
Summary
Teacher educators have argued that lack of a common knowledge base, curriculum, or a common pedagogy in teacher preparation programs has made it challenging to study how content taught in teacher preparation courses supports PSTs to acquire the knowledge, practices, and skills required to effectively enact mathematics instruction as beginning teachers [8,9,10,11,12,13]. A plethora of research findings have linked productive instructional environments to teachers’ knowledge of how to teach elementary mathematics in a way that develops and relates to the benefit of attending to children’s mathematical thinking [20, 22,23,24,25]. Consistent in these studies is teachers’ use of Cognitively Guided Instruction (CGI), a framework that explicates how children’s mathematical thinking develops and provides teachers with a context to interpret children’s strategies, conceptions, and misconceptions in specific mathematical concepts. Franke and Kazemi [23] pointed out that teachers using CGI were well poised to engage in sense making around children’s thinking, continually evaluated children’s understanding, and adapted and built on children’s mathematical thinking
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