Abstract
Problem solving is a core activity in mathematics classrooms at all levels of schooling across the world. Problems are central to mathematics teaching and learning and constitute the basis for intellectual activity in the classroom (Lampert, 2001; Stein, Smith, Henningsen, & Silver, 2000). Thus, mathematics problems form the foundation of students’ opportunities to learn mathematics. In turn, the anticipation, examination, and evaluation of students’ work on problems constitute a substantial portion of the work of mathematics teachers. Thus, consistent with the so-called practice-based approach to teacher professional learning, the anticipation and examination of students’ solutions to mathematics problems should be a strategic site for teachers to learn in and from their instructional practice (Kazemi & Franke, 2004; Krebs, 2005). Yet, teacher learning does not occur as an automatic consequence of their using mathematics problems with students or witnessing the attempts of students to solve problems. Opportunities for teacher learning in and through close examination of aspects of instructional practice appear to be dependent on if and how professional development cultivates teacher inquiry and reflection (Little, Gearhart, Curry, & Kafka, 2003).
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Acknowledgments
I thank Valerie Mills, Dana Gosen, and Geraldine Devine—leaders of the DELTA project in Oakland Schools—for graciously agreeing to use the PISA Apples task in their project and making available detailed session records and artifacts. I also thank Patricia Kenney for her assistance in identifying the PISA Apples task as a fruitful candidate for use in this work. Thanks also to Heejoo Suh and Rachel Snider for their assistance with data collection, analysis, and interpretation. This research was supported by the National Science Foundation under Grant No. 1019513 [Using PISA to Develop Activities for Teacher Education] and the Michigan Department of Education for its grant to Oakland Schools [Developing Excellence in Learning and Teaching Algebra]. Any opinions, findings, conclusions, or recommendations expressed here are those of the author and do not necessarily reflect the views of the National Science Foundation and Michigan Department of Education nor those of individuals acknowledged above.
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Silver, E.A. (2016). Mathematical Problem Solving and Teacher Professional Learning: The Case of a Modified PISA Mathematics Task. In: Felmer, P., Pehkonen, E., Kilpatrick, J. (eds) Posing and Solving Mathematical Problems. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-28023-3_20
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