Thinking Practices in Mathematics and Science Learning, 2013
Page 25. CHAPTER 1 MATHEMATICS REFORM AND TEACHER DEVELOPMENT: ACOMMUNITY OF PRACTICE PERSPECTIVE... more Page 25. CHAPTER 1 MATHEMATICS REFORM AND TEACHER DEVELOPMENT: ACOMMUNITY OF PRACTICE PERSPECTIVE Mary Kay Stein Edward A. Silver Learning Research and Development Center, University of ...
The past decade has witnessed a strong, standards-based call for improving what mathematics is ta... more The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study was to contribute to the field’s understanding of (a) the specific coaching practices that help teachers enact more conceptual-based forms of instruction; and (b) how coaches learn to enact those practices. Using a design-based implementation research approach, we trained coaches using a particular model for one-on-one coaching (Content-Focused Coaching); the coaches then worked with teachers to plan lessons aligned with the coaching model. Data consisted of videotapes of pre-lesson conferences that were transcribed and coded according to the model. Analyses of 32 coaches’ practice over a 2-year period suggest that each of the three components of our coaching model (attention to student thinking, pedagogy, and mathematics) demonstrated statistically significant improvement over time. An illustrative analysis of five coaching sessions of one coach revealed a progression over five sessions from planning discussions that stayed at the level of general strategies to more specific conversations about teaching a particular task and then to deeper discussions that integrate attention to mathematical concepts, student thinking, and pedagogical moves. We view this delineation of coach learning as an important first step in laying the groundwork for the design of future coach training.
Journal for Research in Mathematics Education, Mar 1, 2020
A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instr... more A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instructional practices do not always neatly align with their beliefs because of factors perceived as constraints. The purpose of this article is to introduce a new approach for examining the relationship between teachers’ beliefs and practices, an approach that focuses on specific instructional practices that support the development of students’ conceptual understanding and on mismatches that occur between what teachers believe to be important and what they report actually doing in the classroom. We also examine the relationship between teachers’ self-reported constraints and mismatches between teachers’ beliefs and practices.
Conventional mathematics instruction has failed to help many students in urban schools to develop... more Conventional mathematics instruction has failed to help many students in urban schools to develop desirable forms of mathematical proficiency. A promising alternative is offered by instruction that is oriented toward helping students develop a meaningful understanding of mathematical ideas through engagement with challenging mathematical tasks. For 5 years, teachers involved in the QUASAR project have engaged in developing and implementing this alternative style of mathematics instruction in urban middle schools. In this article, some critical features of QUASAR instruction are described and exemplified, and some findings regarding the positive impact of this instruction on students are discussed. Finally, some of the challenges and obstacles encountered in attempting to build the capacity of teachers and schools to offer meaning-oriented mathematics instruction are identified.
Journal for Research in Mathematics Education, 2020
A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instr... more A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instructional practices do not always neatly align with their beliefs because of factors perceived as constraints. The purpose of this article is to introduce a new approach for examining the relationship between teachers’ beliefs and practices, an approach that focuses on specific instructional practices that support the development of students’ conceptual understanding and on mismatches that occur between what teachers believe to be important and what they report actually doing in the classroom. We also examine the relationship between teachers’ self-reported constraints and mismatches between teachers’ beliefs and practices.
We argue that large-scale, standards-based improvements in the teaching and learning of mathemati... more We argue that large-scale, standards-based improvements in the teaching and learning of mathematics necessitate advances in our theories regarding how teaching affects student learning and progress in how we measure instruction. Our theory—an embodiment of the interaction of high and low levels of two constructs that past research has shown to influence students’ development of conceptual understanding (explicit attention to concepts and students’ opportunity to struggle)—guided the development of survey-, video-, and artifact-based measures of teaching. Here, we develop a validity argument for the inferences that can be drawn about teaching from these measures by identifying claims and empirical evidence about the extent to which those claims are born out in practice. Results suggest our theory is capturing four patterns of teaching and that it can successfully predict different types of student learning: skills efficiency measured on the state standardized test and conceptual unde...
Thinking Practices in Mathematics and Science Learning, 2013
Page 25. CHAPTER 1 MATHEMATICS REFORM AND TEACHER DEVELOPMENT: ACOMMUNITY OF PRACTICE PERSPECTIVE... more Page 25. CHAPTER 1 MATHEMATICS REFORM AND TEACHER DEVELOPMENT: ACOMMUNITY OF PRACTICE PERSPECTIVE Mary Kay Stein Edward A. Silver Learning Research and Development Center, University of ...
The past decade has witnessed a strong, standards-based call for improving what mathematics is ta... more The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study was to contribute to the field’s understanding of (a) the specific coaching practices that help teachers enact more conceptual-based forms of instruction; and (b) how coaches learn to enact those practices. Using a design-based implementation research approach, we trained coaches using a particular model for one-on-one coaching (Content-Focused Coaching); the coaches then worked with teachers to plan lessons aligned with the coaching model. Data consisted of videotapes of pre-lesson conferences that were transcribed and coded according to the model. Analyses of 32 coaches’ practice over a 2-year period suggest that each of the three components of our coaching model (attention to student thinking, pedagogy, and mathematics) demonstrated statistically significant improvement over time. An illustrative analysis of five coaching sessions of one coach revealed a progression over five sessions from planning discussions that stayed at the level of general strategies to more specific conversations about teaching a particular task and then to deeper discussions that integrate attention to mathematical concepts, student thinking, and pedagogical moves. We view this delineation of coach learning as an important first step in laying the groundwork for the design of future coach training.
Journal for Research in Mathematics Education, Mar 1, 2020
A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instr... more A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instructional practices do not always neatly align with their beliefs because of factors perceived as constraints. The purpose of this article is to introduce a new approach for examining the relationship between teachers’ beliefs and practices, an approach that focuses on specific instructional practices that support the development of students’ conceptual understanding and on mismatches that occur between what teachers believe to be important and what they report actually doing in the classroom. We also examine the relationship between teachers’ self-reported constraints and mismatches between teachers’ beliefs and practices.
Conventional mathematics instruction has failed to help many students in urban schools to develop... more Conventional mathematics instruction has failed to help many students in urban schools to develop desirable forms of mathematical proficiency. A promising alternative is offered by instruction that is oriented toward helping students develop a meaningful understanding of mathematical ideas through engagement with challenging mathematical tasks. For 5 years, teachers involved in the QUASAR project have engaged in developing and implementing this alternative style of mathematics instruction in urban middle schools. In this article, some critical features of QUASAR instruction are described and exemplified, and some findings regarding the positive impact of this instruction on students are discussed. Finally, some of the challenges and obstacles encountered in attempting to build the capacity of teachers and schools to offer meaning-oriented mathematics instruction are identified.
Journal for Research in Mathematics Education, 2020
A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instr... more A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instructional practices do not always neatly align with their beliefs because of factors perceived as constraints. The purpose of this article is to introduce a new approach for examining the relationship between teachers’ beliefs and practices, an approach that focuses on specific instructional practices that support the development of students’ conceptual understanding and on mismatches that occur between what teachers believe to be important and what they report actually doing in the classroom. We also examine the relationship between teachers’ self-reported constraints and mismatches between teachers’ beliefs and practices.
We argue that large-scale, standards-based improvements in the teaching and learning of mathemati... more We argue that large-scale, standards-based improvements in the teaching and learning of mathematics necessitate advances in our theories regarding how teaching affects student learning and progress in how we measure instruction. Our theory—an embodiment of the interaction of high and low levels of two constructs that past research has shown to influence students’ development of conceptual understanding (explicit attention to concepts and students’ opportunity to struggle)—guided the development of survey-, video-, and artifact-based measures of teaching. Here, we develop a validity argument for the inferences that can be drawn about teaching from these measures by identifying claims and empirical evidence about the extent to which those claims are born out in practice. Results suggest our theory is capturing four patterns of teaching and that it can successfully predict different types of student learning: skills efficiency measured on the state standardized test and conceptual unde...
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