Curricular resources include the different kinds of materials (digital or physical) that teachers use in or for their teaching (textbooks, lesson plans, etc.) and have a significant influence on students' opportunities to learn. At the same time, teachers play a crucial role as interpreters of such materials, so there is a complex relationship between curricular resources and their classroom use. This book aims to bridge these rather disconnected but highly related programs of research by describing, comparing, and exemplifying new research approaches for studying, in connected ways, both curricular resources and their classroom use, thereby supporting also investigation of the complex interplay between the two. In addition to implications for research, the book has implications for curriculum development and teacher education. Specifically, the book deepens understanding of how curriculum developers can better exploit the potential of curricular resources to support classroom work, and how teacher educators can better support teachers to use curricular resources in the classroom.
Sharpen concrete teaching strategies that empower students to reason-and-prove How do teachers and students benefit from engaging in reasoning-and-proving? What strategies can teachers use to support students’ capacity to reason-and-prove? What does reasoning-and-proving instruction look like? We Reason & We Prove for ALL Mathematics helps mathematics teachers in grades 6-12 engage in the critical practice of reasoning-and-proving and support the development of reasoning-and-proving in their students. The phrase "reasoning-and-proving" describes the processes of identifying patterns, making conjectures, and providing arguments that may or may not qualify as proofs – processes that reflect the work of mathematicians. Going beyond the idea of "formal proof" traditionally relegated only to geometry, this book transcends all mathematical content areas with a variety of activities for teachers to learn more about reasoning-and-proving and about how to support students’ capacities to engage in this mathematical thinking through: Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work that features a range of solution strategies, representations, and misconceptions Modifying tasks from curriculum materials so that they better support students to reason-and-prove Evaluating learning environments and making connections between key ideas about reasoning-and-proving and teaching strategies We Reason & We Prove for ALL Mathematics is designed as a learning tool for practicing and pre-service mathematics teachers and can be used individually or in a group. No other book tackles reasoning-and-proving with such breadth, depth, and practical applicability. Classroom examples, case studies, and sample problems help to sharpen concrete teaching strategies that empower students to reason-and-prove!
Curricular resources include the different kinds of materials (digital or physical) that teachers use in or for their teaching (textbooks, lesson plans, etc.) and have a significant influence on students' opportunities to learn. At the same time, teachers play a crucial role as interpreters of such materials, so there is a complex relationship between curricular resources and their classroom use. This book aims to bridge these rather disconnected but highly related programs of research by describing, comparing, and exemplifying new research approaches for studying, in connected ways, both curricular resources and their classroom use, thereby supporting also investigation of the complex interplay between the two. In addition to implications for research, the book has implications for curriculum development and teacher education. Specifically, the book deepens understanding of how curriculum developers can better exploit the potential of curricular resources to support classroom work, and how teacher educators can better support teachers to use curricular resources in the classroom.
Sharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, this book transcends all mathematical content areas with a variety of activities for teachers that include Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.
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