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!

Modifying Tasks to Increase Their Reasoning-and-Proving Potential

chapter 5 modifying tasks to increase their reasoning-and-proving potential

Although we have argued throughout the first four chapters of this book that reasoning-and-proving transcends content and grade level, the reality is that most popular middle and high school textbook series limit the discussion of proof to geometry textbooks. This raises the question regarding how teachers can provide more opportunities to engage students in reasoning-and-proving when their textbooks don’t support it. It is interesting to note that Andrew Wiles, who published the first valid proof of Fermat’s Last Theorem in 1995 at the age of 45 (Fermat made his conjecture in the 1600s), found the theorem in a book in the library as a 10-year-old. He was instantly engaged ...

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