Description

Book Synopsis
College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation.Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned.

Science Of Learning Mathematical Proofs, The: An

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    A Paperback / softback by Elana Reiser

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      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: Publication Date: 07/12/2020
      ISBN13: 9789811225512, 978-9811225512
      ISBN10: 9811225516

      Description

      Book Synopsis
      College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation.Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned.

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