Teaching Math With Examples
- Length: 126 pages
- Edition: 1
- Language: English
- Publisher: John Catt Educational
- Publication Date: 2021-04-06
- ISBN-10: 1913622487
- ISBN-13: 9781913622480
- Sales Rank: #71100 (See Top 100 Books)
Some teachers think that there’s little to say about teaching with examples – after all, everyone uses them. But here are just some of the questions you might have about teaching with worked examples:
- How do we introduce an example?
- What do we ask students to do when studying a solution?
- Should a solution be presented all at once or revealed step-by-step?
- After we study an example, what comes next?
- Does it matter if the solution is presented as if from a fictional student, a real student in class, or from the teacher?
- How do we help students move from understanding someone else’s ideas towards using it on their own to solve problems?
- How do we write a solution in a clear way, that students can learn from?
- When is a good time to offer a worked example? When is it better to let students try a problem?
- Are worked examples more useful for some mathematical content than others?
This book will answer all of these questions. In some cases, research offers answers. Other questions represent gaps in the research literature and the book offers solutions arrived at through experience and trial-and-error and the author’s own process of classroom problem solving.
Welcome to the world of teaching with examples!
Copyright Reviews Epigraph Dedication Acknowledgements Preface: The value of studying examples Introduction: Getting started with examples Preview of what’s to come Chapter 1: How learning from examples works Analyze, explain and apply: Thinking deeply about examples Self-explanation research Notice and remember: Preparing to learn from an example In short Chapter 2: The case for starting with examples Learning from examples and problem solving Examples and creative engagement Problem-solving strategies In short Chapter 3: Routines for learning from examples Slow reveal of the solution Time to quietly analyze the example Explain to a partner Some good prompts Your turn How different should the problem be from the solution? What comes next? In short Chapter 4: Some questions and answers about the routine Q: When do students take notes? Q: Do students write down the answers to the self-explanation prompts, or only discuss them with classmates? Q: Do you always start the routine with a review problem for students to solve? Q: It seems you don’t explain the example to the students before they have studied it. Why is that? Q: In your routine, you first ask students to study a solution. Then, when everyone is finished, you reveal prompts for explanation. Wouldn’t revealing them with the solution help students read it more carefully? Q: Do you leave the example up when students try to solve the “Your Turn” application problem? Q: Does your routine work for online learning? Q: Does it matter whether you associate the solution with a particular fictional student (e.g. “This is how Michael solved the problem”)? Q: Is your routine the only good way to present worked examples? In short Chapter 5: Moving from examples to problem solving Whole-task and part-task practice Technique 1: Meaning-making problems Technique 2: Completion problems Technique 3: Fading out an example Technique 4: Case comparisons Technique 5: Mistake analysis In short Chapter 6: Giving worked examples as feedback A simple theory of feedback A worked example feedback routine Stage 1: Mark it Stages 2 & 3: Focus on a problem; create a worked example Stage 4: Call for revision In short Chapter 7: Designing worked examples Choosing problems for examples The science of example design Structuring a long solution In short Chapter 8: Teaching proof with examples Start with a goal-free problem Preview the structure I think aloud, you analyze Lots of whole-task practice In short Afterword: The big ideas of teaching with examples Further reading Preface Two cultures of mathematics Introduction & Chapter 1 Reviews of the worked example literature How Americans teach Algebra/Math by Example and design-based research Chapter 2 Behaviorism and the emergence of cognitive science John Sweller and cognitive load theory Chapter 3 Can teaching be evidence-based? The importance of self-explanation Chapter 4 Associating strategies with (fictional) students Chapter 5 Whole-task practice and complex learning Chapter 6 Why is feedback research so hard? Chapter 7 Well-designed materials Chapter 8 Goal-free and open-ended problems Michelle Cirilo’s writing on proof About the author Extended description for image on p. 80 Extended description for image on p. 81 Extended description for image on p. 88 Extended description for image on p. 92
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