We want our students to know that learning is as important a goal as problem solving in mathematics. Failing to solve a problem but learning something from studying the solution is not a failure at all.
Because understanding a new idea is itself a creative process, as mathematically impressive as discovering it in the first place. And it's also just as valuable - mathematics needs people who are able to learn challenging ideas with depth.
If what we mainly value is problem solving, studying a solution is just giving up. But if we value achieving mathematical understanding, we can see the studying of a solution for what it is: a core mathematical act.
And that's why studying mathematical examples is so valuable.
"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 "
"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 i