Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures

by Ted Herr, Ken Johnson

Problem Solving Strategies Crossing the River with Dogs and Other Mathematical Adventures Why Teach a Course in Problem Solving? The NCTM Principles andStandards state that problem solving should be integrated throughout all courses and grade levels. For example, guess-and-check is a natural strategy to apply in algebra. Advanced math students often use finite differences to study functions and sequences. And drawing a diagram and using physical representations are commonly employed strategies in many contexts. However, many students never encounter valuable strategies such as matrix logic or unit analysis. And in content-crowded math classes, few students get the concentrated practice or time necessary to fully develop their problem-solving skills. By taking a semester course in problem solving, students can master a multitude of strategies while developing confidence in their problem-solving abilities. Your students will be better prepared to meet the challenges of school and life by taking this course.

Genres: Mathematics, Reference

486 pages, Hardcover

First published January 1, 1994

Reviews

[Andrew · Rating 4 out of 5]

This should be Math 1, or Pre-Algebra, or whatever passes for 7th-9th grade math. At the very least supplementing high school curricula.

The difficulty is that students don't think through problems. We break them down step-by-step and then wonder why the Quadratic Formula is being retaught in Algebra II and Precalculus. Classes move at a snail's pace because the student's don't get how to connect this to that and work to solve a problem with all their tools.

These puzzles work to build skills for thinking through a problem. Not Algebra or Geometry, but organizing information, changing perspective, and thinking through the data. The are no answers in the book, forcing students to discuss the problems in your class. It would be interesting to adapt the skills to the content in class and have students work out both things together.


As an added bonus, the problems dealing with scale modeling included one where the only way to solve it would be to use a compass construction (unless you knew your trigonometry, which would be easier).

Would that I could find better ways to work this into classes. Ah, time, why must you get in the way of good ideas!

[Cody]

Great book! Was originally a college text to study problem solving. I had it but didn't take the course,just thought it was cool. Then did the whole book as part of an endorsement class from cover to cover. No joke. Did every problem in it too. Yes I am a geek.

But this book it totally supported by the Common Core and its 8 Standards for Mathematical Practices. And ways in which we need to encourage our children to think.

Check it out.

Why do I expect Levar Burton to come in after these reviews and then theme music?