I am holding a new small volume by two distinguished professors of mathematics - Edward Burger and Michael Starbird, The 5 Elements of Effective Thinking. I feel like saying a few words that are not directly related to the book proper. But first, let me say that it's a very good book of the self-help variety that I would highly recommend to people in the teaching profession. The authors advance several pedagogical devices that without doubt would enhance any teacher's effectiveness.
I especially loved two - I found them brilliant and pedagogically sound:
Give credit for a useful, quality error. An error detected and dealt with is a very good indicator of student's involvement, progress, and development of effective study habits.
For every class, assign a couple of students - questioners - whose responsibility on that day is to ask at least one good question.
The authors do not limit their advice to the teacher audience. Much of what they wrote is intended for students - how to improve one's study habits and even how better to prepare for the exams. The book distills their vast experience as students, math professors, business consultants, successful authors.
The authors describe behavioral strategies mastering which, i.e., making them into habits, is bound to improve one's thinking. There are four strategies that are associated with four classical elements: Earth, Fire, Air, Water.
Earth: Understand deeply. Ground your thinking on firm foundation.
Fire: Fail to succeed. Ignite insights through mistakes.
Air: Be your own Socrates. Creating questions out of thin air.
Water: Look back, look forward. Seeing the flow of ideas.
The fifth element is a necessary Change that must be desired, pursued, and be expected upon the mastery of the four fundamental strategies. The acquired habits will serve students well beyond college classrooms, help grownups in making good personal and business decisions. As the as authors write,
Our hope is that students will find these elements transformative; instructors will use these lessons to enrich their classes; leaders of society, whether in business, sciences, politics, or the arts, will employ these strategies to become more innovative; and lifelong learners will apply these principles to better live as ever-evolving students of world.
Now to allow for a diversion from the book and self-help thematics, I - on my part - hope that the fact that such a book has been written by two professors of mathematics may weigh on an old discussion that has flourished recently with the publication in the NY Times of the article, Is Algebra Necessary?.
I do not know whether the book will succeed in the marketplace. The competition in the self-improvement market is stiff. And although it is said that a person who bought a self-improvement book is likely to buy another one in the next 18 months, there is a reasonable number of popular and trusted books that fill about the same niche, e.g.,
- E. de Bono, Six Thinking Hats
- R. von Oech, A Whack on the Side of the Head: How You Can Be More Creative
- S. Covey, The 7 Habits of Highly Effective People
- R. Bradbury, Zen in the Art of Writing: Essays on Creativity
- K. H. Blanchard, The One Minute Manager
- B. Edwards, Drawing on the Right Side of the Brain
Be as it may, I find it significant that the two math professors chose a venue other than employing Algebra as a tool for improving their readers' thinking. Had the book been written around an algebra course it would have had no competitors.