I remember when I was in grade school, textbooks weighed about twenty pounds and were chock-full of basic, mechanical exercises. There were around 200 problems at the end of each chapter, and the first 150 of them were questions like 365 ´ 791. We often worked individually on these in class, in silence.
Despite how boring this was, math was always my favorite subject. This was probably because I was good at it and I liked being the best; not necessarily because I enjoyed the actual calculations. But in math class, there should be no “best.” The mechanical, formulaic process of learning categorizes kids into a one-dimensional scale of bad, worse, worst and good, better, best. Students should be able to view the world through the lens of mathematics and form their own unique perspectives that cannot possibly be ranked.
Textbooks like the ones I was used to have deterred students from math, especially when they take control of math learning – often, textbooks dictate lesson plans, in-class work, and homework.* We cannot allow an inanimate object to decide how students learn math.
So, if the textbook is too powerful, what can we do to achieve some balance of power? What should the role of the textbook be if it does not govern math assignments? To answer this, we first need to think about the point of education. This may seem like an even more complex subject, but I think it can help us. There are many uses of education (students learn to collaborate and communicate with others – their peers and teachers – as they would in the “real world”; students understand and appreciate how their country and world came to be; education is a signal to others that the individual is competent; and the list goes on), but one use that is particularly relevant to the role of textbooks is this:
Education provides students a window into the real world. If that window is dirty, foggy, scratched, or covered, students’ perspectives will reflect this for much of their lives.
The role of textbooks should assist in making this window as clear as possible. Certainly, a textbook that mandates students to repeatedly practice mechanical processes will make for a heavily blotched window.** This is why I believe most students do not really understand what math is. Their perceptions have been rigged.
A mathematics textbook should be a collection of prudent information about the world, accompanied by analytical questions that force students to think critically. This critical thinking should involve math. Sometimes, the best way to view a situation is with a mathematical eye. Identifying these special situations would be difficult for teachers to do continuously, so this is where the textbook comes in handy. The Internet, interactive technology, and software used in today’s modern, digital textbooks can provide an even greater window to the world.
In short, textbooks should be real-life, interesting, and informative. No drill and practice, no rote memorization. These are important at times, but will be dealt with outside the realm of textbooks.**
*The dominance of textbooks is why Henri Picciotto founded the Escape from the Textbook! community of educators who meet regularly to give each other ideas on engaging ways to teach important concepts.
**The practice of basic skills and mechanical processes is where certain types of technology come into play. See my post Ideal Math Education Technology in the Digital Age (last paragraph).