For decades many reform educators of math and science have been adopting a practical, relevant, and “real-world” approach to the teaching of abstract ideas. They have called it “hands-on.” The term was (and, in some circles, still is) identified as the only effective way of teaching. In the 1990s, it carried so much clout and attained such a celebrity status that if an author did not use “hands-on” in his/her new introductory physics or math book, few publishers would want to publish the book and fewer teachers would want to adopt it.
What eased the acceptance of this seemingly effective approach to teaching was the rapid growth of technology and its explosive popularity in the art of teaching. In introductory physics, for example, sophisticated graphics and animation software replaced the dreary equations. Students learned to “master” the projectile motion in a hands-on way: instead of learning how to use the equation of a projectile, they became experts in tweaking the initial speed and direction of the projectile in such a way as to hit the target.
The reform movement is not anything new. In the first half of the 20th century, it was the most powerful voice in education. And as it was sweeping across the education landscape — and in the process almost killing mathematics in the US — there were traditionalists who doubted the efficacy of “hands-on.” No educator questions the fact that practical activities can reinforce the learning of abstract ideas. However, they cannot replace the role of manipulation and exercise of abstract symbols in the development of the mind. Abstraction is, after all, a necessary nourishment for the human mind. We don’t substitute pictures and movies for words when we teach a toddler how to speak. As we show the toddler the picture of a tree, we repeatedly pound its brain with the abstract sound of “t-r-e-e.” Similarly, an animation software may reinforce the learning of the motion of a projectile.
But ultimately, we have to pound the brain of the novice repeatedly with the abstract equation if (s)he is to learn the concept of projectile motion.
Words at a higher level of abstraction are learned only by usage, practice, and memorization. There is no “real-world” way of teaching a word like “justice” to an elementary-school student. A thousand pictures and movies of judges, jurors, and courtrooms will not teach the kid the meaning of the word. (S)he needs to hear it, read it in stories and news, memorize its spelling, use it in his/her writings incorrectly, get corrected, and use it again and again until (s)he “gets it.” Confining the instruction to pictures makes the student a master in the “game” of recognizing a courtroom, a judge, and a jury, but deficient in using the word “justice” in a sentence; just as confining a physics novice to the “game” of projectile motion makes him/her proficient in the game, but deficient in solving a simple projectile problem.