[Rescued from my old blog.]
I thought you might enjoy the quote I’m going to use on the blackboard in math class:
The clearer the teacher makes it, the worse it is for you. You must work things out for yourself and make the ideas your own.
—William F. Osgood, quoted in
Out of the Mouths of Mathematicians
by Rosemary Schmalz
…and here is one more, just for fun:
The ultimate goal of mathematics is to eliminate all need for intelligent thought.
—Ronald L. Graham, quoted in
Out of the Mouths of Mathematicians
by Rosemary Schmalz
I think that last quote is a good description of the basic arithmetic algorithms. The reason we learn such things as “borrowing” or long division is so that we can automatically do the calculations without having to think about what the numbers mean. Of course, the algorithms are based on our place value number system, so if we can get students to think intelligently about the “why” behind the algorithms, they will learn a lot about how numbers work.
Denise Gaskins' Let's Play Math 
I agree with what you said about mathematics. I would say that computer science, too, eliminates the need for intelligent thoughts and labor 🙂 It’s only after graduating that I ‘ve discovered that what we were doing at elementary mathematics class, was mere algorithmic. Knowing the “How” without the “Why” is definitely not intelligent. As such, we deprive students from the joy of learning, that of knowing the proof, and how complicated things stems from simple understandable elements. I think that the contrary would empower students to be creative.
I like the quote on teaching, every teacher should know it. Robyn R.Jackson put well this principal from an opposite side in her book title: “Never work harder than your students”. Besides, John Taylor Gatto also assert that we don’t learn by being taught, but we learn by being self-thought. That is, learning is a self-accomplishment.
Thank you for sharing.
A computer science teacher
By the way, this post is thought provoking, at least on me 🙂
I was thinking on the explanation of arithmetics: why we can borrow and restitute in such a way. Don’t laugh on me, but, ironically, it is till now that I can explain what I’ve learned well when I was 6 years old 😀