Quotable: On Teaching

[Photo by City of Boston Archives via Flickr (CC BY 2.0).]

I’ve started collecting quotes about teaching math for the chapter pages in my next Math You Can Play book. Here are a couple snippets that don’t fit the theme of “Multiplication & Fractions,” but they struck my fancy anyway:

If teachers would only encourage guessing. I remember so many of my math teachers telling me that if you guess, it shows that you don’t know. But in fact there is no way to really proceed in mathematics without guessing. You have to guess! You have to have intuitive judgment as to the way it might go. But then you must be willing to check your guess. You have to know that simply thinking it may be right doesn’t make it right.

[Photo by Nathan Russell via Flickr (CC BY 2.0).]

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics.

Leon Henkin
from “Round and Round at the Round Table”
Teaching Teachers, Teaching Students: Reflections on Mathematical Education

Do you have some favorite quotes on math and teaching? I’d love to hear them! Please share in the Comments section below.

4 thoughts on “Quotable: On Teaching”

1. “All freemen I conceive, should learn as much of these [mathematical] branches of knowledge as every child in Egypt is taught when he learns the alphabet. In that country arithmetical games have been invented for the use of mere children, which they learn as a pleasure and amusement. They have to distribute apples and garlands, using the same number sometimes for a larger and sometimes for a lesser number of persons; and they arrange pugilists and wrestlers as they pair together by lot or remain over, and show how their turns come in natural order. Another mode of amusing them is to distribute vessels, sometimes of gold, brass, silver, and the like, intermixed with one another, sometimes of one metal only; as I was saying they adapt to their amusement the numbers in common use, and in this way make more intelligible to their pupils the arrangements and movements of armies and expeditions, and in the management of a household they make people more useful to themselves, and more wide awake; and again in measurements of things which have length, and breadth, and depth, they free us from that natural ignorance of all these things which is so ludicrous and disgraceful.”

Plato, Laws, Book VII [819]

2. Learning with games, as pleasure and amusement. Sounds like my kind of math! The combination of puzzle-solving and real-life math makes a good mixture.

1. When I first found your blog I thought playing math was a new idea. Turns out you’re the truly classical one, and the drill-and-kill method is the modern one. 😉

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