As I continue to polish the manuscript for my math games book, I’ve been looking for short quotations to put at the beginning of each chapter. I’ve gathered a lot of math quotations over the years, from my own reading and from quote-collection websites. But there’s a problem with using most of these in a book, since to do it right I would have to dig up the original source of each quote and then write a letter to the publisher for permission to use it. And pay a fee that, depending on the publisher’s sense of self-importance, can run into the hundreds of dollars. Bother!
So I went digging around my rss reader to see what sort of inspiration I could find. Bloggers love to be quoted, right? And most of them are happy to give permission via email, which makes my job ever so much easier.
Here are some of the gems I’m considering. I’d love to hear your favorite quotes from math bloggers, too — or favorite passages from your own blog. Please comment!
It’s amazing that this vision of math as “getting to the right answer on your first try” even exists. I have to make, unmake, remake so many mistakes to get where I’m going. I think all mathematicians work that way.
Somehow, a big part of the experience of math is trouble. Frustration is the status quo. But when you get something—the thrill!
A child learns to count spoonfuls, learns to count people, learns to count fingers, learns to just plain count, and in the process acquires the abstract concept of, for example, “two.” The child takes ownership of this concept, and can reapply it freely. As adults we may take “two” for granted, but we have never met it, never touched it, never tasted it. It is one of the first completely abstract concepts that we ever owned.
Math is the beautiful, rich, joyful, playful, surprising, frustrating, humbling and creative art that speaks to something transcendental. It is worthy of much exploration and examination because it is intrinsically beautiful, nothing more to say. Why play the violin? Because it is beautiful! Why engage in math? Because it too is beautiful!
Too often, kids learn a distaste for the subject without ever having the chance to see what there is to love in mathematics. For too many, the understanding of math isn’t particularly enduring, while their dislike of the subject is.
The toughest thing for a homeschooler is the same as for a school teacher – shifting from a weak tea vision of math being grinding calculations to a rich frothy mug of math as an active way of thinking.
Math happens when we notice similarities and differences. This is math proper. You purposefully create differences, keeping similarities, and observe what happens.
There are layers and layers of noticing to be had. We need to return to activities again and again to reach more layers. That’s why geeks are often told, “You have too much time on your hands!” when an outsider realizes how much time is spent with a single activity. There are riches to be had ONLY if you spend the time.
Intuition is great. Inductive logic is great. But it just isn’t enough. Back it up. Verify it. Embrace the conflict that arises when what you thought was true turns out to be, well, not so much.
Whatever you do, for goodness sake, don’t tell them the right answer. (Like, ever. Let them come to consensus. Learn how to ask helpful questions without giving away the store.) Unless for some reason you want to completely shut down discussion. And thinking.
— Kate Nowak
Virtual Conference on Core Values: Mistakes are Made
I am in the habit of beginning each class by apologizing to my learners. I’ll teach the class better next time because of what I learn from my interactions with them and from their feedback. I remind them that they are free to take the class next year – when it is improved. No one takes me up on that, but it sets the tone that I expect to grow as an educator.
6 thoughts on “Quotations XXVI: On Teaching Math”
Excellent quotes Denise. I like Kate Nowak’s in particular. Thank you for sharing.
Please note the [Mathematics and Multimedia] carnival schedule has changed.
It will be hosted by Mathematics, Learning & Web 2.0 in August and hosted by Guillermo Bautista in July on Math and Multimedia.
David Cox’s quote says it all: life if full of surprises! What we expect won’t happen and what we didn’t will!
Denise, I wish you all the best with your book! The quotes are wonderful, and there seem to be so many to choose from! Math is our universal language! It is the language that is used in all other areas of our lives. Isn’t it amazing that we can speak, through math, with so many others? Amazing!!
Barry Garelick sent me this quote by email to add to my list:
The amazement I felt at the age of seven when realizing that counting to one hundred twice is the same as counting to two hundred once was no less than when as a sophomore in college I discovered I could prove that the set of non-intersecting circles in a plane is countable.
— from Confessions of a Math Major