Comments on: Misunderstanding Math

By: Larry Stookey

Larry Stookey — Sun, 24 Jul 2011 16:16:47 +0000

I don’t teach math. I teach physics. At the high school level, physics is mostly an “applied math” class, with lots of real-life problems to solve. It’s nice to have students who don’t have to use a calculator to divide two into 3. I have to admit that it’s nice when I can use some of the math “shorthand” vocabulary to talk to my students about problem-solving techniques, such as “Remember to distribute the number 2 across the two terms in parentheses.”
What this requires is that our young must learn the basic math principles using the inquiry methods of which Paul Lockhart is so rightfully fond. There is a tendency nowadays in many school districts to replace content teachers of science or math or English in middle school with K-8 teachers, who frequently have not learned the content knowledge or do not exhibit the interest in math or science to teach anything that is not in the elementary text and consumable workbooks. This is sad, because then these districts have fallen into the trap that Lockhart describes, teaching rote and lifeless facts and formulas.
We can’t tread the paths of mathematicians and scientists of centuries past. We can’t expect students to reinvent and rediscover all math and science, but we can and should show them the path and describe the wonders of the routes taken by these earlier students. And we need to do this earlier rather than later.

By: Phillip Alvelda

Phillip Alvelda — Tue, 05 Oct 2010 23:36:58 +0000

I can’t tell you HOW many people I’ve run into that tell me, “I can’t do math,” or “trigonometry is impossible” and within 15 minutes I can get them to say something like “Really? That’s all there is to it? Why didn’t they explain it that way in high school?” Similarly, I can’t count the number of kids I have tried to explain something to that simply didn’t understand the first route through the problem, and could only get the idea with an approach from a different direction. Some people are much more spatial and benefit from starting with physical objects and moving them around. Others are more comfortable starting with symbology and only thinking about the link to physical objects later, and fundamental truths after that. Some, more rarely, even like the abstract theoretical approach to fundamental ideas from which all else can be derived. Different learning styles and perspectives reach different people.

Sadly, few elementary, middle, or high school math teachers have had enough exposure to mathematics themselves to even realize that there ARE multiple approaches to most math challenges.

By: Phillip Alvelda

Phillip Alvelda — Tue, 05 Oct 2010 23:31:49 +0000

The teacher’s materials do, in fact, contain a lot of text-book style instructions. But the beauty of it is in how, once one understands the concepts that link text-book algebra notation to the physical blocks, and how each illuminates the other, THEN the interactions between the two, and people playing with both becomes magical.

By: Tim Shepard

Tim Shepard — Tue, 05 Oct 2010 22:52:05 +0000

Thank you.

Insightful, articulate, and thought-provoking. Math is a subject which seems to have become razed by the sharp edges of education these days. It is- I believe- the rather paradoxical nature of currently practiced modes of teaching, which has stunted the growth of a more… shall we say natural… or even flexible? … viable means of sparking mathematics with the vitality and authenticity it deserves.

I grew up in an area which (all-too-often), prides itself on providing exemplary education to the public. Yet it seems like so much of the curriculum was founded upon teaching us students what to think, as opposed to how we might actually think. In 8th grade, I was put in an advanced math class. It was called, “Integrated 3″ I believe. All the math classes, until calculus- if you even got that far in High School- were integrated aspects of math. Then in 9th grade, they suddenly changed the system so that classes were apportioned to their respective subject (i.e. algebra, trig, etc..). Next thing I knew, I had come to realize that I sucked at math, and that math was the worst subject ever.

It was until I began school at the University of Washington, when I finally realized that my thinking wasn’t exactly spot-on- so to speak. I read Newman’s Principia Mathematica, and wah-lah! I CAN do math, and so can anyone- and so SHOULD everyone. It can be just as fun and creative as writing, painting, drawing music… it really just comes down to how, not what, we are teaching the subject in schools.

Sorry for the super long post, lol. Loved the article, love the blog, I’ll be checking in frequently to see what’s going on.

Thanks again for this post.

Tim

By: Maths private tutor

Maths private tutor — Mon, 04 Oct 2010 08:01:33 +0000

Great information in this post and I think there are even a number of Universities that don’t really get it (see below). So it’s not really all that surprising that our schools and even our culture at large fail to grasp the significance, the beauty, the elegance, or the joy of practicing mathematics.

By: Juan Hudkins

Juan Hudkins — Thu, 23 Sep 2010 11:55:49 +0000

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By: Chris S.

Chris S. — Fri, 06 Aug 2010 21:37:49 +0000

Very informative. So far you succeeded in opening my mind to what “Math” could really become.

…So far, I’m still on the search for a “solution” as to what can/needs to be done. I am tired of reading stories; essays; scripts; books, about the problems with how mathematics are taught now-a-days. I need answers!!! Answers!!….And more answers!

SN: By the way: Henri Piccioto’s Algebra Lab materials looks like a regular school textbook (Not very stimulating to the mind if you ask me) :/

By: My Bonus

My Bonus — Tue, 22 Jun 2010 21:15:46 +0000

I’ve been thinking the exact exact issue myself recently. Glad to determine someone around the same wavelength! Good content.

By: Cindy Murphy

Cindy Murphy — Sun, 04 Jan 2009 22:49:18 +0000

Music to my ears!! I’ve been fighting this fight for many years — convincing students one at a time — that the art of math is actually tons on fun and meant for we mortals to enjoy.

I ran across “The Mathematician’s Lament” a while ago — it brought tears to my eyes. Even when the idiots were getting me down, and I thought all was hopeless, I’d see the look in a student’s eyes who really got it — magical! It will keep me going spreading this gospel for the rest of my life!

By: Phillip Alvelda

Phillip Alvelda — Sun, 02 Nov 2008 23:31:24 +0000

Absolutely love it. Are you getting response? Dad