Archive for: January 2008

If you’re new here, you may want to subscribe to my RSS feed. Thanks for visiting!

I’ve just been perusing a very interesting blog (and a great resource for teachers in public schools). It’s called MathNotations.

This post intrigued and annoyed me, though. (Hey, maybe that’s a sign that it is a good blog!) It’s a poll about which method should be used to teach multidigit multiplication, like 48*73, for example. (If you do go to the link, make sure you scroll down and read the comment on Jan 30th by Michael Paul Goldenberg. It is excellent.)

Unfortunately, this poll is guilty of the same myopia as the American school system in general. It’s about creating a “standard.” Standard is just another word for limitation for people who really don’t know how to excel.

In the case of this poll, it is about choosing (out of an artificially limited group of choices - which is the logical fallacy of “false dichotomies”) how multidigit multiplication should be taught.

The wording of the poll is:

“Here are your options regarding your preference for how multidigit multiplication should be taught in Grades 3-5:”

Um, here are my options? I think not.

One of the great problems in (at least) American education today is that we’re firmly locked, sealed, and vacuum-packed into the box of pedagogical dogma.

(more…)

A reader in China asked about how to change fractions…not just simple ones, into percent.

“I am trying to assist my 6th grader and my way of doing math works, but it appears complicated when I explain it….”

Professor Homunculus replies:

I know what you mean. I used to be a math teacher, and I understand that each child needs his own method of explanation. There is no “one right way,” but I have learned that there is a need for at least one simple, core explanation (a sort of “summary” or “schematic” explanation) that each teacher can build on.

So, for how to change fractions into percent, I have come up with this:

Read the rest here

A girl recently asked for some help multiplying.

Professor Homunculus replied:

I have lots of questions to ask you, but first, here is something you can do right away to help you learn multiplication by 2, 3 and 4:

Get out a deck of cards. Make sure they are all (52) there. Now count them by twos. If you end up saying “fifty-two,” and have no cards left, you got it right.

Now try by threes. If you end up saying “Fifty-one”, and have one left over at the end, you got it right again.

Now try by fours. If you end up at “fifty-two” and have none left over, you’re right again.

Now do that over and over. Always count by twos, threes, and fours, no matter what you are counting from now on.

If you get a group of coins, like pennies, as change, count them by threes.

If you have to count the amount of kids in a class, count by threes or twos.

And so on.

Actually counting things in groups is a lot better than looking at tables, and parroting them back.

If you really want a great way to learn to multiply very fast and easily, consider getting a copy of “Numbers Juggling - Times without the Tables.”

You can find a link to it on the right-hand side of each page of these Math Mojo Chronicles.

Also, have you checked out MathMojo.com? Go there and click on the link for “speed multiplication by 11 and 12″. (It’s down the page a bit).

Then, check out:
http://www.squidoo.com/multiplication/
It will teach a cool multiplication trick, but you’ll only be able to do it if you first learn (and practice) what you learn at the “speed multiplication by 11 and 12″ link, above.

You are actually in luck. Recently a new book came out, and I have to say, it is a great book for girls to learn math from.
It’s called “Math Doesn’t Suck,” and it was written by an actress who is also (of all things) a mathematician. It’s a pretty awesome book.

Now for my questions:

How are you at addition? How are you at your other subjects in school? How are you with sports? Do you practice anything regularly (a sport, musical instrument, game?)

When you wrote the comment, were you aware of your misspellings and grammar mistakes? I’m not asking to judge you, just for info for how to help you.

Any answers to those questions will help me figure out how to help you better.

A reader wrote in the following request:

I need to know what would be a good activity to use with preschool and primary students to help them grasp the concepts of the following:
1. Centering
2. Reversibility
3. Conservation of
-amount
-length
-number
-liquid
-area
I would really appreciate any suggestions!

Professor Homunculus replies:

The best activity would be for you to be able to explain those concepts to yourself without using any words like the ones you used in the question.
Considering these things as “concepts” and trying to teach preschoolers “concepts” is a self-defeating concept itself.

Put the things you want them to understand in simple layman’s terms. Don’t worry, you are not simply going to “explain” them to the kids, but you need to stop thinking in terms of “concepts” yourself when you are dealing with children. It is fine to talk about those things at conferences, where teachers have to pretend they understand things.

On the other hand, you cannot pretend to a kid. Get the Ideas in simple laymans terms in your own head, and keep them only in those terms while you are among children.

After you have done that, you will find plenty Ideas for “activities” (a pedagogic magic-bullet word, which doesn’t mean a thing to children in the real world) flowing from your own imagination. Those are the only ones that count.

“Activities” created by people who have different representations of concepts than you do are not the right activities for you to share with others. You have to share what’s in your brain.

Yeah, it’s harder work for you, but it gets the only results that really count for the kids.

As you may know, the motto of Math Mojo is “Making Math Meaningful.”One of meaningful things about math, is that it is communication between humans about representing and understanding our world. Is is the humanity of the communication that makes education fun and meaningful. Any time we take that out, and defer to “curriculum” or “standards,” we are getting away from the deeper meaning of math.

Math with no meaning is, well, meaningless. Keep it human.

I hope this helped,

Hi - Ho!

Professor Homunculus

As loyal readers know, I am a semi-retired professional magician. I live in rural upstate New York, where there’s not a lot of work for magicians, except at birthday parties, weddings, etc. I’d rather eat a raw frog than perform at functions like that, so I don’t get a lot of gigs up here.

So I was happily surprised yesterday, around 2 pm, when Ken, the owner of the Night Eagle Cafe in Binghamton, NY, called me out of the blue, and asked if I would perform that evening as an opening act for Leon Redbone.

Would I open for Leon Redbone? Is 2 a prime number?

(more…)

Recently an interested reader (a teacher) wrote in a great question. I thought you might be interested in it, too. Here it is:

I ran across your website of mathematical terms. Is there a specific name for the division bracket? We are introducing 3rd graders to the vocabulary and symbols. Thank you.

Haven’t you ever wondered about things like that? They may not be earth-shattering like learning math concepts, but I think little things like that make math more interesting.

Whenever you introduce a little thing that makes a child (or anyone else go, “Yeah…I wonder why…” you’ve helped them get a bit more curious - and that’s what it’s all about.

So, if you’re curious to find out the answer, I’ve put up a little post where you can read more about it at MathMojo.com

Happy pondering!

The Professor