Category: math education

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Recently I got an request to review my booklet, “Numbers Juggling - Times without the Tables.” Request came from Sol Lederman, who runs the “Wildaboutmath” blog.

I’d heard that name before, but really couldn’t remember much about Sol, so I checked out his blog to see how serious it was.

Wow, it’s a great blog, full of lots of valuable information about math, how to learn and teach math, and the joy of math. You should definitely check it out.

Sol reviewed the booklet, and you can read his review here.

The review was generally positive, but Sol had a very valid and important criticism. Since the greatest value of the booklet is really in the seven follow-up e-mails in the e-mail course, it should be marketed as a course, rather than a booklet.

That got me thinking (as every good book-review should do). So now I am developing real, in-depth, home-study courses for each of the basic operations of arithmetic.

Each will be about thirty modules long. The modules will walk you through the basics to absolutely turbo-charged speed-math methods.

I’ll be telling you more about it as it develops. If you are interested drop me an e-mail. (Use the contact box near the upper right corner of this page).

Now on to the ADD part of this post. Many people who have problems with math have problems with attention, focus, concentration, etc. I am one of them. I have suffered with ADD for as long as I can remember. It was only “officially” diagnosed a few years ago.

As it happens, Sol suffers from it as well. Or suffered. He has a blog dedicated to journaling his recent “cure.” I have not met Sol, and cannot vouch for anything, but he seems very dedicated to describing his experiences honestly.

Let me say that I am a skeptic, down to my bones, and hope you take everything with a grain of salt. But I would investigate what he has to say. I have subscribed to the RSS feed to his site, and intend to look into the methods he as used. You might want to take a look as well.

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Original Photo by Norsehorse Edited by Brian

Ah, I love it when readers beat me to the punch!

The comments to the original post pretty much sum up the paradox and it’s solution very well.

Khaled’s and Mark’s comments illustrate perfectly one of the things I wanted to point out about this puzzle. That point is:

Just because something is phrased a certain way is not reason to assume that that phrasing is the best way to represent the problem. And one way to critically examine the situation is to reframe it in a mathematical equation.

Khaled said, “Interesting how, once you assume that you can implicitly trust a given source, you can be led through any logic, or illogic, and have a lot of trouble pulling yourself back to a critical mindset.”

How true. Then Mark gave a good method to understand how to see where the paradox lies when he said, “I started to write an equation, because properly written equations can solve all counting problems, but then realized that this was pointless, because adding 2 dollars to the 27 dollars the guests paid did not reflect what happened.”

Exactly! The question was phrased to lead you to believe that because the facts were a certain way (which it accurately represented) you had to see it in a certain way (which was anything but accurate).

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I found this on a weird little personal blog:

Why has math been hated by some?

Because it requires them to think and forces them to give the correct and exact value. Math has a clear distinction of right and wrong. Most people love to speak about any issue, but hate to accept that they’re wrong.

That’s the beauty of math… right is right and wrong is wrong.

Concise and true, isn’t it? So many people hate the way their parents, teachers, politicians, and salespeople waffle and prevaricate, yet they don’t like their Ideas to be held up to scrutiny. They are going to grow up just like the people they are complaining about now, unless they learn a system of honest critical-thinking. Math and logic are just the ticket.

Math is the great equalizer. You don’t have to be rich or privileged to excel at it. Some of the greatest mathematicians started out as sons or daughters of poor, rural families. Curiosity and a local library are all you need to get you on your way.

Once again I am going to suggest the greatest introductory math book I know, “The Realm of Numbers,” by Isaac Asimov, even though it is out of print. Google it. Get it.

It is written for non-math people. It will take you from counting to algebra, in plain terms, without “worksheets.”

Don’t take my word for it. It’s a great book. Go now, and google it.

Hotcha!

Brian

Are you a homeschool parent struggling to teach your child math? Or are you just frustrated by the way your kid’s school teaches math? You’re definitely not alone, and you’re in great company.

Here is part of a story from a father who faced the same thing. It’s a comment left by Mark, a reader at the MathNotations blog.

You should read the entire article, then scroll down to the comments where the exchange between Paul Michael Goldenberg and myself (Brian) begins. Read them to understand the background to the great comment by Mark, which is partially reproduced here:

“I had a 4th grader who was being just totally crushed. I tried to help with math homework, but the assignments were chaotic. He just finally refused to even try to do his math homework. To see tears in his eyes and protest, “I’m not good in math, Dad!” broke my heart.

“I took him home, and found out that he could do not complete a 10 x 10 multiplication table or do any long division. I concocted a non-stressful systematic build-from-a-foundation scheme. We used a variety of manipulatives, including an abacus for computation. (I guess you and I think alike, eh?) I taught him basic algebra using a balance and weights: keep the pans level, and that’s an equation analogue.

“Upshot: he started calculus at age 16.”

Amazing! What a motivation for you to try your own ways (with or without Math Mojo methods) to help your child. Of course, not everyone can know as much math as Mark (I sure don’t!) but you can do plenty with the methods you can find on this site, and in Mark’s comments (click the link to MathNotations, above, to get there).

So head out there and read them now.

Wait! The author of that comment just left a terrific comment below. Make sure you read it if you are trying to teach your child math.


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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.

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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.

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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

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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

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While listening to “Morning Edition” on National Public Radio awhile ago, I heard a report about self-esteem in the workplace, and how Gen-Xers need constant praise for the simplest of accomplishments in order to feel appreciated.

Oh, my! The poor darlings are in the workforce now and now there are actually consulting firms that deal with how to keep the delicate little flowers happy, to retain them as workers, powered by constant praise, awards ceremonies and cookies and milk, I guess.

My first reaction was, “How idiotic. Just don’t hire the little turdblossoms in the first place, and the problem’s over.”

As usual, my first reaction is pretty useless. It seems that a great majority of gen-xers suffer from this self-esteem pathology, and if you aren’t going to hire gen-Xers, you are going to severely limit your pool of potential employees, some of whom may be genuinely talented for the job, despite their self-esteem problem.

So what do you do?

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(Continued from the previous three posts.)

the reader replied to my answer:

thank you professor for answering all of my future qustions, but u never answered my old answer though. What happens if i fail math 9 of coruse ill be end up in emath10 whats emath10 (doesn’t sound good though)Like do i get to go to collage but if u can’t answer that qustion ill ask someone else. Heres a qustion for you though what good paying job are there in this world without math like doesn’t require math because u told me everything involes math. but i am asking you to name some jobs thats don’t require math as a requirement. I am asking you all these qustions because i am scared the world might be a different place when i grow up so i am just prepareing for the future.

Professor Homunculus’s reply:

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