Category: memory techniques (mnemonics)

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To check multiplication of single digits by longer numbers with playing cards:

We’re going to use what I call “numbers crunching” to check. That is the same as using the nines-remainders. You do know how to get the nines-remainder of a number, don’t you? It’s very simple, but it takes a bit of explaining.

It also pays to know why checking with nines-remainders works. Both of those things are beyond the scope of this article, but I’m working on a booklet and a video about how to check your answers for all of the basic operations of math using “number crunching”. There are lots of tips and shortcuts that make this method absolutely simple and effective. Let me know if you’re interested by using the “Contact” box near the upper right hand corner of this page.

(This video will be re-edited and uploaded by the end of Wednesday, April 30)

If you know about crunching, you’ll be interested to know that practicing with cards like this is perfect for checking with crunching. It turns out that if you crunch all the digits from zero to nine, you get a crunch number of 0.

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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 just read an interesting and valuable post by a concerned parent at “Mindless Math Mutterings” (which are anything but). I like that blogger’s thoughtful posts about education.

This particular post was about becoming and expert with math “facts.”

I have one observation that I feel has been terminally left out of this discussion, though:

Although the basic building blocks must be able to be used immediately when needed, what we generically call “memorization” is a dead-end for most people.

We require children to sit and “memorize” in order to learn, but we don’t teach them how to memorize. Memorization is a skill, just like other thinking skills, that needs learning and tweaking. Rote memory is a terrible myth. I mean, it works for some, but it is not the only, nor is it the best, way for most people. (more…)

Just had a great evening mulching and edging our apple tree. I ran out of mulch and ground paper, but I can get more tomorrow.

As I worked, I used a catch (see last post) to collect my thoughts. The one I used is my favorite - it’s a mnemonic device. I used the rhyming peg method, (”one is the sun, two is a shoe, three is a tree,” etc.) and only needed to get to “door” for the four Ideas I had been mulling over.

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I was out mulching our apple tree in the front yard, when some thoughts came to me. One of them was that I can see how gardening can be such great contemplative avocation.

I’m not a gardener, and have never been very good at things like that, but I can weed, I can mulch, and I can mow the lawn. All of which are sort of brain-dead activities which can lead you into a trance-like state.

If you had been contemplating something just before you get into that state, or have had something preying on your mind, it is easy to let thoughts about it come to you while you are in that state. They can wash over you in a pleasant way. The trick is to catch them, and get them recorded somehow, so you can recall them later, and work them into something and take advantage of them.

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I recently read a post on another blog concerning the two most important elements that children should master in math in order to succeed. The author suggests that basic skill with multiplication and basic mastery of fractions are the two essentials.

I am of the same opinion. The author also thinks that memorization and drills are the best way. On that, I’m not so sure. Yes and no.

Here’s my take:

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Have you ever heard of Hintikka’s Paradox? In a nutshell, it’s about, “Is it immoral to ask someone to do something that can’t be done?”

It’s so easy to say, “Just memorize it.” That’s the cry of people who want you to learn your “math facts.”

But do they ever teach a child how to memorize? How cruel to would it be to grade a kid on his reading ability if you never taught him how to read?

That’s the paradox of the memorization problem. Not every child even knows how to memorize.

There are lots of solutions, but I’ve never seen any good ones on math sites, or ever heard of teachers really using any. Let’s think about our part of helping out before we prescribe solutions we don’t provide.

Personally, I think rote memory is one rotten way to learn. Learning mnemonics is so much more fun, creative and effective. I don’t mean silly mnemonics that are taught in some of the baby-style trendy math methods that are out there. I mean a concerted effort to learn serious memory techniques. My favorite book to learn memory from is “How to Develop a Super Power Memory,” by Harry Lorayne. He’s written more since then, but despite its hokey title, it is the most straightforward of all the books I’ve read.

One solution for learning multiplication without rote memory is the method taught in my booklet “Numbers Juggling - Times Without the Tables.” the link for it is on the top of the right-hand column of this blog. I think this is the best solution for anyone who is dissappointed with the traditional “just shut up and memorize it” method.

Make sense?

Trust your brain - learn mental math and memory methods!

… a kiss is but a kiss. But on the other hand, a number can be many things. And there are many ways to remember numbers.

In lesson 3 of “Eating Math For Breakfast” you’ll learn a very basic but effective way to memorize a string of digits in order to do more math mentally.

Eventually Math Mojo will incorporate more mnemonic (memory) techniques into the website, but for now, this method will do. Mnemonics is a very powerful tool for magicians and is vastly underutilized in our education system.

In case you didn’t know, Math Mojo is part of Magic and Learning, a company that uses methods of magicians to teach thinking skills.

Today I have to start working on the “Math Mojo Monthly - Comes out quartly mostly” newsletter, to let subscribers know that the Chronicles have been reincarnated, and that these “Eating Math for Breakfast” lessons are available. .

I hope you have been trying out the lessons. They will become more fun to do in the near future, as I am adding a weirdness-factor to them as we go along.

(What the heck could that mean?)