Is this problem correct or incorrect, and why? (Please don’t answer just yes or no, withouth the “why,” OK?)

Please leave [...]]]> I just wanted to try this little experiment with readers. I came across this little problem recently, and I have to admit, it gave me pause. I wanted to know what readers think.

Is this problem correct or incorrect, and why? (Please don’t answer just yes or no, withouth the “why,” OK?)

Please leave your thoughts about this in a comment below.

A concerned parent wrote in:

Hello, I was never very good at algebra. I managed to get by,and it has haunted me ever since. My daughter is in the eighth grade and wants my help with homework. Now, I feel really dumb, any suggestions. Thanks.

A concerned parent wrote in:

Hello, I was never very good at algebra. I managed to get by,and it has haunted me ever since. My daughter is in the eighth grade and wants my help with homework. Now, I feel really dumb, any suggestions. Thanks.

Professor Homunculus replies:

Thanks for your question. It’s a problem a lot of parents come across, and I think your question will resonate with many people. And by the way, no need to feel dumb – it’s the people who don’t try to help their kids with learning that are dumb.

An old version of Algebra the Easy Way is the one I used to learn algebra, when I was in my forties, is the one I’d recommend. It’s written a little bit “childish” (but not too childish for a forty-year-old), but it is not as boring and pedantic as most texts. It was published by Barrons Education Series, Inc., and the author was Downing. the edition I have was printed in 1984. (No, I wasn’t in my forties back then – I just bought this old edition when I was in my forties!) Maybe you can find an old copy online.

I’m not a fan of textbooks, because they tend to be uninspiring, too politically correct (caring more about diversity than math – don’t get me wrong, I’m a proponent of diversity, but many modern schoolbooks are embarrassingly pandering to the extent that there’s almost no math in them), or the opposite – too rigid and authoritarian (“Here’s the rule kid – just shut up and memorize it. If that was good enough for me and my pappy, it’ll be good enough for you!”)

So besides the above-mentioned book, as far as textbooks, it’s hit or miss. I figure your child’s teacher will have enough boring textbooks in the classroom, so a good way to attack the problem from your angle is to get some fun, inspiring books into your home. The library is a great place to go poking around. Not just the math section, but the “recreational math” section (around the 793.7 section in the Dewey Decimal System) as well. By the way, “recreational math” is in the same section with magic and games books. That should tell you that math isn’t always the big boring pain that schools often make it.

A big help can be the book, “Innumeracy” by John Allen Paulos. It’s not a textbook, and you will learn things about math that actually make sense (Imagine that!) It’s probably your best bet to start with.

Got a good used bookstore in your neighborhood? Scour it for old math or recreational math books. You can find real gems there. Maybe I’m getting old (aren’t we all?) but I find it kind of cool to find “lost knowledge” in old books.

There is a classic, honest mistake that many parents make when trying to help their children learn math – They try to match the way they kid is taught in school, and teach that way. It’s a losing proposition. If it isn’t working in school, it probably won’t work for you, because, face it, the teacher is a professional. The best method of attack is by the flank. Find an entirely different method, or set of books, than the school uses. Make sure the child understands that the school method is fine, but if you learn an alternative (a good alternative, not some airy-fairy trendy junk) you will be able to gain insight into the actually math, and thereby understand the school method even better.

A great advantage to this is that your daughter will learn a lot of stuff that the teacher probably isn’t aware of. That is a totally empowering feat for a kid.

Pre-empt the child’s probably protests of “…but we don’t do it the way you’re showing me…!” by explaining that you don’t want her to do it in class the way you are teaching, but you want her to try it and learn it because will help her with the school way. She may not be able to grok that right away, but don’t give up. It is a lesson in maturity to find out that a frontal attack on abstract knowledge is not usually the best way. By eighth grade, this is a lesson your daughter should be able to “get” with some patient guidance.

This is a longer process than just going over what’s taught in school, but odds are, you’ll only have to do it once, and when it works, your child will have a method of self-learning that will help her in every subject, for the rest of her life. It’s a great lesson.

By the way, I think it’s a lucky father who’s eighth grade daughter asks him for help with anything.

One last thing: Math can really be an inspiring, romantic, artistic subject. Keep at it with your daughter. The day the “Aha!” lightbulb goes on in her brain about it might be one of most wonderful experiences you share together.

I wish you and your daughter all the best in your learning/teaching endeavors.

Brian (a.k.a. Professor Homunculus)

Original Photo by Norsehorse Edited by Brian

There’s a braintwister that’s been going around the internet, well, probably ever since there was an internet. It’s actually probably thousands of years old in one version or another. You may have seen it phrased like this:

Three men go into a motel. The man behind [...]]]>

Original Photo by Norsehorse Edited by Brian

There’s a braintwister that’s been going around the internet, well, probably ever since there was an internet. It’s actually probably thousands of years old in one version or another. You may have seen it phrased like this:

Three men go into a motel. The man behind the desk said that the room costs $30. So each man paid $10 and went to the room.

Later, the desk clerk realized that the room was only $25. So he sent the bellboy to the men’s rooms with five one-dollar bills.

The bellboy couldn’t figure out how to split five dollars evenly three ways, so he gave each man one dollar, and kept the other two for himself.

This meant that the three men had each paid $9 for their rooms, which makes a total of $27 dollars. Adding the two dollars that the bellboy kept would make a total of $29 dollars.

So where is the other dollar?

My advice to anyone trying to solve anything like this, or trying to think about anything at all, for that matter, is not to jump to conclusions.

Want to give it a try and add your thoughts in a comment? Go for it! I’m not asking for the solution, just some thoughts about the meaning of the puzzle – how it relates to life, logic, decision-making and understanding your world. I am not putting this up as a trivial puzzle.

My comments will be in the next post.

(Note: When I originally posted this, there were a few typos and other mistakes in it. If you busted your head over it till now, please accept my apologies. It should be correct now.)

I get alerts on topics like “homeschool math” and “basic math.” The second of those two alerted me to a [...]]]> For those who are not aware of it, you can get daily e-mails updates to online articles, web-pages, blog posts etc., that have been recently posted, about any subjects you like, through google alerts.

I get alerts on topics like “homeschool math” and “basic math.” The second of those two alerted me to a great blog post at Joie de vivre – Algebra. Her motto is “Stories only happen to the people who can tell them.” Manifique!

Her post was about math ed and algebra, their relevance, and how they’re pretty well murdered in public schools.

The question at the end of the article, “Are there not enough math teachers because no one learns math well enough to teach it? Or does no one learn math well because there aren’t enough teachers?” is interesting. It meant to be a rhetorical “chicken/egg” question, and as such, it a good one.

I (humbly) submit for consideration, though, that this question may not the most useful one. I think there actually are enough math teachers, but there are three other factors at work:

One factor is that many of them can’t teach very well and/or don’t know math very well.

The second is that those who can and do, aren’t allowed. They are forced to follow some shallow curriculum that the district, state, or whatever ordains. A psychologist friend of mine calls this CDD (or Curriculum Dysfunction Disorder).

The third, and maybe most important, is not that there is any inherent problem in how we teach algebra (well, of course there is, but it may not be as bad as this third factor). It is that we send each child through elementary schools where they are taught math by a “normal” teacher, not a math specialist.

Many (most?) of those teachers have no particular fondness for math, nor an aptitude to understand or teach it. It’s not their faults, either, it’s the way things are set up by a culture that likes to talk about education, but hated to think about it (see also politics, morals, etc. ad nauseum).

Therefore, most students don’t learn an adequate appreciation for the basics, and many don’t learn the basics at all.

If students don’t get the basics, it is absolute cruelty to expect them to use them to understand concepts which build upon them. (Ever hear of Hintikka’s Paradox?) We are setting these kids up to hate school (and society) and then blaming them for it. This is the greatest, most hypocritical crime you can commit on young people in a culture. Why do we love to do it and defend it?

As the author of the article points out, if we were taught algebra well, it would “Excellent! Wonderful! The real world! Teach me this stuff, it sounds great! Except that’s not how we get taught algebra, is it?”

How true! It’s not the algebra, it’s the damned dumb way our administrators and policy makers in the schools think about it.

It’s become “subject in school” instead of the wonder that it really can be.

This is something Plutarch once wrote about the great mathematician Archimedes:

“…Archimedes, although he achieved fame by his mechanical inventions, believed that pure mathematics was the only worthy pursuit. Again Plutarch describes beautifully Archimedes attitude, yet we shall see later that Archimedes did in fact use some very practical methods to discover results from pure geometry:-

Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, the beauty and grandeur of the subjects examined, of the precision and cogency of the methods and means of proof, most deserve our admiration.
”

Beauty! Grandeur! That’s the ticket!

If you are really interested in “why algebra?” one of the best tips I can give you is to check out The Algebra Project’s website. The Algebra Project is the brainchild of Robert Moses, who was a Freedom Rider and is a great civil rights activist. He considers algebra a civil right, and his reasoning is a great lesson in math, philosophy, how to develop great societies, and much more. As I write this, I realize more and more the value of what he is trying to get across. Please visit that site.

Now, if I may, I’d like to tell a little about my own math journey.

A long time ago, I was a mathephobic, unconfident student. Then I learned math through alternative means. Actually, I learned math through magic books. I am a professional magician.

Now who would have thought that a magician would ever benefit from learning math? When I was a kid, sitting in the psycho-nazi math teacher from hell’s class, I kept thinking, “Who needs this stuff? I’ll never need it, I know I’m going to be a magician.”

Since then, as part of my act, I have done simple mental calculations, like 946 times 873, in seconds, to the amazement of audiences all over the world.

This isn’t being said to impress you with how “smart” I am. The truth is, I get a little sad each time I get great applause for tricks like that, because in fact they are so much easier than the high-end sleight-of-hand I practice for hours each day.

Anyone could do the mental juggling I do if we were adequately taught. And it is fascinating to learn. There is no “boredom factor” when you learn easy, sensible methods.

To that effect, I began developing the Math Mojo and Math Mojo Chronicles website and blog.

I know I ought to get more actual teaching and strategy done here on these sights, but I subscribe to those cool google alerts, which send me to off to cool blogs, which in turn set me off on these tangents.

OK, I’ll get off it now and go develop some more pages on speedmath for you. Or as Frank Zappa would say, “Shut up ‘n’ play yer guitar.”

P.S. Referenced in Joie de vivre’s post is an article in the L.A. Times that deals with algebra and drop-out rates in L.A. schools. Fascinating stuff.