Archive for: June 2008

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photo by lsiegert

A curious reader asked this question:

What is a base?? I’m sorry but I’m in the sixth grade and never heard of a base and then all of the sudden it’s in my homework. Will you please explain to me in easy fifth or fourth grade words what a base is? Pretend I’m stupid or something!

 Professor Homunculus replies:

Well, that’s going to be hard to pretend, because you are obviously smart enough to ask for help. You also did a good job expressing your question, so here goes:

Bases are different ways to express numbers. Like languages are different ways to express thoughts. You could say, “butterfly” in English, or “mariposa” in Spanish, “papillion,” in  French, or “schmetterling,” in German, but they would all mean the same thing, just different names for it.

You can write the number 11 in base ten, or as 21 in base five, or as A in base eleven, and they all stand for the same amount.

Just as in different languages, there are specific times you need to use different bases. That is a little hard to understand, right now, I know, but first you must learn how to translate into different bases, before you can understand anything about them.

Fortunately, it is much, much easier to learn how to translate from base to base than from language to language.

A base is the amount of digits we use to represent our numbers with.

We normally use what it called the base ten system. As you know, we normally use only ten digits - 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to make up all of our numbers. After 9, we have to start a new column (called the “tens” column, because it tell us how many tens we have). 

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Tags: base 10 , base 2 , bases , what are bases , what is a base

Hey, you droogs,

There was an interesting post on the Whallah! blog about an article in the Associated Press, concerning the education of math teachers in public schools.

Apparently the National Council on Teacher Quality has done a comprehensive study to come to the conclusion that everyone who is not an “expert” has known for years: Teachers are not being taught math adequately, and generally fail to teach it well to their students. (Do tell…)

Isn’t it funny that the “establishment” will never admit that? It takes an expensive academic “study” to show what is already known, yet Universities (in general) will not do anything about the way they teach teacher how to teach math. They will try some new, expensive methods that some textbook company has lobbied for, of course. But they won’t try anything that might actually work.

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Tags: math ed , math education , math pedagogy , multiplication , public schools

A mom recently wrote in to ask this question about standard and expanded notation.

“How do you know when you are writing in standard form, expanded form? For example, is the expanded for of 30,048
30000 + 40 + 8 ?
Or for 29,486, the expanded form = 20000 + 9000 + 400 + 80 + 6 ?”

Professor Homunculus replies:

Precisely! Oddly enough, there is no “standard” for “standard.” What I mean is, for 30,048 the standard form could also be considered:

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photo by jonathan229

I haven’t been posting much. Sorry. Been in a kind of existential funk.

But today I had to include this. It is a link to an article that was in our local paper today, about a heinous phenomenon in a local school. Apparently, some second-graders have been actively plotting to kill a little girl in the school. You can read about it in this digg.com post.

OK, no big deal right? After all, this is America, where everyone is “entitled” to their lunacy, no matter how depraved.

But this is in a rural, upstate New York school. No inner-city, no whacked out Waco, no out-in-the-hills survivalist community.

I have done afterschool Math Mojo programs in this school. It is a nice place with (generally) nice kids. I’m not amazed, though, because our society has become all about abuse of power, from the highest, to the lowest, levels.

I know that you can’t make a sweeping judgement about public schools in general from a local anecdote. But the anectodes are getting to be pretty thick in our public schools.

It is depressing as hell. I don’t mean to depress you. There has got to be a solution, and I believe that readers of this blog are generally part of it. Homeschooling, unschooling and afterschooling are good, positive movements.

The big difference is the amount of parental involvement. If your child knows that you truly take an interest in them by spending time with them, your conscience becomes part of their conscience, without having to lecture them or make them feel “watched.”

But you know that. I just want to say that from the comments this blog gets, and the e-mails I receive, it’s people like you that give me hope. I hope I give you some to, at least as far as encouraging you to play around with math.

To that end, I went out and bought a cool little piece of software at the Apple Store yesterday. It’s a Wacom writing tablet, and I hope to make some really easy-to-follow math tutorials for you with it in the next few days. I’ll have one up here by tomorrow probably.

See you then (if I didn’t bum you out too much.)

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