November 10, 2006

On Textbooks

Bob Dixon, on math textbooks:

And speaking of asking kids to do something they haven't been taught, "critical thinking" problems are a regular part of the text. Those problems are much like the ones we'd see in a book of brainteasers. Here's one:
Work with a partner. [Good idea, especially if your partner is an adult who knows how to do problems like this.] Arrange the digits 1, 2, 3, 4, 5, 6, 7, and 8 into two decimals so that their sum is as close to 1 as possible. Use each digit only once. The sum cannot be equal to or greater than 1.
They [also] have these "critical thinking" problems along the lines:
Jane is 7 years older than her brother, and the sum of their ages, plus 5, multiplied by 4, is the age of their house. How old is everyone and everything?
The people who author these books are the same ones who look back derisively at my mathematics education because we had to figure out when a couple of trains, leaving opposite coasts and going different speeds, would meet up. The problem wasn't all that authentic, but I think the algebra for solving it was. I have nothing against the "Jane is 7 years ..." problem per se. If you've taught the algebra for solving ... just about anything ... then no problem. But in my daughter's text, "critical thinking" means "something relatively difficult to do that we haven't taught anyone how to do, mostly because we don'’t know how to do that."

4 comments:

Anonymous said...

Jane is 7 years older than her brother, and the sum of their ages, plus 5, multiplied by 4, is the age of their house. How old is everyone and everything?

Two equations and three unknowns.

Is this a trick question, or is this in an actual algebra class and the answer is a set of equations?

-Mark Roulo

rightwingprof said...

"Jane is 7 years older than her brother, and the sum of their ages, plus 5, multiplied by 4, is the age of their house. How old is everyone and everything?"

"Is this a trick question, or is this in an actual algebra class and the answer is a set of equations?"

Good question, though these people are always talking about real world problems, and how, exactly, would something like this pop up in the real world?

Aus_Autarch said...

Everytime I visit these edblogs, I shudder. I am a teacher in Australia, and as inevitably as winter follows autumn, what fails in the U.S.A migrates southwards to be inflicted on Australian students and teachers.

Already, university education lecturers (education "experts") (more like ex-spurts, ex as in has-been, spurt as in a drip under pressure) rave about "Authentic Learning" and "Critical Thinking" aleardy infests curriculum design documents. ("Three-storey intellect", "Habits of Mind").

It makes me wonder: exactly how did people think *before* we had these people telling us how to think? We currently have the state government mandating (now there is an abused word) and education model based on how all ideas interact - strands and dimensions of learning are all the rage: the Victorian Essential Learning Standards (VELS). Previous to this we had the prosaic curriculum standards framework (CSF, CSF2)which "merely" indicate what a student was expected to be able to know and do at all age levels - but this was not "authentic".

Bah! It's like looking into a crystal ball, reading the edblogs - and it is not predicting a rosy future for Australian students and teachers.

Anonymous said...

Hey, please don't blame us (US) for everything... we got Whole Language from you guys! (Well, you neighbours, the sheep growers :-)

As to how did we think before the "experts," the answer is simple -- that we didn't. Any educrat worth his salt will easily prove it to you by the fact that we still have war and poverty. And in some sense he will be right -- after all, HE also is the result of the pre-expert period :-)