Things That Shouldn't Be Dictionaries

[livingdeb]

I'm reading about teaching. I read a blog entry where someone was complaining about how stupid it was that they were forced to teach math with group learning and no practice and the kids were all confused. So the writer, who was planning to teach for only three years (as part of the Americorp program, I think), just ignored that and did what would work, but the people who wanted to be career teachers were afraid to disobey like that, so they just struggled along.

So I looked up the math textbooks in use for my local school district and found them in the library and thumbed through one.

It didn't have that problem, but it did have the same problem as the sociology text my students had when I was student teaching. Sociology is one of the most fascinating fields ever, though we don't yet know much. But there was almost no hint of that in the text. It was just a pile of terms and their definitions. The whole time I was teaching I was able to stomach using the text only once. For all the other lessons, I went back to materials that had made me think the topic was interesting and figured out a way to modify those for high school use. I slept only four hours on weeknights.

But hey, math textbooks are better, right? At the very least, they have a lot of problems in them, and all you have to do is make sure they are all solvable and that the answers in the back are all correct (because all texts are full of typos, right?).

Well, can you believe you can design a math book to be nothing but a pile of terms and their definitions? I looked closely at a unit on angles. Do they talk about the fascinating problem of measuring an angle? (Finding some sort of length to measure just doesn't work. You can't just use two points like you're used to, but you can use three points, so long as those equate to the right parts of a circle. Who would ever guess that?) Do they talk about how all triangles, no matter how ordinary or how wacky, have angles whose measures add up to the same number? No, it's all about what are complimentary angles and supplementary angles (I had actually forgotten those terms) and right angles, acute angles, scalene triangles. Bleh. It was hard for me to even remember that there was anything interesting about angles after looking at that chapter.

No sleep would be had trying to teach from that book.

Comments

[llcoolvad.livejournal.com]

Don't forget, most of those "textbooks" also have companion workbooks. See, that way the publishing houses sell you TWO things instead of one. And in the workbooks are all the spiffy problems.

When I was a kid they were doing experimental stuff with us, and I remember 5th grade math was out of a box. Like a recipe box, with tabs and such. You'd find your place, and just start working forward from there. The teacher would teach the theoretical stuff, but then during work time we'd have to work on stuff on our own. I finished the box in something like two weeks; they had to go unwrap the next box just for me. Ah, back when I liked math!

[llcoolvad.livejournal.com]

I know this also because comp sci books are like that. At least at the college level they are. Big honking textbook, maybe some problems in it, but then supplemental workbook, and usually some additional materials on the book's website.

[livingdeb.livejournal.com]

I liked those lessons out of a box. I'm not sure if I had any in math. I definitely had some in reading several times.

[livingdeb.livejournal.com]

Bleh, what a waste. And they fill up all the extra space they aren't using with pictures. It doesn't really make the book look all that much more user-friendly, though.

[(Anonymous)]

It's difficult for me not to respond to this at great length because I am actually helping write the second edition of a math textbook as my summer job and I've spoken with about a dozen math teachers on what does and doesn't work in the classroom in their experience (as well as with a guy who used to head the math and science curriculum evaluation team for one of the national foundations).

For what it's worth, they do have to teach vocabulary like complementary (not complimentary! commonly confused word alert!) angle in order for kids to be prepared for the TAKS, and in general, it's important IMO for people in any field to be conversant with the jargon that's used. I'm not saying vocabulary should crowd out other stuff, but it does seem like a relevant part of the mix. A lot of that geometry vocab is boring and hard for even me to remember, though. But it's actually better - as in, there is less of it - than when we studied geometry; they have dropped a lot of the terms describing very specific angle types.

I find it sort of hard to believe that the textbook does not actually talk about the sum of the angles of a triangle always being the same [specific] number. That's a pretty fundamental point. Our textbook (geared for 6th and 7th graders) has an exercise in which students end up deriving for themselves that the sum of the angles of a polygon is (n-2)*180, for instance.

I can't speak for the text you looked at (which one, for what grade level?), but generally there is a lot of stuff that doesn't end up in the student edition of a textbook. Our book comes with a pretty beefed up teachers edition that includes a lot of direction for class discussions to occur in conjunction with the book, a CD full of suggested activities, etc. So the overall curriculum may be more interesting than the student edition would suggest.

This being said, a lot of math textbooks are boring and ineffective and rely on the teacher really filling the gap and creating interest and excitement. This is particulary hard for new teachers to do.

I think group learning is a complex topic. To be effective, I think it requires an environment that not all teachers are capable and motivated to create in their classroom, and it's not something that every child will find helpful (any more than every child finds any given pedagogical approach helpful). And there are serious challenges to discovery-based learning compared to drill/plug-and-chug based learning, not the least of which is that it takes longer. But it seems to me that there is a way to move forward from the (flawed) Connected Math program that does not require going back to an era of passive memorization and doing 8,000 identical (and boring) problems. (I assume the blogger you read about was doing CMP or one of its close relatives, since the big criticism of it I am aware of is that it does not do a good job of tying the investigative approach to the explicit underlying mathematics.)

One potential danger is that assessment (whether formal testing or teacher observation of student learning) in a given classroom is very short-term oriented. The issue is not just how well students are doing right now, but how they will do in future math courses (and whether they bother to take them and make an effort in doing well).

For example, I am slower than a current, primed trig student who has spent a lot of time recently practicing writing down the values of various trig functions from a memorization process, but a gazillion years removed from my trig course, I can still come up with the correct values in about 5 seconds because I invested the time early on in truly understanding the unit circle. This discovery process could easily look like a waste of time in the short run (why bother developing it myself when I could just copy and memorize) but is hugely valuable in the long run. (I recently felt that my unit circle memory was fading but I realized it was just lack of recent practice. The underlying stuff is still there.)

Of course, determining what kind of teaching is the most "successful" requires operationalizng "success" (including specifying a population, a time frame, etc.) and is ultimately an empirical question.

(sally)