Algebra tile template

The algebra tile template I've used earlier has a minor error in it - the last row is too wide, so that the last two x²-pieces are not square and are different from the first two. Here is a revised version, with a separate template for negative terms.

Models, moderation, and climate change

How would the climate change debate change if it focused more on behaviors and less on ideas? Ilan Chabay visited the University of Oslo two weeks ago ¹ to talk about “improving how we learn for sustainability,” emphasising the value and necessity of models to deal with complex issues. There was a pronounced exasperation in the audience at large at the unwillingness of much of American society to seriously address humanly induced climate change, and much of the discussion centered on cognitive shifts needed toward a greater respect for scientific results.

Being a middle school teacher, I kept expecting the conversation to turn toward the teaching of sustainable behaviors, but this was dealt with only in a closing comment. Strictly, however, beliefs or models are hardly what cause pollution, depletion of resources, or climate change. Actions, purchases, behaviors are what cause these things.

And is there really that much reason to believe that modifying the former will result in changes in the latter? As far as I can see, people who are more educated in general, who are more knowledgeable about models of climate change, are no less - and are frequently more - inclined to fly frequently, enjoy foods imported from distant places, and consume electronics whose production involve environmental hazards. On the other extreme, the Amish, while likely not overly receptive to the science of climate change, probably also contribute less to the problem than does anyone who uses an electronic device to read this entry. The connection, then, between understanding of science on the one hand, and sustainable practices on the other, is not straightforward.

I do see that groups who are outright hostile to science and who also engage fiercely in politics do thwart necessary political efforts. However, I am not convinced that insisting on a common understanding on the way the natural world works, an agreement on metaphysical issues, is the only common ground worth seeking. Could some basis for agreement on careful and moderate consumption be found elsewhere? Could there be some convergence on how we will behave without agreement on why we would do so?

I would like to think that devoting resources to the development of measured skepticism, to the appreciation of the strengths and weaknesses of models of climate change, would result in more rational decision-making and in behavior directed toward limiting the problems. But I don’t know that there’s overwhelming evidence that this would be more effective an approach than eclectically building on whatever various motivations for moderation that one might find.

¹And due to that delightful arrangement, the Fall Break in Norway, I could attend! Yay for whoever decided we’d continue to have a week off in October even though most kids don’t need to help their families harvest potatoes at that time anymore.

Two years of silence and scrambling

I've started my third year at a Norwegian middle school (that is, my students are in grades 7 - 10, so some are in the "high school" age range - things are divided up differently here). This year I'm teaching 10th grade math and science, a course on nutrition and cooking for a 9th grade class, a small elective on electronics, and special ed math group for some 7th and 8th grade kids.

What we teach changes every year here. Last year I had a lot of 9th grade science and math, and the topics were mostly different from what they are this year. To some extent we follow classes we teach from year to year, which is nice in that we get to know the students better. Lots of random factors also affect what courses we're assigned to teach too, though. My first year I had several sections of remedial English. The cooking/nutrition and electronics courses are new to me this year.

A sweet thing about this system is the variety of interesting new things a teacher gets to learn every year. Last year I learned new things about the brain, the neural system and the endocrinological system, because those topics happened to be in the 9th grade curriculum. We dissected fish heads to find the brain and sensory organs, and I did a few practice runs before the actual class, having never taken biology before myself, not even in high school. The other major topics that year, electricity and chemistry, were more familiar. This year I'm learning about genetics and cytology, human reproduction, possibly something about the petroleum industry, while also teaching more familiar stuff on kinematics, gravity, organic chemistry, and optics. Science up to and including the 11th grade here is always integrated science, and not in the sense of every year having an integrative theme, but in that a wide range of disparate topics are covered.

A major drawback of this approach will be evident to any teacher familiar with the American system, where a teacher is responsible for a relatively small number of courses that is usually taught every year. Here, all my lessons have a kind of first draft quality to them. I do find all these various science topics to be intensely interesting, and might have become bored with the US approach of doing Algebra over and over and over again, but I do often feel bad about how little topic-specific pedagogy I know. In math, of course, typical pitfalls are easy to predict now that I have taught the same material a number of times, and I know a lot about what to do about them. But I really have no idea what will go wrong when we start working on DNA replication - I'll just have to try it out and see. We muddle along, learning as we go.

Teaching this way rarely results in any kind of polished approach that seems worth writing up for publication on a blog for other teachers. Nor does it leave much time for writing. This entry has been penned in the middle of our Fall Break, a Norwegian arrangement that originally was put in place to accommodate farmer kids who needed this time for harvesting potatoes. Now, I find it a good time for regrouping and for replanning new courses, after six weeks of getting a sense of what they are about. And perhaps for writing a little.

By the end of this school year I'll have completed a three-year science cycle, having had one group of kids from 8th through 10th grade in math and science. Then (depending on what teaching assignment I get) I just might teach a science course for the second time around.

I'd do 8th grade science very differently, though. The unit on evolution, for example, really didn't work at all.

¹ These courses aren't scheduled every day, though. In fact, two of them meet only once a week, and several meet only twice weekly. That's what makes planning it all remotely possible.