Posts Tagged ‘curriculum’

linear combination

At a meeting earlier this week, some of the other math teachers were saying that they didn’t teach their kids about the LCM or how to choose a variable to eliminate when solving systems by linear combination.  I was stunned.  Instead of using the LCM, they said they told the kids to always swap the x coefficients and multiply, being sure to make one equation positive and the other negative.  Let’s leave aside the sloppiness of the language here for a minute.  I can’t really imagine using an approach geared to the lowest level students.  It doesn’t seem fair to everyone else to present material that ignores what ought to be prior knowledge, and after all “Algebra 2” means something. 

But they went on to say that students picked up on the variations on their own.

So, this is a dilemma: should I present a severely dumbed-down approach, hoping that students will make the extensions themselves, or be more comprehensive in my presentation?

If I’m serious about students deciding what and how and how much they will learn, I have to be willing to take the risk of them being lazy.  So I did that today.  The thing is that they’ve seen this before, in Algebra 1.  So, I don’t know how it would have worked with a class that had not seen the technique before.  Luckily (hah) I have an Algebra 1 class too, and can try it there later this year.


curriculum choices

I’m trying to find ways to get my students involved in the curriculum that I teach them.  To that end,  I would like to ask this question:

Is there anything in your daily life that you think has something to do with math, but you don’t know what it might be?  Something that you’re wondering about?

The old way of using a question like this is to try and find matches between their interests and the planned curriculum.  That’s fine as far as it goes.  Teachers can also ask students about this kind of thing as the class progresses, which would be called “making it relevant to their world.”  I don’t think that goes far enough either, but at least it’s not me finding applications.

The danger here (danger!) is that the things they identify are over their heads.  That’s entirely possible.  So what’s the right answer to that?  You don’t know enough math yet.  Investigate that on your own (hah.)

And the challenge, if it’s completely unrelated to the planned curriculum, is to find time to address whatever part of these answers can be brought into their zone of proximal development.  Even assuming that they all have the same proximal zone is a huge error.

What to do…


What difference does it make if I’m more creative as a teacher?  There’s no guarantee that creative lesson planning leads to growth in creativity for my students.  I could use super creative methods to bring students along rails to an objective that I’ve designed, but it’s still me making the hard decisions for them.  If we’re interested in promoting creativity in students, we need to think about curriculum development.

Contrariwise, I could use the same approach every day with open ended tasks that allowed free form solutions, but those wouldn’t always go where I wanted them to.  So that’s not a problem unless you’re determined to control the outcome.  But that’s not how creativity works, right?  You don’t go in looking for a certain and specific outcome.  You don’t need to be creative to get an outcome that you can see in advance.