One of the reasons I wanted to teach 9th grade when I first started was because I wanted to, eventually, know all the students in the school. (There were other reasons, but that’s one of them.) So after four years, I’ve taught everyone math and really enjoy knowing all the students well. (Well, I didn’t teach everyone – the students who skipped me to go straight to Geometry, but I managed to get to know most of them in other ways.)
So, because of that, I’ve taught a new batch of students every year, and every year I can refine my routines, toss what didn’t work, keep what did, and try out new things.
But next year there’s a very good chance I’ll be teaching Algebra II – the first time I’m teaching the course (and any main math course besides Algebra I). And that means my students will be the current sophomores, who I taught last year. And I’m wondering, how does that work? What can I carry over easily? Will transferring routines and getting started be faster (not just because they know the routines but are also older)? Will it be harder to toss out routines they liked that I didn’t because they know them? Will the honeymoon period at the beginning of the year be shorter, or longer?
I don’t know, but I’m hoping some people will having some insight. What do you do when you teach the same kids again?
So there’s a good chance I’ll be teaching Algebra II next year (will everyone leading a morning session in TMC14 change courses before it arrives?) and so I was thinking about my future routines. My students will be (mostly) students that I taught last year, plus the current freshmen who are advanced in Geometry. Last year and this year I was big on Estimation180 but, because I was so big on it, they’ve seen a lot of it. There’s still plenty they haven’t seen, but I wanted to expand. I remember reading someone who said they used Estimation180 one day, Visual Patterns another, Counting Circles another, and I think there was a fourth but I don’t remember what. I thought it sounded like a good idea.
I was hesitant about counting circles at first because, yeah, my students do need to boost their mathematical fluency, number sense, and mental math, and that is always helpful, but it’s a lot of time to spend on stuff that is technically not part of the curriculum. But then I started to think about all the things we could count that would specifically enhance the Algebra II curriculum, and I got excited.
Things We Can Count
- Monomials (2x, 4x, 6x, 8x…)
- Polynomials (a + 2x, 2a + 4x, 3a + 6x…)
- Fractions of etc)
- Sin/Cos/Tan values of those values above
- Imaginary numbers
- Complex numbers
- Geometric Sequences (1, 2, 4, 8….)
- Geometric Sequences with Negative Ratios (1, -2, 4, -8….)
- Monomials geometrically (x, x^2, x^3, x^4…)
- Irrational numbers (…)
What else could we count?