My issue wasn’t that they weren’t learning. My issue was that they were learning something that leads nowhere.

Maths is a series of skill that build on each other. We teach factorising, which allows us to later teach solving quadratics. This is the reasons we have a curriculum, which we are obliged to follow.

Why can’t we teach an engaging lesson on factorising?

They have been engaged, they have learned, and I have failed in my job. Because my job isn’t to have them learning, it is have them learning the specified material, in the specified order.

Now many Maths teachers argue that we shouldn’t be go guided by what the curriculum says, and we should teach for learning’s own sake. But that is not what we are paid to do. Nor do I ever want to say to some kid that doesn’t pass a required exam that they shouldn’t complain that they can’t become the electrician/doctor/pilot they wanted to be because we put engaging learning above curriculum learning.

I’m sure lots of high school teachers will recognise the situation where kids turn up at your door on day one who love Maths — but can’t actually do any. They’ve had loads and loads of side-tracks, exploring shapes and patterns, collecting and plotting data, playing maths games. Activities like our square cakes. It leads to twelve year olds who think they are good at Maths but who can’t add two negative numbers — because drill is boring, and primary school teachers don’t do boring.

@Dan: I can’t really have an engaging lesson on factorising, because I pretty much never teach a “lesson on factorising”. It is done mixed it with other things as we make our way through Algebra.

I rarely think much at the lesson level, because I want everything to cohere into related strands, and focusing on lessons devoted to one thing doesn’t do that. Things are taught spread across lessons, easing them in, going back constantly to revise, and sprinting ahead sometimes to where we will be going. I do have “activities”, but they are invariably very short — 15 minutes tops.

One key is there’s always something for them to be doing, and I keep mixing it up. I would argue that the key to useful engagement in Maths is negative — preventing confusion or boredom — rather than finding things that naturally motivate them. My aim is to have a class where kids enjoy themselves and enjoy learning, but enjoying an individual lesson, as such, isn’t part of that.

The bulk of the engagement, of course, comes from the joyful feeling of success when they “get it”. The less time spent getting to that point, the better — and drill gets them there quickest, so I’m happy to have large bursts of drill. (There’s a myth that kids don’t like drill, but there’s drill they don’t mind and there’s drill they hate.)

@Tracey

Hanging out in a High School staff room at the start of the year you might hear different comments compared to a blog like this.

Every year our new school entrants complete an AsTTle test before they start, which includes questions on they judge their ability and attitude to maths. Since they have no teacher that they feel have to be polite to, they can be honest. The correlation between their attitude to Maths and their skills is weak. Worse, their self-assessment of how good they are is also weak — many of them really don’t know that they haven’t been taught any real Maths yet.

I taught my first two years of high school math at a school for “alternative” (i.e., “at risk”) kids. Virtually all tested at a grade 4 level or less in math and literacy. Attendance was sporadic, behavior was a nightmare, getting most of them to do any work was a fool’s errand and I was that designated fool for math (no colleagues in the school, in other words). After one semester of flailing with no set curriculum, I tried CPMP, aka Core-Plus. The first semester was a disaster, though at least I had something to focus on. The second semester (fall of my second year) wasn’t much better. Then, I hit on the idea of skipping to the unit on discrete math, which deal with, among other things, Euler paths and circuits, critical path diagrams (pretty much of a waste) and graph coloring. A few students got the Euler path and circuit stuff reasonably well, but the winner was the graph coloring sub-unit. That got one girl to suddenly write a legitimate A exam after having failed test after test with less than minimal effort. I presented on this at an NCTM annual meeting in 2000 or 2001 in which I urged people interested in using integrated curricular materials with challenging (and challenged) students not to repeat my mistakes (which were legion).

In retrospect, I would be prepared to experiment and try to find a unit that you think would get students excited. The beauty of the graph coloring and other discrete math topics is that they don’t depend so heavily on student success in other topics. Counting is counting, and there is a lot of inherent play in things like graph-coloring problems. Art gallery problems can be a lot of fun and still lead to deep mathematical thinking and learning, done right. Joe Rosenstein at Rutgers has a self-published textbook I’m going to be reviewing soon that has all sorts of material that I believe students could succeed with even if they’ve not done well in math before.

Finally, group work takes enormous seed-planting, cultivation, nurturing, and patience to be successful, even with students who have decent mathematical backgrounds. You should likely not make it the mountain you and your students die on.