Practicing Teaching Analysis
During my clinical observations at a couple of different schools, I had the opportunity to watch a couple of teachers really making an intentional effort to help their students with learning vocabulary.
In a middle school class I observed, I watched as the teacher and students worked through a problem of factoring a quadratic and then finding the zeros. After finding them, however, he told the class, that these were called the "zeros" or they can also be called "solutions" or "roots."
There are so many times that we toss around different words for things, without even realizing it, but without letting the students know that we may be using more than one word to mean the same thing, and thus we lead them to be confused. Simply doing as this teacher did and instructing them right up front that these words can be used interchangeably I am sure helped them avoid a lot of confusion. (And in fact, I'm sure my deduction is correct as I hear that his students consistently are the high scorers on the end of level tests they are required to take--and one thing that tends to be difficult on those tests is when differently terminology is used from the stuff you are familiar with, even if you understand the concept.)
I also sat in on a geometry class. I sat in on a lesson introducing tangent lines to circles and was VERY impressed by what I saw. The idea was not introduced by displaying an abstract picture of a circle with a line tangent to it, or with a lecture. Instead, the teacher had a real picture demonstrating circles with lines tangent to them (I think it was a picture of something with pipes, if I remember right). Then someone came up and pointed out what they thought the tangent was. Then there was a discussion, along with more real life pictures demonstrating circles and tangents to them. I was actually kind of blown away by how good this was! This of course made it so much more real to students. After discussing the idea in terms of real life pictures, some abstract ones were brought in, but still with real life pictures that showed the same idea as the abstract drawings. I was impressed by what I saw, and all the different ways that the teacher had found where circles and their tangent lines were found in real life things we encounter. It made the lesson he was teaching seem so much more relevant and important, even to me, so I'm sure to the students! I loved the way this was taught. There are many skills in math that students need to learn in order to be successful in higher math classes, but which they may not see any immediate use for at all. Getting students thinking about things they have encountered already in their lives, that demonstrate this idea, before abstracting the concept was so helpful to both making it seem important, and to making the idea easy to grasp.