Graphical Organizer Charts

One of the teachers I work with closely at my school has sheets and sheets of handouts on the theories behind various concepts. Over the years, she has polished her theory handouts and they seem to work very well for her classes. Although it's not my preferred method of teaching, observing her handouts has gotten me to think about how I can use graphical organizers to help elucidate certain confusing concepts to the students.

For example, my students and I developed some notes together in December on how to look at graph of f(x) and use it to generate rough estimates of the graphs of f'(x) and f"(x). And we also started with a graph of f'(x) and worked our way to developing f(x) and f"(x) graphs. Keeping those notes in a 3-column format helps the kids see side-by-side the correspondence between the graphs.

As another example, one thing that I was nervous about was teaching integral Calculus concepts for the first time this year. I read up on various resources from Sam's Virtual Filing Cabinet, and decided that I liked the suggestion of first introducing integration techniques before discussing the meaning of integrals. So, I created this worksheet. The kids started with the middle column and first differentiated to get the left column answers. This was a mini-review because it had been a few weeks since I had seen the kids (Christmas vacation). And then, I urged them to observe the pattern and to work backwards to find the indefinite integral column.

It was great! The kids were certainly able to figure out some of the simple ones on their own, but in general, they found it helpful to think about what dy/dx is, before thinking about how to "work backwards" to find the indefinite integral. They carried that technique with them later on even when they weren't given a grid to work with. We still needed a couple more days of practice before they felt comfortable with the idea of "working backwards" to un-do differentiation, but this was a good way to introduce it without introducing much fear.

Another attempt at teaching schematically is this: a framework for taking notes on wave transformations. I haven't actually used this yet, but I think it's definitely an improvement over whatever I did last year. We will start by seeing/comparing how sine and cosine waves are similar under each simple transformation, and then work our way to seeing how they transform under a series of steps and under complicated IB language. Then, the kids will work backwards, going from waves to equations to solidify their understanding.

Do you teach with graphical organizers? If so, for which concepts?