In response to connections, fluency, coherence

With the last post in place I started the term with my year 10s in mind. With trigonometry in mind. With understanding in mind. I felt a panic/rush/excitement/worry about this and about problems that I may have caused with previous lessons.

We started the lesson with a discussion of what trigonometry evoked in the students: I asked them to think and discuss for a few minutes. Students suggested triangles, angles, labelling sides, lengths, inverses, right angles... they also suggested SOH CAH TOA... "But what does that mean" a lot of them asked. A good question. What does that mean?

The students were then asked to think of questions in which they would use trigonometry (they have had some experience of it before). Lots of triangles were drawn (right-angle on the right). "OK... what can you do now? Try something!" Most students' examples gave the lengths of 2 sides (e.g. opposite and hypotenuse) and an angle to which they were trying to apply sine. "But what do I have to work out?" This gave a good discussion point...why use sine here when you have the angle, the opposite and the hypotenuse? What do you want to work out? Why would you want to include an unknown? How would that help?

Rearrangement of the quotients led to discussion. "Why have you done it like that?" "I looked at what I did before and I swapped them" It seemed that thinking of sin 46 as a number proved challenging. Thinking of sin as a function was also challenging: "Can you divide sin x by sin to get x?"

There was a lot of positive discussion and a lot of challenge. The class were at such different points in this topic that using this method of teaching gave the class an opportunity to work on aspects which they themselves found challenging. Whilst I took this opportunity to clarify some methods and why we did them, some students plotted sine as a graph and experienced it as a function.

The richness of looking at a small group of functions for an extended period of time excites me and helps me to realise connections and coherence. I also see points at which other 'topics' can be assessed as they come into use throughout. I can see myself doing Trigonometry for a while!