About 2 minutes before the show started, I had a panicked thought. "Reduction formulae is such a small section, what if we run out of things to talk about?" But, at the end of the show, I had to cut the conversation short due to lack of time. The beauty of this section really came alive for me as I spoke to Robyn. | |

I suppose, as a teacher, I got lost along the way. Of course I told my learners that trig graphs and equations were connected, but I'm not convinced that I ever showed them how, or how beautiful the connection is.

As you know, Grade 11s are busy finishing off trig graphs. Robyn spoke about revising the CAST diagram before starting reduction formulae. Through the discussion, we then decided it would be a better idea to revise the CAST diagram while teaching the graphs.

You'll remember in last week's show, Craig spoke about linking the trig parent graphs to the unit circle. He directed us to the following links to help:

Unit Circle and Sine Graph

Unit Circle and Cosine Graph

Unit Circle and Tangent Graph

If this teaching approach is used in the Grade 11 classroom, it would be quite easy to revise the CAST diagram at the same time.

Robyn then spoke about the learners doing an investigation to discover the reduction formulae themselves. She used the investigation in Everything Maths as an example, but did also suggest that teachers draw up their own investigations. I would agree with her. The link supplied is a good one, but doesn't go into too much depth. Maybe you'll make a great one and share it with us? If you do, I'll certainly post a link to it on this blog.

I must stop typing now, otherwise I might as well just put down a transcript the show. If you want to know more about it, please watch the clip. Let's move on to the other links.

You'll remember in last week's show, Craig spoke about linking the trig parent graphs to the unit circle. He directed us to the following links to help:

Unit Circle and Sine Graph

Unit Circle and Cosine Graph

Unit Circle and Tangent Graph

If this teaching approach is used in the Grade 11 classroom, it would be quite easy to revise the CAST diagram at the same time.

Robyn then spoke about the learners doing an investigation to discover the reduction formulae themselves. She used the investigation in Everything Maths as an example, but did also suggest that teachers draw up their own investigations. I would agree with her. The link supplied is a good one, but doesn't go into too much depth. Maybe you'll make a great one and share it with us? If you do, I'll certainly post a link to it on this blog.

I must stop typing now, otherwise I might as well just put down a transcript the show. If you want to know more about it, please watch the clip. Let's move on to the other links.

Mindset resources for reduction formulae:

www.youtube.com/watch?v=PgubJofzbvs

www.youtube.com/watch?v=FocBOlJ3PQc

www.youtube.com/watch?v=PgubJofzbvs

www.youtube.com/watch?v=FocBOlJ3PQc

Other resources that may help:Notes and examples on trigonometric reductions: http://cnx.org/content/m38870/1.1/

Summary table of the trigonometric reductions: http://www.bymath.com/studyguide/tri/sec/tri7.htm

Summary table of the trigonometric reductions: http://www.bymath.com/studyguide/tri/sec/tri7.htm

Robyn's 5 point teaching strategy:

- Make sure you have the basics right. Do learners know the trig ratios and how they work in the Cartesian Plane?
- Do an investigation or discover exercise into trig ratios on the Cartesian Plane.
- Create a table or list of all the reduction formulae which have been investigated.
- Explore how these can be used in problems.
- Explain how reduction formulae can be used "in reverse", ie breaking up a large or obscure angles.

Robyn's 3 pressure points:

- Be aware of letting learners learn the reduction formulae "by heart" instead of teaching learners HOW they work.
- Teachers should teach by letting learners do investigations. While doing examples is good, it should not be the only method of teaching.
- It is very easy to see reduction formulae as a separate topic. It's very important to be able to link the CAST diagram with the graph of the trig function.

I know I should say good bye now, but I am delaying it. My problem is, I really want to talk more about this topic. Anyone want to join me? Use #vtmaths or just comment below. (This is going to be REALLY awkward if no one does... on such a public forum...)

Until next time, happy teaching!

Until next time, happy teaching!