As I drag the corner of the right-angled triangle on my whiteboard, creating an infinity of similar triangles, I draw the students’ attention to the calculation of the ratio of the lengths of two of the sides. Yes, through all this change, it remains constant. How do I envisage my students reacting? I want them to say what they think, not what they think I want to hear. What is a reasonable reaction to my use of a dynamic geometry software package? Well, ‘so what?’ springs to mind.
Mathematically, the proportionality of similar shapes is interesting. My lesson, or my demonstration invites a termination to the discourse. I ask the question, how do I teach the students trigonometry? Steer, de Vila & Eaton (Mathematics Teaching 214) describe a method referred to as ‘MNO’ (Burke and Olley, 2008). I will describe and exemplify this method for teaching Trigonometry at GCSE, and then ask whether this still invites a shrug of the shoulders.
The M in MNO stands for map, and what I want to do here is lay down the maths that is Trig at GCSE level. I have clustered these around nodes, the clusters representing maths that I think can be taught concurrently, and by implication, the separation indicating the maths that I think can’t. My map is not set in stone, is negotiable and evolving.
I move onto the N, the narrative. I think that most maths could be introduced from a historical perspective, in this case, the trig ratios from Antiquity, and the relatively modern view of Trigonometry as a Function. I have decided to take a problem solving approach this time, therefore, the History is bypassed. My narrative looks like this:
The O is for Orientation, I want the students to engage with the maths I want them to learn by doing something. This is where the plethora of activities for learning maths that has been built up over the years comes in. One of my first stops will be www.resourceaholic.com . The activities I get my students to do will include the use of problems to be solved (first stop nrich.maths.org), as well as class textbooks. All this will be clarified by my strong explanatons, and students will have plenty of time to reflect and ask questions. I will write about the activities I use another time.
So can the students still reasonably respond with ‘so what?’ Of course they can, they can say* and think what they want. Given the thought I have put into my plan for teaching the topic, I am confident that I can contextualise their concerns and reorient them towards mastering trigonometry.
*Clearly there are some things one can’t say in a classroom, a reorientation towards the maths seems to me to be the best response.