I have two classes of MYP 5 Plus mathematics, which we call Integrated Mathematics 10+ at our school.

To follow the previous day’s spaghetti task, I posted the graphs of the three trig functions the students had created, and asked for them to contribute their observations and thoughts.

I asked them to tell me what they **see** (observe, notice). I gave them about 5 minutes to make contributions which I documented on the whiteboard.

Then, after the flow of observations seemed to have been exhausted, I asked them to tell me what they **think** about these graphs (what might happen in the parts of the domain that we cannot see, etc.). I liked that both classes figured out the properties of trig functions (such as domain, range, amplitude, period, negative angles) without me telling them anything at all. Kids were adding to others’ thoughts and collectively agreeing on the properties of the trig functions.

Finally, after plenty of time, the students were asked to tell me what they **wondered** from all of this. This part gave me ideas on how to direct the inquiry for this unit. I was quite amazed by some of the questions: What would the graphs of inverse trig functions look like? How can we make this graph be like the ultra violet rays, gamma rays, etc, that we viewed on the Scale of the Universe? It also allowed me to see what questions I might need to address, such as a lack of clarity on the definition of “exponential”.

Perhaps the **Wonder ** section went a bit too long for the second group, as some students lost focus and interest near the end. There were also some slightly irrelevant wondering questions, which were really about triangle trig. I think next time I will have them do the routine, or part of the routine (eg wonder only) in table groups.

But most importantly, to me, it gave students the opportunity to **own the learning**. They had physically created the graphs in the previous lesson, and now they were deciding the patterns and properties for these graphs.

All I did was facilitate.* *

I feel like this kind of learning is how it should be all the time.

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## About eadurkin

Originally a HS Mathematics teacher from New Zealand, currently working as Associate Principal in the Secondary School at Canadian Academy, an international school in Kobe, Japan. Married with two children.