## Getting High School Kids To Talk “Math”

Today I had the pleasure of working with a dedicated and gifted first year teacher. Tim is doing an impressive job teaching pre-calculus grade 11 and 12 math; he has well prepared lessons and examples, clear explanations and solid answers to student questions. Tim invited me into his classroom to work with him and his students to develop some mathematical discourse with the kids.

The unit of study for todays grade 11’s was circle geometry; students had to learn, prove and apply both the Tangent Radius Theorem and Equal Tangents Theorem

The lesson played out as shown below. Keep in mind the focus is on student talk.

**Part 1 – Modelling** Teachers (Tim and I) stated the Equal tangents theorem for the students, and walked them through the logic of the proof

**Part 2 – We Do Together **Teachers stated the Tangent Radius Theorem and elicited ideas from the whole class regarding their understanding of the theorem, the diagram, assumptions, and conjectures. Students were encouraged to use relevant math terms and were probed with open ended questions to guide their thinking.

**Part 3 – You Do Together (whole class)** a) Students solved a problem that most students could easily prove. b) Then, as a class (this is the “do together” part) students brainstormed relevant terminology and theorems used to do the example proof.

**Part 4 – You Do Together (Pairs) **Students had 60 seconds to use a diagram and the terms from part 3 to explain/prove the problem to a partner – after 60 seconds they switched roles from listened to speaker.

During part one of the lesson no students used the language of mathematics verbally. During part two, students struggled to use the language (either they weren’t comfortable doing so or they didn’t know how). By part four of the lesson students were very talkative and on topic. The sentences formed by students seemed to be perfectly logical and mathematically correct. It was quite exciting for both Tim and I to see how quickly students became engaged in mathematical discourse when given clear structures and expectations. Tomorrow we will be trying out a write-around (recently called paper-blogging in the blogosphere) and I am quite excited to see the results. My personal agenda is to get students using social media to engage in discourse by the third lesson (approximately 160 minutes of lead up instruction time).

If you’ve been wanting to get students to talk more in your math classes – just give it a try. A couple of simple structures and a few minutes of planning seems to go a long way!

I would have killed to get this kind of education in high school. Would have prepared me for my Engineering math 10 years down the road.

Hey Patrick! I couldn’t agree with you more – that is why these types of changes are occuring. Classrooms have changed since you and I were in school, and so have the expectations. This is quickly becoming more representative of what happens in school. I’m excited to be a part of it!