## Observing a maths lesson

by Cordelia Myers, Sep 2018

**Context:**

This thinking was initiated by the Fenland Headteachers. They asked me to consider: “What does an effective maths lesson look like with the new emphases?” They wanted to know what to look for in an observation and how should this be different from previous observations.

This is an exciting question and I have enjoyed thinking about what constitutes effective maths teaching.

**In the observation:**

In many ways it is very simple: Are students thinking?

The new curriculum has an increased emphasis on problem solving and reasoning. Tasks like the one we started with are examples of reasoning practice (a futoshiki ). They may not even contain much traditional “maths”. Teachers won’t be systematically setting problems and asking for answers. They might be giving answers and asking for problems. They should ask open-ended questions: What can we find out from this information? What can’t we find out from this information?

Observers should be looking for coherence and connection rather than memorised procedures and tricks or short cuts.

**What does this look like in the classroom?**

- Dialogue between students and between students and their teacher
- Misconceptions will be revealed and discussed
- Links will be made between different branches of maths
- Mistakes are treated with respect and interest
- All students have the opportunity to articulate their thoughts
- “Don’t know” is not permitted unless there is a valid mathematical explanation for not knowing (eg insufficient information is provided)
- Intelligent practice takes place
- Students will be working on fewer tasks in a lesson, to greater depth.
- It may be noisy

**Lessons I am proud of**

Personally, the lessons with which I am most pleased are those in which mathematical argument breaks out. Usually this starts between neighbours. They disagree on an answer and discuss why. This is often resolved quickly because of a numerical error. If not, students start to talk with those around them. This can spread wider in the classroom and can result in a fruitful and intelligent mathematical discussion. I try hard not to intervene. However, I confess that, at this point, I sometimes dread someone walking in. It may appear chaotic but both I and the students know that actually something substantial is being achieved. Students have moved on in their thinking and have a deeper understanding of the problem – through defending their solution (whether correct or not).

I think those in leadership play a vital role in allowing staff to let this happen and affirming those who do. That sets us free to take risks and push students’ thinking. Feedback focused on this is appreciated by teachers – more than generic feedback. Clearly there needs to be competent behaviour management but, assuming this in place, a noisy, seemingly chaotic classroom should be a place of thinking, learning and new discovery.