What is a good maths teacher?

Over this week I’ve been reflecting on what Sir Michael Wilshaw, the HM Chief Inspector of Education, said about what makes a good teacher. He speaks for the first 9 minutes on the video below but I highly recommend listening to the entire discussion.

He talked about two teachers who he had experience working with, both of whom were great teachers in completely different ways. One of the teachers had a more didactic style and the other preferred to facilitate learning. Whilst they had very different styles, they held similar values on what makes a good teacher. Some examples of these values include:

1. Planning should be detailed but also flexible enough to adapt to the students’ needs.

2. Success is measured on how much students learn and progress.

3. Teaching is a constant learning process. Being reflective about the lessons that you have taught is a key attribute in improving how you help students make progress.

Holding these values helped to make both of these teachers equally succesful at maximising student progress in a style which worked for them. This reminded me of what Jo Boaler said in her wonderful book, The Elephant in the Classroom.

In some educational debates, traditional teaching is placed at one end of a pole, and progressive teaching at the other. In my research I have found that such categories do not mean much, and that both camps include effective and ineffective teaching.

This view of placing yourself into a certain category of teaching fortunately seems to be outdated now. I’m sure that many teachers nowadays hold a similar view to mine in that the way in which we teach our students is dependent on what topic we are teaching and who we are teaching. If we want our learners to make maximum progress we have to think carefully about which activity, which resources and which way of learning will help us reach that goal. There is no point in talking about different styles of teaching; there is only room for discussion on how to maximise learning.

Up to this point, I have simply established something that we all know to be true i.e. that good teaching is less about adopting one correct style and more about the values you hold as a teacher.

Over the years I’ve developed a set of values/pointers which are based on my own experiences, books, research and blog posts which I’ve read. They are always attached to my desk so that I can read them on a regular basis and also revise them when necessary. I think every teacher should have their own set of values and pointers at hand to help focus their lessons onto maximising the learning of their students.

As a side note, I also think that many of us go through ‘cycles’ in teaching. By this I mean that we often get an idea into our head about one thing we want to improve upon or utilize more, and we end up focusing on that for a while. For example, when Dan Meyer’s 101 questions site was first introduced I probably over-used it a little at first because I think it’s an excellent idea to get students posing their own questions. Having the set of values and pointers on my desk helped to remind me that there are other things that I want to focus on other than promoting curiosity.

So, here’s my list on what I think helps make me a better teacher. The points are in no particular order, the values and pointers are mixed up and they certainly overlap, expecially in terms of formative assessment. There are probably too many but I see no reason to whittle it down to a list of 10 as I wouldn’t want to miss any of these out of my teaching. If you have any personal values or pointers which aren’t on this list, It’d be great to hear about them.

1. Always promote understanding. Try to get them to ask why.

2. When students believe that success is possible, they will try.

3. Reward students for doing something which is difficult for them as an individual. Don’t reward speed in calculating.

4. Don’t worry about covering every single thing. Teach skills and concepts and teach the students how to learn.

5. Always be enthusiastic about every topic in every lesson.

6. Help them realise that mathematics is just as much about posing questions as answering them. Promote curiosity and the questions will follow.

7. Help them understand that mathematics is not a rigid topic with one correct approach. They can use mathematics as a tool to solve problems in the way that best suits them.

8. The method is often more interesting than the answer. Promote multiple methods and celebrate different students methods.

9. Establish an environment in which they know that making mistakes is a necessary part of the learning process.

10. Establish an environment in which collaboration and communication is key to aid understanding and improve retention.

11. Provide feedback which improves their learning. What’s the point in marking if it doesn’t help them improve. Never put a grade on classwork or homework.

12. Promote pupil autonomy and provide opportunites for the students to act on feedback and reflect on learning in class. They identify their own weaknesses and work to improve on them.

13. Make them struggle with problems first. Make them think for the majority of the lesson. Once they’ve struggled, get help off peers before asking me.

14. Have a big goal for exam classes and share this goal with the students on a regular basis.

15. Share objectives with students which are concepts focused, not context focused. Show them where we are in the learning journey, where we’re going and why we’re learning it.

16. Provide model answers so that students know your expectations of quality. Try to use other students work for this.

17. Like language learning, try to connect current concepts and topics to previous ones to help students remember and retain previous topics.

18. Teach topics in different ways using different activities so that student construct them differently increasing the liklihood of understanding and retention.

19. Provide choices, even if at times they’re artificial.

20. Help them to realise that learning is not fixed but incremental. See a challenge in a positive way to improve learning rather than a negative experience.

21. Persist, write down ideas and change ideas when working on a difficult problem.

22. Try to incorporate rich tasks (low floor, high ceiling) which stretch all learners. Observe learners working before jumping in with questions.

23. Understand the process involved when working on a problem or investigation: Tinkering, Organising, Pattern Searching, Generalizing.

24. Plan a few higher level questions and questions which address misconceptions. Let students figure out misconceptions for themselves using these questions.

25. Spend a lot of time building strong relationships with students outside of the classroom. Friendly and caring but also professional.

26. Use real life examples but do not promote the fake version of mathematics which does not make sense in the real world.

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