Teaching Mathematics Ch 10: Continuing Professional Development

  • When assessing your lessons, focus on the quality of teaching and the quality of learning.
  • As you become more experienced, reflection will become less formal but no less important for improvement.
  • Generally, trainees feel that they most in the early months of training their: ability to structure a lesson; and class management. To a lesser extent they develop time management, relating to pupils, and learning to pitch the lesson at the right level.
  • The Career Entry and Development Profile (which you complete at the end of your first year) is designed to help bridge the gap between your training and your first year in teaching.
    • You can use it to reflect on your strengths and weaknesses at the end of your training.
    • It helps the school to coordinate your induction year.
    • It also offers you a chance to specify where you would like further experience to develop your expertise.

Reflecting well

It feels a little ironic to write a reflective diary entry on reflection! But I am conscious that it is a very, very important element of my development as a teacher. I’m also conscious that at times in the past I have found myself ‘going through the motions’ with reflections, particularly at UTSAM in Ecuador. The reasons for this were twofold: I was very busy, and didn’t prioritise my reflections sufficiently; and I got into a routine with my classes and found it hard to keep my reflections fresh.

Solutions to this are various:

  • Recognising it as an issue should help me to avoid it next time.
  • Planning dedicated time to reflect (a) on individual lessons and (b) every fortnight or so to reflect on the past couple of weeks and set goals for the next couple of weeks.
  • Doing ‘hot debriefs’ on some lessons, following the model of my CELTA course – this gets the reflection done quickly, but allows me to draw out the learning from it while it’s fresh in my mind.
  • Assigning myself particular topics to reflect on, so that I’m not always trying to reflect on the lesson as a whole.

An interesting blog post argues that the quality of reflection is limited by our memories, our limited perspective (that of the teacher), and perhaps focusing on the wrong things. The solution is to record the lesson, and use this recording to objective analyse the lesson according to the learning objectives (or, indeed, any specific objectives I may have had).

So another solution for me is to use video as a reflection tool from time to time. One really interesting way to develop this and to link it to my objectives around student involvement and building trust with students is to ask them to video me in the lesson, and then to analyse my teaching for strengths and weaknesses.

Finally, I think a solution comes from building my own template for what a meaningful reflection should focus on. A useful starting point is the questions in this blog post. From these, I can build a basic template for my classroom reflections:

  • What’s one thing I was trying to achieve in this lesson? Why?
  • In what ways did I achieve it? In what was didn’t I achieve it? How do I know?
  • What would I do the same or differently if I had another chance to achieve this objective? Why?
  • What might have been the root cause of my success or failure? How do I know/why do I think this?
  • How can I respond to this root cause in my next lesson?
  • What assumptions did I make in the lesson? What impact did those assumptions have on my teaching/students’ learning? Do I need to change these assumptions? Why?
  • How did this lesson contribute to my overall vision for (a) my teaching (b) my students (c) this year? How did it contribute to one or more of my students’ visions for themselves? How do I know?
  • What one thing can I change in my teaching tomorrow?
  • What one thing can I improve for the next term?
  • What one thing should I keep doing?

Obviously I won’t answer each of these questions every time, but by putting them in a ‘reflection master document’ I can refer to them easily whenever I am reflecting.

Being a Number

The NCETM CPD module for ITE students has directed me towards this great video ‘Being a Number’

The module asks you to plan a lesson in your head using the numbers in the video

Outline activity plan (assuming a reasonably high level KS3/4 class)

Give pupils each a number and do some quickfire mental arithmetic as a starter: each pupil must choose another pupil and an operation on the two numbers – the answer starts the next operation.

Put pupils in groups of same coloured numbers, and ask them to spend five minutes exploring what we can say about those numbers e.g. they all end in 1 or 6. Ask pupils to look for other examples. Highlight previously agreed rules for group working.

Bring pupils back together and share examples, perhaps using an IWB setup. If it hasn’t come up, elicit the idea that all the green numbers are multiples of five. Then ask, if all green are multiples of five, how we can write that as an algebraic expression.

Then ask what we can say about the other colours, based on greens being multiples of five. Elicit the algebraic expressions for the other colours, with assistance.

Put pupils in groups of 5 consecutive numbers, and ask them to spend five minutes exploring what operations they can do with their five numbers, and any interesting patterns them come up with. Model one pattern e.g. red and blue added together gives green. Ask students to look for other patterns. Assign one member from each group to feed back their patterns.

Feed back patterns to class, and ask students whether those patterns will always hold, and why.

What do I want students to learn during the lesson?


CPD module continued

Continuing with NCETM CPD module: Exploring the tension between theory and practice in the classroom

B – What happened in some classrooms, and what might happen?

Activity 3

Some great videos on teachers teaching, which help me to see how you might react or not react when pupil responses aren’t what you expect. The challenge here is that I can watch and analyse these, and say that I will be open to students’ responses, avoid saying an answer is wrong etc. and yet it isn’t until I get into a classroom that I can try these things out. Nevertheless, it’s good to see other teachers’ reactions and consider whether I would react in the same way.

Really inspiring videos though!

Activity 4

This was an interesting situation where the students got, and reinforced, an incorrect idea. It showed how much lessons can be thrown off if they don’t go the way you want them to. These situations are hard to predict, but I think the solution is often to find a student who has the correct answer and get them to explain it, and/or to find a way to get students to investigate their misconception.

C – What might be a cause of tension, and what can you do about it?

I will need to return to this once I start teaching – it’s not something I can do already.

At the same time, because my internet is slow, I’m reading ‘Inside the Black Box’ about the importance of formative assessment. In reading this, many of the themes I’ve already come across are coming out again: the importance of AfL, active involvement of students, the importance of self-assessment. This sparks two thoughts: (a) I may have got close to reading enough for now, and (b) the challenge is going to be in making my practice fit with the theory that I think I understand and agree with. It’s all very well recognising the value of AfL. The difficulty is going to be putting it into practice in a valuable, consistent way.

How can I do this? I suspect there isn’t an easy answer, but lots of observation before Teach First, and getting teachers to observe me, asking them specifically to assess how I use assessment to develop my teaching practice, will be important aspects. It sounds as though Dylan Williams’ Embedded Formative Assessment book will also be very useful, so I’ll put that on the list to buy…

Separately I’ve read the latest edition of Equals from the MA. It has a lot on the overall purpose of school, and is a really useful reminder of the big picture – I’m so absorbed trying to develop my subject knowledge that I need to step back occasionally and remember why I’m a teacher in general, not a maths teacher in particular.

Equals also talks about motivating students which really resonates with me. In the article it says we can’t try to convince students they’ll use the maths we’re teaching them, but rather than maths as a subject is incredibly useful to society as a whole, and abstractly it is useful to them to help them develop thinking skills etc. This helps me imagine how to motivate students – I can imagine picking a lower ability student and convincing the class he’s going to be a computer programmer etc. and making the point it could be any of them.

Lastly I LOVE the idea of Maths fiction – creating worlds where e.g. circles are banned to develop students’ use of geometry.

CPD for ITE students

I’ve found a CPD module on NCETM specifically designed for ITE students, so this reflective diary is a reflection on that CPD module.

Why do you want to teach maths?

Why is maths so important? Firstly because it is used so often in our daily lives. Basic mathematical ability is essential to make sense of money issues, risks etc. And yet lots of the maths we do in school isn’t directly related to daily life. Why is this important? I don’t feel as though I have an adequate answer to this yet, although I imagine it has to do with the thinking and problem-solving skills that the subject can help us to develop.

Activity 1: of the two statements I agree with elements of both, but I think statement B is closer to the truth. A lot of what we learn isn’t that useful in daily life. But what is useful is the ability to problem-solve and the ability to understand the world around us – e.g. trigonometry allows us to make sense of the built environment. Yet even as I write this I don’t find it that convincing.

How much of the importance statement would I have agreed with? Not much! Why? Not because I think it’s wrong, but just because as an 11-year old the statement wouldn’t be very meaningful to me. The concepts of participation, or even of different jobs, would feel quite alien and remote. The statement sounds like a good rationale to adults, but not for 11-year olds.

Activity 2:

Most students think that maths:

– is about remembering rules

– is about getting the right answer

– is about thinking hard

– is very complicated

– is doing questions from a textbook

– is something that you do on your own

Most teachers think that maths:

– is about getting the right answer

– is doing questions from a textbook

– is something that you do on your own

– can stimulate moments of pleasure

– is a tool for science to use

– is about solving problems

– is about a few big ideas being used in many contexts

I think that maths:

– is about thinking hard

– can stimulate moments of pleasure

– is a tool for science to use

– is about solving problems

– is about a few big ideas being used in many contexts

– is a creative discipline

– is about independent thinking

I think that maths is a difficult but very rewarding discipline, valuable for its own sake as well as for its role in science, and that is surprisingly creative and enjoyable as long as it is taught in an effective way.

Why do I want to become a teacher?


  Teaching Learning
Whistling dog cartoon ·      Not relevant to them

·      Something done to them

·      Something that doesn’t involve them

·      Something controlled by the teacher

·      Not something they understand

‘Understanding the score’ extract ·      Responsive to the learner

·      Differentiated

·      High expectations

·      Challenging, not spoon-feeding

·      Adaptable

·      Rewarding!

·      Active, interesting, exciting, unexpected

·      Relevant to each learner

·      Task- and problem- based

·      Difficult, requires tenacity

I think… Teaching is something that is deeply responsive to the learner, and informed by best practice. It is differentiated, and makes sense to learners. Learning is something that you can sink your teeth into. It’s challenging but not scary, and it is based on investigations and rich tasks, not just learning from the textbook. It surprises and occasionally delights you.
I want to become a teacher because…

I think I can inspire students to see the value of and interest in maths, and if I can do this I will find it an incredibly rewarding job.



The remainder of the activities in this introductory section I will need to come back to once I’ve been into a school.