How an activity feels to pupils

I saw some truly excellent teaching whilst training with Teach First, and had some brilliant tutors. Some of the very best where when I as a participant or as an observer felt comfortable with the pace of the lesson, and felt that the activities were really meaningful.

Which led me to reflect on how activities can feel to pupils:

  • Do they have time to get on with the activity?
  • Am I disrupting the whole class repeatedly?
  • Are they writing how they really want to write or performing to success criteria set by me or someone else?

Some of these points were quite subtle – for instance even when the pace was great, and the activity useful, sometimes I found that I wasn’t producing outputs that were meaningful to me, because I knew that the teacher was looking for a specific type of ‘answer’ i.e. they were defining the success criteria, not me.

A good example of someone else setting success criteria is our reflective diary entries – Teach First structure these so that you are directed to answer specific questions each week. Great to get you thinking about different aspects of pedagogy or professionalism, but often I found myself wanting to reflect on something different – and there was no space for this. In the end I would often write a ‘tick box’ reflection for Teach First, and then write a meaningful reflection myself in a separate entry.

In terms of my own teaching, then, I need to consider how I can plan activities that feel well-paced and meaningful to students. But I’m realising how hard this is to do – the way an activity feels is dependent on so many different factors. In turn this means that perhaps the best way for me to check how activities feel is to ask students themselves regularly.

Boaler: What is maths? And why do we all need it?

Another recommended reading from Teach First. Selected quotes below:

Mathematics is a performance, a living act, a way of interpreting the world. Imagine music
lessons in which students worked through hundreds of hours of sheet music, adjusting the notes
on the page, receiving ticks and crosses from the teachers, but never playing the music. Students
would not continue with the subject because they would never experience what music was. Yet
this is the situation that continues in mathematics classes, seemingly unabated.
Those who use mathematics engage in mathematical performances, they use language in all its
forms, in the subtle and precise ways that have been described, in order to do something with
mathematics. Students should not just be memorizing past methods; they need to engage, do, act,
perform, problem solve, for if they don’t use mathematics as they learn it they will find it very
difficult to do so in other situations, including examinations.

We cannot keep pursuing an educational model that leaves the best and the only real taste
of the subject to the end, for the rare few who make it through the grueling eleven years that
precede it. If students were able to work in the ways mathematicians do, for at least some of the
time – posing problems, making guesses and conjectures, exploring with and refining ideas, and
discussing ideas with others, then they would not only be given a sense of true mathematical
work, which is an important goal in its own right, they would also be given the opportunities to
enjoy mathematics and learn it in the most productive way.

Boaler’s vision is an inspiring but ambitious one. Like Swan, Boaler discusses the end goal of a maths classroom without always making explicit the precursors necessary to allow students to work like mathematicians. Working like a mathematician is hard and, amongst other things, requires grit, persistence and a willingness to be wrong before being right. None of these things will come naturally to a mathematics student.

On the other hand, each of these things can be encouraged. The challenge is that it will take time, persistence and agility on my (the teacher’s) part to encourage students to work like mathematicians. It isn’t easy, but if Boaler is to be believed it’s worth the effort.

Boaler: What is Maths? And why do we all need it?

Swan: Collaborative Learning in Mathematics

From Swan’s paper (available below):

Teaching is more effective when it …

  • builds on the knowledge students already have;

  • exposes and discusses common misconceptions

  • uses higher-order questions

  • uses cooperative small group work

  • encourages reasoning rather than ‘answer getting’

  • uses rich, collaborative tasks

  • creates connections between topics

  • uses technology in appropriate ways.

Types of teaching activities that can achieve these principles:

  • Classifying mathematical objects
  • Interpreting multiple representations
  • Evaluating mathematical statements
  • Creating problems
  • Analysing reasoning and solutions

But what are the precursors to this? Swan talks about the challenge of ensuring all group members participate, and some ways to encourage this, but reflecting on what I’ve heard from other teachers in the past few weeks, I think we need to take another step back first.

The challenge that I’ve seen and heard from several teachers is to create the conditions within their classroom that allow productive collaborative work, rather than students spending group work time chatting about something other than maths.

Those classes that have used group work time productively have all had some common features:

  • The level of challenge is just right – students want to do the work because they want to find a solution to the problem the teacher poses.
  • There is a balance between letting students spend quality time on a difficult problem, but not letting activities run for so long that attention wanders.
  • Most importantly, the teacher has a good, professional, mutually respectful relationship with the class.

These points are hard as a teacher to achieve, but worth working on when I get to school in September. The last one, particularly, is what I keep coming back to – mutual respect and a professional relationship with the class are absolutely central to good teaching.

Another reflection is that the stuff Swan is suggesting is tough for students too. That’s part of the point of his activities. But if my classes are to have success with strategies like this, I need to scaffold them through Friday skills lessons or similar. Asking students to undertake activities like this when they’re not used to them will take time and effort on both our parts.

Swan: Collaborative Learning

Quiet disaffection

Quiet disaffection in the maths classroom is the title of a research report by Nardi and Steward.

The authors propose a model for many of the quieter students in maths classrooms: T.I.R.E.D. The model is below, as well as quick thoughts as to how I could respond.

Tedium: students can’t see the relevance of the maths they’re learning, and so find it tedious.

Response: I want to make clear to students that they can always ask me what’s the point of a topic – I might not be able to answer immediately, but I will get them an answer.

Isolation: There is seen to be little opportunity to work with peers.

Response: Build a relationship with the class so I’m comfortable designing group tasks without feeling I’ll lose the ability to facilitate the class. Tolerate on topic discussions between students, even if my instinct is to ask for silence. Make clear to students when they can talk, and when they should be silent. Encourage 3B4ME.

Rote learning: Students feel that a teacher will only allow one way to solve problems, and will ask for repetitive, context-free practice.

Response: Seek out the thinking behind student methods that are different to my own. Encourage student explanations of their approaches, rather than my own explanation (but need to balance with clarity of explanation). Get students to set their own questions.

Elitism: Students tend to think only exceptionally intelligent people can succeed at maths.

Response: Promote a growth mindset. Ban ‘I can’t’. Praise effort not just correct answers. Promote getting stuck and unstuck.

Depersonalisation: Students tend to feel that the maths classroom rarely caters to their individual needs.

Response: Keep a log of students’ interests. Contextualise the maths using this. Ask students what their individual needs and difficulties are regularly. Use rich tasks and real-life contexts.

Emotional Constancy

Teach Like a Champion Technique 47: Emotional Constancy

Modulate your emotions and tie them to student achievement not to your own moods or the emotions of your students.

  • For example ‘I expect better of you’ not ‘I’m really disappointed in you’.
  • Emotional constancy builds trust and helps students return to productivity quickly.