This blog post is written by Chris Shore, Senior Enterprise Fellow and PhD student at Loughborough University. Chris is also a tutor and module leader on the Outstanding Mathematics PGCE at Loughborough University (webpage linked at the bottom of this blogpost). Edited by Dr Bethany Woollacott.

How do you sustain a long career in any profession, especially one as demanding as secondary school teaching? We believe that one way to do this is by developing as a reflective teacher, so that each year is different from the last. In fact, the joke often goes that the best teacher experiences 20 different years in school rather than just one year repeated 20 times!

This belief in reflective practice is embedded in the Mathematics Post Graduate Certificate in Education (PGCE) here at Loughborough, such that our university-based modules are called ‘The reflective mathematics teacher’ and ‘Developing as a reflective mathematics teacher’. This short blog post will outline some views of reflective practice and discuss a model we use in our work with student (pre-service) teachers.

What is reflective practice?

Firstly, reflective practice is more than thinking deeply about the knowledge base of your particular discipline. Donald Schön¹, one of the significant thinkers about reflective practice noted:

In the varied topography of professional practice, there is a high hard ground overlooking a swamp. On the high ground, manageable problems lend themselves to solution through the application of research‐based theory and technique. In the swampy lowland, messy, confusing problems defy technical solution.

Schön¹, p. 3

So, thinking about your domain of knowledge (the hard high ground) is a useful practice to develop, and one of the key ways that we learn new ideas and skills. But on its own, it may not be sufficient to make progress in your chosen field.

Secondly, it is different from merely noting anecdotes from within your working day (the swampy lowland). Again, this may be a good thing to do, especially if they are amusing, but it is unlikely to lead to developing expertise in your career. Instead, it is the bringing together of these two: the integration of your professional knowledge base and your experiences of practice.

Models of reflective practice

There are almost as many models of reflective practice as there are reflective practitioners! For example, Kolb’s Experiential Learning Cycle² lists four stages to effective reflection:

1. concrete experience,
2. reflective observation,
3. abstract conceptualisation,
4. and active experimentation.

Whereas, Gibb’s Reflective Cycle³ features six:

1. description,
2. feelings,
3. evaluation,
4. analysis,
5. conclusion,
6. and action plan.

Schön⁴ suggested two types of reflective practice:

1. reflection-in-action
2. and reflection-on-action.

Reflection-in-action is an immediate act of reflection during an activity or task. Reflection-on-action is a post-hoc practice, involving reviewing professional decisions and then analysing any resulting actions.

Experiences, issues, actions

It is this reflection-on-action that we embed as a central practice on the mathematics PGCE; we use a model that we call Experience → Issues → Actions, broadly based on a professional development programme called Develop your Teaching⁵.

Experience

The idea is that student teachers pick a significant experience to reflect upon as they encounter different aspects of the PGCE. This could be from taught university sessions, school lessons that they are observing, or lessons that they are planning and teaching. By significant experience, we mean something that stood out for them and something that they could describe such that someone else could recognise it. Significant does not necessarily mean earth-shattering or a hinge event which turned the whole lesson. It could be any single instance: positive or negative. For example, it could be an interaction with a pupil or a sequence of events from a lesson, it could be a question asked or an answer given, a decision made or an explanation given. It could be a big event (e.g., teaching trigonometry for 2 weeks to a year 10 class) but it is most likely to be a small event (e.g., the numbers chosen for a trigonometry worked example).

Issue

Whatever experience is identified, the student teacher should consider what issue is raised by the experience. Again, an issue is not necessarily negative: it might be something which highlights an area or skill that they would like to get better at, but it also could be something positive arising from the experience (e.g., noticing how a teacher uses a school’s reward system to encourage pupil motivation). Sometimes, different issues might be raised from one shared experience. For example, in one PGCE cohort, we all observed a teacher in a local school explain upper and lower bounds to his year 8 class. From that observation, one student teacher realised that this area of the year 8 curriculum felt unfamiliar to them, therefore identifying a gap in their own subject knowledge as an issue. Another student teacher identified a different issue, noticing the teacher’s pedagogical choice of mathematical representation during the explanation. Two different issues were raised by different student teachers from having the same experience, and this is one of the things that makes this model of reflection powerful.

Action

Finally, from these issues, the student teachers should formulate a concrete set of actions. In the example above, the student teacher who identified their lack of subject knowledge as an issue might choose to work on a mathematical task or textbook exercises around the topic area. The student teacher who identified the issue about mathematical representations could choose to work with their placement mentor on how different representations afford different opportunities for learning, or plan lessons trialling different representations to understand how pupils respond to each one. Each issue could result in multiple different actions.

Here is another example which describes two student teacher’s reflections after encountering the same experience whilst they were teaching at their placement schools. These reflections are normally written in more detail (eg a paragraph), but they are summarised here to give an example.

As you can see, the same type of incident was experienced by different teachers in different schools, and they were able to draw out their own relevant issues and formulate some actions. This model of ‘experience to issues to actions’ is cyclical in nature as classroom problems are encountered, dealt with, and re-encountered. The goal is bridging the gap between the high ground of educational theory with the swampy lowlands of classroom practice, such that the student teacher can progress and flourish in the workplace. As Sellars⁶ notes:

This approach allows for contextually orientated experimentation in problem solving; it is a way of using past experiences, reflection and action to experimentally problem solve ‘on the spot’ where the circumstances are confused or unclear.

Sellars⁶, p.5

If you are interested in becoming a mathematics teacher, use the links below to email Tom or Chris, or apply on our website.

References

[1] Schön, D. (1987). Educating the Reflective Practitioner: Toward a New Design for Teaching and Learning in the Professions. San Francisco, Calif: Jossey-Bass.

[2] Kolb, D. A. (2014). Experiential learning: Experience as the source of learning and development. FT press.

[3] Gibbs, G. (1988). Learning by doing: A guide to teaching and learning methods. Further Education Unit.

[4] Schön, D. (1983). The Reflective Practitioner: how professionals think in action. New York, Basic Books.

[5] The Mathematical Association (1991). Develop your teaching: A professional development pack for mathematics – and other – teachers. Oxford: Stanley Thornes.

[6] Sellars, M. (2017) Reflective practice for teachers. London: SAGE Publications Ltd.