I have just finished reading Being Alongside by @AlfColes. It's an excellent book full of interesting reflections on developing teaching, particularly through the use of video. His work with video is based on this paper, and more generally, John Mason's Discipline of Noticing. In his approach, teachers create accounts-of (reconstruction), followed by accounting-for (interpretation). The aim of this process is to:
...focus on the articulation of a purpose arising out of the detail of observations.
A purpose is 'an emergent description of the sorts of guiding principles that student teachers found energising when learning from their own experience'. They are similar to Rosch's basic-level objects, which can be described as 'easily stated labels, linked to action'.
Here is a list of some basic-level actions that I have noticed from my own practice:
- Being alongside - being alongside as opposed to being in-front-of learners
- Natural powers - explicitly tapping into students 'natural powers' in the classroom
- Pre-telling problems - giving students problems that require independent study
- Tutorial - using lessons as tutorials, with students learning facts/procedures etc. beforehand
- Recording/repeating without rephrasing - recording/repeating student responses in their own words, not mine
- Multiple solutions - recording all student responses and then discussing (as a group) which makes sense and why
- Opening-not-closing - asking students 'what do we think about this?' instead of closing down a line of inquiry
- Elaborate/cumulate - encouraging students to build on their own, and each other's, views
- Student voice - asking students how they would like to proceed, or whether something is useful
- Allow space for... - create opportunities for students to explore/discuss ideas in more depth
- Step back and listen - monitor students working together, resist the temptation to intervene
- End of sentence - wait until the end of someone's sentence, not interrupting before responding
- Conversation - create an environment where class discussions take the form of conversations not interrogations
- Wait time: students - allow students time to answer questions, perhaps by discussing in pairs first
- Wait time: teachers - pause before choosing how to act
- Slow down - slowing down discussion or exposition in order to draw attention to what is significant
- Re-group - take some time to form a new plan in the moment, to address an unexpected difficulty
- Ebb and flow - be aware of and allow for ebbs and flows in people's attention
- Time out - take a minute out of a lesson to rest/pause, especially if there is a lot of new information to be learned
- Direct attention - use a range of gestures to attract attention to what is significant
- Reduce variation - reduce complexity in order to stress key points (and ignore what is less significant)
- Awareness of metaphor - be aware of possible (negative) implications of using certain metaphors
- Authentic questions - field or ask questions for which the answer is not known in advance
- Points of departure - pose problems that admit various possible approaches and responses
- Undoing problems - pose problems containing minimal information, that require students to undo processes
- Partial attempts - praise partial solutions as such, rather than as incorrect or containing misconceptions
- Messy solutions - praise non-neat working as containing valuable thought processes
- Conjecture and public revision - promote the language of conjecture and revision
- Re-drafting - encourage re-drafting of partial solutions following feedback
- No blanks - encourage students to always attempt problems, do not accept blank responses
- Make good ideas public - bring good ideas to the fore (especially during group discussions)
- Assign multiple competencies - praise a range of abilities in an attempt to address status imbalance
- Working as a group, not in a group - create group-worthy tasks that require interdependence
- Curiosity - be mathematical in front of learners, allow them to see you (as teacher) solving a (difficult) problem
- Make thinking visible - find ways to make other's thinking more visible, e.g. through use of whole-class whiteboards
As you can see, there are lots here. To what extent might they be useful for others?
It must be noted here that these basic-level actions have arisen solely from noticing patterns in my own teaching. The next stage is to work with my department to discuss and collate a list of actions that we all use regularly, perhaps by adding to or subtracting from this list.
We must then try to work out when and how to use them (this feels very similar to the difficulty in arriving at useful problem-solving heuristics). I think the use of video is a crucial aspect in this process, and am going to explore the possibilities in more depth.
Towards a coherent theory of practice
What ties these basic-level actions into a coherent theory? Perhaps it is best encapsulated in Barbara Rogoff's metaphor of teaching as an apprenticeship, and the concepts of guided participation and participatory appropriation:
The metaphor of apprenticeship provides a model in the plane of community activity, involving active individuals participating with others in culturally organized activity that has as part of its purpose the development of mature participation in the activity by the less experienced people. Apprenticeship as a concept goes far beyond expert-novice dyads; it focuses on a system of interpersonal involvements and arrangements in which people engage in culturally organized activity in which apprentices become more responsible participants.
The concept of guided participation refers to the processes and systems of involvement between people as they communicate and coordinate efforts while participating in culturally valued activity. This includes not only the face-to-face interaction, which has been the subject of much research, but also the side-by-side joint participation that is frequent in everyday life... The "guidance" referred to in guided participation involves the direction offered by cultural and social values, as well as social partners; the "participation" in guided participation refers to observation, as well as hands-on involvement in an activity.
The concept of participatory appropriation refers to how individuals change through their involvement in one or another activity, in the process becoming prepared for subsequent involvement in related activities. With guided participation as the interpersonal process through which people are involved in sociocultural activity, participatory appropriation is the personal process by which, through engagement in an activity, individuals change and handle a later situation in ways prepared by their own participation in the previous situation. This is a process of becoming, rather than acquisition…
This view of learning as an apprenticeship, as a process of becoming, is echoed in Being Alongside. But what are we aiming to become? Better mathematicians? More independent? More resilient? More open-minded? More tolerant? Better listeners? A closer community? Better people?