Which one is the best?:
Analysing classroom interaction through emotional orientations, purposes and somatic markers, implications for teacher education
Laurinda Brown (University of Bristol, UK) and David A Reid (Acadia University, Canada)

Abstract: Learning to teach is learning to make the decisions in classroom situations that are the decisions teachers make. In this article, we explore a theoretical basis for describing this process of coming to decide as a teacher does, and illustrate the discussion with a classroom episode and follow-up interview of one teacher’s decision-making. We also show how we use these theories,  the analysis of observations and videos of teachers’ practises, and reflections on these, to inform our work with student teachers.

The question that informs our learning as teacher educators is: “How is it possible to work with people on our courses so that they learn about children learning mathematics, when we are not offering a single ‘right’ way to teach?”  Experienced teachers deal with situations where there are many different possible responses all the time. How do they decide what to do? 

Mr. Hatt is an experienced grade eight mathematics and science teacher in Canada whose classes David Reid observed as part of a research project on reasoning. He teaches two groups of students, his “homeroom” class, and one other. The following episode is from his introductory lesson for a unit on using algebraic expressions to describe mathematical situations. The students are building “trains” of trapezia of ever increasing length (see Fig 1) and calculating the perimeters.  He has asked each group to give him an arithmetic expression that describes the calculation they did to find the perimeter of a train of six trapezia, and he has written these expressions on the chalkboard (see Fig 2). He has also asked them to use their expressions to calculate the perimeter of a train of eight trapezia.  He is now discussing each expression in turn and has come to the last one.
Mr. Hatt: 	Which one does that kind of resemble?
Students:	The first one.
Mr. Hatt: 	The first one, the first one, OK.
Student: 	Which one’s the best?
Students:	 Ours, ours.

Mr. Hatt does not have time to think about his response. He acts, not on the basis of conscious reflection, but on the basis of predispositions that have developed over his lifetime. There are many things we can imagine Mr. Hatt doing after the transcript above. He could walk out of the room, saying nothing. He could say any number of things:
•	“‘Best’ is a moral judgement; this is a mathematics class.”
•	“I won’t tell you.”
•	“I’m not so sure we’re at the best one yet.”
•	“I’m asking the questions here!” 
•	“In what way does this one resemble the first one?” (ignoring the question entirely)
•	“Strawberry Fields Forever.”
•	“Summum bonum.”
•	“The homeroom class had a better one.”
•	“The third one is the best. Now, how does this one resemble the first one?”
•	“Which one’s the best?  Good question. Let’s discuss that.”

Some of the possible responses listed above may have seemed less likely to you than some others.  Why was this so?  

Damasio (1996) has studied the making of such decisions through the neurological characteristics of people who no longer seem able to make them. He has put forward the somatic marker hypothesis to explain what he has observed.  The term “somatic marker” is used for the juxtaposition of image, emotion and bodily feeling we have that informs our decision-making:
Because the feeling is about the body, I gave the phenomenon the technical term somatic state (“soma” is Greek for body); and because it “marks” an image, I called it a marker. Note again that I use somatic in the most general sense (that which pertains to the body) and I include both visceral and nonvisceral sensation when I refer to somatic markers (Damasio, 1996, p.173). 
We would suggest that your somatic markers come into play when you judge some actions to be likely actions of a teacher and others to be unlikely. In their work on teachers’ complex decision-making, Brown and Coles (2000) state:
Somatic markers act to simplify the decision as to which behaviour to try. Negative somatic markers mean that the behaviours do not even come to mind as possibilities for action. A positive somatic marker means that the behaviour becomes one of a number available for use (p.168). 
You have a constellation of somatic markers that are active in teaching situations. While another teacher would make different decisions than you would, at the same time you can recognise similarities in the choices your somatic markers would guide you towards. 

How do we use these ideas in our work as teacher educators? When we met we had different frames through which we viewed our work. David was concerned with developing ‘emotional orientations’ and Laurinda was interpreting the development of teachers in terms of ‘purposes.’ 
Through our collaboration (reported also in Brown & Reid, 2003) our initial theoretical ideas have come together through a connection with Damasio’s hypothesis of somatic markers. In the next two sections, in our own voices, we introduce our separate theoretical frames.
David: Emotional Orientations
I have lately come to see a constellation of somatic markers as what Maturana (1988) would call by the name “emotional orientation”.  An emotional orientation is what characterises someone’s actions as appropriate to a context, like teaching.

Maturana would call teaching a “domain of explanation”, characterised by a community whose members can recognise in others behaviours appropriate to the community, although they probably could not give specific criteria for doing so.  Many communities are like this, and communities can overlap, contain other communities, or subtly blend into other communities according to the behaviours different members accept as legitimate.  For example, algebra is a domain of explanation, just as teaching is:
…if someone claims to know algebra, that is, to be an algebraist, we demand of him or her to perform in the domain of what we consider algebra to be, and if according to us she or he performs adequately in that domain, we accept the claim.  (Maturana, 1988b, p. 3)   
In responding to his student’s question “Which one’s the best?” Mr. Hatt can act in many ways, but as a teacher you might not recognise some of the responses listed above as appropriate.  As we noted before, Mr Hatt’s choice must be based on something other than conscious reflection as there is no time for conscious reflection here.  Instead something like a somatic markers, or a constellation of somatic markers, must be at work, and in the larger context of all his teaching the somatic markers that guide Mr. Hatt implicitly define a preference for certain behaviour he, and we, would see as appropriate for a teacher.
…whether an observer operates in one domain of explanations or in another depends on his or her preference (emotion of acceptance) for the basic premises that constitute the domain in which he or she operates. Accordingly, games, science, religions, political doctrines, philosophical systems, and ideologies in general are different domains of operational coherences in the praxis of living of the observer that he or she lives as different domains of explanations or as different domains of actions (and therefore of cognition), according to his or her operational preferences. (1988a, pp. 33-34)
Maturana suggests the phrase “emotional orientation” to name the set of criteria (which we read as somatic markers) appropriate to a domain of explanations.  He uses “emotional” because it is a bodily predisposition rather than conscious reflection that is operating when we perceive some behaviours as appropriate and others as not.  
As different kinds of explanations are appropriate to different domains of explanation we have different emotional orientations appropriate to each domain.  We observe the actions of others as being appropriate to a particular domain according to our own emotional orientation for that domain.  So a mathematical emotional orientation allows us to recognise the activity of others as being mathematical, and hence to identify those people as mathematicians.  A teacherly emotional orientation allows us to recognise the activity of others as being teacherly, and hence to identify those people as teachers.  We have many emotional orientations as we belong to many communities, characterised by different (probably overlapping) constellations of somatic markers. 

This invites the question: How do we work with student teachers so that they develop constellations of somatic markers in relation to teaching mathematics, i.e., a mathematical teacherly emotional orientation?
Laurinda: Purposes
When asked about my practice when teaching I would often say ‘come and see what I do’; the practice remained largely ‘tacit knowing’ (Polanyi, 1966). I had a lot of experience, not only as a teacher but also as a curriculum developer and in-service provider when I took up my post as a teacher educator. I made a conscious decision to try to be aware of my practice in this new post in a way in which I had not been as a teacher. With my first group of student teachers I used my previous experience to offer activities that I knew worked with practising teachers when encouraging them to share their practice. There was one major problem with this approach, however: I was not working with practising teachers. These students did not talk like teachers, nor did they react like teachers. When I left that first session I remarked to my experienced colleague that I now believed that teacher education courses did something but that I was still not sure what. 
Out of my developing awarenesses grew a theory-in-action (Schön, 1991) in which I started to use the word ‘purposes’. Purposes emerged for me as a description of the sorts of guiding principles which student teachers found energising in terms of their own learning. These principles are neither philosophical descriptions of their attitudes and beliefs in relation to the teaching and learning of mathematics and of mathematics itself, nor the detailed ‘tips for teachers’ i.e. particular examples of behaviours that seem to be incapable of adaptation to new circumstances.
Working with groups of student teachers a routine developed of them describing the details of their practice, discussing incidents that seemed to them to be in some way similar. From these discussions a vocabulary of what they considered to be important would develop, such as ‘sharing responses’ or ‘how do I know what the pupils know?’. Such phrases are examples of what I call purposes, although I do not call them by name in my work with the student teachers. Discussions at the level of purposes, seemingly somewhere between philosophy and behaviours, did seem to be effective in allowing a group of students to begin to collect together a range of strategies for use, and so their beliefs and attitudes began to adapt. The purpose for the year suggested to the students was to work on gaining a sense of the teacher they wanted to become
I found such a hierarchy discussed in the work of Rosch (Lakoff, 1987; Varela, Thompson, Rosch, 1995). Rosch reported that basic-level categories are ‘the generally most useful distinctions to make in the world’ (Lakoff, 1987, p. 49). Having been shown the picture of a dog we are able to recognise it as such and most people would use the word ‘dog’ to describe the picture. This is the ‘basic level category’. There would be some individuals who might know that particular dog and so use its name as a descriptor and be able to give details of that dog’s individual characteristics and behaviours (interactional properties, p. 51). There are also people who would describe dog in a more general, technical way (superordinate categories, p. 51). This gave some additional support for the evidence I had of teachers talking in terms of ‘purposes’ in what appeared to be the most useful and most easily expressed distinctions that described and motivated the student teachers’ teaching actions. There was again this feeling of being between detail and abstraction.

	Rosch categories	Brown teaching strategies 	
Abstract layer (mind)	superordinate	teachers’ images of mathematics and mathematics teaching		
In between layer (most useful distinctions in the world)	‘basic-level’	‘purposes’	
Detail layer (actions)	interactional properties	behaviours	

In the transcript Mr. Hatt’s behaviour after the student says ‘The first one’ is to repeat that phrase twice and say ‘OK.’ We have no access from this extract to his purpose in doing this. It could be that he has learned that the students might say some more if he repeats the statement. He might have worked in the past on the purpose of  ‘facilitating discussion’. Who knows? And if interviewed, Mr. Hatt himself might not be able to answer the question “Why did you do that?’
So, here’s another question: How do we work with student teachers so that they recognise purposes for their teaching? In doing this they will then develop a range of behaviours for this purpose. This seemed to be related to the constellations of somatic markers in relation to teaching mathematics, i.e., a mathematical teacherly emotional orientation.

Seeing somatic markers

So, what does an experienced teacher do when asked “Which one’s the best?”
Mr. Hatt: Which one does that kind of resemble?
Students: The first one.
Mr. Hatt: The first one, the first one, OK.
Students: Which one’s the best?
Students: Ours, ours.
Mr. Hatt: I’m not so sure we’re at the best one yet.
Students: Both.
Mr. Hatt: But, I’m not sure, uh, my home room had – I think – I believe there were two different ones here – Now, the question is this – you then had to turn it up a notch and I asked you to go to (SS: 8) – 8. Did your method work? Yeah.
Students: Yeah.
Mr. Hatt: Did it?
Students: Well what was the answer?  26?
Mr. Hatt: Yeah. The answer is 26.
Student: Then it worked.

What can we say about Mr. Hatt’s somatic markers based on his response to the question Which one is the best? This is not easy to answer without collecting more information from somewhere, because you cannot see somatic markers directly in the same way as you cannot see purposes. We can, however, begin to speculate and raise questions. It was clear to us (from our emotional orientations as teachers of mathematics) that this teacher does not want the groups to end their work yet. One other strand of our discussion at the time came from noticing that Mr Hatt did not always use questions to support the discussion. He also used statements (such as “The first one, the first one” and ‘I’m not so sure we’re at the best one yet.’). How aware is he of using statements to support the questioning of his students? Is this something he does in other lessons? Has he a gut feeling that he does not want to answer the question yet? Was Mr. Hatt aware of using statements? Or was this simply what he did? How could we find out more about this? In the end we decided to talk with the teacher.
Interview with teacher … teachers in practice
The interview was semi-structured in that we knew that we were going to invite the teacher to talk about the details of his practise. Although the lessons we had viewed on video had been given some two years beforehand, the same focus had been used recently for a sequence of lessons. The teacher, consequently, spoke out of his recent experience. He made the following comments, chosen to illustrate a range of what was talked about, related to supporting discussions and questioning:
• Students have to be actively engaged or they are not learning.
• …, they want you to tell them, but they don’t learn unless they are actively engaged.
• I like to begin most things with a physical hands on activity, then to have a lot of representations, pictorial symbolic, students can flip back and forth.
• Can … they come up with expressions, then explain to the class how they obtained their expressions.  And there are a number of explanations. 
• They are formulating in their own minds the easy way to do it. Then they are going to ask me, but I don’t answer their questions. [LB Why don’t you answer?] They would like the easy way out, but they have to have time to know that it is a problem.  That it isn’t as simple as they might have thought.  I provide very little information until they have found a method.  There are a lot of methods.
• My biggest nightmare would be if everyone did 3 n plus 2.  I’d ask them to come up with another.  And they might say ‘Why, I have one that works?’.
• I might have my own method, but then I saw an easier way, so they write that, but others might stay with a more difficult way that they understand. In a 14 year old mind they are not always willing to accept a different picture of what is happening.
• To them they think the formula has to work for everything, so when they find the formula is different this is a discrepant event.
• If they ask me ‘why?’ I turn it back to the class.  I think that comes up in their groups.  They come and ask me why, but I want them to go work on that.  
• A friend of mine who is a doctor works with Medical students and he focuses on questioning.  And he says if you don’t know the questions and you don’t know the answers you’d better listen.  
• Don’t be too quick to answer questions, or to ask them.  The psychiatrist doesn’t answer the question “Am I mad?”  He invites the patient to tell more.
When he was invited to give detailed descriptions of his practice, Mr Hatt spoke of his intentions in a way that we would call speaking of purposes.  He gave insight into what motivates his teaching through some strong images.  For example, he expressed a belief in beginning with something physical, in looking for different solutions and in finding ways of getting students to be more engaged. The influence of somatic markers is not revealed here by a behaviour we observed.  Instead , there are images, like the physicist unasking the question, that point to purposes, like not being too quick to answer.  Given this conversation, our analysis of the lesson is that Mr Hatt operates to support the continuing discussion of many different strategies, not rushing to fix on one alone. The actual form of the statements and range of responses is not fixed, but contingent upon what happens.   Purposes suggest the presence of somatic markers that point to the behaviours that might actually happen, and as a method we can go back to the videotapes to check those out.
Teachers in preparation
The process of coming to be a teacher can be seen as a process of developing a teachers’ emotional orientation through an accumulation of appropriate somatic markers.  As experienced teachers continue to learn about teaching they continue to accumulate somatic markers (from among those appropriate to teachers) that guide them to make decisions differently than when they were new teachers.  Our awarenesses are there throughout — here’s a story from 
Laurinda:
I was interviewing people for the teacher education course. The woman I was talking to told a powerful story of how her own ideas of what mathematics was had undergone change when she was at school. She was ‘put down’ a set from the top set after which she found the teaching of her new teacher effective for her and she came top of the year in the next year’s examinations. Recently she had had the opportunity of going back to the school and had observed this teacher. She described the teacher teaching angle by starting by asking the children what they knew about angle. This was a description of behaviour. She immediately said ‘to connect with what they already know’ and then described more of the lesson, making these shifts in level as she commented on what she had seen. I was encouraging her to talk and stay with the detail.  Because of who I now am having lived these ideas I was able to ask her to think of herself as the teacher and asked her to imagine other ways of knowing what the children know (as a purpose - not made explicit at that stage). We brainstormed other ways in which this could be done and how, no matter what her initial ideas on teaching were, there might be a range of strategies which could be employed to achieve this. 
Conclusion
The experiences that student teachers undergo are important in beginning that process and the identification of the motivations that will direct their accumulation of effective behaviours for those motivations. The parallel with teaching mathematics is apparent to us, as teachers we support learners in making their own connections and exploring a range of methods of solution to problems, why not work on transcripts with student teachers and allow them to think through a range of responses for different purposes? The journey that we are on as teacher educators is of developing our own awarenesses of ways of working with student teachers who are working on the teaching and learning of mathematics.

Mr Hatt answered the questions of “Which one is best” by making it an invitation to the students to continue to think about the situation, by suggesting that the “best” might not yet have emerged. We see a parallel with the questions “Which one is best” often asked by beginning teachers trying to choose ways of introducing a topic, developing a  skill, evaluating understanding, or expanding their students’ competencies. Seeing learning to teach as acquiring and refining somatic markers appropriate to a teacherly emotional orientation through focusing on purposes.  The three theoretical elements, somatic markers, emotional orientations and purposes arose in very different contexts, but all claim to say something about how people come to behave in the ways that they do. Rather than trying to answer “which one is the best” by claiming that one of these is somehow better than the others, and better than the many other theoretical constructs that have been proposed to explain how people come to behave in the ways that they do, we chose to take the question as an occasion to continue to think about the situation.  We suggest that a complex situation cannot be understood through a single optimal perspective, but rather that multiple perspectives, each good enough to shed light on some aspect of the situation, are needed. 

References

Brown, L. and Coles, A. (2000). Complex decision-making in the classroom: The teacher as an intuitive practitioner.  In T. Atkinson and G. Claxton (eds.), The intuitive practitioner: On the value of not always knowing what one is doing (pp. 165-181).  Buckingham: Open University Press.  
Brown, L. and Reid, D. (2003). Somatic markers: Teachers’ decision-making and students’ emotioning in mathematics classrooms. In S. Pope (ed.), Proceedings of the British Society for Research into Learning Mathematics, 22(3), 7-12.
Damasio, A. (1996). Descartes’ error: Emotion, reason and the human brain. London: Papermac. 
Lakoff, G. (1987). Women, fire and dangerous things.  Chicago: University of Chicago Press.
Maturana, H. (1988a). Reality: The search for objectivity or the quest for a compelling argument.  The Irish Journal of Psychology, 9, 25-82.
Maturana, H. (1988b) Ontology of observing: The biological foundations of self consciousness and the physical domain of existence: Conference workbook: Texts in cybernetics. American Society for Cybernetics Conference, Felton, CA., USA. Retrieved April 6, 2005 from the World Wide Web: http://www.Inteco.cl/biology/ontology/index.htm
Polanyi, M. (1966). The tacit dimension. Garden City, New York: Doubleday.
Schön, D. (1991). Introduction. In Schön, D. (Ed.), The reflective turn. New York, Teachers College Press.
Varela, F., Thompson, E. and Rosch, E. (1995). The embodied mind. Cambridge: The MIT Press.