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Re-cognising Learning and Teaching: Opening the Space of Possibility

Re-cognising Learning and Teaching: Opening the Space of Possibility

In S.Voller, E.Blass and V.Culpin (Eds) (2011). The Future of Learning: Insights and Innovations from Executive Development. New York: Palgrave Macmillan. 131-149.


Re-cognising Learning and Teaching: Opening the Space of Possibility


Chris Breen, University of Cape Town



Oriented by complexivist and ecological discourses, teaching and learning seem to be more about expanding the space of the possible and creating the conditions for the emergence of the as-yet unimagined, rather than about perpetuating entrenched habits of interpreta­tion. Teaching and learning are not about convergence onto a pre­-existent truth, but about divergence – about broadening what is know­able, doable, and beable. The emphasis is not on what is, but on what might be brought forth. Thus learning comes to be understood as a recursively elaborative process of opening up new spaces of possibility by exploring current spaces.                          (Davis 2004, 184)


This chapter will explore some of the implications of the above quotation for the future of learning with a specific focus on executive education. The initial part of the chapter will be located in the author’s long past experience as a mathematics educator in the South African context. It will then outline some recent learning and teaching theories that have emerged from complexity science and ecosystemic thinking. With these foundations, the author will ground some implications and possibilities in practical examples drawn from his current work in executive education.

The attempt to do justice to the subtleties and nuances of the topic in a linear piece of writing will not be easy.  The challenge will be to remain true to the complex swirl of events and situations that are indicated by the root of the word complex – ‘plex’ to ‘weave’ – and try to introduce suitable and helpful threads that will allow the reader to tug gently and uncover the inevitable connections and mutual dependencies.


Insights from an Educational Past

Everything said is said by an observer (Maturana 1987).

Maturana’s above statement challenges the existence of a detached and totalized knowledge that can be objectively described. This means that, as author, I am irrevocably entwined in the words that follow. This places an onus on me to provide the reader with some upfront access to the sources of my entanglement, especially those from the initial phases of my working career – first as a high school mathematics teacher (7 years), and then as a university mathematics educator (25 years).

As a successful mathematics student at school (regularly winning prizes), I enjoyed the status that success in mathematics gave me. I learnt that the correct way to learn was to follow the teacher carefully and adapt given procedures so as to be fast in getting to the correct answer (Breen 1990). After school I decided to study chemical engineering – mainly because I was told that it was the most difficult course at university that used mathematics! The reader will be able to recognize a well-developed sense of confidence in personal ability and a willingness to accept the toughest challenge possible. After completing my university studies, this same approach followed me into the teaching profession where I initially endeavoured to produce student clones who could succeed in working quickly, logically and accurately. In this way, both they and I could be seen to be successful high achievers.


Getting Complicated

Davis and Sumara (1997) introduce the term ‘Complicated’ to describe this ego-centred problem-solving world-view and teaching approach which is rooted in the simple mathematical equations of Newton and Descartes’ ‘I think therefore I am’. They later table additional features of this Complicated paradigm (Davis and Sumara 2008) as being based on machine metaphors aligned to concepts of input and output; as well as the use of linear imagery as one moves from A to B as efficiently and effectively as possible with the aim of progress. Problems can be solved by reducing them to their component parts. Measurement is an important component which aims to give us stability and control through prediction and routine. Best practice is the target at which everyone aims.

Davis (2004) grounds teaching approaches from this Complicated paradigm as coming from epistemic considerations of rationalism and empiricism where logical procedures are used to see the light of reason and the logic of mathematics is used as the core model. Teaching as Instructing or Telling (rationalism) and Teaching as Training (empiricism)  are the main modes for the classroom and what is taught is independent of who is taught (Davis 2004, 63 – 90).

During my short high school teaching career, I became aware of some deficiencies in the above approach, but the cracks really started opening up when I was appointed as a university mathematics educator in 1982 in a context of increasing political turmoil in South Africa.

A devastating challenge to the sovereign rule of mathematics in my life came from Julian David (1992), a Jungian analyst, at an open evening talk in Cape Town. As part of his speech, he focused on the damage that he believed that an over-emphasis on Logic has caused in the world. Amongst a great deal more, he said the following:

Western worship of intellect goes back to Socrates and Plato. The leading element was Logic – causality in the abstract – and this gave birth to the industrial revolution. Psychologically it conferred power… The founding principle of Logic is that opposites exclude each other. So Logic whips through the world dividing things… Logic classifies, and within classes, everything must be the same. Logic encour­ages separateness, class war and apartheid. Logic lacks humanity…

Logic is crucial in developing effective ego-conscious­ness. Logic gave Plato stability. Its abstractions offered a more satisfactory world altogether – a world of eternal truths, where there would be no change… The other functions of the psyche – feeling, sensation and intuition – were the dross. Without feeling, thinking is necessarily destructive.

Thinking without feeling is not the God Plato thought it would be; it is closer to the Antichrist…

These were shocking but deeply resonating words to a mathematics educator who on the one hand inevitably privileged Logic as part of his teaching, yet on the other was appalled by the horrors being carried out in the name of apartheid and had been gearing his work towards preparing teachers for a future democratic South Africa (Breen 1992, 1993).

Further reflection on this theme highlighted the way in which the dominant teaching methodology and context helped shape students views of themselves and their abilities. For example, one of the key features of mathematics learning is the test and the subsequent marking process. The dynamics of achievement and the positioning of students by ability that follows when these ‘marks’ become public became a growing concern. An example of the insidious nature of this positioning is shown in a piece of research where student teachers wrote a test to examine their knowledge of the school syllabus (Breen 2004a). Students were asked to predict which of them would achieve the top marks and which of them would do badly. They were quite happy to enter into this artificial game even though they had no evidence other than their verbal class interactions of the past few months. The surprise result was the success of Fred, the only quiet black African student in the class whose silent predisposition did not fit into the dominant expectation of extroversion in class being a good guide to achievement. No-one correctly predicted that he would finish as one of the top three students. More worrying was that Fred had also quite clearly undervalued his own ability and did not consider that he might feature in the top group of achievers. In contrast, Ross, an extrovert white male, was outspoken in class and the whole class consequently deferred to him when he appeared convinced of a viewpoint. Almost everyone placed him at the top of the class when in fact his final result was in the bottom half of the class.

David Henderson (1995, iv), a mathematics lecturer at Cornell University, highlights the loss of intellectual capital that can result from such a limited view of ability and value.

I have been teaching a geometry course based on the material in this book for a long time now. One might expect that I have seen everything. But every year, about one-third of the students will show me a meaning or way of looking at the geometry that I have never thought of before and thus my own meaning and experience of geometry deepen. Looking back I notice that these students who have shown me something new are mostly persons whose cultural backgrounds or race or gender are different from mine; and this is true even though most of the students in the class and I are white males… Note that this conclusion implies that I must listen particularly carefully to the meanings and proofs expressed by females and persons from other cultures and races because there is much which they see which I do not see.

Similarly, experiences with students such as Marissa (Breen 2004b, 2008a) and Portia (Breen 2008b) demonstrated the serious damage to self-esteem that resulted from their early and continued failure in mathematics, a subject which has been used as a filter mechanism for career choices. Failing students became withdrawn in class and extremely hesitant to offer an answer.


Into the Complex

Complexity theorists draw a distinction between the descriptors complicated and complex. This new interdisciplinary field begins by rejecting the modernist tendency to use machine-based metaphors in characterizing and analyzing most phenomena. Machines, however complicated, are always reducible to the sum of their respective parts, whereas complex systems – such as human beings or human communities – in contrast, are more unpredictable, more alive. (Davis & Sumara 1997: 117)

My growing understanding of the above deficiencies of the dominant teaching and learning methodologies arising from a Complicated paradigm and the drastic imperatives of the contested South African context led me to introduce some new innovations to my teaching curriculum (Breen 1992, 2008b).  It was only much later that I found a theoretical basis for many of these ideas in a Complex paradigm. The Complex paradigm is located in the area of adaptive systems and draws on ecosystem rather than machine metaphors. The imagery here is cyclical with a focus on feedback loops that aim at sufficiency and growth and the whole cannot be compressed into individual parts. The key value comes from newness and surprise and the focus is on adaptability and growth through an application of the most appropriate practice for the local context and participants (Davis and Sumara 2008).

Complexity paradigm discourse stems from two major conceptual orientations (Davis 2004) – complexity science and ecological discourses – that have their roots in an inter-objective orientation in the world in which attention is placed on both the cultural and the biological as well as to both the announced and enacted (Merleau-Ponty 1962). Similarly, a strong move is made to bring mind and body together as the embodied mind (Varela, Thompson & Rosch 1991). A complexity science orientation lead to a conception of Teaching as Occasioning where occasioning signals the participatory and emergent natures of learning engagements, pointing to both the deliberate and accidental qualities of teaching (Davis 2004, 215). Ecological discourses take a different route. While they share with complexity a conviction that all forms and events are intimately intertwined, this conviction has become more oriented to ‘questions of meaning, ethical action, spiritual entanglement and mindful participation in the evolution of the cosmos’ as it reasserts the role of human consciousness (Davis 2004, 161). This leads to Teaching as Conversing where conversations are ‘an emergent form, one whose outcome is never pre-specified and (which) is sensitive to contingencies’ (Davis 2004, 177).  Teaching as Conversing aims to indicate the notion of mindful participation in the unfolding of personal and collective identities, culture, intercultural space and the biosphere.  This approach has prompted more of a concern for ethical know-how than the complexity thinking-oriented practical know-how.


Enacted Teaching

A key learning theory with its roots in these ideas has variously become known as the Santiago Theory of Cognition (Capra 1997) or enactivism (Davis 1996). These terms refer to the work started by two Chilean theoretical biologists, Humberto Maturana and the late Francisco Varela (Maturana and Varela (1986), Varela, Thompson and Rosch (1991)).

One of the key concepts of this theory is one’s structure. Varela, Thompson and Rosch (1991, xv) describe the term ‘structure’ as a fluid and temporal self, which is formed ‘by the combined influence of one’s biological constitution and one’s history of interaction with the world’ (Davis 1996, 9). The enormous influence that this has on the way in which each one of us sees the world is emphasised in the following quotation:

In the enactive approach reality is not a given: it is perceiver-dependent, not because the perceiver ‘constructs’ it as he or she pleases, but because what counts as a relevant world is inseparable from the structure of the perceiver.                (Varela 1999, p. 13)

Since the structure of each individual is so strongly in place at an invisible level, any input from the teacher will be uniquely processed by each learner through the lens of their own structure – a process to which the teacher has no access at all. This means in effect that the teacher can realistically have little impact on the outcome of the lesson so can more usefully focus on paying attention to the input she gives to the session which will aim to perturbate the learner.

The perturbations of the environment do not determine what happens to the living being; rather it is the structure of the living being that determines what change occurs in it. This interaction is not instructive, for it does not determine what its effects are going to be…. The changes that result from the interaction between the living being and its environment are brought about by the disturbing agent but determined by the structure of the disturbed system.    (Maturana and Varela 1986, p.96)

Not only did this theory give me a theoretical foundation for the work I was already doing, but it also gave me permission to move more assertively into new territory. From this perspective, my task as teacher is to become ‘a disturbing agent’ in the classroom where the changes (which I take to be the learning) will be determined by the structure of the learner. In essence, the theory says that I can only have a limited influence on what actually gets taken up in the classroom and my control over the outcomes is almost non-existent.

These insights gave me the freedom to pursue my interest in becoming a better perturbator in order to challenge the status quo in South African mathematics classrooms with relish!


Consciously Perturbating Executive Education

The Initial Invitation

At the start of 2001, I was invited by Kurt April, one of my past mathematics education students, to teach a few sessions on his MBA module. He knew that I was exploring ideas from complexity and had had first-hand experience of my perturbatory teaching methods! Sitting in on his class in order to get a sense of the students before making my own contribution, I discovered some very familiar dynamics from the class of mainly white male students. Students were seated in a large lecture theatre with fixed seats facing the front. There was overt competition for teacher’s attention with a palpable pride in right answers. Fear of being wrong led to a hesitance to commit to an answer. Students from minority groups in the class were generally less vocal. Few seemed concerned about the contributions of others as they tried to be the first to give a correct answer or offer evidence of their superior knowledge and insights.

I decided to try to disturb some of these normalities in my session and so offered the class an activity based on a videotape of people in black and white T-shirts passing around two basketballs (Simons 2007).

I set the class the challenge for everyone in the class to be able to get the same correct answer for the total number of passes made by the people wearing white T-shirts. The stakes were high as no-one wanted to be the person who let the class down. The focus was absolute. When it came to give answers, there was a surprisingly large range from 12 passes to 22 passes. I asked the class if anyone had noticed anything unusual while watching the film. There were one or two answers such as a shot which bounced off someone’s head; or where a black T-shirted person received a pass from a white T-shirted person. Eventually, after the volunteered answers had dried up and nothing new was being offered, I decided to ask Nombeko, the only black woman in the class whether she had noticed anything. Very hesitantly and reluctantly she offered that she thought she had seen an extra person. Intensive further questioning led her to gradually extend this to an extra person wearing black; an extra person dressed up as an animal; as a jungle animal; as a monkey; and finally as a gorilla! At this stage, as she no doubt anticipated, the rest of the class burst into laughter – no way could they have missed a gorilla! No-one believed her.

On replaying the video, someone dressed in a gorilla suit is seen to walk across the front of the screen and beat his chest before walking off screen. The immediate responses came thick and fast. ‘You’ve changed the video’. My response of “How did Nombeko know there would be a gorilla the second time if it wasn’t there the first?” was met with a conspiracy theory of my having cued her during the tea break! Next came: ‘We were doing what you told us to do’ to which I asked whether they didn’t think it might possibly be useful to be aware if there is a gorilla in the room?). And finally when cornered one person said, ‘Yes, but what answer did Nombeko get – she probably wasn’t concentrating on the task so was one of the ones who let us down!’

And even when it turned out that Nombeko had the correct answer and the questioner the wrong answer, his final statement on going to tea was that he had learnt that he had to be on his guard so that I didn’t catch him out again!

The disturbing echoes from my mathematics education past as outlined earlier  are frightening. The majority of these business school students who display a comfortable (at times arrogant) regard for their own abilities and a reluctance to turn to others for advice, turn out to have been successful students at mathematics at school. They report that they were rewarded for displaying their abilities in class. There is no understanding that the other presents an ideal additional source of data – especially if their life story is different.


Exploring the literature

A short while after this MBA experience, I was asked to teach on another business school leadership course and these requests started coming with increasing frequency until I eventually decided to make the move from mathematics education to executive education in 2008.

It became important to familiarize myself with relevant literature and one of my first sources was Dee Hock, who had successfully overseen the birth of VISA, and subsequently written a book in which he told his story and outlined the crucial theoretical insights that he gained from the experience.  In essence he sets the challenge for future leaders to let go of the dominant mechanistic paradigm and embrace new ideas which he believes belong to what he calls the ‘chaordic age’ (Hock 1999). The following two quotes give the reader an idea of his views on two of the topics under consideration – the Complicated paradigm and the ego-drive to succeed.

This separatist, mechanistic concept is a powerful way of viewing the world, a useful way of perceiving some aspects of real­ity and a practical aid in day-to-day activities. Difficulty begins when it is held forth as the best way of perceiving reality. Destruction begins when it is held forth as the only way. It is only one perspective; only one way of perceiving reality. And it is the best way only for narrow, limited, quantifiable purposes.                                   (Hock 1999, 288)

Success, while it may build confidence, teaches an insidious lesson: to have too high an opinion of self.  It is from failure that amazing growth and grace so often come, provided that one can only recognise it, admit it, learn from it, rise above it, and try again. There is no reason to be discouraged by shortcomings.                   (Hock 1999, 71)

He also makes a telling comment that speaks to the MBA gorilla experience.

Fascinating patterns began to emerge. Most women seemed to understand the concepts quickly, deeply, and intuitively. People raised in Eastern cultures and religions were also swift to understand. Native peoples had no trouble at all…Those who had the most difficulty with the concepts were often Caucasian men from Western societies in positions of power. People like me! (Hock 1999, 199)

The following diagram, adapted from Dalmau (1995) and Kimberley and Fernbach (2006) offers a sharp focus to my experience of the different styles of learning and focus of the Complicated and Complex paradigms as well as their implications for the business world. The diagram associates the rational, complicated paradigm with management and the key areas of structures, systems and processes. This is the territory of traditional mathematics and executive education teaching. It is the section below the line that excites me most. Leadership is explicitly linked to a Complex paradigm and the key areas of relationship, intent and information. The challenge for me becomes one of using my insights from complexity and mathematics education to inform my ‘below the line’ teaching and learning in executive education?

Fig. 1.


A crucial additional element from the literature came from a book which began to speak directly to my growing understanding of the nature of ‘below the line’ work in business education (Senge, Scharmer, Jaworski and Flowers 2004). Only on my second reading of the book did I notice that the book was dedicated to the memory of Francisco J. Varela, which explained my excitement at the ideas being expressed! This book introduced the concept of the Theory of the U (Senge et al 2004, 83) which Scharmer later developed in more detail (Scharmer 2007). A representation of the opening process of the U is given in the figure below (Scharmer 2007, 37-40)


Fig. 2.


The visible section above the line represents our unconscious responses to situations. We draw heavily on our lived experience which has been strongly formed by our exposure to learning in the complicated paradigm. The result is that we respond by automatically downloading and reacting in a set, unconscious way. He believes that working for change requires one to move into the unconscious or invisible areas and journey through a process where we have to open our minds, hearts and wills as we move down the U.


First Challenging Steps

The range of what we think and do is limited by what we fail to notice. And because we fail to notice that we fail to notice, there is little we can do to change; until we notice how failing to notice shapes our thoughts and deeds.                                               (Goleman 1997, 24)

Repeated work using the gorilla movie with business leaders at all levels showed that the MBA experience was not an aberration. The same features of blind certainty coupled with a reluctance to listen to others – especially if they were not from a similar background – could be found at all levels of leadership.

I decided to take up the task of challenging the download-react unconscious behavior and attempt to work on Scharmer’s first invisible level – that of Open Mind. In doing this, I wanted to work from the enactivist perspective which  moves the central position from ‘I think therefore I am’ to ‘I act therefore I am’. I decided to take up the complexity science invitation of Teaching as Occasioning and set tasks which would ask participants to work in real time to get a lived experience of the concept under study. In this way they could participate as full subjects in their own learning. By including the ecological Teaching as Conversing perspective, they are able to keep a careful watch on themselves in action, and enter into post-activity reflective conversation which would be uniquely personal.

In the South African context, diversity has become the subject of many workshops and participants readily accept theoretical arguments about the need to listen to others to gain new ideas. One of the biggest challenges I face in my initial encounters with new classes is to get participants to become aware of the unconscious negative consequences that inevitably come from an education system that has placed a total emphasis on the rational, complicated world and how these consequences include a general inability to move beyond an ego position and take the views of others seriously. The activity described below gives a brief idea as to how the above ideas from complexity allow me to take an awareness-intending perturbating teaching role.

The class is asked the number of times the letter ‘f’ appears in a short sentence that is displayed on the screen for a short period. Participants write down their answers without consulting or showing their answers to others. In the crucial next step, I ask each person to match their degree of certainty with an imaginary bet in the local currency (in South Africa this is Rand (R)). If they are 100% certain they must bet R100; 50% certainty means a bet of R50; etc. After the first viewing of the sentence generally only 20% of the class is willing to bet R100 (10 people in an assumed class of 50). I show the sentence again and challenge them to be true to themselves and have the courage of their convictions. The percentage of people who are 100% certain of their answers generally rises to about 70% at this stage.

Now we start exploring answers as I ask those who have seen 0 ‘f’ to come forward to stand in front of the class, and build this up by one each time. The first person generally comes up when I reach two ‘f’s. One can see the look of surprise when they see that there are only 2 of them in the class of 50 who have seen 2 ‘f’s. As they stand in front f the class, I ask them to tell us how much they bet. They are then asked if they want to change their bet. Those who have bet R100 and are 100% certain of their answer very seldom change their answer – even though 96% of the class has seen more than they have! And they won’t even back down when I present them with a logical argument why they cannot remain 100% sure that 96% of the class can be wrong. They know what they saw and do not regard their colleagues as data. The only way they say they will change their bet is if they see what they regard as the data – the original sentence – again. And of course, when I give them the chance to see the sentence again, they almost always make the same oversight. They will even step forward on invitation by me and tell each one of the rest of the class who have seen more f’s than they have, that they are wrong and are stupid! And the same pattern continues as we increase the number of f’s going as high as some who have seen 8 ‘f’s. Very seldom does anyone seem to learn and accept colleagues’  observations as valid and a possibly superior data source.

The debrief conversation that they have with colleagues after everyone has been able to agree on the correct answer allows them to explore the dynamics that were going on at both individual and collective levels. The implications of their ego-centred stance and disregard for others highlight the absence of an open mind. With them thinking they have learnt the lesson, I generally move on to the gorilla movie mentioned earlier and the shocks continue! The gorilla serves as an excellent metaphor for threats, weaknesses and opportunities that are around us and that we fail to notice.

A further building block is provided by the following activity (Breen 2001)  which works with the concept of structure introduced earlier, and the way in which what we perceive to be reality is strongly influenced by our lived experience and genetic predispositions.

I show a brief excerpt from a concert where Hugh Masekela is performing. At the end of the showing each viewer is asked to select an image that stood out for them and write down as much detail about that image as they can. The range of differing facts reported on a particular image can be seen to be strongly influenced by the individual observer’s own particular lived experience and assumptions of that image. It is only when they share their certainties with the rest of the group that the very subjective nature of their ‘factual’ descriptions of what they saw becomes apparent. For example, there is an image of some policemen standing on a hill looking at the concert. This image has been variously described as consisting of: 3 bored policemen; 4 policewomen; 4 policemen with an Alsatian; or 5 armed policemen looking for trouble. Each of these descriptions can be shown to have a strong link to the viewer’s personal experiences with authority and police in the past!

Once the majority of the class has accepted the deficiencies of an ego-centred source of data and their limited experience, they are ready to move onto activities which highlight the benefits that can come from a careful consideration of those who think differently than they do.

I project a section of the 9 times table (up to 10 x 9) on the screen and ask participants to work individually and write down everything that they notice about the table. First attempts are very poor with the maximum number of observations being in the region of 4 or 5. Those who would describe themselves as mathematically able generally have the shortest list that starts with the label that this is the 9 x table and not much more.

The second half of the exercise gives each person the task of offering a new observation that has not been said before. Before we start, I ask those who see themselves as being useless at or scared of mathematics to stand up. As non-experts they then take the privileged position of being asked to answer first and, in addition, they are given a wild card to jump the queue whenever they have a new insight. The main instruction given is that they must hide their original answers and not compete with each other, but rather to listen carefully to what each person says and explore the new possibilities that each observation opens up. The class is amazed at the list of over 50 observations that are made, and particularly that it is the self-proclaimed non-experts who often lead the way in creative observations!

These examples have been offered in an attempt to give the reader access to the different type of real life/real time classroom interactions that might be occasioned by foregrounding an enactivist perspective of teaching and learning – they are certainly not intended to be templates for best practice! Each activity is aimed at holding up a mirror that allows participants to observe, think about and discuss their own actions in the moment. This initial work with a group in executive education usually spans one or two full days and my intention is to finish the process where each participant has a new awareness of their blind spots and a willingness to start working on opening their minds to the possibility that they are mistaken and that others may be able to assist.

It is always very sobering to experience the willingness of participants to move to the edge and engage with these ideas and this very different teaching style. The following selection of journal comments from a group of senior executives from a variety of backgrounds and contexts is intended to give the reader an insight into the courage, honesty and responsibility that participants take for their reaction to the experience.

The first session with Chris was brutal to my ego and what I originally saw as strong points. The no.1 MAJOR challenge is to accept that I need to change if I want to learn. (IJ)

I have become aware that the gap between what I may say and what I actually do is big. My insistence, in the face of strong contrary views, that I had seen three ‘F’ characters has jolted a realization of the extent of my arrogance through the dismissal of any sense that others could in fact have been correct in what they saw. (CD)

Before our session, diversity was a de facto state of my mind as long as I am not racist, anti-gay or anti-anything that is different from my attributes.  I didn’t know that I was not embracing diversity in the true sense because races and ethnic groups are simply the first layer of diversity. I have been running away from the real world. A world of feelings, relationships, true human values, intents and information that I had forsaken or tried to forget because I programmed myself to be an outcome-driven and performance-driven person. This is why I was associating myself only with people that are like me, who think like me and who see the world like me. (EF)


My career has been pretty remarkable – but I question as to how much of my drive was because I wanted to do it, and how much was because success would impress others? Probably the latter I think. The corporate ladder places great emphasis on the car you drive, the size of the office, the fact as to whether you have a personal assistant or not and so on. (AB)

I take away some wonderful tools as well, that will allow me to self discipline and hence to lead my team better. These include the vision exercises, where I have always argued about being right in terms of seeing the same picture with somebody else, without willing to be disturbed and hence accepting that I could have missed the ‘gorilla’. Playing the 9 times table today, it dawned on me that I could have been shutting a whole lot of creativity and value creation out there by being the dominant speaker because I saw quite a number of ways that one can see patterns evolving within a simple exercise like that. Thus an environment needs a leader to create it, to unleash the potential of the whole team. It requires of me to play a critical balance below or above the line. Indeed I have been failing to notice what I fail to notice. (GH)


Digging Deeper

The inevitable question that emerges from participants after this type of work is how they can begin working with this new awareness to try to change some of these actions and their taken-for-granted assumptions and unconscious beliefs. This has become the exciting aspect of my current work as it opens up the space for new beginnings and continues the challenge of teaching through occasioning and conversing. The remaining part of this chapter will try to put down some markers that begin to illuminate a possible path that I have been exploring.


Entering the Complex Space

Man’s worst sin is unconsciousness, but it is indulged in with the greatest piety even by those who should serve mankind as teachers and examples.                                       Jung (in Hollis 2003, 21)

Psychoanalytic ideas point to a different understanding of complex-ity  – Jung’s concept of the complex – an autonomous, affect-laden idea which has a life of its own and, when unchallenged, puts one’s life on automatic pilot. It is a mythological subsystem that is the result of the accretion of personal experience around a certain idea. (Hollis 2003, 15). These complexes are at the root of our patterns of choice and have ‘invisible filaments reaching down into history and replicating its dynamics if not its surface appearances’ (Hollis 2003, 21)

Digging deeper involves inviting participants on courses to start paying attention to these complexes which appear as charges or unexpected energies. These charges are ‘an embodiment of the invisible’ (Hollis 2003, 26) and provide us with an opportunity to locate and work with what are also known as blind spots or triggers. Wheatley (2005, 212) similarly invites us to be willing to be disturbed and actively pay attention to events that surprise or disturb us and use these occasions as opportunities to initiate non-judgmental conversations about the disturbance.

In similar vein, Varela (1999) introduces the concept of immediate coping as we engage with the world. He claims that we have a readiness-for-action (micro-identity) proper to every lived situation (microworld). His interest is in the hinge moments where we move between microworlds and choose an appropriate microidentity. If this is generally determined by the ‘common-sense emergence of an appropriate stance from an entire history of the agent’s life’ (Varela 1999, 11) – a seemingly clear link to Jung’s complex – the challenge becomes one of finding ways in which we can become aware and increase our possibilities for action at a hinge moment.


Becoming More Aware

I first began working with these ideas in the Researching Teaching module on a taught Masters programme in Teaching at the University of Cape Town at the beginning of the century (see Breen 2000 and 2002 for the background to the introduction of this course). The main methodology for this work is based on the Discipline of Noticing (Mason 2002) which asks participants to collect charged situations (critical incidents) in the form of brief-but-vivid accounts-of which removed all emotion, assumptions and personal bias from their reporting  and which stopped at the hinge moment. These accounts-of are then offered to others in conversation in what Varela calls ‘second person research – an exchange between situated individuals focusing on a specific experiential content developed from a first-person position’ (Depraz, Varela and Vermersch 2003, 81). This interaction gives the participant access to different interpretations and possible future actions to change the automatic download response. In Breen (2005), I give an extended example of a teacher, Nicky, as she chooses to work on her reaction to students coming to her for extra mathematics lessons who trigger her when they arrive for class without having done the homework that she had set them in their previous session.

In my work with executives, I have streamlined this process to initially focus on incidents where they have lost their temper with someone else – at work or at home. They are asked to re-enter the experience and explore aspects such as: what is happening in their body; whose behavior from their own childhood are they reminded of as they swing into action; what fear was present in them just before they lost it; etc.

The task between sessions then is to collect a series of accounts-of situations where they lose it or where they behave in a way that they would like to change. What is going on? What themes and similarities do they notice? This links with Scharmer’s advice to enter the unknown and, in the first instance, observe, observe, observe and become one with the environment.

Working on one’s own practice, especially when one is trying to change habitual responses, is an extremely difficult task. Participants are introduced to mindfulness practice and body awareness techniques to help them catch the hinge moment as it happens, pause, take a deep breath and then consciously choose a different learning rather than judgment course of action. Once again the willingness of executives to undertake this work and pay attention to their own complexes with honesty and integrity is remarkable. The following two examples come from participants on an extended course who were given an assignment to select an aspect that they wanted to work on and implement some small win change procedures as an action research project.

Freda sees herself as an introvert and perfectionist who is not good with people. At work she runs on autopilot but can feel her body is tense. She is irritated by what she sees as inefficiency in her workers and sees all feedback as being negative criticism. Her collection of critical incidents highlights her sarcastic and defensive interactions with others. She begins a short daily mindfulness practice each day to still the mind after which she prioritises for the day. She introduces open communication sessions with her workers where her task is just to listen to them. She finds herself becoming less tense and less pressurized and stops blocking others. The biggest gain comes from what should have been a tough meeting with union officials where she was able to let go of her defensiveness and fear and listen careful and ask useful exploratory questions.


John is surprised to discover that nearly all his critical incidents centre around his wife. She is a very capable woman who gave up her career to stay at home and look after the children. She gets rattled when she is under pressure. Looking at his incidents, he recognizes that each time he judges his wife as if he is smarter than her. He remembers that his father was very judgmental of his mother and that he grew up knowing that he had to be strong and perfect to be appreciated.

He becomes aware of what goes on in his body as he reaches a hinge moment – his head feels as if it is swelling and his chest expands as if it is going to burst. And then he loses it and the results are devastating. His wife closes off and a think tension is in the air. The children change behavior and become tearful and withdrawn. When he gets to work he is already in an emotional state and is impatient and easily frustrated.

He works on becoming more aware of his body and asks his wife to assist him in changing his attitude to her. A new situation arises when he is typing his assignment. His wife is next to him and moves – spilling her coffee over herself and some of his notes. He feels his head start to swell and manages to catch the moment. He breathes in and, instead of following his normal route of blaming her for her irresponsible juvenile behavior, he tells her that it doesn’t matter as he has finished with that information!

John reports that the consequences of his awareness work are immediate and dramatic. He and his wife become closer and the children happier as they sense fewer tense moments between father and mother. Leaving the house in a happy frame of my mind, has led to his having fewer hinge moments with colleagues which has encouraged more cooperation and consultation in decision making. The benefit to the company has been that his project team can now effectively sit around the table and give their individual input to a decision ensuring that it is the best for the company.


Concluding Thoughts

I have previously reported (Breen 1992) how I started this journey into finding a more effective form of teaching in 1986 in the South African context of severe political contestation. The impetus came from my desire to prepare mathematics teachers for an as yet unimagined future with a majority government. Traditional teaching methods that appealed to logic were not working as I saw each student filter the content through their own taken-for-granted assumptions. The challenge was to enter the unknown and explore the possibilities of what was doable and beable. The words of the opening quotation by Davis, written 18 years later, resonate strongly.

Varela (1999, 27) refers to Mencius’s comparison of a truly wise person and the village honest person. The village honest person is someone who will know what to do in a specific situation provided that there is sufficient time to think about it and to make a considered decision. The truly wise person, in contrast, does not have to stop and consider what action to take. Through a process which he describes as consisting of extension, attention and intelligent awareness, the truly wise person just acts in accord with the situation.

The traditional complicated teaching and learning that has formed the majority of school mathematics and executive education instruction seems to be geared towards the development of village honest people. Leaders with this training are able to make excellent decisions when given the time to consider their options. Their default behaviours in familiar situations generally fall into the download-react category and are governed by taken-for-granted assumptions and unconscious complexes.

This chapter has used a theoretical and practical base to explore some of the possibilities that open up when these invisible foundations are explored from a complex teaching and learning perspective. The move from receptive learning to active participation in real life and real time activity provides the condition for learning in the moment. The perturbations create occasions where the unconscious can be made visible. Once participants have acknowledged their need to notice more, they can choose to take control over the changes they wish to make. The importance of having the space to enter into conversation – especially with those who have different life experiences is crucial as is a willingness to be disturbed. In this way, each session is co-determined by the participants, the teacher and the context which allows different possibilities to emerge at individual and group levels.

The changes described in this chapter point to the education of more truly wise executives who are aware of their actions in the moment and able to choose to act naturally as required in each situation. The initial results of the work reported in this chapter are extremely encouraging in this regard.



Breen, C. (1990). A Cautionary Tale about Rabbits, Moles and Choices. Pythagoras, 23, 20-22.

Breen, C. (1992). Teacher Education: Confronting Preconceptions. Perspectives in Education, 13, 1, 33 – 44.

Breen, C. (1993). Holding the Tension of the Opposites. For the Learning of Mathematics, 13, 1, 6-10

Breen, C. (2000). Re-Searching Teaching: Changing Paradigms to Improve Practice. In M.A. Clements, H. Tairab & W. K. Yoong (Eds.), Science, Mathematics and Technical Education in the 20th and 21st Centuries (pp. 94-103). Department of Science and Mathematics Education: Universiti Brunei Darassalam.

Breen, C. (2001). Researching Teaching: Telling the hole’d truth and nothing but my truth, in A. Rogerson (ed.) Proceedings of the 3rd Mathematics Education into the 21st Century Project conference. Palm Cove, Cairns, Australia, August 19-24, 2001

Breen, C. (2002). Researching Teaching: Moving from gut feeling to disciplined conversation. South African Journal of Higher Education, 16, 2, 25-31.

Breen, C. (2004a). Perturbating the Assessment of Individuals and Groups: Listening for Challenges to Mathematics Teacher Educators. Pythagoras 60, December 2004, 2 – 12.

Breen, C. (2004b). In the Serpent’s Den: Contrasting scripts relating to fear of mathematics. In M.Høines and A. Fuglestad (Eds.) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Volume 2, 167-174, 2004: Bergen, Norway.

Breen, C. (2005). Promising Practices in Teaching and Learning. In C. Kasanda (Ed.) Proceedings of the 13th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education, January 2005, Safari Conference Centre, Windhoek, Namibia.

Breen, C. (2008a). Tugging at Psychological Threads in Mathematics Education. In T. Brown (Ed.) The Psychology of Mathematics Education: A Psychoanalytic Displacement. Sense: Rotterdam. 219 – 230

Breen, C. (2008b). The Hole is More than the Sum of its Parts: Mathematics Teacher Education in a Complex World. Notices of the South African Mathematical Society, 39, 1, April 2008, 15-30.

Capra, F. (1997). The Web of Life. London: Harper Collins.

Dalmau, T. (1995). The Six Circle Lens. Retrieved from http://www.dalmau.com/pdfs/six_circle_lens.pdf on 9 July 2010.

David, J. (1992). Unpublished lecture notes on Plato and Logic. Public lecture given at the University of Cape Town, July 1992.

Davis, B. (1996). Teaching Mathematics: Towards A Sound Alternative. New York: Garland Publishing.

Davis, B. (2004). Inventions of Teaching: A Genealogy. London: Lawrence Erlbaum.

Davis, B. and D. Sumara (1997). Cognition, complexity, and teacher education. Harvard Educational Review, 67(1), pp. 104–125.

Davis, B. and D. Sumara (2008). Innovation and Complexity Thinking 2.0. Retrieved on 9 December at


Depraz, N., F. Varela and P. Vermersch (2003). On Becoming Aware. Amsterdam: John Benjamins.

Goleman, D. (1997). Vital Lies, Simple Truths. New York: Bloomsbury Publishing.

Henderson, D. (1995). Experiencing Geometry: On Plane and Sphere. New York: Prentice-Hall.

Hock, D. (1999). The Birth of the Chaordic Age. New York: Berrett-Koehler.

Hollis, J. (2003). On This Journey We Call Our Life. Toronto: Inner City Books.

Kimberley, H. and M. Fernbach (2006). Research in the middle: the link between issues and actions in equity research. Paper presented at AVETRA conference, 19-21 April 2006. Retrieved from http://www.avetra.org.au/ABSTRACTS2006/PA%200057.pdf on 8 July 2010.

Mason, J. (2002). Researching Your Own Practice: The Discipline of Noticing. London: RoutledgeFalmer.

Maturana, H. (1987).Everything said is said by an observer. In W.I. Thompson (Ed.) Gaia: a way of knowing. New York: Lindisfarne Press.

Maturana, H & Varela, F. (1986). The Tree of Knowledge. New York: Shambhala.

Merleau-Ponty, M. 1962. Phenomenology of Perception. London: Routledge.

Senge, P., Scharmer C.O., Jaworski, J. and B.S. Flowers (2004). Presence: Human Purpose and the Field of the Future. Cambridge, Massachusetts: Society for Organisational Learning.

Scharmer, C. Otto (2007). Theory U: Leading from the future as it emerges. Cambridge, Massachusetts: Society for Organisational Learning.

Simons, D. (2007). Gorilla movie viewable at  http://viscog.beckman.illinois.edu/flashmovie/15.php

Varela, F. 1989. Laying down a path while walking. In W. E. Thompson,

(Ed.), Gaia (pp. 48-63). Cambridge, MA.: Shambhala.

Varela, F.J. (1999). Ethical Know-How. Stanford: Stanford University Press.

Varela, F. J., Thompson, E. & Rosch, E. (1991). The Embodied Mind: Cognitive science and human experience.  Cambridge, MA: The Press MIT.

Wheatley, M. (2005). Finding Our Way: Leadership for an Uncertain Time. New York: Berrett-Koehler.