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Teaching and Learning

Some Reflections on Teaching and Learning

October 4, 2017, Author: Chris Breen

When I was at school I learnt the trick of getting good marks in maths. Listen carefully to the teacher and crack the code of what s/he was teaching and then practice practice practice to make sure I could do the sums in the way teacher wanted as quickly as possible. The teacher always had a formula, an algorithm that I had to follow – don’t ask questions as to why, just do it! And I did perfect this art to the extent that I became a maths fundi in the eyes of my peers.  And then I moved on to become a mathematics teacher and I did my best to find a whole set of ´fool-proof´ formulae/recipes that my students could adopt that would give them excellent results if they just did what I told them to do. And they did generally follow my recipe and so they got good results and I became known as a god teacher! Of course, I didn´t succeed with everyone, but I quickly learnt to avoid time and energy on these students by labeling them as being too lazy, stupid or disruptive to do the work properly.

After a few years of teaching like this I signed on to do an overseas Master´s degree in the Teaching of Mathematics at Exeter University and my safe and certain world of teaching and learning was shattered. I learnt ideas such as ´only awareness is educable´ and ´the challenge of subordinating teaching to learning´ which seriously shifted my perspective from the teacher to the learner. I’ve written about some of this journey in an article called Rabbits and Moles. After this revelation I returned to teaching in South Africa and started experimenting with a methodology which took responsibility for putting learning and the learner at its centre as I worked to develop a wider range of teaching possibilities in my own resource folder. I focused on listening more carefully to the learner so that I could select a teaching methodology that suited each individual learner rather than just continue with my one-size-fits-all approach. I started designing activities which took students to the core of the concept being studied. In many ways I was already experimenting with biocentric education.

And then in 1984 I took on the challenge of preparing mathematics teachers for a future post-apartheid South Africa in my new position as Mathematics Didactics and Teacher Educator. I began a journey of trying to find a way to prepare future maths teachers for the challenges they would face – particularly in a hopefully post-apartheid society, which miraculously did happen a decade later. I started an NGO which focused entirely on addressing the challenges facing teachers in township schools. Since those early days I have been obsessed with this challenge of creating an optimal learning space for each and every one of the learners in my classes to maximise their own unique learning potential. It has been an epic and lonely quest that has seen many ups and downs as I experimented with a range of different methodologies and content foci – and I am still hard at work trying to reach this elusive goal that seems to get further away the more proficient and knowledgable I become! Those interested can read an article I wrote for the journal, Thinking Classrooms, in which I tried to map some of the key points that marked the initial phases of this still ongoing journey.

For this particular blog reflection, I want to focus on one of the most effective assignments I first gave to the B.Ed. class of experienced mathematics teachers almost 25 years ago. I asked them to learn a totally new skill and to keep a reflective diary during the period of the assignment. I asked them to track their progress in learning this new skill, their emotions as they mastered the material, and their preferred learning strategies and environment. I then asked them to compare all this with what the same factors that they had created in their own mathematics classrooms. Several of the teachers were shocked to come to the conclusion that they would possibly have failed if they had been a student in their own class. Most said that their prefered learning strategies and environments were nothing like the dull, teacher-dominated chalk-and-talk monologue that dominated the teaching of recipes that occurred in their own mathematics classrooms.

I can remember deciding to learn to play the flute at the same time as one B.Ed. class was doing this assignment so that I could re-experience the learning. My first step was to sign on for lessons with a teacher once I was the proud owner of a new (Yamaha!) flute. After the first minutes of my introductory lesson, I realised that one of us was going to go insane pretty quickly! I could not make a sound from the flute! My teacher tried to get me to pinch my cheeks, purse my lips and blow gently so as to produce a melodic note. No amount of puffing and panting was producing any worthwhile product and my teacher kept repeating the same instructions – more loudly and slowly – as to what I should be doing with my cheeks, lips and breath. I felt pressurised and totally incompetent as I kept failing this simple initial task. I wasn’t getting anywhere and this was not what I thought learning should be about. So I decided to withdraw from this ‘lesson’ process immediately and get to know my flute in my own way for a while. I took on the task of experimenting with different lip and cheek positions until I achieved my objective of getting a reasonable sound from my flute. And even then I did not rush back to lessons – I took pleasure for a while in just re-appreciating my ´brilliance´ in making a sound.

So a couple of months later I went back to my teacher with much more confidence – only to be offered the scales to practice both in the lessons and for homework. Her theory was that you must know the basics before you can start to do anything with the flute! And I was immediately taken back to my piano lessons as a child where I was taught with the same approach and had the scales thrust down my throat at all times in class and at home with my mother and teacher taking turns at shouting at me about my lack of commitment and ability to these damn scales! And that was the end of my intended career as a concert pianist! (Even then I obviously had dreams that learning should not be painful and stressful).

Back to the flute. Enough was enough and I did not want to revisit those piano times so I decided to change teachers. I found a wonderful man who approached my lessons very differently. He could hear my determination to learn to play this instrument and could recognise my passion for the music that experts could play on this instrument. He could also see my willingness to work hard at learning this skill. So he devised a double-pronged approach in which I spent equal amount of time on the basics (those scales!) and on beginning to learn a few recognisable songs (such as my first epic – Baa Baa Black Sheep). And even 20 years later I recall my pleasure at being able to play tunes such as Ode to Joy and an extract from Dvořák´s New World Symphony (poorly but, to me, recognisably).

These distant memories are all coming back to me as I experience teaching and learning all over again – but this time as a student. I have signed on for a teacher training programme to become a biodanza facilitator – and I am struggling! The teacher is a gifted practitioner whose expertise in running actual biodanza classes is quite clearly firmly located in her entire body. It is a joy to watch her craft a lesson in an instant, or switch plans in the moment as she intuitively picks up what the class needs. I can recognise that skill and know that it takes years to get to this place. It’s what I have spent my life learning to do in my own different field.

I have entered this course filled with passion for this field of biodanza and biocentric education. I have been working with most of the underlying theory of biodanza for almost 20 years and have taken to the biodanza classes from the start like a duck to water. I now want to learn how to create lessons that will serve to deepen the teaching that I already do and I am very willing to learn the craft.

But I am struggling to access the subtleties of putting together a class and can see that I am rapidly becoming labelled as the deviant in the class!

And as I’ve started observing and thinking about this state of affairs in terms of teaching and learning, I have been reminded just how difficult it is for a gifted practitioner to pass on the nuances of their craft to others. The subtleties have their roots in deeply lived experiences that cannot easily be packaged into an ordered cognitive chunk of knowledge. I understand again why it is that I always baulk when asked what I am doing to pass on my own craft of teaching to others as a legacy. I reconnect with the essential problem that I cannot easily offer any learner the same lived experience and practice that underpins my choices.

And I realise that our biodanza teacher is trying to bypass this hurdle by offering us a ‘formula’ for running a biodanza class. But it’s a different sort of formula from the one I know in maths classes.  And unlike maths, there is no easily recognisable correct end product. In maths there is an external answer that can be verified by everyone – not just the teacher, whereas in designing a biodanza class the formula’s successful implementation is mediated by the subjective lens of the teacher. So I know there is a structure embedded in what we are being offered, but so far I can´t get a grip on the nuances that would give me access to a finer degree of judgment. Over the years I´ve developed what is to me the helpful strategy of screening out some of the confusing additional words so that I can access some of the core concepts that have formed the centre of my mathematics content offerings. But I feel the sand shifting beneath my feet each time I think I am getting somewhere.

And I realise I have spent the past 37 years experimenting on an almost daily basis with these ideas of teaching and learning – ever since my Exeter revelations. I have discovered that I really do like learning in a particular way that foregrounds understanding and connectivity. At the moment it seems impossible for me to go back to learning something almost by rote without understanding the ‘why’ of the greater generalisable concept and schema that underpins this formula. It doesn´t help me to learn a formula or recipe off by heart. I want to reach out and try to touch the heart of core of the craft. I want to work with what I already know and have accumulated over the years rather than pretend I am a tabula rosa. And I want to work on parallel tracks so that while my main focus is on learning the basics (the scales), I also get the chance to jump tracks from time to time to feed my passion for the future (the Baa Baa Black Sheep approach).

Inevitably my life experiences as a mathematics teacher and Didactics lecturer have influenced my approach to teaching and I believe the challenge for all teachers is in lines with Kierkegaard who asks the teacher to be a learner in the first place.

But of course I cannot impose that on another teacher, so I try to feel my way forward as if I am blindfolded remembering the wonderful words of the David Waggoner poem, Lost, which tell me to let the forest find me! So I try to keep quiet and observe and pick up the gems that will help me find my way in the forest. I look around and see the variety of responses in the class. Many seem to have slotted right in there and are bounding ahead learning the recipe. Others who seem to share some of my difficulties have put these aside and are focusing on learning the scales in order to pass the exam, while a couple of fellow scientists unsuccessfully attempt to draw structural mind maps of every twist and turn in the path,

And I think back to the many learners in mathematics classrooms around the country who are not able to think like teacher and take on board the recipes that they are being handed to solve mathematical problems. I think of the many questioning young minds who ask uncomfortable questions and who get into trouble for asking ‘why’, or for forgetting the teacher’s recipe. How many of them have given up after believing the label that they were too lazy, stupid or deviant to learn maths. Of course the irony is that when they come to write their exams they quickly discover that if they have not remembered the full recipe, they have nothing within themselves that will allow them to create a solution on their own.

And I realise how lucky I am to have this opportunity to be a learner again and struggle with these nuanced aspects of teaching and learning. Twenty years later after taking on that flute challenge, I am once again learning another new skill and being asked to make choices and reflect on how I prefer to learn!

Maybe I´ll see if my flute is still lying around somewhere and I can still play Baa Baa Black Sheep or dare I hope – Dvořák.