I [...] spoke
for the first time
after all these years
in my own voice.

All the True Vows


All the true vows
are secret vows
the ones we speak out loud
are the ones we break.

There is only one life
you can call your own
and a thousand others
you can call by any name you want.

Hold to the truth you make
every day with your own body,
don’t turn your face away.

Hold to your own truth
at the center of the image
you were born with.

Those who do not understand
their destiny will never understand
the friends they have made
nor the work they have chosen

nor the one life that waits
beyond all the others.

By the lake in the wood
in the shadows
you can
whisper that truth
to the quiet reflection
you see in the water.

Whatever you hear from
the water, remember,

it wants to carry
the sound of its truth on your lips.

in this place
no one can hear you

and out of the silence
you can make a promise
it will kill you to break,

that way you’ll find
what is real and what is not.

I know what I am saying.
Time almost forsook me
and I looked again.

Seeing my reflection
I broke a promise
and spoke
for the first time
after all these years

in my own voice,

before it was too late
to turn my face again.

~ David Whyte ~

On Questions

Here, where I am surrounded by an enormous landscape, which the winds move across as they come from the seas, here I feel that there is no one anywhere who can answer for you those questions and feelings which, in their depths, have a life of their own….
I would like to beg you, dear Sir, as well as I can, to have patience with everything unresolved in your heart and to try to love the questions themselves as if they were locked rooms or books written in a very foreign language. Don't search for the answers, which could not be given to you now, because you would not be able to live them. And the point is, to live everything. Live the questions now. Perhaps then, someday far in the future, you will gradually, without even noticing it, live your way into the answer.

- Rainer Maria Rilke

I have already signalled that my time at Exeter University transformed my thinking about teaching. In addition to the powerfully disruptive lecturing style of Dennis Crawforth, it was the exposure to Caleb Gattegno and his two aphorisms, ‘Only awareness is educable’ and ‘The subordination of teaching to learning’, that saw me return to school teaching in South Africa with new resolve.

I had the opportunity to experiment with these ideas at high-school level for the next six years before deciding I was ready to take the next step by exploring ways in which I could train future mathematics teachers using these new insights for learning mathematics.

My next step was to head overseas again for some more learning. This time I registered at Churchill College, Cambridge for a Master’s degree in Research in Mathematics Education with Alan Bishop. While studying overseas, I successfully applied for a Senior Lecturer’s post in Mathematics Education at the University of Cape Town (UCT).

I started my new adventure with what the reader will no doubt now recognise as predictable foolhardiness. Within a couple of years, I had designed and introduced two new teaching mathematics education programmes (at B.Ed. and M.Ed. levels), and I had initiated a teaching support project in township schools through the appointment of a former B.Ed. student as a full-time fieldworker in the Mathematics Education Project (MEP).

The latter move heralded a speedy and shocking personal exposure to the realities of apartheid education and police brutality in the face of student unrest. The fieldworker (who was also chairperson of the local radical teachers’ union) was soon placed in detention, and several student teachers were suddenly missing from my class because they were in prison.

My immediate response was to start lecturing about research and theory to do with political dimensions of mathematics education linked to frameworks such as the one outlined in Paolo Freire’s Pedagogy of the Oppressed (1970). This did not have the desired results of open enquiry that I had hoped for! It seemed as if the right-wingers rejected everything I was saying and labelled me a ‘bloody communist’, while the more radical students shouted, ‘Viva, comrade, viva’ in support! Nothing was changing. Theory and logic seemed to be irrelevant change agents – especially in a time of conflict!

I became even more disturbed by the challenge when I noticed that regardless of their political beliefs, the majority of these student teachers seemed to take an extremely authoritarian approach towards learners when I observed them in school classrooms during teaching practice.

This motivated me to start focusing my research endeavours on developing a classroom methodology for transformation, using my own Method of Mathematics classroom as a laboratory and source of data.

This was a lonely journey as I was working in a way that was not aligned with the dominant priorities and theoretical gaze of my fellow education academics. Welcome respite from this local academic alienation came when the end of apartheid gave me direct in-person access to international colleagues who were interested in similar questions.

Once the academic boycott was over, my first international conference, on the topic ‘Political dimensions of mathematics education’, took me to London. A quotation from Gattegno’s work in my paper sparked a meeting with two fellow American attendees who insisted I follow them on an extraordinary journey down to Wiltshire to meet their friend and colleague, Dick Tahta. Dick had worked intensively with Gattegno, and unknown to me, had been lecturing just up the hallway in Exeter University when I was a student there. Dick was later lauded by Stephen Hawking as his best teacher who had opened his eyes to the power and beauty of mathematics.  Dick quickly became a friend and a mentor and pushed me hard to overcome my academic insecurities and submit my first international journal article. He also later visited South Africa as my guest to work with my students and MEP teachers. He was also instrumental in introducing me to John Mason whose work on the Discipline of Noticing became my chosen appropriate methodology for my classroom research.

These international links emboldened me to find an intellectual and collegial home in the International Group for the Psychology of Mathematics Education (PME), attending the organisation’s annual conferences every year from 1993 (Tsukuba, Japan) to 2008 (Morelia, Mexico). This contact introduced me to the work of Brent Davis, who provided me with the missing theoretical link by pointing me towards enactivism and the Santiago Theory of Cognition – the work of Francisco Varela and Humberto Maturana.

These strong international connections encouraged me to face the local challenge of expanding my space back home at UCT. Together with a few academic colleagues whose focus remained on classroom practice, we managed to overcome internal opposition and start a Master’s degree in Teaching. Offering a module called ‘Researching Teaching’ gave me the incentive to read more widely and argue the theoretical case for my work . The enthusiasm with which students welcomed this work and started researching their own practice for their dissertations was highly encouraging, although it did open up another site of contestation with some of my colleagues.

I became President of PME in 2004, and spent my term of office working to open up the organisation’s field of research reporting to include frameworks other than strict psychology and ensuring that members from less-represented countries were warmly welcomed and initiated into the group.

My term of office as PME President ended in Seoul in 2007 with a new challenge. The local organiser took exception to my refusal to let him change the ground rules governing how he, as host, was allowed to run the conference on PME’s behalf. He was not used to being opposed and was particularly frustrated by the rule that PME retiring presidents (in other words, myself!) had to be invited to give one of the plenary papers. By a wonderful coincidence, the theme of the Seoul conference highlighted humanistic mathematics education, echoing the theme of my very first conference paper and my subsequent work. Everything seemed to fall into place, and I found the determination to use this opportunity to reflect on my 25 years of work in the field of mathematics education. My presentation consisted mainly of photos of people and stories and music – a methodological alignment with my content. My voice was at last loud and clear!

After obtaining a UCT Distinguished Teacher’s Award in 2000, one of my past mathematics education students, Kurt April, opened the path for me to run some teaching sessions at UCT’s Graduate School of Business. The reflective space provided by my Seoul paper encouraged me to look for a new teaching challenge. I took early retirement from UCT and mathematics education in 2008 and started freelance teaching at the GSB and various corporate organisations. 

My full list of mathematics education Publications includes several papers that are accessible on these website pages. Please make contact with me if there is a particular paper you cannot locate.