Reflections on the Working Group

I am in 'awe' of the capacity of human beings over the centuries. Thank you to the working group leaders and the participants; I am grateful for the contributions that each individual made to the occassioning spaces that were created in our discussions and actions.

We saw examples of the ways in which human beings have brought forward 'tools' that served in a variety of ways. For example, the quipu, the stick maps, and Greenland coastal maps. For me, these were 3 examples of tools that communicated a narrative in some way. However, I imagine that the communication really did happen within cultural settings. In order to fully understand the narrative that was shared by these particular tools one needed to be a part of the cultural settings.

In other examples we examined 'tools' that are often 'included' in mathematics classrooms. Tools, such as fractions strips, circles, grid paper, fraction flags, and string. In some ways these tools help to make visible particular aspects of mathematical concepts; and. at the same time these 'tools' might hide other mathematical aspects. It is only working with the tools, with the images that we have about the concepts, and the language that we can bring forward the meanings of the tools.

On the third day we explored tools that, for me, were developed to 'ease' a human being in terms of repeated tasks. An image of a cherry pitter, and cigar cutter, and then we looked at the ways in which we could compute the value of square root 2. We looked at representations that is some early methods of approximation, and finally at a slide rule. The whole discussion around square root of 200 brought back early school memories for me where I learned about different algorithms for calculating the square root of a number and then I was introduced to the slide rule. My how I thought that I had a fantastic 'tool' in my hands. Yet, 4 decades later, as we explored the slide rule this week, the slide rule seemed to no longer be the 'tool' that I thought it was.

I am in awe of human beings' and how we are given the gifts of thinking and creation. I am also so aware that the 'tool' may be an extension of our entire body as a learning system - this includes not only physical acts but also mental acts. I wonder if the maps, the quipu, the algorithms, the slide rules, the ploughs, the hoes are all tools to make visible the narratives that live in our bodies? Human beings create tools in order to communicate the ideas and actions that they live. Even 'numbers' in this sense can be tools as I believe that they were developed to 'make visible' the meaning of quantity. A formula can be a tool, as it makes visible a relationship that human beings have discovered. Eventually some 'tools' are 'taken up' as signifying something of significance for the collective; or for the community.  However, other 'tools' are developed and not taken up as they do not emerge as 'significant' at the collective, or communal, level.