Brian -

Thirty years ago, I chanced upon the following assertion by Spengler (in Bloor 1983) that:

"... if we appreciate each culture in its individuality we will realise that the unshakable truths and convictions of its members are but expressions of one specific existence and one only ... [for example] Mathematics is not a universal thing; there is not, and cannot be, number as such. There are different number worlds and the character of a piece of mathematics depends wholly on the culture in which it is rooted, the sort of mankind it is that ponders it ..."

Bloor, D. (1983) Wittgenstein: a social theory of knowledge. Columbia: Columbia University Press.

Thirty years later, through reading the current iteration of your paper - and grasping (for example) the significance of Figure 4 - I finally understand what Spengler was talking about. Thank you.

While it is not a standard ‘EJOLTS’ account of a living theory research enquiry, for me, your paper ‘works’ - but within its own frame of reference. This is where I have an area of concern. The Abstract states – “This article sets out to investigate the relationship between Living Theory and mathematics”. The Keywords section includes ‘Mathematics’ and ‘Living Educational Theory’. However, a word search for ‘living’ within the main text highlights: ‘Living Mathematics’; ‘Living Values’; Living Contradiction; ‘Living Visual Taxonomy’; ‘Living Narrative’. By contrast, there are just four instances of the term ‘living [educational] theory’. i.e.

1. This is suggesting that living [educational] theories can be built on the top of a mathematical form.

2. I believe that using a mathematical lens to gain an awareness of the world outside of myself, for example, the learning interactions of others or of quantitative genetics, can be made more beneficial by the living theory methodology.

3. Integrative education: I can suggest ways in which art and my living educational theories can support the ST∑@M (Science Technology Engineering Art and Mathematics) integrative education movement (Yakman, 2008) potentially empowering learners to engage with mathematics communicating their lived experiences through the integration of a range of artistic medium …

4. Reverse-engineering: … concepts that are traditionally mathematically sophisticated may be more clearly understood, unravelled and demystified, using the living theory approach.

None of these references engages directly with the “… relationship between Living Theory and mathematics” as stated in the Abstract.

The conclusion states: “This article has argued that a collaboration between living theory, applied statistics and mathematics may enrich the applicability, validity and purposefulness of mathematical models as a creative medium and an organic tool.” The main text uses the terms ‘Living Mathematics’, ‘Living Values’, Living Contradiction, ‘Living Visual Taxonomy’ and ‘Living Narrative’ - I would like to see a firmer connection with your own living-educational-theory or with the overarching Living Educational Theory per se. This firmer connection could be achieved with the help of just four additions to the quotations 1-4 above to make these oblique references to living theory explicit to your practice.

In short, my question is: What makes this paper a living theory research paper? Apart from this lingering question - I like it; I think that it ticks all the review criteria . . . but in a round-about sort of way. Can you make it more head-on?

Best wishes

- Pete