Plant construction simulation was conducted by the Homer software, and all three modes of the mathematical models were coded in MATLAB.
The main objective is to develop modes of thinking about mathematical subjects.
Moreover, there is no guarantee that in the future we will not make some kind of breakthrough placing chaos models on a much sounder first principles footing, so there does not seem to be much substance to the claim that chaos explanations are different in kind from other modes of explanation in mathematical physics.
Watson and Barton (2011) might consider this outcome to be the consequence of failing to view mathematical modes of enquiry as fundamental to all mathematical working.
Mathematical modes of enquiry, in contrast, tend to point to mathematical practices as fundamental to developing mathematical understanding.
The case is framed thus because the ways in which mathematical practices and/or mathematical modes of enquiry played out within this dataset was the 'phenomenon … in a bounded context' (Miles and Huberman 1994, p. 25) that I was interested in.
In this 'separate and integrative' frame, where mathematical practices are selectively, rather than fundamentally, drawn upon, it would appear that a possible outcome of sporadic absence of explicit attention to mathematical practices is the disruption of mathematical modes of enquiry.
In combination, a highly localized approach to techniques is seen and further, thinking about quantitative relations appears to come into play only when a procedure is not immediately at hand, pointing to a prioritization of content and techniques over a more fundamental integration of mathematical modes of enquiry.
Thus, while relevant reasoning practices are sporadically evident here relating to rounding and possibly scaling up and reversing downwards, these are not set holistically within either the quantitative reasoning (Schifter 2011) or the strategic working (Kilpatrick et al. 2001) that are described as part of the mathematical practices canon or mathematical modes of enquiry frame.
However, comments from other teachers suggest that the phenomena that he provided a case of - the ability to produce and expand a repertoire related to some mathematical practices without an overall shift in orientation towards mathematical modes of enquiry - were more widespread.
