Social foundations of the mathematics curriculum: a rationale for change

The nature of educational aims as criteria for worthwhile curriculum practice is explored and a cross-section of aims for mathematics education is discussed. An aim for mathematics education which emphasises the social aspect of the subject in its being, its conduct and its applications is identified and epistemological foundations for such a view of the nature of the subject are explored. It is argued that such an epistemological perspective of mathematics would be reflected in the social context of the mathematics classroom, arising from a methodology in which the subject would become more problematic and open to change, investigation and hypothesis. The aims of two major mathematics curriculum development projects (the Nuffield Mathematics Project and the School Mathematics Project) are examined to determine the extent to which their aims may take the 'social' nature of mathematics into account. The probable social context of mathematics classrooms using their materials is postulated in an attempt to characterise the nature of the subject as it is reflected in these materials. A view of the nature of mathematics held by practising teachers and by pupils is then established by drawing upon, and extrapolating from, evidence relating to the social context of mathematics classrooms at primary and secondary level. Conclusions follow, which suggest that fundamental change in mathematics education requires, as a first step, the adoption of a new epistemological perspective of the subject in order that the pursuit of the aim which emphasises the social nature of mathematics is achieved. It is suggested that this, in turn, ultimately could lead to the desired balance in the mathematics curriculum which hitherto has been lacking

Quantitative agreement in the detection of the N1 peak (primary outcomes).

<p>The boundaries of the boxes indicate the 25^th and 75^th percentiles, the line within the box marks the median, the whiskers indicate the 10^th and 90^th percentiles and the circles above and below represent outliers (<i>n</i> = 16 for each index). Horizontal lines on top of the bars represent statistically significant post hoc differences between pairings (Student-Newman-Keuls, <i>p</i> < 0.05). LoA: limits of agreement, CV: coefficient of variation.</p

Effects of stimulation intensity on event-related potential (ERP) recordings.

<p>Each panel shows the average ERP of all available trials from each subject (color-coded) for a single stimulation intensity. The overlapping thick black line represents the grand average of all subjects (<i>n</i> = 16). RTh: nociceptive withdrawal reflex threshold.</p

Single-trial peak amplitude and latency values and number of peaks detected with each method, averaged across stimulation intensities and subjects.

<p>Values are presented as mean ± SD.</p><p>Single-trial peak amplitude and latency values and number of peaks detected with each method, averaged across stimulation intensities and subjects.</p

Categorical agreement in the detection of the N1 peak (primary outcomes).

<p>The boundaries of the boxes indicate the 25^th and 75^th percentiles, the line within the box marks the median, the whiskers indicate the 10^th and 90^th percentiles and the circles above and below represent outliers (<i>n</i> = 16 for each index). Horizontal lines on top of the bars represent statistically significant post hoc differences between pairings (Student-Newman-Keuls, <i>p</i> < 0.05). <i>p</i>_<i>pos</i>: positive percent agreement, <i>p</i>_<i>neg</i>: negative percent agreement, κ: Cohen’s kappa.</p

Comparison of manual and automated ERP feature detection/estimation methods.

<p><b>A)</b> Trial-by-trial image of ERP responses of a single subject elicited with the highest stimulation intensity (20 trials). <b>B-E)</b> Performance of OBS1, OBS2, DRIV and WVLT methods, respectively, on the detection/estimation of single-trial ERP features of a single subject elicited with the highest stimulation intensity. Crosses, circles and asterisks represent single-trial N1, N2 and P2 features, respectively, while the blue trace is the average of 20 trials. Note that WVLT algorithm did not detect the N2 peak in <b>E)</b>.</p