British Academy published today report Society Counts: Quantitative Skills in the Social Sciences and Humanities (link to full text). A quote:

20. The British Academy has frequently emphasised the need for well-rounded graduates, equipped with core skills, if the UK is to retain its status in research and higher education.
21. These core skills start with quantitative methods. The skills standardly deployed, for example, in the natural sciences and engineering are no longer synonymous with or restricted to particular subjects; these skills are now relevant and necessary well beyond traditional science, technology, engineering and mathematics (STEM ) subjects. The changes required to develop these skills in graduates is relevant across the university curriculum. We must therefore seek to apply some of the methods and thinking

that are being used to bring about curriculum change through the STEM initiative.

(Link to full text of the Report)

# School maths is failing children – a US and Australian perspective

A post by Jon Borwein and David H. Bailey in The Conversation. A quote:

## Pedagogy and mathematics

It is undeniably important that mathematics teachers have mastered the topics they need to teach. The new Australian national curriculum is misguidedly increasing the amount of “statistics” of the school mathematics curriculum from less that 10% to as much as 40%. Many teachers are far from ready for the change.

But more often than not, the problem is not the mathematical expertise of the teachers. Pedagogical narrowness is a greater problem. Telling that there is a correct idea in a wrong solution to a problem on fractions requires unpacking of elementary concepts in a way that even an expert mathematician is not usually trained to do.

One of us – Jon – learned this only too well when he first taught future elementary school teachers their final university mathematics course.

Australian teachers at an elite private school could not understand one of Jon’s daughter’s Canadian long-division method nor her solution techniques for many advanced school topics. She got mediocre marks during the year because of this.

# Distribution of abilities

From the Abstract of the paper The best and the rest: revisiting the norm of normality of individual performance, Ernest O’Boyle Jr. and Herman Aguinis:

We revisit a long-held assumption in human resource management, organizational behavior, and industrial and organizational psychology that individual performance follows a Gaussian (normal) distribution. We conducted 5 studies involving 198 samples including 633,263 researchers,
entertainers, politicians, and amateur and professional athletes. Results are remarkably consistent across industries, types of jobs, types of performance measures, and time frames and indicate that individual performance is not normally distributed—instead, it follows a Paretian (power law) distribution. Assuming normality of individual
performance can lead to misspecified theories and misleading practices. Thus, our results have implications for all theories and applications that directly or indirectly address the performance of individual workers including performance measurement and management, utility
analysis in preemployment testing and training and development, personnel selection, leadership, and the prediction of performance, among others.

I am all in marking exams just now and am not able to look into the paper carefully.

Some thoughts though.

The general thesis of non-normality is fine but it is like claiming that the Earth orbits the Sun.

Calibrated measures, such as IQ and many psychological tests, almost by definition are normal in populations (in fact, in the population for which they are developed). There are underlying assumptions, of course, but the point is that they are taylored to be such. Also, exam performance may be calibrated to look like normal by appropriate choice of the set of questions and allocation of marks.

Looking at Study 1, for example, it is ridiculous to talk about normal distribution. Firstly, before looking at the data we know that they are non-negative and generally with small values. The methodology of selecting “leading” journals” makes the numbers even smaller. Before critisising I should think more but a selective procedure invalidates basic assumptions about validity of normal approximation.

The histograms shown towards the end of Study 1 clearly show this. These histograms should have been put at the beginning of the study. The mean and the standard deviation are almost meaningless for this kind of data (counts, maximum at low values). If anything, the histograms suggest starting with exponential or Gamma, and discard the normal outright. Pareto is fine, as well.

Also, using $$\chi^2$$ to evaluate the quality of the fit is primitive.

By the way, the fact that Pareto is better than normal does not show that it is any good. Any of the distributions mentioned above will be better than normal.

As it happens, I recently a second year Assignment for Practical Statistics, where students do this kind of thing (fitting exponential distributions, evaluating the fit). They would not have got good marks for using $$\chi^2$$ test. QQ-plots and Kolmogorov Smirnov type tests are much better.

Students certainly do not get good marks if they simply fit a distribution and do not evaluate the quality of the fit.