Mathematical anxiety is linked to reduced cognitive reflection: A potential road from discomfort in the mathematics classroom to susceptibility to biases

Background
When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181–185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25–42, 2005). The CRT is a measure of a person’s ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking.

Methods
In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs.

Results
Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1–3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection.

Conclusions
Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals’ ability to make advantageous choices and good decisions.

Late industrialization and the increased merit selection hypothesis - Ireland as a test case

The Irish case provides a particularly appropriate test of the increasing merit selection hypothesis deriving from the liberal theory of industrialization. This is so not only because the lateness and speed of economic change allows us to capture such change through a set of national surveys conducted in the past three decades, but also because such change was based on a sustained policy of increased openness to international competitive forces. The functional requirements of the economy and a rapid increase in the supply of those with higher educational qualifications provided an ideal context in which to observe the movement from ascription to achievement predicted by the liberal theory. However, while changes in the class structure and a rapid expansion of educational opportunity had significant consequences in terms of absolute mobility, there was no evidence of a significant shift towards meritocratic principles. At the same time as the service class increased their advantage over other classes in the pursuit of educational qualifications, the impact of educational qualifications on class destination diminished. Controlling for education, we find that the impact of class origin effects is substantial and shows little sign of diminishing over time. In our conclusion we discuss the implications of our findings in the context of the recent debate on meritocracy.

Summary statistics, educational achievement gaps and the ecological fallacy

Summary statistics continue to play an important role in identifying and monitoring patterns and trends in educational inequalities between differing groups of pupils over time. However, this article argues that their uncritical use can also encourage the labelling of whole groups of pupils as ‘underachievers’ or ‘overachievers’ as the findings of group-level data are simply applied to individual group members, a practice commonly termed the ‘ecological fallacy’. Some of the adverse consequences of this will be outlined in relation to current debates concerning gender and ethnic differences in educational attainment. It will be argued that one way of countering this uncritical use of summary statistics and the ecological fallacy that it tends to encourage, is to make much more use of the principles and methods of what has been termed ‘exploratory data analysis’. Such an approach is illustrated through a secondary analysis of data from the Youth Cohort Study of England and Wales, focusing on gender and ethnic differences in educational attainment. It will be shown that, by placing an emphasis on the graphical display of data and on encouraging researchers to describe those data more qualitatively, such an approach represents an essential addition to the use of simple summary statistics and helps to avoid the limitations associated with them.