This paper is about teaching probability to students of philosophy who don’t aim to do primarily formal work in their research. These students are unlikely to seek out classes about probability or formal epistemology for various reasons, for example because they don’t realize that this knowledge would be useful for them or because they are intimidated by the material. However, most areas of philosophy now contain debates that incorporate probability, and basic knowledge of it is essential even for philosophers whose (...) work isn’t primarily formal. In this paper, I explain how to teach probability to students who are not already enthusiastic about formal philosophy, taking into account the common phenomena of math anxiety and the lack of reading skills for formal texts. I address course design, lesson design, and assignment design. Most of my recommendations also apply to teaching formal methods other than probability theory. (shrink)

There is a growing consensus that math anxiety highly correlates with trait anxiety and that the emotional component elicited by math anxiety affects math performance. Yet few studies have examined the impact of “specific math anxiety” on math performance and the underlying physiological and affective mechanism. The present study examines the mediation effect of heart rate variability—an affective measurement indexed by respiratory sinus arrhythmia —in the relationship between specific math anxiety and arithmetic speed. A total of 386 junior high school (...) students completed a self-reported questionnaire to measure their anxiety level. Among this sample, 29 individuals with specific math anxiety, 29 with specific reading anxiety, 24 with specific trait anxiety, and 22 controls were selected to participate in an arithmetic task and a reading task while RSA was recorded when they performed the tasks. Results revealed that individuals with specific math anxiety showed lower RSA and longer reaction time than the other three groups in the arithmetic task. Regression and mediation analyses further revealed that RSA mediated the relation between specific math anxiety and arithmetic speed. The present study provides the first account of evidence for the affective hypothesis of specific math anxiety and suggests that affective responses may be an important mechanism underlying the detrimental effect of specific math anxiety on math performance. (shrink)

The under-representation of women in Science, Technology, Engineering, and Mathematics is ubiquitous and understanding the roots of this phenomenon is mandatory to guarantee social equality and economic growth. In the present study, we investigated the contribution of non-cognitive factors that usually show higher levels in females, such as math anxiety and neuroticism personality trait, to numeracy competence, a core component in STEM studies. A sample of STEM undergraduate students, balanced for gender and Intelligent Quotient, completed online self-report questionnaires and a (...) numeracy cognitive assessment test. Results show that females scored lower in the numeracy test, and higher in the non-cognitive measures. Moreover, compared to males’, females’ numeracy scores were more strongly influenced by MA and neuroticism. We also tested whether MA association to numeracy is mediated by neuroticism, and whether this mediation is characterized by gender differences. While we failed to detect a significant mediation of neuroticism in the association between MA and numeracy overall, when gender was added as a moderator in this association, neuroticism turned out to be significant for females only. Our findings revealed that non-cognitive factors differently supported numeracy in females and males in STEM programs. (shrink)

This study examined the effects of opportunity to learn or the content coverage in mathematics on student mathematics anxiety, problem-solving performance, and mathematics performance. The pathways examining the influences of OTL on student problem-solving performance and mathematics performance via mathematics anxiety were also tested. A sample of 1,676 students from Shanghai-China, and a sample of 1,511 students from the United States who participated in the Programme for International Student Assessment 2012 were used for the analyses. The results from multilevel models (...) and path models supported our hypotheses that OTL not only showed significant direct effects on student mathematics anxiety, problem-solving performance, and mathematics performance, but also presented indirect effects on student problem-solving performance and mathematics performance via mathematics anxiety in both Shanghai-China and United States, controlling for student gender, grade, and socioeconomic status. The practical implications of the current results were also discussed. (shrink)

It is well established that math anxiety has a negative relationship with math performance. A few theories have provided explanations for this relationship. One of them, the Attentional Control Theory, suggests that anxiety can negatively impact the attentional control system and increase one's attention to threat-related stimuli. Within the ACT framework, the math anxiety —working memory relationship is argued to be critical for math performance. The present meta-analyses provides insights into the mechanisms of the MA—MP relation and the mediating role (...) of WM. Through database searches with pre-determined search strings, 1,346 unique articles were identified. After excluding non-relevant studies, data from 57 studies and 150 effect sizes were used for investigating the MA—MP correlation using a random-effects model. This resulted in a mean correlation of r = −0.168. The database search of WM as a mediator for the MA—MP relation revealed 15 effects sizes leading to a descriptive rather than a generalizable statistic, with a mean indirect effect size of −0.092. Overall, the results confirm the ACT theory, WM does play a significant role in the MA—MP relationship. (shrink)

Many studies have indicated that mathematics anxiety, and other negative attitudes and emotions toward mathematics, are pervasive and are associated with lower mathematical performance. Some previous research has suggested that working memory is related to both mathematics anxiety and mathematics. Moreover, both gender and chosen course of study appeared likely to influence students’ attitudes to mathematics. In the present study, 40 university undergraduates completed a battery of assessments investigating working memory, attitude to mathematics, test anxiety. and mental and written arithmetic. (...) Attitudes to mathematics were significantly associated with the other variables: working memory, test anxiety, and both measures of mathematical performance. The other variables were not strongly associated with one another. There were no gender differences in mathematical performance, but females exhibited more negative attitudes to mathematics and higher test anxiety than males. After controlling for test anxiety, there ceased to be significant gender differences in attitudes to mathematics. Science students had more positive attitudes to mathematics than humanities students, but the groups did not differ in test anxiety, Science students were better at written but not mental arithmetic. They were also better at working memory, but this was not a significant covariate when the groups were compared on mathematical performance and attitudes to mathematics The results are discussed, with particular focus on implications for future research on influences on mathematics anxiety. (shrink)