Math anxiety

Mathematics is often perceived as a difficult subject by many students, parents and teachers alike. Difficulties with the subject are most often attributed to cognitive factors (lack of ability, preparedness, practice and knowledge). Emotional factors are often overlooked and are easily written off as potential persistent and serious causes of mathematical learning difficulties. However, it is increasingly recognized in psychology and education that several students have serious negative emotional reactions to mathematics. These emotional problems can lead to performance difficulties and/or can become obstacles that discourage students from further mathematics training even if their performance is good. This debilitating emotional reaction to mathematics is termed “mathematics anxiety” (MA). MA is “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in… ordinary life and academic situations” (Richardson and Suinn, 1972). MA ranges from the feeling of mild tension to experiencing strong fear. MA is not restricted to classroom situations or to children. Rather, MA can generalize to out of school situations and can affect adults. For example, MA can manifest itself in everyday situations about handling numbers such as when counting change in shops or doing basic mathematics under time pressure. MA is often present in normally performing students, discouraging them from choosing math related careers. A structured universal prevention program for MA does not yet exist. Most of the activities we suggest here are based on the principles of Cognitive Behavioural Therapy (CBT) and the Rational Emotive Behaviour Therapy (REBT). These methods help individuals to identify self-defeating thoughts and feelings, challenge the rationality of those feelings, and replace them with more productive beliefs

A Tutorial on Hunting Statistical Significance by Chasing N.

There is increasing concern about the replicability of studies in psychology and cognitive neuroscience. Hidden data dredging (also called p-hacking) is a major contributor to this crisis because it substantially increases Type I error resulting in a much larger proportion of false positive findings than the usually expected 5%. In order to build better intuition to avoid, detect and criticize some typical problems, here I systematically illustrate the large impact of some easy to implement and so, perhaps frequent data dredging techniques on boosting false positive findings. I illustrate several forms of two special cases of data dredging. First, researchers may violate the data collection stopping rules of null hypothesis significance testing by repeatedly checking for statistical significance with various numbers of participants. Second, researchers may group participants post hoc along potential but unplanned independent grouping variables. The first approach 'hacks' the number of participants in studies, the second approach 'hacks' the number of variables in the analysis. I demonstrate the high amount of false positive findings generated by these techniques with data from true null distributions. I also illustrate that it is extremely easy to introduce strong bias into data by very mild selection and re-testing. Similar, usually undocumented data dredging steps can easily lead to having 20-50%, or more false positives.DS is supported by the James S. McDonnell Foundation

Statistical reform and the replication crisis

The replication crisis has prompted many to call for statistical reform within the psychological sciences. Here we examine issues within Frequentist statistics that may have led to the replication crisis, and we examine the alternative---Bayesian statistics---that many have suggested as a replacement. The Frequentist approach and the Bayesian approach offer radically different perspectives on evidence and inference with the Frequentist approach prioritising error control and the Bayesian approach offering a formal method for quantifying the relative strength of evidence for hypotheses. We suggest that rather than mere statistical reform, what is needed is a better understanding of the different modes of statistical inference and a better understanding of how statistical inference relates to scientific inference

When Null Hypothesis Significance Testing Is Unsuitable for Research: A Reassessment.

Null hypothesis significance testing (NHST) has several shortcomings that are likely contributing factors behind the widely debated replication crisis of (cognitive) neuroscience, psychology, and biomedical science in general. We review these shortcomings and suggest that, after sustained negative experience, NHST should no longer be the default, dominant statistical practice of all biomedical and psychological research. If theoretical predictions are weak we should not rely on all or nothing hypothesis tests. Different inferential methods may be most suitable for different types of research questions. Whenever researchers use NHST they should justify its use, and publish pre-study power calculations and effect sizes, including negative findings. Hypothesis-testing studies should be pre-registered and optimally raw data published. The current statistics lite educational approach for students that has sustained the widespread, spurious use of NHST should be phased out

Understanding Mathematics Anxiety: Investigating the experiences of UK primary and secondary school students

The project investigated individuals’ attitudes towards mathematics because of what could be referred to as a “mathematics crisis” in the UK. Evidence suggests that functional literacy skills amongst working-age adults are steadily increasing but the proportion of adults with functional maths skills equivalent to a GCSE grade C has dropped from 26% in 2003 to only 22% in 2011 (National Numeracy, 2014). This number is strikingly low compared with the 57% who achieved the equivalent in functional literacy skills (National Numeracy, 2014)

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature.

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth "strategy selection") in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research

Motor conflict in Stroop tasks: Direct evidence from single-trial electro-myography and electro-encephalography

Several brain imaging studies have assumed that response conflict is present in Stroop tasks. However, this has not been demonstrated directly. We examined the time-course of stimulus and response conflict resolution in a numerical Stroop task by combining single-trial electro-myography (EMG) and event-related brain potentials (ERP). EMG enabled the direct tracking of response conflict and the peak latency of the P300 ERP wave was used to index stimulus conflict. In correctly responded trials of the incongruent condition EMG detected robust incorrect response hand activation which appeared consistently in single trials. In 50–80% of the trials correct and incorrect response hand activation coincided temporally, while in 20–50% of the trials incorrect hand activation preceded correct hand activation. EMG data provides robust direct evidence for response conflict. However, congruency effects also appeared in the peak latency of the P300 wave which suggests that stimulus conflict also played a role in the Stroop paradigm. Findings are explained by the continuous flow model of information processing: Partially processed task-irrelevant stimulus information can result in stimulus conflict and can prepare incorrect response activity. A robust congruency effect appeared in the amplitude of incongruent vs. congruent ERPs between 330–400 ms, this effect may be related to the activity of the anterior cingulate cortex

An event-related brain potential study of arithmetic syntax

Number cognition is important both for the society and for the individual. The disorder of number cognition (developmental dyscalculia) can have major impact on individual life quality. Several children and adults experience problems with one aspect of ‘arithmetic syntax’, the representation of place value structure. Here we provide the first cognitive neuroscience investigation of place value representation. Our study systematically contrasted semantic (the numerical distance effect) and syntactic (place value structure) violations in a mental addition verification task. Participants verified additions with four-digit numbers. Semantic incongruencies elicited the N400 ERP effect. A centro-parietal (putative P600) effect to place-value violations was not related to arithmetic syntax. Rather, this effect was an enlarged P3b reflecting different surprise values of place value vs. non-place value violations. This potential confound should be considered in numerical cognition experiments. The latency of the N400 and P3a effects were differentially affected by place-value analysis. The amplitude of the P3a and that of a fronto-central positive effect (FP600) was sensitive to place value analysis and digit content. Results suggest that ERPs can index the syntactical analysis of multi-digit numbers. Both ERP and behavioral data confirmed that multi-digit numbers were decomposed into their constituent digits, rather than evaluated holistically. These findings enable the detailed investigation of place value representation in both normal and dyscalculic populations

Maths anxiety and subjective perception of control, value and success expectancy in mathematics

Peer reviewed: TruePublication status: PublishedMathematics anxiety (MA) is an academic anxiety related to doing, learning and testing mathematics. MA can negatively affect mathematics performance, motivation and maths-heavy science and technology-related career choices. Previous data suggest that subjective perceptions and interpretations of students are key in the genesis of MA. Here, based on expectancy-value and control-value theory, we aimed to identify potential, theoretically based subjective factors probably key to understanding MA. We analysed data from 151 745 fifteen-year-old children from 65 ‘countries and economies' from the Programme for International Student Assessment (PISA) 2012 dataset. Subjective self-perceptions had a stronger relationship with MA than maths achievement. We found that higher MA was associated with lower perceived control over maths activities and lower subjective expectation of success. Surprisingly, children with higher subjective valuation of maths had higher MA for similar levels of subjective control and success expectancy in maths. Results offer an improved understanding of potential antecedents of MA and suggest that effective interventions could be based on gradual confidence building in maths. These could primarily draw on a deeper understanding of the subject improving subjective success expectancy and feeling of control over maths activities. Cultural variation in findings is discussed