The development of reasoning skills during compulsory 16 to 18 mathematics education

Keogh

Eccleston

2019

PAIN

Self Cite

Pain disrupts attention in order to prioritise avoidance of harm and promote analgesic behaviour. This could in turn have negative effects on higher-level cognitions which rely on attention. In the current paper we examined the effect of thermal pain induction on three measures of reasoning: the Cognitive Reflection Test, Belief Bias Syllogisms task, and Conditional Inference task. In Experiment 1, the thermal pain was set at each participant's pain threshold. In Experiment 2, it was set to a minimum of 44°C or 7/10 on a VAS scale (whichever was higher). In Experiment 3, performance was compared in no pain, low intensity pain, and high intensity pain conditions. We predicted that the experience of pain would reduce correct responding on the reasoning tasks. However, this was not supported in any of the three studies. We discuss possible interpretations of our failure to reject the null hypothesis and the importance of publishing null results.

Section: Reasoning In Painmentioning

confidence: 99%

Section: Belief Bias Syllogisms Taskmentioning

confidence: 99%

Section: Raven's Matricesmentioning

confidence: 99%

See 1 more Smart Citation

An investigation of the effect of experimental pain on logical reasoning

Keogh

Eccleston

2019

PAIN

Self Cite

“…It is quite plausible, for instance, that different mathematical topics, pedagogies or cultures support the development of different general reasoning skills: perhaps the study of core topics in A-level mathematics improves conditional reasoning, but other topics have better effects for this or other types of task. For example, in Cyprus where the 16-18 mathematics curriculum has a substantial deductive geometry component, students' abstract conditional reasoning skills improved in line with the normative model of the conditional to a greater extent than in A-level students in the UK (Attridge, Doritou & Inglis, 2015;Attridge & Inglis, 2013). The Cypriot students also showed a reduction in belief bias on a thematic syllogisms task (Attridge, Doritou & Inglis, 2015).…”

Section: Discussionmentioning

confidence: 97%

“…For example, in Cyprus where the 16-18 mathematics curriculum has a substantial deductive geometry component, students' abstract conditional reasoning skills improved in line with the normative model of the conditional to a greater extent than in A-level students in the UK (Attridge, Doritou & Inglis, 2015;Attridge & Inglis, 2013). The Cypriot students also showed a reduction in belief bias on a thematic syllogisms task (Attridge, Doritou & Inglis, 2015). Possibilities of this nature should truly interest mathematics education advocates, who could use evidence to provide detailed recommendations about preparation that might benefit students with different existing skills and different career aspirations.…”

Section: Discussionmentioning

confidence: 99%

Support with caveats: advocates’ views of the Theory of Formal Discipline as a reason for the study of advanced mathematics

Wainwright

Research in Mathematics Education

Wainwright

et al. 2017

Self Cite

The Theory of Formal Discipline (TFD) suggests that studying mathematics improves general thinking skills. Empirical evidence for the TFD is sparse, yet it is cited in policy reports as a justification for the importance of mathematics in school curricula. The study reported in this paper investigated the extent to which influential UK advocates for mathematics agree with the TFD and their views on the arguments and evidence that surround it. Quantitative and qualitative analysis of data from structured interviews revealed four themes: broad endorsement of the TFD; reference to supportive employment data; the possibilities that mathematics education might not always effectively develop reasoning and that study of other subjects might have similar effects; and concerns about causality and the extent of the evidence base. We conclude that advocates broadly support the TFD despite being aware of its limitations.

Refutations and Reasoning in Undergraduate Mathematics

Alcock

Int. J. Res. Undergrad. Math. Ed.

2023

This paper concerns undergraduate mathematics students’ understandings of refutation and their related performance in abstract conditional inference. It reports on 173 responses to a refutation instrument that asked participants to: 1) state ‘true’ or ‘false’ for three statements, providing counterexamples or reasons if they thought these false (all three were false); 2) evaluate possible counterexamples and reasons, where reasons were ‘corrected’ versions of the statements but not valid refutations; and 3) choose which of the counterexamples and the corrected statements were better answers, explaining why. The data show that students reliably understood the logic of counterexamples but did not respond normatively according to the broader logic of refutations. Many endorsed the corrected statements as valid and chose these as better responses; we analyse their explanations using Toulmin’s model of argumentation. The data further show that participants with better abstract conditional inference scores were more likely to respond normatively by giving, endorsing, and choosing counterexamples as refutations; conditional inference scores also predicted performance in a proof-based course.