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A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students.

ABSTRACT: School mathematics comprises a diversity of concepts whose cognitive complexity is still poorly understood, a chief example being fractions. These are typically taught in middle school, but many students fail to master them, and misconceptions frequently persist into adulthood. In this study, we investigate fraction comparison, a task that taps into both conceptual and procedural knowledge of fractions, by looking at performance of highly mathematically skilled young adults. Fifty-seven Chilean engineering undergraduate students answered a computerized fraction comparison task, while their answers and response times were recorded. Task items were selected according to a number of mathematically and/or cognitively relevant characteristics: (a) whether the fractions to be compared shared a common component, (b) the numerical distance between fractions, and (c) the applicability of two strategies to answer successfully: a congruency strategy (a fraction is larger if it has larger natural number components than another) and gap thinking (a fraction is larger if it is missing fewer pieces than another to complete the whole). In line with previous research, our data indicated that the congruency strategy is inadequate to describe participants' performance, as congruent items turned out to be more difficult than incongruent ones when fractions had no common component. Although we hypothesized that this lower performance for congruent items would be explained by the use of gap thinking, this turned out not to be the case: evidence was insufficient to show that the applicability of the gap thinking strategy modulated either participants' accuracy rates or response times (although individual-level data suggest that there is an effect for response times). When fractions shared a common component, instead, our data display a more complex pattern that expected: an advantage for congruent items is present in the first experimental block but fades as the experiment progresses. Numerical distance had an effect in fraction comparison that was statistically significant for items without common components only. Altogether, our results from experts' reasoning reveal nuances in the fraction comparison task with respect to previous studies and contribute to future models of reasoning in this task.

SUBMITTER: Morales N

PROVIDER: S-EPMC7315778 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students.

Morales Nicolás N Dartnell Pablo P Gómez David Maximiliano DM

Frontiers in psychology 20200618

School mathematics comprises a diversity of concepts whose cognitive complexity is still poorly understood, a chief example being fractions. These are typically taught in middle school, but many students fail to master them, and misconceptions frequently persist into adulthood. In this study, we investigate fraction comparison, a task that taps into both conceptual and procedural knowledge of fractions, by looking at performance of highly mathematically skilled young adults. Fifty-seven Chilean ...[more]

PMID: 32625137

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Project description:ObjectivesTo investigate levels of distress, depression, anxiety, stress and perception of their current study situation during the COVID-19 pandemic among undergraduate dental and medical students.DesignObservational, cross-sectional study including two consecutive surveys (May and July 2020).SettingA large medical school in Germany.ParticipantsAll first year dental and medical students were invited. 132 participating first year students (44 dental, 88 medical) from the first survey and 150 students (50 dental, 100 medical) from the second were included in our analyses.Primary and secondary outcome measuresMental burden (distress thermometer, Patient Health Questionnaire-4, Perceived Stress Scale-4) and self-reported changes in mental health and perception of study situation during the COVID-19 pandemic (self-developed items) were compared. Open-ended questions were analysed by conventional content analyses.ResultsA considerable proportion of students (t1: May 2020: 84.1%; t2: July 2020: 77.3%) reported distress levels above cut-off. In July 2020, dental students reported significantly higher distress scores than medical students (dental: M=7.0, SD=2.3; medical: M=5.7; SD=2.1; p<0.001). More dental than medical students reported mild, moderate and severe levels of anxiety and depression symptoms. The majority stated that their mental health and study motivation had not changed during the pandemic. Logistic regression showed that being a dental student was significantly associated with a higher likelihood for serious worries regarding the study situation during COVID-19 at t1 (OR 4.0; 95% CI 1.1 to 14.2). At t2 higher distress was significantly associated with a higher likelihood for experiencing serious worries (OR 1.8; 95% CI 1.3 to 2.5). Regarding current concerns related to the pandemic, students most frequently reported difficulties with self-regulated learning (15.2%), study-related worries and uncertainty (14.4%), missing feedback of students and lecturers (11.4%) and lack of practical training (9.8%).ConclusionThe results suggest that high mental burden and the lack of practical training among medical and dental students is an increasing problem, with a possibly even higher urgency in dental students. Tailored psychological and educational support offers during and after the COVID-19 pandemic might help them as they progress through (medical and) dental school.

Dataset Information

A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students.

Publications

A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students.

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