Profiles of Cognitive Flexibility in Arithmetic Reasoning: A Cross-Country Comparison of German and American Elementary Students

doi:10.26711/007577152790009

Cited by 7 publications

(2 citation statements)

References 14 publications

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“…Which aspects can be promoted in the development of an understanding of numbers and arithmetic with the help of the fingers, which cannot? While neuroscientific and cognitive-psychological studies often seem to focus exclusively on the correctness of the result (e g., Käser et al, 2013 ), the declared aim of mathematics education is the development of flexible mental calculation and thus the focus on diverse solution paths from the very beginning (e g., Selter, 2000 ; Anghileri, 2001 ; Baroody, 2003 ; Rathgeb-Schnierer and Green, 2017 ).…”

Section: Beyond Cardinal and Ordinal Aspectsmentioning

confidence: 99%

The Benefits of an Interdisciplinary Approach to Mathematics Education on Issues Around Computation in School

Martignon

Rechtsteiner²

2022

Front. Psychol.

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We present arguments in favor of an interdisciplinary approach in mathematics education. As an instance, we briefly recall how cognitive neuropsychologists promoted intense finger gnosis acquisition, i.e., acquiring the ability to mentally represent one’s fingers, at an early age. Mathematics educators definitely recommended the development of finger gnosis but examined its limits. They also presented arguments in favor of developing flexible mental calculation as a goal of arithmetical instruction in elementary school. In this context we describe the training of “Zahlenblick” as a way to foster flexible mental calculation and connect it with concepts from the theory of metacognition. We illustrate how precisely this branch of metacognition demands further interdisciplinary research. In our analysis, “Zahlenblick” extends to acquiring an eye for proportions, beyond just whole numbers. We illustrate how useful it would be to better understand the neural underpinnings responsible for the advantages of so-called natural frequencies, compared with percentages or probabilities, and of icon arrays for representing them. Such natural frequencies are adequate formats for the early confrontation with decision-making under risk.

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Section: Beyond Cardinal and Ordinal Aspectsmentioning

confidence: 99%

The Benefits of an Interdisciplinary Approach to Mathematics Education on Issues Around Computation in School

Martignon

Rechtsteiner²

2022

Front. Psychol.

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“…Observou-se também que todos os recursos do raciocínio por características do problema foram usados pelos dois anos escolares, com menores proporções no 2º ano e maiores no 4º ano, ou seja, de modo geral, estes recursos cognitivos, ou ações mentais, já estavam disponíveis para as crianças mais novas e o seu uso foi ampliado pelas crianças mais velhas (Caviola et al, 2018;McMullen et al, 2016). Acredita-se que tal achado esteja relacionado ao nível de experiência numérica dos estudantes (Rathgeb-Schnierer & Green, 2017). Embora o conhecimento numérico tenha se destacado nos resultados, os procedimentos de solução também evidenciaram as fragilidades deste conhecimento nos estudantes brasileiros, pois houve alta proporção de contagem, considerada a mais imatura das estratégias de cálculo (Threfall, 2002).…”

Section: Considerações Finaisunclassified

Different Profile of Cognitive Flexibility in Brazilian Students of 2nd and 4th Years of Ensino Fundamental

Teixeira Nunes,

De Assis,

Vellinho Corso

2022

RELIME

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Este artículo tiene como objetivo identificar, caracterizar y comparar el perfil de flexibilidad cognitiva los cálculos mentales de los estudiantes brasileños, en función del análisis de elementos cognitivos, a saber, las características de los problemas y los procedimientos de solución, utilizados durante la resolución de cálculos aritméticos. La muestra de este estudio incluyó 42 estudiantes de segundo año (7 a 8 años) y 42 estudiantes de cuarto año (9 a 11 años), de cuatro escuelas públicas en Porto Alegre. Se alentó a cada niño a clasificar 12 cálculos aritméticos, demostrando su conocimiento numérico al explicar el razonamiento involucrado en la resolución, a través de un instrumento de evaluación específico sobre la flexibilidad cognitiva. Los resultados revelaron que las diferencias en las proporciones de uso del conocimiento numérico diferenciaban los perfiles de flexibilidad cognitiva: flexible, mixto o rígido.

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Danish third, sixth and eighth grade students’ strategy adaptivity, strategy flexibility and accuracy when solving multidigit arithmetic tasks

Jóelsdóttir,

Andrews

2023

Eur J Psychol Educ

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In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn from twenty demographically different schools. Drawing on a tri-phase assessment tool, each student completed a series of tasks designed to elicit shortcut strategies. First, students solved each task by means of their preferred strategy; those using shortcut strategies were construed as adaptive for that task. Second, students solved the same tasks by means of whatever alternative strategies they had available; those offering at least two strategies were construed as flexible for that task. Third, for each task, students were asked to indicate which of their strategies they believed was optimal. Across all grades, students were more flexible than adaptive. Overall, sixth graders exhibited higher levels of flexibility than third graders and marginally lower levels than eighth graders. Sixth graders exhibited higher levels of adaptivity than those in either grade three or grade eight. Students’ accuracy, which improved with maturation, was influenced positively by both adaptivity and flexibility, with flexibility having the greatest influence in grade three and adaptivity in grade six. The findings raise further questions concerning, inter alia, culture’s influence on students’ strategy choices and the interaction of adaptivity, flexibility and maturity on accuracy.

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Profiles of Cognitive Flexibility in Arithmetic Reasoning: A Cross-Country Comparison of German and American Elementary Students

Abstract: Flexibility in performing mental calculations has become an important topic for research in mathematics education

Cited by 7 publications

References 14 publications

The Benefits of an Interdisciplinary Approach to Mathematics Education on Issues Around Computation in School

The Benefits of an Interdisciplinary Approach to Mathematics Education on Issues Around Computation in School

Different Profile of Cognitive Flexibility in Brazilian Students of 2nd and 4th Years of Ensino Fundamental

Danish third, sixth and eighth grade students’ strategy adaptivity, strategy flexibility and accuracy when solving multidigit arithmetic tasks

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