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. 2020 Dec 18:11:574366.
doi: 10.3389/fpsyg.2020.574366. eCollection 2020.

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

Bert Jonsson  1   2 , Carina Granberg  1   2 , Johan Lithner  2   3
Affiliations

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

Bert Jonsson et al. Front Psychol. .

Abstract

In the field of mathematics education, one of the main questions remaining under debate is whether students' development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students' math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students' performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students' learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension.

Keywords: cognitive proficiency; creative mathematical reasoning; fluid intelligence; rote learning; working memory.

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Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Figures

FIGURE 1
FIGURE 1
(A–C) Examples of AR and CMR practice tasks and how they were presented to the students on their laptop screen. (A) AR practice task; (B) CMR practice task; (C) CMR task asking for the formula.
FIGURE 2
FIGURE 2
(A–D) Examples of test tasks and how they were presented to the students on their laptop screen. (A,C) Practiced test tasks and (B,D) transfer test task.
See this image and copyright information in PMC

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