Abstract
A large portion of mathematics education centers heavily around imitative reasoning and rote learning, raising concerns about students’ lack of deeper and conceptual understanding of mathematics. To address these concerns, there has been a growing focus on students learning and teachers teaching methods that aim to enhance conceptual understanding and problem-solving skills. One suggestion is allowing students to construct their own solution methods using creative mathematical reasoning (CMR), a method that in previous studies has been contrasted against algorithmic reasoning (AR) with positive effects on test tasks. Although previous studies have evaluated the effects of CMR, they have ignored if and to what extent intrinsic cognitive motivation play a role. This study investigated the effects of intrinsic cognitive motivation to engage in cognitive strenuous mathematical tasks, operationalized through Need for Cognition (NFC), and working memory capacity (WMC). Two independent groups, consisting of upper secondary students (N = 137, mean age 17.13, SD = 0.62, 63 boys and 74 girls), practiced non-routine mathematical problem solving with CMR and AR tasks and were tested 1 week later. An initial t-test confirmed that the CMR group outperformed the AR group. Structural equation modeling revealed that NFC was a significant predictor of math performance for the CMR group but not for the AR group. The results also showed that WMC was a strong predictor of math performance independent of group. These results are discussed in terms of allowing for time and opportunities for struggle with constructing own solution methods using CMR, thereby enhancing students conceptual understanding.
Highlights
A solid grasp of mathematics is a valuable life skill and a foundational goal of the Swedish national curriculum (Skolverket, 2019; The Swedish National Agency for Education)
Mathematical Reasoning education still centers around memorization and repetition, denoted as rote learning, rather than conceptual understanding (Bergqvist, 2007; Bergqvist and Lithner, 2012; Boesen et al, 2014)
Based on previous finding that cognitive ability is a strong predictor of performance but is independent of practice conditions (CMR/algorithmic reasoning (AR)) and the assumption that practicing with creative mathematical reasoning (CMR) tasks include struggle and that high Need for Cognition (NFC) is associated with more complex task solving strategies, we posed three hypotheses: (1) practicing with CMR tasks is hypothesized to be superior to practicing with AR tasks on subsequent test performance (2) working memory capacity (WMC) is hypothesized to significantly predict test performance, independent of group
Summary
A solid grasp of mathematics is a valuable life skill and a foundational goal of the Swedish national curriculum (Skolverket, 2019; The Swedish National Agency for Education). In a study by Jäder et al (2019) examining mathematic textbooks from 12 countries, it was discovered that most tasks (79%) could be solved using predefined solutions or algorithms, and an additional 13% of tasks required only minor tweaking of a previously provided template This reliance on rote learning and imitation-based reasoning implies that when facing a task, students often problem-solve by recalling and applying algorithms they have previously memorized, based on perceived similarities to older tasks, but with little conceptual understanding of those algorithms (Lithner, 2008; Boesen et al, 2010). Based on previous finding that cognitive ability is a strong predictor of performance but is independent of practice conditions (CMR/AR) and the assumption that practicing with CMR tasks include struggle and that high NFC is associated with more complex task solving strategies, we posed three hypotheses: (1) practicing with CMR tasks is hypothesized to be superior to practicing with AR tasks on subsequent test performance (2) WMC is hypothesized to significantly predict test performance, independent of group. (3) NFC is hypothesized to significantly predict test performance for the CMR group but not the AR group
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
