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Translating Cyclic Mathematical Representations: Effects on Students' Learning Outcomes and Cognitive Processes in Covariation Problem-Solving

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Title: Translating Cyclic Mathematical Representations: Effects on Students' Learning Outcomes and Cognitive Processes in Covariation Problem-Solving
Language: English
Authors: Abdul Wahab, Subanji, Sisworo
Source: Journal of Teaching and Learning. 2026 20(2):119-137.
Availability: Journal of Teaching and Learning. 401 Sunset Ave. Faculty of Education, University of Windsor, Windsor, Ontario, Canada N9B 3P4. Tel: 519-253-3000 Ext. 4068; e-mail: jtl@uwindsor.ca; Web site: https://ojs.uwindsor.ca/index.php/JTL
Peer Reviewed: Y
Page Count: 19
Publication Date: 2026
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Problem Solving, Cognitive Processes, Outcomes of Education, Mathematics, Mathematics Instruction, College Students, Foreign Countries, Graphs, Tables (Data)
Geographic Terms: Indonesia
ISSN: 1492-1154
1911-8279
Abstract: Research on students' understanding of covariation has primarily focused on static, linear models, overlooking the cognitive challenges of translating dynamic and cyclical representations. Despite their relevance to real-world applications, few studies have examined how students process covariational relationships in cyclic contexts, thereby limiting the development of effective strategies to improve their problem-solving abilities. Using a sequential mixed-methods design, the study was conducted with 53 first-semester students at STKIP PGRI Sumenep in Indonesia, during the 2024/2025 academic year. Data were collected through pre-tests and post-tests to measure changes in problem-solving performance, along with a closed-ended questionnaire administered to all students and structured interviews with six selected participants, which provided deeper insights into the cognitive processes involved. The findings revealed significant improvements in students' ability to interpret and solve covariation problems after engaging in tasks that required translating between cyclic graphical and tabular representations. Specifically, students demonstrated improved learning outcomes in recognizing periodicity, understanding variable interdependence, and applying functional reasoning in cyclical contexts. The cognitive analysis indicated that tasks involving representation translation helped students engage more deeply with the cyclical nature of mathematical relationships. These results suggest that focused instruction on representation translation can foster stronger cognitive engagement with complex mathematical concepts. The study emphasizes the importance of incorporating cyclic models into early mathematics instruction and recommends that curriculum developers prioritize representational fluency. Further research is needed to explore the broader implications of such instructional strategies in diverse mathematical contexts. [Note: The page range (119-139) shown on the PDF is incorrect. The correct page range is 119-137.]
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1508176
Database: ERIC
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  Data: Journal of Teaching and Learning. 401 Sunset Ave. Faculty of Education, University of Windsor, Windsor, Ontario, Canada N9B 3P4. Tel: 519-253-3000 Ext. 4068; e-mail: jtl@uwindsor.ca; Web site: https://ojs.uwindsor.ca/index.php/JTL
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  Data: Research on students' understanding of covariation has primarily focused on static, linear models, overlooking the cognitive challenges of translating dynamic and cyclical representations. Despite their relevance to real-world applications, few studies have examined how students process covariational relationships in cyclic contexts, thereby limiting the development of effective strategies to improve their problem-solving abilities. Using a sequential mixed-methods design, the study was conducted with 53 first-semester students at STKIP PGRI Sumenep in Indonesia, during the 2024/2025 academic year. Data were collected through pre-tests and post-tests to measure changes in problem-solving performance, along with a closed-ended questionnaire administered to all students and structured interviews with six selected participants, which provided deeper insights into the cognitive processes involved. The findings revealed significant improvements in students' ability to interpret and solve covariation problems after engaging in tasks that required translating between cyclic graphical and tabular representations. Specifically, students demonstrated improved learning outcomes in recognizing periodicity, understanding variable interdependence, and applying functional reasoning in cyclical contexts. The cognitive analysis indicated that tasks involving representation translation helped students engage more deeply with the cyclical nature of mathematical relationships. These results suggest that focused instruction on representation translation can foster stronger cognitive engagement with complex mathematical concepts. The study emphasizes the importance of incorporating cyclic models into early mathematics instruction and recommends that curriculum developers prioritize representational fluency. Further research is needed to explore the broader implications of such instructional strategies in diverse mathematical contexts. [Note: The page range (119-139) shown on the PDF is incorrect. The correct page range is 119-137.]
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      – Text: English
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      – TitleFull: Translating Cyclic Mathematical Representations: Effects on Students' Learning Outcomes and Cognitive Processes in Covariation Problem-Solving
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