Comparing the type of thinking and answers of students in solving proportional problems based on dual processing theory

Subject Areas :

Ali Mohammadian Khatir ¹ , Amir Ali Tabatabaei Adnani ² , Ali Barahmand ³ , Mohammad Ali Faribourzi Araghi ⁴

1 - Ph. D. Candidate in Mathematics Education, Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 - Assistant Professor of Mathematics, Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
3 -
4 - Associate Professor of Mathematics, Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2024-12-23 Accepted : 2025-02-21 Published : 2025-02-23

Keywords: dual processing theory, direct and inverse proportion, disproportion problems.,

Abstract :

Purpose: The purpose of this study is to investigate the type of thinking and responses of seventh grade male and female students based on dual processing theory in solving direct and inverse proportional problems and non-proportional problems and comparing them with each other.

Method: The method of this research was quantitative-descriptive and practical in terms of purpose. Data were collected from 16 seventh grade students from two different public schools from the first period of secondary school. Students were asked to solve 9 open-ended problems, which included 3 direct proportional problems, 3 inverse proportional problems, and 3 non-proportional problems.

Findings: The results showed that in direct and inverse proportional problems and non-proportional problems, the students of both groups answered the questions correctly. In the section of intuitive and inferential answers related to all three types of problems, the group of boys answered the questions more intuitively than the group of girls, but the correct intuitive and inductive answers of the group of girls were more than the group of boys. Also, in non-proportional problems, most of the intuitive and inferential answers of both groups were incorrect. Also, in the examination of 9 questions, it was found that there is a significant difference in questions 3 and 4, and most of the students of the two groups used the intuitive method to answer the questions. But in the rest of the questions, there was no significant difference in students' answers to the questions with intuitive and inferential methods. Conclusion: It can be concluded that the type of thinking used by seventh grade male and female students in solving direct and inverse proportional problems and non-proportional problems based on dual processing theory can lead to better results in education.

References:

احمدی، غلامعلی، ریحانی، ابراهیم، نخستین روحی، ندا. (1394). تأثير آموزش مبتني بر گفتمان رياضي بر توانايي استدلال رياضي دانش‌آموزان دوره ي متوسطه. مجله ي روان شناسي مدرسه، 4(1): 22-37.
اسکمپ، ریچارد. (1989). " فهم رابطه‌ای و فهم ابزاری، ترجمه رضا حیدری قزلجه، گویا، زهرا. (1381). مجله رشد آموزش ریاضی، 15-4.
بازرگان، عباس. (1387). مقدمه‌ای بر روش‌های تحقیق‌های کیفی و آمیخته، رویکردهای متداول در علوم رفتاری. تهران: انتشارات دیدار.
خاکی، غلامرضا. (1383). روش تحقیق در مدیریت، مرکز انتشارات علمی دانشگاه آزاد اسلامی، چاپ سوم.
شیخ الاسلامی، علی، امیدوار، عظیم. (1396). اثربخشی آموزش تفکر انتقادی بر سبک حل مساله‌ی (کارآمد و ناکارآمد) دانش‌آموزان. مجله‌ی روان‌شناسی مدرسه، 6(2): 83-99.
طاهرزاده بروجنی، نسترن و ربیعی، مهدی. (1390). مروری بر حل مساله ریاضی در دوره ابتدایی. مجله آموزش ریاضی، 28(4): 28-50.
گویا، زهرا (1377). نقش فراشناخت در یادگیری حل مساله ریاضی. مجله رشد آموزش ریاضی، 11(3): 20-32.
گویا، زهرا (1377). نقش فراشناخت در یادگیری حل مساله ریاضی. مجله رشد آموزش ریاضی، 11(3): 20-32.
Attridge, N., & Inglis, M. (2015). Increasing cognitive inhibition with a difficult prior task: implications for mathematical thinking, 47(5), 723-734.
Ayan, R., & Işıksal-Bostan, M. (2019). Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement. International Journal of Mathematical Education in Science and Technology, 50(1), 65-81.
Bago, B. (2018). Testing the corrective assumption of dual process theory in reasoning (Doctoral dissertation, Sorbonne Paris Cité).
Beckmann, S. (2011). From the common core to a community of all mathematics teachers. The Mathematics Educator, 20(2), 100-124.
Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36(3), 247-273.
Borodin, A. (2016). The need for an application of dual-process theory to mathematics education. Cambridge Open-Review Educational Research e-Journal, 3(4), 12-25.
Burton, L. (1984). Mathematical thinking: The struggle for meaning. Journal for research in mathematics education, 15(1), 35-49.
Cramer, K., Post, T., & Behr, M. (1989). Interpreting proportional relationships. Mathematics Teacher, 82(6), 445-452.
Cramer, K. A., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications: Middle grades mathematics. In Research ideas for the classroom: Middle grades mathematics (pp. 159-178). Macmillan Publishing Company.
Cramer, K., Post, T., & Graeber, A. O. (1993). Connecting research to teaching: Proportional reasoning. The Mathematics Teacher, 86(5), 404-407.
Ersoy, E., & Guner, P. (2015). The place of problem solving and mathematical thinking in the mathematical teaching. The Online Journal of New Horizons in Education-January, 5(1), 120-130.
Evans, J. S. B. (2003). In two minds: dual-process accounts of reasoning. Trends in cognitive sciences, 7(10), 454-459.
Evans, J. S. B. (2010). Thinking twice: Two minds in one brain. Oxford University Press.
Evans, J. S. B., & Stanovich, K. E. (2013). Dual-process theories of higher cognition: Advancing the debate. Perspectives on psychological science, 8(3), 223-241.
Frankish, K. (2015). Dennett’s dual-process theory of reasoning. In Content and consciousness revisited (pp. 73-92). Springer, Cham.
Gillard, E., Van Dooren, W., Schaeken, W., & Verschaffel, L. (2009a). Dual processes in the psychology of mathematics education and cognitive psychology. Human Development, 52(2), 95-108
Gillard, E., Van Dooren, W., Schaeken, W., & Verschaffel, L. (2009b). Proportional reasoning as a heuristic-based process: time constraint and dual task considerations. Experimental Psychology, 56(2), 92-99.
Gómez-Chacón, I. M., García-Madruga, J. A., Vila, J. Ó., Elosúa, M. R., & Rodríguez, R. (2014). The dual processes hypothesis in mathematics performance: Beliefs, cognitive reflection, working memory and reasoning. Learning and Individual Differences, 29, 67-73.
Heller, P. M., Ahlgren, A., Post, T., Behr, M., & Lesh, R. (1989). Proportional reasoning: The effect of two context variables, rate type, and problem setting. Journal of Research in Science Teaching, 26(3), 205-220.
Lamon, S. J. (1995). Ratio and proportion: Elementary didactical phenomenology. Providing a foundation for teaching mathematics in the middle grades, 167-198.
Lamon, S.J. (2012). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Routledge.
Leron, U., & Hazzan, O. (2006). The Rationality Debate: Application of Cognitive Psychology to Mathematics Education. Educational Studies in Mathematics, 62(2), 105–126.
Lim, K. H. (2009). Burning the candle at just one end. Mathematics Teaching in the Middle School, 14(8), 492-500.
Özgün-Koca, S. A., & Kayhan-Altay, M. (2009). An investigation of proportional reasoning skills of middle school students. Investigations in Mathematics Learning, 2(1), 26-48.
Park, J. S., Park, J. H., & Kwon, O. N. (2010). Characterizing the proportional reasoning of middle school students. Seoul National, University Journal of Education Research, 19(5), 119–144.
Pişkin-Tunç, M. (2020). Investigation of Middle School Students’ Solution Strategies in Solving Proportional and Non-proportional Problems. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 1-14.
Watson, A. (2001). Instances of mathematical thinking among low attaining students in an ordinary secondary classroom. The Journal of Mathematical Behavior, 20(4), 461-475.