Designing and validating a mathematics education model based on multiple solutions to develop the creative thinking of high school students
Subject Areas : Research in Curriculum Planningmasomeh moasenzadeh 1 , Nematollah Mousapour 2 , sadegh nasri 3 , maryam safarnavadeh 4
1 - PhD student in Curriculum Planning, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Professor of Curriculum Development, Farhangian University, Tehran, Iran
3 - Associate professor of Psychology, Shahid Rajaiee Teacher Training University, Tehran, Iran
4 - Associate Professor, member of the academic faculty of the Ministry of Health, Medicine and Medical Education, Tehran, Iran
Keywords: creative thinking, problem posing, Mathematics Education, Multiple solutions tasks,
Abstract :
The overall purpose of the present study was to design and validate a mathematics education model based on multiple solutions to develop creative thinking in high school students using a mixed exploratory research approach. In the qualitative section, the statistical population consisted of experts, experts and teachers of mathematics, 12 people were selected by purposive non-random sampling. Data collection tools were in-depth and semi-structured interviews based on the foundation data approach. Delphi technique was used to analyze the data, survey method was used for validity by the interviewees and retest reliability methods were used to calculate the reliability.Qualitative data analysis identified 16 themes. Among the themes, the main themes of selective procedure include solution of non routine problems (open - ended), multiple solution tasks and problem posing. In the quantitative part, to confirm the conceptual model, confirmatory factor analysis was used using Smart PLS software. The results showed that the degree of fit of the measurement model indices was optimal.
Ahmady, G., Reyhani, E., & Nakhostin Roohi, N. (2015). The Impact of mathemtical communication-based training on the Mathemthical reasoning ability among high-school students. Journal of School Psychology, 4(1), 22-37. [Persian]
Amir Ahmadi, Y., Iravani, Sh., Sharafi, M. (2012). Content analysis of science textbook of the elementary school fifth grade based on Dewey’s problem-solving model. Research in Curriculum Planning, 8 (35), 86-95. [Persian]
Aphrodite, M. A., & Rita, P. (2021). Young Students' Ability on Understanding and Constructing Geometric Proofs. Social Education Research, 121-133.
Ardiansyah, A. S., & Asikin, M. (2020). Challenging students to improve their mathematical creativity in solving multiple solution task on challenge based learning class. In Journal of Physics: Conference Series (Vol. 1567, No. 2, p. 022088). IOP Publishing.
Azizi Mahmoodabadi, M., Lighatdar, M. J., & Oreyzi, H. R. (2020). Investigating the effectiveness of schematic representation-based instruction on the ability of solving non-routine problems in mathematics. Research in Curriculum Planning, 17(64), 151-166. [Persian]
Bicer, A. (2021). A Systematic Literature Review: Discipline-Specific and General Instructional Practices Fostering the Mathematical Creativity of Students. International Journal of Education in Mathematics, Science and Technology, 9, 252-281.
Bingolbali, E. (2020). An analysis of questions with multiple solution methods and multiple outcomes in mathematics textbooks. International journal of mathematical education in science and technology, 51(5), 669-687.
Çetin, A. Y., & Dikici, R. (2021). Organizing the mathematical proof process with the help of basic components in teaching proof: Abstract algebra example. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 235-255.
Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. sage.
Creswell, J. W. (1998). Qualitative inquiry and research design: Choosing among five raditions. CA: Sage.
Dafei, Hamid (2017) Multiple representation in mathematics education. National conference on mathematics education in elementary school in 2016. [Persian]
Gall, M., Walter, B., Joyc, G. (2008). Educational Reseach an Introduction. Translated by Ahmadreza Nasr. Tehran. Samt. [Persian]
Gridos, P., Avgerinos, E., Mamona-Downs, J., & Vlachou, R. (2021). Geometrical Figure Apprehension, Construction of Auxiliary Lines, and Multiple Solutions in Problem Solving: Aspects of Mathematical Creativity in School Geometry. International Journal of Science and Mathematics Education, 1-18.
Gruntowicz, B. (2020). Mathematical Creativity and Problem Solving. (Masters Thesis). University of Montana. Retrieved from https://scholarworks.umt.edu/etd/11562
Hakimzadeh, Rezvan (2019). The facts that times 2019 revealed for Iran. Tasniews agency, Februery 18, 2019. Available: https://tn.ai/2445802 [Persian]
Hamdani, D., Subarinah, S., & Triutami, T. W. (2021, February). Construction Scheme of Proof Based on Assimilation and Accommodation Processes: Theorem of Number Theory. In Journal of Physics: Conference Series (Vol. 1776, No. 1, p. 012004). IOP Publishing.
Hatisaru, V. (2020). Exploring evidence of mathematical tasks and representations in the drawings of middle school students. International Electronic Journal of Mathematics Education, 15(3), em0609.
Homan, H. (2013). Knowing the scientific method in behavioral sciences (research foundations). Tehran. Samt. [Persian]Homan, H. (2018). Modeling structural equations using Lisrel software.Tehran. Samt. [Persian]Kerlinger, F. (2020). Foundations of behavioral research. The second volume. Translated by Hasan Pasha Sharifi. Avai Noor Publications. Tehran. [Persian]Kiamanesh, A., Sfarkhani, M., Aghdasi, S., Mohsenpour, M., Kabiri, M., Mahdavi, H., Sangari, A., & Atashak, M.(2011). Examining the process of educational changes in the period of 2014-2016 based on the findings of international studies of Thames in Iran and the countries of the region, according to the goals of the twenty-year vision document (eighth grade). A joint project of Educational Research and Planning Organization and Tarbiat Moalem University. [Persian]
Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424.
Levav-Waynberg, A., & Leikin, R. (2012). Using multiple solution tasks for the evaluation of students’ problem-solving performance in geometry. Canadian Journal of Science, Mathematics and Technology Education, 12(4), 311-333.
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Beverly Hills, CA: Sage.
Lynch, K., Star, J.R. (2013). Views of struggling students on instruction incorporating multiple strategies in Algebra I: An exploratory study, Journal for Research in Mathematics Education.
Mehrabi, M. (2012). The effect of the active teaching method (problem solving) on the creativity and academic progress of the first grade male middle school students of Euclid city in the academic year of 1990-1991. Master's thesis, Islamic Azad University, Maroodasht branch, Faculty of Education and Psychology. [Persian]
Minggi, I., Mulabar, U., & Assagaf, S. F. (2021). Learning Trajectory in Mathematical Proof. In Journal of Physics: Conference Series (Vol. 1752, No. 1, p. 012081). IOP Publishing.
Naderi Buanlu, Sona (2013) Examining the problem-solving ability of students. Master΄s thesis in mathematics education. Shahid Rajaee Tarbiat University, Faculty of Basic Sciences, Tehran. http://ganj.irandoc.ac.ir [Persian]
National Council of Teachers of Mathematics (NCTM). (2020). Standards for the preparation of middle-level mathematics teachers. Authors: Rasch, K., BayWilliams, J. M., Cruz-White, I., Lynch, M., Ramirez, N., Roy, G. J, & Barnes, D.
National Council of Teachers of Mathematics. (2014). Principles to actions. National Council for Teachers of Mathematics.
Nooriafshar, M., Haghverdi, M., & Komijani, A. (2017). Multiple Representations in Teaching and Learning: Reflection of Practical Experiences. Journal of New Approaches in Educational Administration, 8(31), 29-54. [Persian]
Rahimi, Zahra (2015) Designing a teaching model based on multiple solutions, to realize mathematical thinking in middle school students. Doctoral thesis of Educational Science, Tarbiat Modares University, Faculty of Humanities. [Persian]
Reyhani, Ebrahim (2019) A review of the structures and educational approaches of Iranian math books. Ebrahim Reyhani Webinar, Tarbiat Dabir Rajaee University. https://www.sru.ac.ir/wp-content/uploads/ 2020/08/sakhtar-2.pdf [Persian]
Reyhani, Ebrahim, Bakhshalizadeh, Shahrnaz and Eskandari, Mojtaba. (2013). Investigating the performance of third-year middle school students in math problem-solving situations. Journal of Education and Learning Studies, 6(1), 67-93. [Persian]
Saputri, M.D., Pramudya, I., & Slamet, I. (2020). Analysis of Mathematic Creative Thinking Ability of 10th Grade High School Students about Solution Mathematics Problems. International Journal of Multicultural and Multireligious Understanding, 7, 314-320.
Schindler, M., & Lilienthal, A. J. (2020). Students’ creative process in mathematics: insights from eye-tracking-stimulated recall interview on students’ work on multiple solution tasks. International Journal of Science and Mathematics Education, 18(8), 1565-1586.
Schoevers, E. M., Kroesbergen, E. H., & Kattou, M. (2020). Mathematical creativity: A combination of domain‐general creative and domain‐specific mathematical skills. The Journal of Creative Behavior, 54(2), 242-252.
Schukajlow, S., & Krug, A. (2012). Effects of Treating Multiple Solutions While Solving Modelling Problems On Students’self-Regulation, Self-Efficacy Expectations And Value. Proceedings of Pme 36, 4, 59-66.
Sdat Mir, Zohre (2009) Comparison of creative and critical thinking in third-year female students of secondary mathematics and humanities in District 14 of Tehran. Thesis of Islamic Azad University - Islamic Azad University, Central Tehran Branch – Faculty of Psychology and Educational Sciences. [Persian]
Shayan, M., Yaftian, N., Ebrahimi, M. (2016). Evaluation of the performance of mathematics teachers of the first year of high school in the mathematics literacy test. 14th Iranian Mathematical Education Conference, Shiraz. [Persian]
Shimizu, Y., Vithal, R., Ruiz, A., Cuoco, A., Bosch, M., Gholamazad, S., Morony, W., Zhu, Y., & Arzarello, F. (2017). School mathematics curriculum reforms: challenges, changes and opportunities. ICMI Study 24. International Commission on Mathematical Instruction.
Shirvani, Nematullah (2015). The relationship between learning styles and creativity with the academic achievement of mathematics course of high school students in Ghaemiyeh city. Thesis of Islamic Azad University, Marvdasht Branch, Faculty of Basic Sciences. [Persian]
Shorakaei Ardakani, J., Reyahinejad, H., Razaghi, H. (2013). The set of approvals of the Supreme Council of Education. Secretariat of the Supreme Council of Education. Burhan School Cultural Institute (School publications), Tehran. [Persian]
Skandari, Mojtaba (2012). Investigating the effect of developing math problem solving skills on middle school students΄ problem solving ability. Master΄s thesis in mathematics education, Tehran: Shahid Rajaee Tarbiat Dabir University, Faculty of Basic Science. http://ganj.irandoc.ac.ir [Persian]
Strauss A. & Corbin J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory, CA: Sage Publications.
Tan, C. P., Van der Molen, H. T., & Schmidt, H. G. (2016). To what extent does problem-based learning contribute to students' professional identity development?. Teaching and Teacher Education, 54, 54-64.
Yaftian, N. (2018). Effective Conditions and Strategies for Presenting Creative Solutions in Solving Mathematics from Creative Graduate Students Viewpoints. New Educational Approaches, 12(2), 60-76. [Persian]
Zahra, G. Evolution and formation of school mathematics curricula in Iran. The growth of mathematics education. 28(4). 4-12. [Persian] Zeybek Simsek, Z. (2021). "Is It Valid or Not?": Pre-Service Teachers Judge the Validity of Mathematical Statements and Student Arguments. European Journal of Science and Mathematics Education, 9(2), 26-42.
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