Abstract
Reasoning is the process of thinking used to make claims and reach conclusions. It is among the first skills that should be taught to students in mathematics lessons and contributes to the creation and development of mathematical foundations. This study identifies evolution and trends in research on mathematical reasoning over the last four decades. Bibliometric analysis was used to reveal the intellectual architecture of the field, as it provides a comprehensive method for exploring and analyzing large volumes of scientific data. The research is organized in a four-step framework, namely, investigation, representation, characterization, and confirmation. This study, which reveals other concepts in which mathematical reasoning is associated with the developmental stages, can help academics, instructors, students, and policymakers in mathematics and other fields obtain insight into areas that need additional research, as well as paving the way for future studies.
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References
Alkan, H., & Güzel, E. B. (2005). Development of mathematical thinking in the student teachers. Gazi University Journal of Gazi Educational Faculty, 25(3), 221–236.
Amsterlaw, J. A., (2004). Development of children’s beliefs about everyday reasoning. (Unpublished doctoral dissertation). Michigan University.
Andrian, D., Azmi, M. P., Amir, Z., & Nurdin, E. (2019). Development of a definition maps-based plane geometry module to improve the student teachers’ mathematical reasoning ability. International Journal of Instruction, 12(3), 541–560.
Apperly, I. A., Warren, F., Andrews, B. J., Grant, J., & Todd, S. (2011). Developmental continuity in theory of mind: Speed and accuracy of belief desire reasoning in children and adults. Child Development, 82(5), 1691–1703. https://doi.org/10.1111/j.1467-8624.2011.01635.x
Arık, İ. A. (1987). Yaratıcılık-Üç Derleme [creativity-three compilation]. Kültür ve Turizm Bakanlığı Yayınları.
Ayal, C. S., Kusuma, Y. S., Sabandar, J., & Dahlan, J. A. (2016). The enhancement of mathematical reasoning ability of junior high school students by applying mind mapping strategy. Journal of Education and Practice, 7(25), 50–58.
Aydoğan Yenmez, A., & Gökçe, S. (2022). Matematiksel Akıl Yürütme [mathematical reasoning]. Anı Publications.
Bakker, M., van den Heuvel-Panhuizen, M., & Robitzsch, A. (2016). Effects of mathematics computer games on special education students’ multiplicative reasoning ability. British Journal of Educational Technology, 47(4), 633–648. https://doi.org/10.1111/bjet.12249
Bansilal, S. (2012). Arriving at the starting point? Exploring a teacher’s use of circular reasoning in a mathematics classroom. Education as Change, 16(1), 35–49. https://doi.org/10.1080/16823206.2012.691706
Battey, D., Bartell, T., Webel, C., & Lowry, A. (2021). Understanding the impact of racial attitudes on preservice teachers’ perceptions of children’s mathematical thinking. Journal for Research in Mathematics Education, 52(1), 62–93. https://doi.org/10.5951/jresematheduc-2020-0207
Benbow, C. P. (1988). Sex differences in mathematical reasoning ability in intellectually talented preadolescents: Their nature, effects, and possible causes. Behavioral and Brain Sciences, 11(2), 169–183. https://doi.org/10.1017/S0140525X00049244
Bitner, B. L. (1991). Formal operational reasoning modes: Predictors of critical thinking abilities and grades assigned by teachers in science and mathematics for students in grades nine through twelve. Journal of Research in Science Teaching, 28(3), 265–274. https://doi.org/10.1002/tea.3660280307
Brahmia, S. W., Olsho, A., Smith, T. I., Boudreaux, A., Eaton, P., & Zimmerman, C. (2021). Physics inventory of quantitative literacy: A tool for assessing mathematical reasoning in introductory physics. Physical Review Physics Education Research, 17(2), 1–17. https://doi.org/10.1103/PhysRevPhysEducRes.17.020129
Brodie, K. (2009). Teaching mathematical reasoning in secondary school classrooms (Vol. 775). Springer Science & Business Media.
Bundy, A. (1983). The computer modelling of mathematical reasoning (Vol. 10). Academic Press.
Bundy, A., Basin, D., Hutter, D., & Ireland, A. (2005). Rippling: meta-level guidance for mathematical reasoning (Vol. 56). Cambridge University Press.
Callingham, R., & Siemon, D. (2021). Connecting multiplicative thinking and mathematical reasoning in the middle years. The Journal of Mathematical Behavior, 61, 1–12. https://doi.org/10.1016/j.jmathb.2020.100837
Casey, M. B., Nutall, R. L., & Pezaris, E. (2001). Spatial-mechanical reasoning skills versus mathematics self-confidence as mediators of gender differences on mathematics subtests using cross-national gender-based items. Journal for Research in Mathematics Education, 32(1), 28–57. https://doi.org/10.2307/749620
Çüçen, A., & Ertürk, E. (2008). The role of logical and mathematical knowledge in abstract reasoning. Kaygı. Bursa Uludağ University Faculty of Arts and Sciences Journal of Philosophy, 11, 247–268.
Davidson, A., Herbert, S., & Bragg, L. A. (2019). Supporting elementary teachers’ planning and assessing of mathematical reasoning. International Journal of Science and Mathematics Education, 17(6), 1151–1171. https://doi.org/10.1007/s10763-018-9904-0
DeTemple, D. W., Long, C. T., & Millman, R. S. (2015). Mathematical reasoning for elementary school teachers. Pearson Education.
Develaki, M. (2020). Comparing Crosscutting Practices in STEM Disciplines. Science & Education, 29(4), 949–979. https://doi.org/10.1007/s11191-020-00147-1
Donthu, N., Kumar, S., Mukherjee, D., Pandey, N., & Lim, W. M. (2021). How to conduct a bibliometric analysis: An overview and guidelines. Journal of Business Research, 133, 285–296. https://doi.org/10.1016/j.jbusres.2021.04.070
Drachova, S. V., Hallstrom, J. O., Hollingsworth, J. E., Krone, J., Pak, R., & Sitaraman, M. (2015). Teaching mathematical reasoning principles for software correctness and its assessment. ACM Transactions on Computing Education (TOCE), 15(3), 1–22. https://doi.org/10.1145/2716316
Embretson, S. E. (1995). Measurement model for linking individual learning to processes and knowledge: Application to mathematical reasoning. Journal of Educational Measurement, 32(3), 277–294. https://doi.org/10.1111/j.1745-3984.1995.tb00467.x
English, L. D. (2004). Mathematical and analogical reasoning of young learners. Routledge.
English, L. D. (2013). Mathematical reasoning: Analogies, metaphors, and images. Routledge.
Eriksson, H., & Sumpter, L. (2021). Algebraic and fractional thinking in collective mathematical reasoning. Educational Studies in Mathematics, 108(3), 473–491. https://doi.org/10.1007/s10649-021-10044-1
Erkek, Ö., & Bostan, M. I. (2019). A different look at the reasoning process of prospective middle school mathematics teachers: Global argumentation structures. Education and Science., 44(199), 75–101.
Evans, J. S. B., & Over, D. E. (2013). Rationality and reasoning. Psychology Press.
Fathima, S., & Rao, D. B. (2008). Reasoning ability of adolescent students. Discovery Publishing House.
Francisco, J. M., & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. The Journal of Mathematical Behavior, 24(3–4), 361–372. https://doi.org/10.1016/j.jmathb.2005.09.001
Gökçe, S., & Güner, P. (2021). Forty years of mathematics education: 1980–2019. International Journal of Education in Mathematics, Science and Technology, 9(3), 514–539. https://doi.org/10.46328/ijemst.1361
Goldstone, R. L., Marghetis, T., Weitnauer, E., Ottmar, E. R., & Landy, D. (2017). Adapting perception, action, and technology for mathematical reasoning. Current Directions in Psychological Science, 26(5), 434–441. https://doi.org/10.1177/0963721417704888
Goos, M., & Kaya, S. (2020). Understanding and promoting students’ mathematical thinking: A review of research published in ESM. Educational Studies in Mathematics, 103(1), 7–25. https://doi.org/10.1007/s10649-019-09921-7
Gouet, C., Carvajal, S., Halberda, J., & Peña, M. (2020). Training nonsymbolic proportional reasoning in children and its effects on their symbolic math abilities. Cognition, 197, 1–13. https://doi.org/10.1016/j.cognition.2019.104154
Hand, V. (2012). Teaching mathematical reasoning in secondary school classrooms. Educational Studies in Mathematics, 79(1), 149–156.
Henderson, P. B., Hitchner, L., Fritz, S. J., Marion, B., Scharff, C., Hamer, J., & Riedesel, C. (2002). Materials development in support of mathematical thinking. ACM SIGCSE Bulletin, 35(2), 185–190. https://doi.org/10.1145/782941.783001
Herawati, S., & Amelia, P. (2021). Analysis of student’s mathematical reasoning ability in solving mathematical problem based on HOTS. Prima: Jurnal Pendidikan Matematika, 5(2), 1–15. https://doi.org/10.31000/prima.v5i2.3661
Herbert, S., Vale, C., Bragg, L. A., Loong, E., & Widjaja, W. (2015). A framework for primary teachers’ perceptions of mathematical reasoning. International Journal of Educational Research, 74, 26–37. https://doi.org/10.1016/j.ijer.2015.09.005
Herman, T. (2018). Analysis of students’ mathematical reasoning. Journal of Physics: Conference Series, 948(1), 1–7.
Hilton, A., & Hilton, G. (2019). Primary school teachers implementing structured mathematics interventions to promote their mathematics knowledge for teaching proportional reasoning. Journal of Mathematics Teacher Education, 22(6), 545–574. https://doi.org/10.1007/s10857-018-9405-7
Hughes, E. M., Riccomini, P. J., & Lee, J. Y. (2020). Investigating written expressions of mathematical reasoning for students with learning disabilities. The Journal of Mathematical Behavior, 58, 1–14. https://doi.org/10.1016/j.jmathb.2020.100775
Huincahue, J., Borromeo-Ferri, R., Reyes-Santander, P., & Garrido-Véliz, V. (2021). Mathematical thinking styles-the advantage of analytic thinkers when learning mathematics. Education Sciences, 11(6), 1–15. https://doi.org/10.3390/educsci11060289
Hunt, J. H., Martin, K., Patterson, B., & Khounmeuang, A. (2021). Special educators’ knowledge of student mathematical thinking. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-021-09508-1
Jablonka, E. (2020). Critical thinking in mathematics EDUCATION. Encyclopedia of Mathematics Education (pp. 159–163). Springer.
Jamnik, M. (2001). Mathematical reasoning with diagrams. University of Chicago Press.
Jansson, L. C. (1986). Logical reasoning hierarchies in mathematics. Journal for Research in Mathematics Education, 17(1), 3–20. https://doi.org/10.5951/jresematheduc.17.1.0003
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/s10649-017-9761-8
Jiménez-Fanjul, N., Maz-Machado, A., & Bracho-López, R. (2013). Bibliometric analysis of the mathematics education journals in the SSCI. International Journal of Research in Social Sciences, 2(3), 26–32.
Johnson-Laird, P. (2008). How we reason. Oxford University Press.
Johnson-Laird, P. N., & Ragni, M. (2019). Possibilities as the foundation of reasoning. Cognition, 193, 1–19. https://doi.org/10.1016/j.cognition.2019.04.019
Julius, R., Abd Halim, M. S., Hadi, N. A., Alias, A. N., Khalid, M. H. M., Mahfodz, Z., & Ramli, F. F. (2021). Bibliometric Analysis of research in mathematics education using scopus database. EURASIA Journal of Mathematics, Science and Technology Education, 17(12), 1–12. https://doi.org/10.29333/ejmste/11329
Kılıç, R. (2023). Broadening the perspectives of primary school mathematics: Past, present and further. Education and Information Technologies, 28(3), 3329–3357. https://doi.org/10.1007/s10639-022-11302-2
Köknel, Ö. (2003). Akıl ile Düşünce Gücü [Mind and thought power] (2. Basım). Altın Kitaplar Yayınevi.
Kollosche, D. (2021). Styles of reasoning for mathematics education. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-021-10046-z
Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281–310. https://doi.org/10.3102/00028312040001281
Kramarski, B., Mevarech, Z. R., & Lieberman, A. (2001). Effects of multilevel versus unilevel metacognitive training on mathematical reasoning. The Journal of Educational Research, 94(5), 292–300. https://doi.org/10.1080/00220670109598765
Kramarski, B., & Zoldan, S. (2008). Using errors as springboards for enhancing mathematical reasoning with three metacognitive approaches. The Journal of Educational Research, 102(2), 137–151. https://doi.org/10.3200/JOER.102.2.137-151
Kuo, E., Hull, M. M., Gupta, A., & Elby, A. (2013). How students blend conceptual and formal mathematical reasoning in solving physics problems. Science Education, 97(1), 32–57. https://doi.org/10.1002/sce.21043
Lange, M. (2021). Inference to the best explanation is an important form of reasoning in mathematics. The Mathematical Intelligencer. https://doi.org/10.1007/s00283-021-10112-7
Lee, M. Y. (2021). Using a technology tool to help pre-service teachers notice students’ reasoning and errors on a mathematics problem. ZDM-Mathematics Education, 53(1), 135–149. https://doi.org/10.1007/s11858-020-01189-z
Lehrer, R., & Schauble, L. (2000). Developing model-based reasoning in mathematics and science. Journal of Applied Developmental Psychology, 21(1), 39–48. https://doi.org/10.1016/S0193-3973(99)00049-0
Lesh, R. A., Hamilton, E., & Kaput, J. J. (Eds.). (2020). Foundations for the future in mathematics education. Routledge.
Lithner, J. (2000). Mathematical reasoning in school tasks. Educational Studies in Mathematics, 41(2), 165–190. https://doi.org/10.1023/A:1003956417456
Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52(1), 29–55. https://doi.org/10.1023/A:1023683716659
Lithner, J. (2004). Mathematical reasoning in calculus textbook exercise. Journal of Mathematical Behavior, 23(4), 371–496. https://doi.org/10.1016/j.jmathb.2004.09.003
Lithner, J. (2005). A framework for analysing qualities of mathematical reasoning: Version 3. Research Reports in mathematics education 3, Department of mathematics, Umea University.
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276. https://doi.org/10.1007/s10649-007-9104-2
Liu, Z., Moon, J., Kim, B., & Dai, C. P. (2020). Integrating adaptivity in educational games: A combined bibliometric analysis and meta-analysis review. Educational Technology Research and Development, 68, 1931–1959. https://doi.org/10.1007/s11423-020-09791-4
Llinares, S. (2018). Mathematics teacher’s knowledge, knowledge-based reasoning, and contexts. Journal of Mathematics Teacher Education, 21(1), 1–3. https://doi.org/10.1007/s10857-018-9399-1
Mandacı Şahin, S., & Baki, A. (2016). Assesment of Mathematical Power. Journal of Bayburt Education Faculty, 8(1), 195–215.
Marzano, R. J., & Heflebower, T. (2011). Teaching & assessing 21st century skills. Solution Tree Press.
Masfingatin, T., & Murtafiah, W. (2020). Exploring the creative mathematical reasoning of mathematics education student through discovery learning. AKSIOMA: Jurnal Program Studi Pendidikan Matematika., 9(2), 296–305. https://doi.org/10.24127/ajpm.v9i2.2714
Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186. https://doi.org/10.1007/s10649-017-9773-4
Mevarech, Z. R., & Kramarski, B. (2003). The effects of metacognitive training versus worked-out examples on students’ mathematical reasoning. British Journal of Educational Psychology, 73(4), 449–471. https://doi.org/10.1348/000709903322591181
Miller, P. H., & Aloise, P. A. (1989). Young children’s understanding of the psychological causes of behavior: A review. Child Development. https://doi.org/10.2307/1130975
Mills, C. J., Ablard, K. E., & Stumpf, H. (1993). Gender differences in academically talented young students’ mathematical reasoning: Patterns across age and subskills. Journal of Educational Psychology, 85(2), 340–346. https://doi.org/10.1037/0022-0663.85.2.340
Ministry of National Education [MoNE]. (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı [National mathematics curriculum (grades 5, 6, 7 and 8)]. TC Milli Eğitim Bakanlığı. Talim ve Terbiye Kurulu Başkanlığı.
Mullis, I. V., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). TIMSS 2003 International Mathematics Report: Findings from IEA's Trends in International Mathematics and Science Study at the Fourth and Eighth Grades. International Association for the Evaluation of Educational Achievement. TIMSS and PIRLS International Study Center.
National Assessment of Educational Practices. (2002). Mathematics framework for the 2003 national assessment of educational progress. National Assessment Governing Board.
National Council of Teachers of Mathematics [NCTM] (2000). Principles and Standards for School Mathematics. Author.
National Council of Teachers of Mathematics [NCTM] (2013). Curriculum and Evaluation Standards for School Mathematics. Author.
Nunes, T., & Bryant, P. (2015). The development of mathematical reasoning. In L. S. Liben, U. Müller, & R. M. Lerner (Eds.), Handbook of child psychology and developmental science: Cognitive processes (pp. 715–762). Wiley.
Powell, S. R., Berry, K. A., & Barnes, M. A. (2020). The role of pre-algebraic reasoning within a word-problem intervention for third-grade students with mathematics difficulty. ZDM Mathematics Education, 52(1), 151–163. https://doi.org/10.1007/s11858-019-01093-1
Ritchhart, R. (2002). Intellectual character. Wiley.
Rizki, L. M., & Priatna, N. (2019). Mathematical literacy as the 21st century skill. Journal of Physics: Conference Series, 1157(4), 1–5.
Rourke, B. P., & Conway, J. A. (1997). Disabilities of arithmetic and mathematical reasoning: Perspectives from neurology and neuropsychology. Journal of Learning Disabilities, 30(1), 34–46. https://doi.org/10.1177/002221949703000103
Saif, A. N. M., & Purbasha, A. E. (2023). Cyberbullying among youth in developing countries: A qualitative systematic review with bibliometric analysis. Children and Youth Services Review, 146, 106831. https://doi.org/10.1016/j.childyouth.2023.106831
Schliemann, A. D., & Carraher, D. W. (2002). The evolution of mathematical reasoning: Everyday versus idealized understandings. Developmental Review, 22(2), 242–266. https://doi.org/10.1006/drev.2002.0547
Shanta, S., & Wells, J. G. (2020). T/E design based learning: Assessing student critical thinking and problem solving abilities. International Journal of Technology and Design Education, 32, 267–285. https://doi.org/10.1007/s10798-020-09608-8
Shejwal, B. R., & Purayidathil, J. (2006). Television viewing of higher secondary students: Does it affect their academic achievement and mathematical reasoning? Psychology and Developing Societies, 18(2), 201–213. https://doi.org/10.1177/097133360601800203
Siregar, N. C., Rosli, R., & Maat, S. M. (2020). The effects of a discovery learning module on geometry for improving students’ mathematical reasoning skills, communication and self-confidence. International Journal of Learning, Teaching and Educational Research, 19(3), 214–228.
Smit, R., Bachmann, P., Blum, V., Birri, T., & Hess, K. (2017). Effects of a rubric for mathematical reasoning on teaching and learning in primary school. Instructional Science, 45(5), 603–622. https://doi.org/10.1007/s11251-017-9416-2
Somuncu, B., & Aslan, D. (2021). Effect of coding activities on preschool children’s mathematical reasoning skills. Education and Information Technologies, 27, 877–890. https://doi.org/10.1007/s10639-021-10618-9
Soulé, H., & Warrick, T. (2015). Defining 21st century readiness for all students: What we know and how to get there. Psychology of Aesthetics, Creativity, and the Arts, 9(2), 178–186. https://doi.org/10.1037/aca0000017
Sterner, G., Wolff, U., & Helenius, O. (2020). Reasoning about representations: Effects of an early math intervention. Scandinavian Journal of Educational Research, 64(5), 782–800. https://doi.org/10.1080/00313831.2019.1600579
Stiff, L. V., & Curcio, F. R. (1999). Developing Mathematical Reasoning in Grades K-12. 1999 Yearbook. Reston, VA: National Council of Teachers of Mathematics.
Stocker, J. D., Hughes, E. M., Wiesner, A., Woika, S., Parker, M., Cozad, L., & Morris, J. (2021). Investigating the effects of a fact family fluency intervention on math facts fluency and quantitative reasoning. Journal of Behavioral Education. https://doi.org/10.1007/s10864-020-09422-1
Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258–288. https://doi.org/10.1080/10986060903253954
Suh, J., Matson, K., Seshaiyer, P., Jamieson, S., & Tate, H. (2021). Mathematical modeling as a catalyst for equitable mathematics instruction: Preparing teachers and young learners with 21st century skills. Mathematics, 9(2), 162. https://doi.org/10.3390/math9020162
Thompson, P. W. (1996). Imagery and the development of mathematical reasoning. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 267–285). Lawrance Erlbaum Associates Inc.
Turner, N. E., Macdonald, J., & Somerset, M. (2008). Life skills, mathematical reasoning and critical thinking: A curriculum for the prevention of problem gambling. Journal of Gambling Studies, 24(3), 367–380. https://doi.org/10.1007/s10899-007-9085-1
Uhden, O., Karam, R., Pietrocola, M., & Pospiech, G. (2012). Modelling mathematical reasoning in physics education. Science & Education, 21(4), 485–506. https://doi.org/10.1007/s11191-011-9396-6
Umay, A. (1996). Mathematics education and measurement. Hacettepe University Journal of Education, 12, 145–149.
Umay, A. (2003). Mathematical reasoning ability. Hacettepe University Journal of Education, 24, 234–243.
Umay, A. (2007). Eski Arkadaşımız Okul Matematiğinin Yeni Yüzü [Our Old Friend The New Face of School Mathematics]. Aydan Web Tesisleri San. Ltd.
Van den Eynde, S., Schermerhorn, B. P., Deprez, J., Goedhart, M., Thompson, J. R., & De Cock, M. (2020). Dynamic conceptual blending analysis to model student reasoning processes while integrating mathematics and physics: A case study in the context of the heat equation. Physical Review Physics Education Research, 16(1), 1–18. https://doi.org/10.1103/PhysRevPhysEducRes.16.010114
Van Eck, N. J., & Waltman, L. (2010). Software survey: VOSviewer, a computer program for bibliometric mapping. Scientometrics, 84(2), 523–538. https://doi.org/10.1007/s11192-009-0146-3
Van Eck, N. J., & Waltman, L. (2013). Vosviewer manual. Leiden: Universiteit Leiden, 1(1), 1–53.
Van Eck, N. J., & Waltman, L. (2014). Visualizing bibliometric networks. In Y. Ding, R. Rousseau, & D. Wolfram (Eds.), Measuring scholarly impact: Methods and practice (pp. 285–320). Springer.
Van Eck, N. J., Waltman, L., Dekker, R., & Van den Berg, J. (2010). A comparison of two techniques for bibliometric mapping: Multidimensional scaling and VOS. Journal of the American Society for Information Science and Technology, 61(12), 2405–2416. https://doi.org/10.1002/asi.21421
Varma, S., & Schwartz, D. L. (2008). How should educational neuroscience conceptualise the relation between cognition and brain function? Mathematical reasoning as a network process. Educational Research, 50(2), 149–161. https://doi.org/10.1080/00131880802082633
Verma, S., & Gustafsson, A. (2020). Investigating the emerging COVID-19 research trends in the field of business and management: A bibliometric analysis approach. Journal of Business Research, 118, 253–261. https://doi.org/10.1016/j.jbusres.2020.06.057
Waltman, L., Van Eck, N. J., & Noyons, E. C. M. (2010). A unified approach to mapping and clustering of bibliometric networks. Journal of Informetrics, 4(4), 629–635. https://doi.org/10.1016/j.joi.2010.07.002
Webb, J. (1985). College mathematics achievement and logical reasoning. Perceptual and Motor Skills, 61(1), 15–22. https://doi.org/10.2466/pms.1985.61.1.15
Woods, T., Williams, G., & McNeal, B. (2006). Children’s mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222–255. https://doi.org/10.2307/30035059
Yeşildere, S. (2006). The investigation of mathematical thinking and knowledge construction processes of primary 6, 7 and 8th grade students who have different mathematical power. (Unpublished doctoral dissertation). Dokuz Eylül University, Institute of Educational Sciences.
Zhao, H., Alexander, P. A., & Sun, Y. (2021). Relational reasoning’s contributions to mathematical thinking and performance in Chinese elementary and middle-school students. Journal of Educational Psychology, 113(2), 279–303. https://doi.org/10.1037/edu0000595
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Aydoğan Yenmez, A., Gökçe, S. Pursuing the traces of mathematical reasoning. Asia Pacific Educ. Rev. (2023). https://doi.org/10.1007/s12564-023-09895-5
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DOI: https://doi.org/10.1007/s12564-023-09895-5