RESEARCH PAPER
The causes of changes in student positioning in group discussions using Polya’s problem-solving and commognitive approaches
 
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1
Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Malang, East Java, INDONESIA
 
2
College of Teacher Training and Education (STKIP) Taman Siswa Bima, NTB, INDONESIA
 
 
Publication date: 2024-09-10
 
 
EURASIA J. Math., Sci Tech. Ed 2024;20(9):em2506
 
KEYWORDS
ABSTRACT
This study aims to describe the causes of changes in student positioning during group discussions utilizing Polya’s problem-solving method and commognitive principles. The subjects of the study are mathematics education students from STKIP Taman Siswa Bima. Two groups were selected from 30 participants, each consisting of three individuals representing the roles of expert, facilitator, and novice. The research approach employed was qualitative exploratory. The findings indicate that changes in positioning were due to role shifts among group members, where group 1 changed from an initial positioning of EP1FP1NP1 to F’P1E’P1NP1, incorporating complete stages of Polya’s problem-solving process and commognitive components. Group 2 transitioned from EP2FP2NP2 to F’P2FP2NP2, reflecting an incomplete application of Polya’s problem-solving stages and commognitive components. Future research recommendations include examining how changes in student positioning occur in algebra problem-solving discussions using Polya’s problem-solving strategies and commognitive components, with a focus on individual student problem-solving within groups.
REFERENCES (60)
1.
Alvermann, D. E., Unrau, N. J., Sailors, M., & Ruddell, R. B. (2018). Theoretical models and processes of literacy. In Theoretical models and processes of literacy. https://doi.org/10.4324/978131....
 
2.
Anderson, J. (2009). Mathematics curriculum development and the role of problem solving. ACSA Conference 2009, 1, Article 8.
 
3.
Apriliyanto, B., Saputro, D. R. S., & Riyadi. (2018). Student’s social interaction in mathematics learning. Journal of Physics: Conference Series, 983, Article 012130. https://doi.org/10.1088/1742-6....
 
4.
Azmitia, M. (2016). Peer interaction and problem solving: When are two heads better than one? Child Development, 59(1), 87-96. https://doi.org/10.1111/j.1467....
 
5.
Campbell, T. G., & Hodges, T. S. (2020). Using positioning theory to examine how students collaborate in groups in mathematics. International Journal of Educational Research, 103, Article 101632. https://doi.org/10.1016/j.ijer....
 
6.
Caspi, S., & Sfard, A. (2012). Spontaneous meta-arithmetic as a first step toward school algebra. International Journal of Educational Research, 51-52, 45-65. https://doi.org/10.1016/j.ijer....
 
7.
Chong, M. S. F., & Shahrill, M. (2016). The use of an emerging framework to explore students’ cognitive competency. Indian Journal of Science and Technology, 9(16). https://doi.org/10.17485/ijst/....
 
8.
Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (2012). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28(3), 258-277. https://doi.org/10.2307/749781.
 
9.
Cole, M. (2010). Reflections on the discussion reflections on the discussion. Comparative and General Pharmacology, 9039(917682025), 2-27.
 
10.
Daher, W. (2020). Students’ positioning and emotions in learning geometric definition. Journal on Mathematics Education, 11(1), 111-134. https://doi.org/10.22342/jme.1....
 
11.
Deal, L. J., & Wismer, M. G. (2010). NCTM principles and standards for mathematically talented students. Gifted Child Today, 33(3), 55-65. https://doi.org/10.1177/107621....
 
12.
DeJarnette, A. F. (2018). Using student positioning to identify collaboration during pair work at the computer in mathematics. Linguistics and Education, 46, 43-55. https://doi.org/10.1016/j.ling....
 
13.
DeJarnette, A. F., & González, G. (2015). Positioning during group work on a novel task in algebra II. Journal for Research in Mathematics Education, 46(4), 378-422. https://doi.org/10.5951/jresem....
 
14.
Esmonde, I. (2013). Mathematics learning in groups: Analyzing equity in two cooperative activity structures. Journal of the Learning Sciences, 18(2), 247-284. https://doi.org/10.1080/105084....
 
15.
Flood, V. J. (2018). Multimodal revoicing as an interactional mechanism for connecting scientific and everyday concepts. Human Development, 61(3), 145-173. https://doi.org/10.1159/000488....
 
16.
Forman, E. A., & Larreamendy-Joerns, J. (2015). Learning in the context of peer collaboration: A pluralistic perspective on goals and expertise. Cognition and Instruction, 13(4), 549-564. https://doi.org/10.1207/s15326....
 
17.
Francisco, J. M. (2013). Learning in collaborative settings: Students building on each other’s ideas to promote their mathematical understanding. Educational Studies in Mathematics, 82(3), 417-438. https://doi.org/10.1007/s10649....
 
18.
Gagné, R. M., & Smith, E. C. (1962). A study of the effects of verbalization on problem solving. Journal of Experimental Psychology, 63(1), 12-18. https://doi.org/10.1037/h00487....
 
19.
Harré, R. (2015). Positioning theory. The International Encyclopedia of Language and Social Interaction, 2009, 1-9. https://doi.org/10.1002/978111....
 
20.
Herbel-Eisenmann, B. A., Wagner, D., Johnson, K. R., Suh, H., & Figueras, H. (2015). Positioning in mathematics education: Revelations on an imported theory. Educational Studies in Mathematics, 89(2), 185-204. https://doi.org/10.1007/s10649....
 
21.
Herbst, P. G. (2003). Using novel tasks in teaching mathematics: Three tensions affecting the work of the teacher. American Educational Research Journal, 40(1), 197-238. https://doi.org/10.3102/000283....
 
22.
Johnson, D. W., Johnson, R. T., & Smith, K. A. (2014). Cooperative learning: Improving university instruction by basing practice on validated theory. Journal of Excellence in College Teaching, 25, 85-118.
 
23.
Kavanagh, S. S., Metz, M., Hauser, M., Fogo, B., Taylor, M. W., & Carlson, J. (2020). Practicing responsiveness: Using approximations of teaching to develop teachers’ responsiveness to students’ ideas. Journal of Teacher Education, 71(1), 94-107. https://doi.org/10.1177/002248....
 
24.
Kayı-Aydar, H. (2019). Positioning theory in applied linguistics. In Positioning theory in applied linguistics (pp. 1-26). Springer. https://doi.org/10.1007/978-3-....
 
25.
Kim, D.-J., Choi, S., & Lim, W. (2017). Sfard’s commognitive framework as a method of discourse analysis in mathematics. International Journal of Cognitive and Language Sciences, 11(11), 481-485.
 
26.
Lederman, E. (2009). Journey into problem solving: A gift from Polya. The Physics Teacher, 47(2), 94-97. https://doi.org/10.1119/1.3072....
 
27.
Lee, C. I. (2017). An appropriate prompts system based on the Polya method for mathematical problem-solving. EURASIA Journal of Mathematics, Science and Technology Education, 13(3), 893-910. https://doi.org/10.12973/euras....
 
28.
Lee, J., & Martin, L. (2017). Investigating students’ perceptions of motivating factors of online class discussions. International Review of Research in Open and Distributed Learning, 18(5), 148-172. https://doi.org/10.19173/irrod....
 
29.
Mueller, M., Yankelewitz, D., & Maher, C. (2012). A framework for analyzing the collaborative construction of arguments and its interplay with agency. Educational Studies in Mathematics, 80(3), 369-387. https://doi.org/10.1007/s10649....
 
30.
Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of calculus. Research in Mathematics Education, 16(2), 182-198. https://doi.org/10.1080/147948....
 
31.
Nilsson, P., & Ryve, A. (2010). Focal event, contextualization, and effective communication in the mathematics classroom. Educational Studies in Mathematics, 74(3), 241-258. https://doi.org/10.1007/s10649....
 
32.
Okafor, T. U. (2019). Effect of Polya’s problem solving technique on the academic achievement of senior secondary school student in physics. European Journal of Physics Education, 10(1), 38-48.
 
33.
Pimta, S., Tayruakham, S., & Nuangchale, P. (2009). Factors influencing mathematic problem-solving ability of sixth grade students. Journal of Social Sciences, 5(4), 381-385. https://doi.org/10.3844/jssp.2....
 
34.
Polya, G. (1973). How to solve it: A new aspect of mathematical method. Cambridge University Press. https://doi.org/10.1017/CBO978....
 
35.
Retnowati, E., Ayres, P., & Sweller, J. (2017). Can collaborative learning improve the effectiveness of worked examples in learning mathematics? Journal of Educational Psychology, 109(5), 666-679. https://doi.org/10.1037/edu000....
 
36.
Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1-3), 13-57. https://doi.org/10.1023/a:1014....
 
37.
Sfard, A. (2006). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. In Learning discourse (pp. 13-57). Springer. https://doi.org/10.1007/0-306-....
 
38.
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. Journal of the Learning Sciences, 16(4), 565-613. https://doi.org/10.1080/105084....
 
39.
Sfard, A. (2008). Thinking as communicating. Cambridge University Press. https://doi.org/10.1017/CBO978....
 
40.
Sfard, A. (2015). Learning, commognition and mathematics. In D. Scott, & E. ‎Hargreaves (Eds.), The SAGE handbook of learning (pp. 129-138). SAGE. https://doi.org/10.4135/978147....
 
41.
Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, J. (1998). Learning mathematics through conversation: Is it as good as they say? For the Learning of Mathematics, 18(1), 41-51.
 
42.
Shahsavari, H., Zare, Z., Parsa-Yekta, Z., Griffiths, P., & Vaismoradi, M. (2018). Learning situations in nursing education: A concept analysis. Research and Theory for Nursing Practice, 32(1), 23-45. https://doi.org/10.1891/1541-6....
 
43.
Simpol, N. S. H., Shahrill, M., Li, H. C., & Prahmana, R. C. I. (2018). Implementing thinking aloud pair and Pólya problem solving strategies in fractions. Journal of Physics: Conference Series, 943, Article 012013. https://doi.org/10.1088/1742-6....
 
44.
Sriraman, B. (2009). Book review: What’s all the commotion over commognition? A review of Annasfard’s thinking as communicating. The Mathematics Enthusiast, 6(3). https://doi.org/10.54870/1551-....
 
45.
Staples, M. (2014). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2-3), 161-217. https://doi.org/10.1080/073700....
 
46.
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340. https://doi.org/10.1080/109860....
 
47.
Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488. https://doi.org/10.3102/000283....
 
48.
Struyve, C., Hannes, K., Meredith, C., Vandecandelaere, M., Gielen, S., & De Fraine, B. (2018). Teacher leadership in practice: Mapping the negotiation of the position of the special educational needs coordinator in schools. Scandinavian Journal of Educational Research, 62(5), 701-718. https://doi.org/10.1080/003138....
 
49.
Tholander, M., & Aronsson, K. (2014). Doing subteaching in school group work: Positionings, resistance and participation frameworks. Language and Education, 17(3), 208-234. https://doi.org/10.1080/095007....
 
50.
Thoma, A., & Nardi, E. (2016). Routines in the didactical and mathematical discourses of closed-book examination tasks. In Proceedings of INDRUM 2016: 1st Conference of the International Network for Didactic Research in University Mathematics (pp. 411-420).
 
51.
Tohir, M., Maswar, M., Moh, A., Saiful, S., & Rizki Pradita, D. A. (2020). Prospective teachers’ expectations of students’ mathematical thinking processes in solving problems. European Journal of Educational Research, 9(4), 1735-1748. https://doi.org/10.12973/EU-JE....
 
52.
Tuset, G. A. (2018). A commognitive lens to study pre-service teachers ‘ teaching in the context of achieving a goal of ambitious mathematics teaching. In Proceeding, Congress of the European Society for Research in Mathematics Education (pp. 3185-3192).
 
53.
van Langenhove, L., & Harré, R. (1999). Introducing positioning theory. In L. van Langenhove, & R. Harré (Eds.), Positioning theory: Moral contexts of intentional action (pp. 14-31). Oxford Basil Blackwell Publishers. Editors: Luk Van Langenhove, Rom Harré.
 
54.
Viirman, O. (2015). Explanation, motivation and question posing routines in university mathematics teachers’ pedagogical discourse: A commognitive analysis. International Journal of Mathematical Education in Science and Technology, 46(8), 1165-1181. https://doi.org/10.1080/002073....
 
55.
Webb, N. M., Franke, M. L., Ing, M., Turrou, A. C., Johnson, N. C., & Zimmerman, J. (2019). Teacher practices that promote productive dialogue and learning in mathematics classrooms. International Journal of Educational Research, 97, 176-186. https://doi.org/10.1016/j.ijer....
 
56.
Wood, M. B. (2013). Mathematical micro-identities: Moment-to-moment positioning and learning in a fourth-grade classroom. Journal for Research in Mathematics Education, 44(5), 775-808. https://doi.org/10.5951/jresem....
 
57.
Yu, S., & Hu, G. (2017). Can higher-proficiency L2 learners benefit from working with lower-proficiency partners in peer feedback? Teaching in Higher Education, 22(2), 178-192. https://doi.org/10.1080/135625....
 
58.
Zayyadi, M., Nusantara, T., Hidayanto, E., Sulandra, I. M., & Sa’Dijah, C. (2020). Content and pedagogical knowledge of prospective teachers in mathematics learning: Commognitive. Journal for the Education of Gifted Young Scientists, 8(1), 515-532. https://doi.org/10.17478/jegys....
 
59.
Zayyadi, M., Nusantara, T., Subanji, Hidayanto, E., & Sulandra, I. M. (2019). A commognitive framework: The process of solving mathematical problems of middle school students. International Journal of Learning, Teaching and Educational Research, 18(2), 89-102. https://doi.org/10.26803/ijlte....
 
60.
Zhang, S., Chan, M. C. E., & Cao, Y. (2019). Studying student interactive positioning in collaborative mathematics problem solving: The case of four Chinese students. In Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 787-794).
 
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