THINKING INTERACTION OF STUDENT IN SOLVING OPEN-ENDED PROBLEMS

Syarifudin Syarifudin, Purwanto Purwanto, Edy Bambang Irawan, I Made Sulandra, Abdur Rahman As'ari, Subanji Subanji

Abstract


The purpose of this research is to describe the process of thinking interaction of students in solving the open-ended problem. The thinking interaction of students' in this study is defined as an activity of exchanging thoughts between students one with other students through communication to produce the suitability of the thinking process between them through the resolution of open-ended problems. This study was conducted on a group of junior high school students with heterogeneous capabilities, consisting of 5 students, and have taken the material to build space. The data of thought interaction activity is obtained from discussion result in solving open-ended problem analyzed by information processing theory. Students' thinking interaction activities begin from one subject person who gives statement and understanding about the problem provided. Activity mutual ideas, complement or give feedback to other subject's comments, ask questions that have not been understood, or give an explanation in deciding the answer to be agreed. Subsequent activities decide the answer orally to be written by each subject. All subjects poured the agreed result on the answer sheet, but there were still doubts from the two subjects on the answer, so the subject looked back at the answers from other subjects. Some subjects continue to write answers and in the end, each subject has a form of answer in accordance with their respective understanding.

Full Text:

PDF

References


Barnard, T. (2015). Why are proofs difficult ? The Mathematical Gazette, 84(501), 415–422.

Barron, B. (2000). Achieving Coordination in Collaborative Problem-Solving Groups. The Journal of the Learning Sciences, 9(4), 403–436.

Barron, B. (2003). When Smart Groups Fail. The Journal of the Learning Sciences, 12(3), 307–359.

Bishop, J. P. (2014). “ She ’ s Always Been the Smart One . I ’ ve Always Been the Dumb One ”: Identities in the Mathematics Classroom. Journal for Research in Mathematics Education, 43(1), 34–74.

Bishop, J. P., Lamb, L. L., Philipp, R. A., & Whitacre, I. (2014). Obstacles and Affordances for Integer Reasoning : An Analysis of Children ’ s Thinking and the History of Mathematics. The National Council of Teachers of Mathematics, 45(1), 19–61.

Capraro, M. M., Capraro, R. M., & Cifarelli, V. V. (2007). What are students thinking as they solve open-ended mathematics problems ?, 124–128.

Francisco, J. M., & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving : Insights from a longitudinal study ଝ. Journal of Mathematical Behavior, 24, 361–372. https://doi.org/10.1016/j.jmathb.2005.09.001

Gresalfi, M., Martin, T., Hand, V., & Greeno, J. (2009). Constructing competence : an analysis of student participation in the activity systems of mathematics classrooms. Educational Studies in Mathematic, 49–70. https://doi.org/10.1007/s10649-008-9141-5

Hitipeuw, I. (2009). Belajar dan Pembelajaran. Malang: Fakultas Ilmu Pendidikan Universitas Negeri Malang.

Johnson, D. W., Johnson, R. T., & Smith, K. A. (2014). Cooperative Learning : Improving University Instruction By Basing Practice On Validated Theory., 1–26.

Kidron, I., Lenfant, A., Bikner-Ahsbahs, A., Artigue, M., & Dreyfus, T. (2008). Toward networking three theoretical approaches : the case of social interactions. Mathematics Education, 247–264. https://doi.org/10.1007/s11858-008-0079-y

Kieran, C. (2002). The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges. Educational Studies in Mathematics, (1995), 187–228.

Kumpulainen, K. & Wray, D. (2002) Classroom Interaction and Social Learning London: RoutledgeFalmer

Kwon, O. N., Park, J. H., & Park, J. S. (2006). Cultivating Divergent Thinking in Mathematics through an Open-Ended Approach. Asia Pacific Education, 7(1), 51–61.

Lai, K., & White, T. (2014). How groups cooperate in a networked geometry learning environment. Instructional Science, 615–637. https://doi.org/10.1007/s11251-013-9303-4

Leatham, K. R., Peterson, B. E., Stockero, S. L., Zoest, L. R. Van, Leatham, K. R., & Peterson, B. E. (2015). Conceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking. Journal for Research in Mathematics Education, 46(1), 88–124.

Mueller, M., Yankelewitz, D., & Maher, C. (2012). A framework for analyzing the collaborative construction of arguments and its interplay with agency. Educational Studies in Mathematic, 369–387. https://doi.org/10.1007/s10649-011-9354-x

NCTM. (2014). Principles Standards and for School Mathematics.

Nilsson, P., & Ryve, A. (2010). Focal event , contextualization , and effective communication in the mathematics classroom. Educational Studies in Mathematics, 241–258. https://doi.org/10.1007/s10649-010-9236-7

Peterson, B. E., & Leatham, K. R. (2009). Learning to Use Students’ Mathematical Thinking to Orchestrate a Class Discussion Blake E. Peterson Keith R. Leatham, 1–22.

Prusak, N., Hershkowitz, R., & Schwarz, B. B. (2012). From visual reasoning to logical necessity through argumentative design. Educational Studies in Mathematic, 19–40. https://doi.org/10.1007/s10649-011-9335-0

Radford, L. (2011). Book Review : Classroom Interaction : Why is it Good , Really ? Baruch Schwarz , Tommy Dreyfus and Rina Hershkowitz ( Eds .) ( 2009 ) Transformation of knowledge through classroom interaction. Educational Studies in Mathematic, 101–115. https://doi.org/10.1007/s10649-010-9271-4

Ryve, A., Nilsson, P., & Pettersson, K. (2013). Analyzing effective communication in mathematics group work : The role of visual mediators and technical terms. Educational Studies in Mathematic, 497–514. https://doi.org/10.1007/s10649-012-9442-6

Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education : an empirical investigation of teacher learning from a virtual video-based field experience. Math Teacher Educ, 123–140. https://doi.org/10.1007/s10857-007-9029-9

Sawada, M. (1997). Chiral recognition detected by fast atom bombardment mass spectrometry recognition.

Stockero, S. L., & Zoest, L. R. Van. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers ’ practice. Math Teacher Educ, 125–147. https://doi.org/10.1007/s10857-012-9222-3

Watson, J. M., & Chick, H. L. (2001). Factors influencing the outcomes of collaborative mathematical problem solving: An introduction. Mathematical Thinking and Learning, (October 2014), 37–41. https://doi.org/10.1080/10986065.2001.9679971

Webb, N. M. (1989). Peer Interaction and Learning in Small Groups. International Journal of Educational Research, 21–39.

Weber, K. (2002). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematic, 48(1), 101–119.

Weber, K., Maher, C., & Powell, A. (2008). Learning opportunities from group discussions : warrants become the objects of debate. Educ Stud Math, 247–261. https://doi.org/10.1007/s10649-008-9114-8

Zoest, L. R. Van, Stockero, S. L., Leatham, K. R., Peterson, B. E., Atanga, N. A., Ochieng, M. A., … Peterson, B. E. (2017). Attributes of Instances of Student Mathematical Thinking that Are Worth Building on in Whole- Class Discussion. Mathematical Thinking and Learning, 6065(January). https://doi.org/10.1080/10986065.2017.1259786


Refbacks

  • There are currently no refbacks.




International Journal of Insight for Mathematics Teaching