The Learning Trajectory Construction of Elementary School Students in Solving Integer Word Problems

Yıl 2022, Cilt: 9 Sayı: 1, 404 - 424, 01.01.2022

Andi Saparuddin Nur , Kartono Kartono Zaenuri Zaenuri Rochmad Rochmad

https://doi.org/10.17275/per.22.22.9.1

Cited By: 1

Öz

The integer is a basic concept in studying arithmetic and algebra. However, students still frequently experience misconceptions, especially in negative integer, count operations. Traditional games are activities that are often carried out by students in coastal areas so that they are relevant to be used as a tool to construct learning trajectories in solving integer word problems. The aim of this study is to produce a learning trajectory that can be used to solve integer word problems using traditional games. This study used a design-based research. Participants in this study were five grade sixth elementary school students. There are 6 sub-topics studied, i.e., the concept of negative integers, sequence integers, addition and subtraction operations, division and multiplication operations, mixed count operations, and solving problems related to integers. The results of this study obtained student learning trajectories for each sub-topic including the free play, collecting data from the game results, making mathematical relationships, building concepts, and applying them to various problems. Students are able to do problem-solving based on the sequence of tasks but require intervention so they can apply it to other situations without engaging in activities. Further research is required for more in-depth exploration on thinking process, instruction types, and behaviours that students might display independently without using traditional games in solving integer word problems.

Anahtar Kelimeler

learning trajectory, word problem solving, whole numbers

Destekleyen Kurum

This research received financial support from the doctoral program BPPDN scholarship from the Ministry of Research, Technology and Higher Education of the Republic of Indonesia and Musamus University

Proje Numarası

Study assignment SK Number: 37769 / M / KP / 2019

Kaynakça

• Barrett, J. E., Sarama, J., Clements, D. H., Cullen, C., Mccool, J., Witkowski-rumsey, C., & Klanderman, D. (2012). Evaluating and Improving a Learning Trajectory for Linear Measurement in Elementary Grades 2 and 3 : A Longitudinal Study. Mathematical Thinking and Learning, 14(2), 28–54. https://doi.org/10.1080/10986065.2012.625075.
• Clements, D. H., & Sarama, J. (2009). Learning and Teaching Early Math: The Learning Trajectories Approach. New York: Routledge.
• Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics Learned by Young Children in an Intervention Based on Learning Trajectories : A Large-Scale Cluster Randomized Trial. Journal for Research in Mathematics Education, 42(2), 127–166.
• Csíkos, C., & Szitányi, J. (2020). Teachers ’ pedagogical content knowledge in teaching word problem solving strategies. ZDM, 52(1), 165–178. https://doi.org/10.1007/s11858-019-01115-y.
• Elia, I. (2019). Word problem solving and pictorial representations : insights from an exploratory study in kindergarten. ZDM (In Press). https://doi.org/10.1007/s11858-019-01113-0.
• Ellis, A. B., Ozgur, Z., Kulow, T., & Dogan, M. F. (2016). An Exponential Growth Learning Trajectory : Students’ Emerging Understanding of Exponential Growth Through Covariation. Mathematical Thinking and Learning, 18(3), 151–181. https://doi.org/10.1080/10986065.2016.1183090.
• Fonger, N. L., Ellis, A. B., & Dogan, M. F. (2020). A Quadratic Growth Learning Trajectory. Journal of Mathematical Behavior, 59(October 2019), 1–22. https://doi.org/10.1016/j.jmathb.2020.100795.
• Gravemeijer, K. (2004). Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. Mathematical Thinking and Learning, 6(2), 105–128. https://doi.org/10.1207/s15327833mtl0602.
• Howe, R. (2018). Learning and using our base ten place value number system : theoretical perspectives and twenty-first century uses. ZDM (In Press). https://doi.org/10.1007/s11858-018-0996-3.
• Isoda, M. (2010). Lesson Study : Problem Solving Approaches in Mathematics Education as a Japanese Experience. In International Conference on Mathematics Education Research 2010 (ICMER 2010) (Vol. 8, pp. 17–27). Elsevier Ltd. https://doi.org/10.1016/j.sbspro.2010.12.003.
• Land, T. J., Tyminski, A. M., & Drake, C. (2018). Examining aspects of teachers’ posing of problems in response to children’s mathematical thinking. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-018-9418-2.
• Özkubat, U., Karabulut, A., & Rüya, E. (2020). Mathematical Problem-Solving Processes of Students with Special Needs : A Cognitive Strategy Instruction Model ’ Solve It !’. International Electronic Journal of Elementary Education, 12(5), 405–416. https://doi.org/10.26822/iejee.2020562131.
• Rakes, C. R., & Ronau, R. N. (2019). Rethinking Mathematics Misconceptions : Using Knowledge Structures to Explain Systematic Errors within and across Content Domains. International Journal of Research in Education and Science, 5(1), 1–21.
• Simon, M. A. (2018). An emerging methodology for studying mathematics concept learning and instructional design. Journal of Mathematical Behavior, 52(October 2017), 113–121. https://doi.org/10.1016/j.jmathb.2018.03.005.
• Simon, M. A., Placa, N., & Avitzur, A. (2016). Participatory and Anticipatory Stages of Mathematical Concept Learning : Further Empirical and Theoretical Development. Journal for Research in Mathematics Education, 47(1), 63–93.
• Simon, M. A., Placa, N., Kara, M., & Avitzur, A. (2018). Empirically-based hypothetical learning trajectories for fraction concepts : Products of the Learning Through Activity research program. Journal of Mathematical Behavior, 52(October 2017), 188–200. https://doi.org/10.1016/j.jmathb.2018.03.003.
• Sun, X. H. (2018). Bridging whole numbers and fractions : problem variations in Chinese mathematics textbook examples. ZDM (In Press). https://doi.org/10.1007/s11858-018-01013-9.
• Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Toward a Theory of Teaching. Educational Researcher, 41(5), 147–156. https://doi.org/10.3102/0013189X12442801.
• Verschaffel, L., Schukajlow, S., Star, J., & Dooren, W. Van. (2020). Word problems in mathematics education : a survey. ZDM (In Press). https://doi.org/10.1007/s11858-020-01130-4.
• Weber, E., & Lockwood, E. (2014). The duality between ways of thinking and ways of understanding : Implications for learning trajectories in mathematics education. Journal of Mathematical Behavior, 35, 44–57. https://doi.org/10.1016/j.jmathb.2014.05.002.
• Weber, E., Walkington, C., & Mcgalliard, W. (2015). Expanding Notions of “ Learning Trajectories ” in Mathematics Education. Mathematical Thinking and Learning, 17(4), 253–272. https://doi.org/10.1080/10986065.2015.1083836.
• Widodo, S. A., Prihatiningsih, A., & Taufiq, I. (2021). Single subject research : use of interactive video in children with developmental disabilities with dyscalculia to introduce natural numbers. Participatory Educational Research, 8(2), 94–108. https://doi.org/10.17275/per.21.31.8.2.
• Xin, Y. P. (2018). The effect of a conceptual model-based approach on ‘additive’ word problem solving of elementary students struggling in mathematics. ZDM (In Press). https://doi.org/10.1007/s11858-018-1002-9.
• Zhang, S., Cao, Y., Wang, L., & Li, X. (2019). Characteristics of teaching and learning single-digit whole number multiplication in china : the case of the nine-times table. ZDM (In Press). https://doi.org/10.1007/s11858-018-01014-8.