A learning trajectory of integer addition and subtraction using the kempreng game context

Indri Salsabila, Mohammad Faizal Amir, Mahardika Darmawan Kusuma Wardana


Traditional games can be used as a context to understand mathematical concepts. Many studies on learning trajectory (LT), which are set in the context of traditional games, have been carried out. However, no study focuses on using the context of the traditional kempreng game to facilitate primary students in understanding integer addition and subtraction. This research aims to design an LT through traditional game kempreng to help construct students' understanding and mathematical concepts through various activities that have been developed. This study uses design research with stages, namely preliminary design, teaching experiment, and retrospective analysis. This study produces LT which consists of five activities, namely: consisting of calculating addition points through the kempreng context, calculating subtraction (difference) through the kempreng context, performing additional operations on the “same” kempreng card, performing subtraction operations on “different” kempreng, and determining the results of addition or subtraction operations of number cards with the opposing group. In this study, LT set in the traditional game of kempreng can be used as a context in preparing learning designs that could stimulate students thinking in understanding the mathematical concepts of integer addition and subtraction. The impact of the research design also occurs on teachers. Learning becomes a student center, the teacher as a facilitator. The results of this study can have implications as one of the considerations for using contexts with real and cultural backgrounds to reduce or build a meaningful understanding of the concept of integer addition and subtraction for primary students.


addition and subtraction; design research; kempreng game; learning trajectory

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Afriansyah, E. A., & Arwadi, F. (2021). Learning trajectory of quadrilateral applying realistic mathematics education: Origami-based tasks. Mathematics Teaching-Research Journal, 13(4), 42–78. https://commons.hostos.cuny.edu/mtrj/wp-content/uploads/sites/30/2022/01/v13n4-Learning-Trajectory-of-Quadrilateral.pdf

Amir, F., & Amir, M. F. (2021). Action proof: Analyzing elementary school students informal proving stages through counter-examples. International Journal of Elementary Education, 5(2), 401–408. https://doi.org/10.23887/ijee.v5i3.35089

Amir, M. F. (2022). Learner-generated drawings by students with mathematical learning difficulties in finishing open number sentences. Jurnal Elemen, 8(1), 216–230. https://doi.org/10.29408/jel.v8i1.4556

Amir, M. F., Darmawan, M., Wardana, K., Zannah, M., Rudyanto, H. E., & Nawafilah, N. Q. (2022). Capturing strategies and difficulties in solving negative integers : A case study of instrumental understanding. 4, 64–87. https://doi.org/10.17648/acta.scientiae.6432

Bakker, A. (2018). Design research in education : A practical guide for early career researchers. Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 711 Third Avenue, New York, NY 10017 Routledge.

Bofferding, L., & Richardson, S. E. (2013). Investigating integer addition and Subtraction: A task analysis. North American Chapter of the International Group for the Psychology of Mathematics Education, 111–118. https://files.eric.ed.gov/fulltext/ED584472.pdf

Chevalier, M., Giang, C., El-Hamamsy, L., Bonnet, E., Papaspyros, V., Pellet, J. P., Audrin, C., Romero, M., Baumberger, B., & Mondada, F. (2022). The role of feedback and guidance as intervention methods to foster computational thinking in educational robotics learning activities for primary school. Computers and Education, 180(December 2021), 1–15. https://doi.org/10.1016/j.compedu.2022.104431

D’Ambrosio, U. (2016). An overview of the history of ethnomathematics bt - current and future perspectives of ethnomathematics as a program (M. Rosa, U. D’Ambrosio, D. C. Orey, L. Shirley, W. V Alangui, P. Palhares, & M. E. Gavarrete (eds.); pp. 5–10). Springer International Publishing. https://doi.org/10.1007/978-3-319-30120-4_2

Edo, S. I., Tanghamap, K., & Tasik, W. F. (2015). Model pembelajaran penjumlahan dan pengurangan bilangan melalui pendekatan pmri konteks permainan karet gelang [Learning model of addition and subtraction of numbers through the PMRI approach in the context of the rubber band game]. Jurnal Pendidikan Matemtika Sriwijaya, 9(2), 74–99. https://doi.org/https://doi.org/10.22342/jpm.9.2.2428.99%20-%20123

Forgasz, H., & Markovits, Z. (2018). Elementary students’ views on the gendering of mathematics. European Journal of Educational Research, 7(4), 867–876. https://doi.org/10.12973/eu-jer.7.4.867

Gravemeijer, K., & Eerde, D. van. (2009). Design Research as a Means for Building a Knowledge Base for Teachers and Teaching in Mathematics Education. The Elementary School Journal, 109(5), 510–524. https://doi.org/http://dx.doi.org/10.1086/596999

Güc, F. A., & Türker, A. A. (2021). An investigation of the noticing skills of mathematics teachers to their students’ misconceptions in written responses 1. International Journal of Curriculum and Instruction, 13(June 2018), 1309–1323. https://files.eric.ed.gov/fulltext/EJ1292015.pdf

Gurbuz, M. C., & Ozdemir, M. E. (2020). A learning trajectory study on how the concept of variable is constructed by students. World Journal of Education, 10(1), 134–148. https://doi.org/10.5430/wje.v10n1p134

Hadi, S. (2017). Pendidikan matematika realistik (teori, pengembangan, dan implementasinya) [Realistic mathematics education (theory, development and implementation)]. (ed. 1). Rajawali Pers.

Khairunnisak, C., Johar, R., Zubainur, C. M., & Sasalia, P. (2021). Learning trajectory of algebraic expression: Supporting students’ mathematical representation ability. Mathematics Teaching-Research Journal, 13(4), 27–41. https://files.eric.ed.gov/fulltext/EJ1332355.pdf

Kurniawati, L., & Amir, M. F. (2022). Development of learning trajectory of perimeter and area of squares and rectangles through various tasks. Premiere Educandum, 12(1), 41–55. https://doi.org/10.25273/pe.v12i1.12121

Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science, and Technology, 9 (1), 1–21. https://doi.org/https://doi.org/10.46328/ijemst.1111

Makonye, J. P., & Fakude, J. (2016). A study of errors and misconceptions in the learning of addition and subtraction of directed numbers in grade 8. SAGE Open, 6(4), 1–10. https://doi.org/10.1177/2158244016671375

Mania, S. (2021). Teachers ’ perception toward the use of ethnomathematics approach in teaching math. International Journal of Education in Mathematics, Science and Technology, 9 (2), 282–298. https://doi.org/https://doi.org/10.46328/ijemst.1551

Maryati, & Prahmana, R. C. I. (2021). Learning trajectory of dilation and reflection in transformation geometry through the motifs of bamboo woven. Didaktik Matematika, 4185(2018), 134–147. https://doi.org/10.24815/jdm.v8i2.21283

Muslimin, Putri, R. I. I., & Somakim. (2012). Desain pembelajaran pengurangan bilangan bulat melalui permainan tradisional congklak berbasis PMRI di kelas IV sekolah dasar [Design of learning to reduce integers through the traditional PMRI-based congklak game in grade IV elementary school]. Kreano: Jurnal Matematika Kreatif-Inovatif, 3(2), 100–112. https://doi.org/10.15294/kreano.v3i2.2642

Muslimin, Putri, R. I. I., Zulkardi, & Nyimas, A. (2020). Learning integers with realistic mathematics. Journal on Mathematics Education, 11(3), 363–384. https://doi.org/http://doi.org/10.22342/jme.11.3.11721.363 - 384

Nur, A. S., Kartono, K., Zaenuri, Z., & Rochmad, R. (2020). The learning trajectory construction of elementary school students in solving integer word problems. Participatory Educational Research, 9(1), 404–424. https://doi.org/10.17275/per.

Nuraida, I., & Amam, A. (2019). Hypothetical learning trajectory in realistic mathematics education to improve the mathematical communication of junior high school students. Infinity Journal, 8(2), 247–258. https://doi.org/10.22460/infinity.v8i2.p247-258

Nurjanah, I., & Alyani, F. (2021). Kecemasan matematika siswa sekolah menengah pada pembelajaran matematika dalam jaringan [Mathematics anxiety of high school students on online mathematics learning]. Jurnal Elemen, 7(2), 407–424. https://doi.org/10.29408/jel.v7i2.3522

Özdemir, A. Ş., Karaşan, S., & Şahal, M. (2021). An examination of the relationship between secondary school students’ abstract thinking skills, self-efficacy perceptions and attitudes towards mathematics. Participatory Educational Research, 8(2), 391–406. https://doi.org/10.17275/per.

Paliwal, V., & Baroody, A. J. (2020). Fostering the learning of subtraction concepts and the subtraction-as-addition reasoning strategy. Early Childhood Research Quarterly, 51, 403–415. https://doi.org/10.1016/j.ecresq.2019.05.008

Risdiyanti, I., & Prahmana, R. C. I. (2018). Ethnomathematics: Exploration in Javanese culture. Journal of Physics: Conference Series, 943(1), 1–6. https://doi.org/10.1088/1742-6596/943/1/012032

Risdiyanti, I., & Prahmana, R. C. I. (2021). Designing learning trajectory of set through the indonesian shadow puppets and mahabharata stories. Infinity Journal, 10(2), 331. https://doi.org/10.22460/infinity.v10i2.p331-348

Sari, D. L., & Nursyahidah, F. (2022). Learning design for statistics materials using the context of traditional market assisted by interactive videos. Jurnal Elemen, 8(January), 29–42. https://doi.org/https:/doi.org/10.29408/jel.v8i1.4067

Shutenko, E. N., Shutenko, A. I., Kuzmicheva, T. V., Koreneva, A. V., Romanova, G. A., & Talysheva, I. A. (2021). Attractive spheres of students’ self-realization as practices for supporting their psychological well-being in university education. International Journal of Cognitive Research in Science, Engineering and Education, 9(2), 173–188. https://doi.org/10.23947/2334-8496-2021-9-2-173-188

Stephan, M., & Akyuz, D. (2015). A proposed instructional theory for integer addition and subtraction. National Council of Teachers of Mathematics, 43(4), 428–464. https://doi.org/DOI:10.5951/jresematheduc.43.4.0428

Stovner, R. B., & Klette, K. (2022). Teacher feedback on procedural skills, conceptual understanding, and mathematical practices: A video study in lower secondary mathematics classrooms. Teaching and Teacher Education, 110, 1–12. https://doi.org/10.1016/j.tate.2021.103593

Susanti, E. (2020). Eksplorasi etnomatematika konsep operasi hitung dalam permainan tradisional kempreng [Ethnomathematical exploration of the concept of arithmetic operations in the traditional game of kempreng]. Suska Journal of Mathematics Education, 6(1), 1–8. http://ejournal.uin-suska.ac.id/index.php/SJME/article/view/10025

Wessman-Enzinger, N. M. (2019). Grade 5 children’s drawings for integer addition and subtraction open number sentences. Journal of Mathematical Behavior, 53(February), 105–128. https://doi.org/10.1016/j.jmathb.2018.03.010

DOI: https://doi.org/10.29408/jel.v8i2.5541


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