Effects of Think–Pair–Share on Students’ Achievement and Improvement in Mathematical Understanding of Linear Equations

Merlina Dwi Astuti; Attin Warmi; Haerudin

doi:10.31949/dm.v8i2.18704

Authors

Merlina Dwi Astuti Universitas Singaperbangsa Karawang, Indonesia
Attin Warmi Universitas Singaperbangsa Karawang, Indonesia
Haerudin Universitas Singaperbangsa Karawang, Indonesia

DOI:

https://doi.org/10.31949/dm.v8i2.18704

Abstract

Developing students' mathematical understanding remains a persistent challenge in mathematics education, particularly in learning algebraic concepts such as linear equations, where students frequently rely on procedural knowledge rather than conceptual reasoning. This study investigated the effectiveness of the Think–Pair–Share (TPS) strategy in improving students' mathematical understanding of linear equations compared with conventional instruction. A quasi-experimental nonequivalent pretest–posttest control group design was employed involving 74 eighth-grade students from a public junior high school in Karawang, Indonesia. Participants were selected through purposive sampling and assigned to an experimental group (n = 37) and a control group (n = 37). Mathematical understanding was measured using an essay test developed from the National Council of Teachers of Mathematics (NCTM) indicators, and the data were analyzed using independent-samples t-tests and N-gain analysis. The results indicated no significant difference in students' initial mathematical understanding between the groups (p = .604). Following the intervention, students taught through TPS achieved significantly higher posttest scores than those receiving conventional instruction (58.78 vs. 47.30; p = .026) and demonstrated greater learning improvement, with a moderate N-gain (0.391) compared with the control group's low N-gain (0.242; p = .021). The posttest comparison also yielded a moderate practical effect (Cohen's d = 0.53), indicating that TPS produced educationally meaningful improvements in students' conceptual learning. These findings suggest that TPS provides an effective collaborative learning environment for strengthening students' mathematical understanding of linear equations and supports its implementation as a pedagogical strategy for secondary mathematics instruction.

Keywords:

Think–Pair–Share, Mathematical understanding, Cooperative learning, Linear equations, Quasi-experimental study

Downloads

Download data is not yet available.

References

Ahmad, M., & Dogar, A. H. (2023). Effect of collaborative learning on conceptual understanding ability in mathematics among 5th grade neglected children. Annals of Human and Social Sciences, 4(2), 205–213. https://doi.org/10.35484/ahss.2023(4-II)19

Akpan, E. E., & Clark, L. J. (2023). Independent t-test statistics: Its relevance in educational research. International Journal of Eminent Scholars, 10(1), 79–88. https://mail.globalacademicstar.com/download/article/independent-t-test-statistics-it-s-relevance-in-educational-research.pdf

Asria, V. Z. (2019). Improving concept comprehension ability in mathematics by using mathematical model: Think–Pair–Share approach. Journal of Physics: Conference Series, 1402(7), 077083. https://doi.org/10.1088/1742-6596/1402/7/077083

Baxter, J. A., & Williams, S. (2010). Social and analytic scaffolding in middle school mathematics: Managing the dilemma of telling. Journal of Mathematics Teacher Education, 13(1), 7–26. https://doi.org/10.1007/s10857-009-9121-4

Beckmann, A., & Michelsen, C. (2022). Conceptual understanding and mathematical literacy through interdisciplinary activities between mathematics and the sciences—Findings with physics, chemistry, and biology. In C. Michelsen et al. (Eds.), Mathematics and Its Connections to the Arts and Sciences (MACAS) (Vol. 19). Springer. https://doi.org/10.1007/978-3-031-10518-0_20

Bell, C. V., & Pape, S. J. (2012). Scaffolding students’ opportunities to learn mathematics through social interactions. Mathematics Education Research Journal, 24(4), 423–445. https://doi.org/10.1007/s13394-012-0048-1

Booth, J. L., McGinn, K. M., Barbieri, C., & Young, L. K. (2017). Misconceptions and learning algebra. In S. Stewart (Ed.), And the Rest Is Just Algebra. Springer. https://doi.org/10.1007/978-3-319-45053-7_4

Bulus, M. (2021). Sample size determination and optimal design of randomized/non-equivalent pretest–posttest control-group designs. Adıyaman University Journal of Educational Sciences, 11(1), 48–69. https://doi.org/10.17984/adyuebd.941434

Cai, J., & Ding, M. (2017). On mathematical understanding: Perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teacher Education, 20, 5–29. https://doi.org/10.1007/s10857-015-9325-8

Chapman, O. (2013). Mathematical-task knowledge for teaching. Journal of Mathematics Teacher Education, 16, 1–6. https://doi.org/10.1007/s10857-013-9234-7

Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13–20. https://doi.org/10.3102/0013189X023007013

Dewi, I. L. K., Zaenuri, Dwijanto, & Mulyono. (2021). Identification of mathematics prospective teachers’ conceptual understanding in determining solutions of linear equation systems. European Journal of Educational Research, 10(3), 1157–1170. https://doi.org/10.12973/eu-jer.10.3.1157

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/s10649-012-9437-3

Huinker, D. (2018). Principles to Actions: Moving to a framework for teaching mathematics. Teaching Children Mathematics, 25(3), 133–136. https://doi.org/10.5951/teacchilmath.25.3.0133

Jarupunphol, P., Khongman, A., Pibulpol, C., Silhavy, R., & Silhavy, P. (2025). Applying Cronbach's alpha to ensure reliable online testing in e-learning environments. In R. Silhavy & P. Silhavy (Eds.), Artificial Intelligence and System Engineering (Lecture Notes in Networks and Systems, Vol. 1490). Springer. https://doi.org/10.1007/978-3-031-96759-7_8

Kazemi, E., & Stipek, D. (2009). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Journal of Education, 189(1–2), 123–137. https://doi.org/10.1177/0022057409189001-209

Luthfiani, N. L., & Nurjanah. (2022). The effect of Think–Pair–Share cooperative learning on students' mathematical communication ability in Indonesia: Meta-analysis study. AIP Conference Proceedings, 2468(1), 070047. https://doi.org/10.1063/5.0102565

Mathaba, P. N., Bayaga, A., Tîrnovan, D., & Bossé, M. J. (2024). Error analysis in algebra learning: Exploring misconceptions and cognitive levels. Journal on Mathematics Education, 15(2), 575–592. https://doi.org/10.22342/jme.v15i2.pp575-592

Mengistie, S. M. (2020). Enhancing students’ understanding of linear equation with one variable through teaching. International Journal of Trends in Mathematics Education Research, 3(2), 69–80. https://doi.org/10.33122/ijtmer.v3i2.148

Moschkovich, J. N. (2015). Scaffolding student participation in mathematical practices. ZDM Mathematics Education, 47(7), 1067–1078. https://doi.org/10.1007/s11858-015-0730-3

Moschkovich, J., & Zahner, W. (2018). Using the academic literacy in mathematics framework to uncover multiple aspects of activity during peer mathematical discussions. ZDM Mathematics Education, 50(6), 999–1011. https://doi.org/10.1007/s11858-018-0982-9

Ndemo, Z., & Ndemo, O. (2018). Secondary school students' errors and misconceptions in learning algebra. Journal of Education and Learning, 12(4), 690–701. https://doi.org/10.11591/edulearn.v12i4.9556

Niss, M., & Jablonka, E. (2020). Mathematical literacy. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-030-15789-0_100

Oktaç, A. (2018). Conceptions about system of linear equations and solution. In S. Stewart, C. Andrews-Larson, A. Berman, & M. Zandieh (Eds.), Challenges and strategies in teaching linear algebra (ICME-13 Monographs). Springer. https://doi.org/10.1007/978-3-319-66811-6_4

Pulungan, R. R., & Suhendra. (2019). Analysis of student’s misconception in solving system of linear equation in two variables. In Journal of Physics: Conference Series (Vol. 1157, No. 4, Article 042113). IOP Publishing. https://doi.org/10.1088/1742-6596/1157/4/042113

Qetrani, S., Ouailal, S., & Achtaich, N. (2021). Enhancing students’ conceptual and procedural knowledge using a new teaching approach of linear equations based on the equivalence concept. Eurasia Journal of Mathematics, Science and Technology Education, 17(7), Article em1978. https://doi.org/10.29333/ejmste/10938

Rihi, F., & Saija, L. M. (2021). Analisis kemampuan pemahaman matematis peserta didik smp pada materi persamaan garis lurus ditinjau berdasarkan gender. Jurnal Pendidikan Matematika Dan Sains, 9(2), 69-76. http://dx.doi.org/10.21831/jpms.v9i1.44944

Robinson, R. S. (2023). Purposive sampling. In F. Maggino (Ed.), Encyclopedia of Quality of Life and Well-Being Research. Springer. https://doi.org/10.1007/978-3-031-17299-1_2337

Russell, M., O'Dwyer, L. M., & Miranda, H. (2009). Diagnosing students' misconceptions in algebra: Results from an experimental pilot study. Behavior Research Methods, 41(2), 414–424. https://doi.org/10.3758/BRM.41.2.414

Setiawan, R., Wagiran, W., & Alsamiri, Y. (2024). Construction of an instrument for evaluating the teaching process in higher education: Content and construct validity. REID (Research and Evaluation in Education), 10(1). https://doi.org/10.21831/reid.v10i1.63483

Simon, M. A. (2017). Explicating mathematical concept and mathematical conception as theoretical constructs for mathematics education research. Educational Studies in Mathematics, 94, 117–137. https://doi.org/10.1007/s10649-016-9728-1

Siswanto, D. H., & Susetyawati, M. E. (2024). Comparison of the effectiveness of cooperative learning models TPS and GI on students’ mathematical concept understanding ability. International Journal of Scientific Multidisciplinary Research, 2(7), 875–888. https://doi.org/10.55927/ijsmr.v2i7.10034

Smith, M., Bill, V., & Raith, M. L. (2018). Promoting a conceptual understanding of mathematics. Mathematics Teaching in the Middle School, 24(1), 36–43. https://doi.org/10.5951/mathteacmiddscho.24.1.0036

Taguma, M., Makowiecki, K., & Gabriel, F. (2023). OECD Learning Compass 2030: Implications for mathematics curricula. In Y. Shimizu & R. Vithal (Eds.), Mathematics Curriculum Reforms Around the World. Springer. https://doi.org/10.1007/978-3-031-13548-4_32

Talkhan, E., Alhubaidah, S., Muthanna, A., & Qadhi, S. (2025). The effect of cooperative learning toward mathematics achievement of primary students: A systematic review using meta-analysis. Social Sciences & Humanities Open, 12, 102247. https://doi.org/10.1016/j.ssaho.2025.102247

Welder, R. M. (2012). Improving algebra preparation: Implications from research on student misconceptions and difficulties. School Science and Mathematics, 112(4), 255–264. https://doi.org/10.1111/j.1949-8594.2012.00136.x

Wright, V. (2018). Vygotsky and a global perspective on scaffolding in learning mathematics. In J. Zajda (Ed.), Globalisation and education reforms (Globalisation, Comparative Education and Policy Research, Vol. 19). Springer. https://doi.org/10.1007/978-94-024-1204-8_8

Zaki, A., Sahid, S., Nurhaliza, R., Naufal, M. A., Huda, M., & Hassan, M. N. (2024). Enhancing mathematical achievement through the Think–Pair–Share cooperative learning model with Higher-Order Thinking Skills questions. Jurnal Riset Pendidikan Matematika, 11(2), 106–117. https://doi.org/10.21831/jrpm.v11i2.76963