# The Innovative Lesson Study for Enhancing Grade 2 Students’ Multiplication Conception through Open Approach

## Main Article Content

## Abstract

The paper aimed to clarify the innovative lesson study learning activities for enhancing Grade 2 students’ multiplication conception. The paper provided the lesson study environment which allowed the primary school teacher could develop the lesson plan about multiplication conception through open approach. Regarding on the open approach, the cycle of lesson study focused how to provide students’ openly constructing their meaning of multiplication based on everyday life situation. The lesson plans about multiplication concept were developed based on the situations of calculating amount of things in groups that each group has same number of thing. The paper will highlight these situations in order to visualize how they allow students to construct their concepts of multiplication and to generate multiplication symbol. The paper has implications for developing constructivist mathematics learning for Grade 2 students.

## Article Details

*Asia Research Network Journal of Education*,

*3*(3), 108–118. Retrieved from https://so05.tci-thaijo.org/index.php/arnje/article/view/268340

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright: CC BY-NC-ND 4.0

## References

Anghileri, J. (1989). An investigation of young children’s understanding of multiplication. Educational Studies in Mathematics, 20(4), 367–385.

Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2009). The array representation and primary children’s understanding and reasoning in multiplication. Educational Studies in Mathematics, 70(3), 217-241. doi:10.1007/s10649-008-9145-1

Baroody, A., Feil, Y., & Johnson, A. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38(2), 115-131. doi:10.2307/30034952

Battista, M. (1999). The importance of spatial structuring in geometric reasoning. Teaching Children Mathematics, 6(3), 170–178.

Chin, K. E., & Jiew, F. F. (2019). Changes of meanings in multiplication across different contexts: The case of Amy and Beth. EURASIA Journal of Mathematics, Science and Technology Education, 15(8), em1739. https://doi.org/10.29333/ejmste/108440

Clark, F., & Kamii, C. (1996). Identifcation of multiplicative thinking in children in grades 1–5. Journal for Research in Mathematics Education, 27(1), 41–51. https://doi.org/10.2307/749196

Confrey, J., & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26(1), 66-86. doi:10.2307/749228

Downton, A., & Sullivan, P. (2017). Posing complex problems requiring multiplicative thinking prompts students to use sophisticated strategies and build mathematical connections. Educational Studies in Mathematics, 95(3), 303–328.

De Corte, E., & Verschaffel, L. (1996). An empirical test of the impact of primitive intuitive models of operations on solving word problems with a multiplicative structure. Learning and Instruction, 6(3), 219- 242. doi:10.1016/0959-4752(96)00004-7

Ehlert, A., Fritz, A., Arndt, D., & Leutner, D. (2013). Arithmetische Basiskompetenzen von Schülerinnen und Schülern in den Klassen 5 bis 7 der Sekundarstufe. Journal für Mathematik-Didaktik, 34(2), 237–263.

Fischbein, E., Deir, M., Nello, M., & Marino, M. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17.

Götze, D. and Baiker, A. (2021) Language‑responsive support for multiplicative thinking as unitizing: results of an intervention study in the second grade. ZDM, 53: 263–275. https://doi.org/10.1007/s11858-020-01206-1

Gray, E., & Tall, D. (1994). Duality, ambiguity, and flexibility: A "proceptual" view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 116-140. doi:10.2307/749505

Gravemeijer, K., & Doorman, M. (1999). Context problem in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111-129.

Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmillan.

Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, N.J.: Erlbaum.

Inprasitha, M. One feature of adaptive lesson study in Thailand: Designing learning unit. Proceeding of the 45th Korean National Meeting of Mathematics Education (pp. 193-206). Gyeongju: Dongkook University. (2010).

Kim V, Douch M, Thy S, Yuenyong C, Thinwiangthong S 2019. Challenges of implementing Lesson Study in Cambodia: Mathematics and Science Teaching by using Lesson Study at Happy Chandara School. Journal of Physics: Conference Series, 1340 (1), 012071

Larsson, K. (2016). Students’ understandings of Multiplication. Sweden: Holmbergs, Malmö

Larsson, K., Pettersson, K., & Andrews, P. (2017). Students’ conceptualisations of multiplication as repeated addition or equal groups in relation to multi-digit and decimal numbers. The Journal of Mathematical Behavior, 48, 1-13. https://doi.org/10.1016/j.jmathb.2017.07.003

Maciejewski, W., & Star, J. (2016). Developing flexible procedural knowledge in undergraduate calculus. Research in Mathematics Education, 1-18. doi:10.1080/14794802.2016.1148626

Matoba, M. (2005). Improving Teaching and Enhancing Learning: A Japanese Perspective. The First Annual Conference on Learning Study, The Hong Kong Institute of Education, 1-3 December 2005

Mulligan, J., & Watson, J. (1998). A developmental multimodal model for multiplication and division. Mathematics Education Research Journal, 10(2), 61–86.

Nohda, N. (2000). Teaching by open-approach method in Japanese mathematics classroom. Proceeding of the 24th conference of the international Group for the Psychology of Mathematics Education, Hiroshima, Japan, July 23-27, volume 1-39-53.

Nunes, T., & Bryant, P. (2010). Paper 4: Understanding relations and their graphical representation. In T. Nunes, P. Bryant, & A. Watson (Eds.), Key understandings in mathematics learning. Retrieved from http://www.nuffieldfoundation.org/key-understandingsmathematics- learning.

Pape, S., & Tchoshanov, M. (2001). The role of representation(s) in developing mathematical understanding. Theory into Practice, 40(2), 118-127. doi:10.1207/s15430421tip4002_6

Pehkonen, E. (1995). Using open-ended problem in mathematics. Zentralblatt fur Didaktik der Mathematik, 27(2), 67-71.

Phaikhumnam, W. and Yuenyong, C. (2018). Improving the primary school science learning unit about force and motion through lesson study. AIP Conference Proceedings. 1923, 030037-1 – 030037-5.

Richland, L., Stigler, J., & Holyoak, K. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist, 47(3), 189-203. doi:10.1080/00461520.2012.667065

Rittle-Johnson, B., Schneider, M., & Star, J. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587-597. doi:10.1007/s10648-015-9302-x

Ruwisch, S. (1998). Children’s multiplicative problem-solving strategies in real-world situations. In O. Alwyn & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 73–80). Stellenbosch: PME.

Selling, S. K. (2016). Learning to represent, representing to learn. Journal of Mathematical Behavior, 41, 191-209. doi:10.1016/j.jmathb.2015.10.003

Sherin, B., & Fuson, K. (2005). Multiplication strategies and the appropriation of computational resources. Journal for Research in Mathematics Education, 36(4), 347–395.

Siemon, D., Breed, M., & Virgona, J. (2005). From additive to multiplicative thinking. In J. Mousley, L. Bragg, & C. Campbell (Eds.), Mathematics—Celebrating achievement, Proceedings of the 42nd conference of the mathematical association of Victoria (pp. 278– 286). Melbourne: MAV

Simon, M., & Blume, G. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25(5), 472–494. https://doi.org/10.2307/749486.

Singh, P. (2000). Understanding the concept of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics, 14(3), 271–292.

Star, J. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404-411.

Stefe, L. P. (1992). Schemes of action and operation involving composite units. Learning and Individual Diferences, 4(3), 259–309. https://doi.org/10.1016/1041-6080(92)90005-Y.

Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving in the classroom. New York: The Free Press.

Stylianides, G., Stylianides, A., & Shilling-Traina, L. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), 1463-1490. doi:10.1007/s10763-013-9409-9

Suanse, K. ., & Yuenyong, C. (2023). Enhancing Grade 10 Students’ Problem Solving Ability in Basic Knowledge on Analytical Geometry Flipped Classroom. Asia Research Network Journal of Education, 3(1), 13–24. Retrieved from https://so05.tci-thaijo.org/index.php/arnje/article/view/264864

Sullivan, P., Clarke, D., Cheeseman, J., & Mulligan, J. (2001). Moving beyond physical models in learning multiplicative reasoning. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 233–240). Utrecht: PME.

Thompson, P., & Saldanha, L. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 95–113). Reston: National Council of Teachers of Mathematics.

Tupsai, J., Yuenyong, C. , Taylor, P.C. (2015). Initial implementation of constructivist physics teaching in Thailand: A case of bass pre-service teacher. Mediterranean Journal of Social Sciences, 6(2), 506-513.

Woranetsudathip, N. and Yuenyong, C. (2015). Enhancing grade 1 Thai students’ learning about mathematical ideas on addition through lesson study and open approach. Mediterranean Journal of Social Sciences, 6(2S1), 28-33.

Woranetsudathip, N. . (2021). Examine First Grade Students’ Strategies of Solving Open-ended Problems on Addition. Asia Research Network Journal of Education, 1(1), 15–24. Retrieved from https://so05.tci-thaijo.org/index.php/arnje/article/view/250020

Woranetsudathip, N, Yuenyong, C, and Nguyen, TT (2021). The innovative lesson study for enhancing students’ mathematical ideas about addition and subtraction through open approach. Journal of Physics: Conference Series 1835 (1), 012061

Yuenyong, C. and Thathong, K. (2015). Physics teachers’ constructing knowledge base for physics teaching regarding constructivism in Thai contexts. Mediterranean Journal of Social Sciences, 6(2), 546-553.