Students’ Intuition in Mathematics Class Using Lesson Study and Open Approach

Affiliation(s)

^{1}
Doctoral Program in Mathematics Education, Khon Kaen University, Khon Kaen, Thailand.

^{2}
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, Thailand.

^{3}
Center for Research in Mathematics Education, Khon Kaen University, Khon Kaen, Thailand.

ABSTRACT

The objective of this article is to investigate students’ intuition in mathematics class using Lesson Study and Open Approach. The research methodology employed was the qualitative research methods of teaching experiment combined with an ethnographic study. The study’s target group consists of three Grade 2 students at Ban Bueng Niam Bueng Krainoon School in Khon Kaen Province during the 2012 Academic Year. This is the school that participated in the professional development of mathematics teachers with Lesson Study and Open Approach innovation project. The researcher collected data from a mathematics class that taught multiplication learning unit (1) from the mathematics textbook for Grade 2 students. This is the textbook used in the professional development of mathematics teachers with Lesson Study and Open Approach innovation project. The research findings are: Mathematics class using Lesson Study and Open Approach allows students to intuitively learn the content of a basic multiplication unit. Students’ intuition was developed during Step 1 (posing open-ended problems) and Step 2 (students’ self-learning through problemsolving) of the Open Approach process. Students intuitively discovered the repeated addition and multiplication methods in solving multiplication problems.

The objective of this article is to investigate students’ intuition in mathematics class using Lesson Study and Open Approach. The research methodology employed was the qualitative research methods of teaching experiment combined with an ethnographic study. The study’s target group consists of three Grade 2 students at Ban Bueng Niam Bueng Krainoon School in Khon Kaen Province during the 2012 Academic Year. This is the school that participated in the professional development of mathematics teachers with Lesson Study and Open Approach innovation project. The researcher collected data from a mathematics class that taught multiplication learning unit (1) from the mathematics textbook for Grade 2 students. This is the textbook used in the professional development of mathematics teachers with Lesson Study and Open Approach innovation project. The research findings are: Mathematics class using Lesson Study and Open Approach allows students to intuitively learn the content of a basic multiplication unit. Students’ intuition was developed during Step 1 (posing open-ended problems) and Step 2 (students’ self-learning through problemsolving) of the Open Approach process. Students intuitively discovered the repeated addition and multiplication methods in solving multiplication problems.

Cite this paper

Panbanlame, K. , Sangaroon, K. & Inprasitha, M. (2014). Students’ Intuition in Mathematics Class Using Lesson Study and Open Approach.*Psychology, 5,* 1503-1516. doi: 10.4236/psych.2014.513161.

Panbanlame, K. , Sangaroon, K. & Inprasitha, M. (2014). Students’ Intuition in Mathematics Class Using Lesson Study and Open Approach.

References

[1] Anghileri, J. (1989). An Investigation of Young Children’s Understanding of Multiplication. Educational Studies in Mathematics, 20, 367-385.

http://dx.doi.org/10.1007/BF00315607

[2] Baba, T. (2007). Japanese Education and Lesson Study: An Overview. In M. Isoda, M. Stephen, Y. Ohara & T. Miyakawa (Eds.). Japanese Lesson Study in Mathematics: Its Impact, Diversity and Potential for Educaional Improvement (pp. 2-7). Singapore: World Scientific Publishing.

http://dx.doi.org/10.1142/9789812707475_0001

[3] Ben-Zeev, T., & Star, J. (2001). Intuitive Mathematics: Theoretical and Educational Implications. In B. Torff & R. J. Sternberg (Eds.), Understanding and Teaching the Intuitive Mind: Student and Teacher Learning (pp. 29-56). Mahwah, NJ: Lawrence Erlbaum.

[4] Bruner, J. (1960). The Process of Education. London: Oxford University.

[5] Fischbein, E. (1987). Intuition in Science and Mathematics. Dordrecht: Reidel.

[6] Fischbein, E. (1994). The Interaction between the Formal, the Algorithmic, and the Intuitive Components in a Mathematical Activity. In R. Biehler, R. W. Scholz, R. Straber, & B. Winkelmann (Eds.), Didactics of Mathematics as a Scientific Discipline (pp. 231-245). Dordrecht: Kluwer Academic.

[7] Fischbein, E. (1999). Intuitions and Schema in Mathematical Reasoning. Educational Studies in Mathematics, 38, 11-50.

http://dx.doi.org/10.1023/A:1003488222875

[8] Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The Role of Implicit Models in Solving Verbal Problems in Multiplication and Division. Journal for Research in Mathematics Education, 16, 3-17.

http://dx.doi.org/10.2307/748969

[9] Gakkoh Tosho Co., Ltd. (2005). Study with Your Friends MATHEMATICS for Elementary School 2nd Grade. Tokyo: Gakkotosho.

[10] Gelman, R (1980). What Young Children Know about Numbers. Educational Psychologist, 15, 54-68.

http://dx.doi.org/10.1080/00461528009529216

[11] Gelman, R. (1982). Basic Numerical Abilities. In R. J. Sternberg (Ed.), Advances in the Psychology of Human Intelligence (pp. 181-205). Hillsdale, Lawrence Erlbaum Associates.

[12] Ikeda, T. (2010). Roots of the Open-Ended Approach: Introduction. Special Issue (EARCOME5) Mathematics Education Theories for Lesson Study: Problem Solving Approach and the Curriculum through Extension and Integration. Journal of Japan Society of Mathematical Education, 6-7.

[13] Inprasitha, M. (2003). Reforming of Mathematics Learning in School Focusing on Mathematical Process. Khonkhan. Khonkhan Publishing.

[14] Inprasitha, M., & Loipha, S. (2004). Innovative Teachers Professional Development to Promote Mathematics Learning. KKU Journal of Mathematics Education, 1, 18-28.

[15] Inprasitha, M. (2006). Open-Ended Approach and Teacher Education. Tsukuba Journal of Educational Study in Mathematics, 25, 169-178.

[16] Inprasitha, M. (2010). One Feature of Adaptive Lesson Study in Thailand: Designing Learning Unit. In C. S. Cho, S. G. Lee, & Y. H. Choe (Eds.). Proceedings of the 45th National Meeting of Mathematics Education, Korea: Dongkook University, Gyeongju, 193-206.

[17] Kilpatrick, J. (1992). A History of Research in Mathematics Education. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 3-38). New York: Macmillan.

[18] Mulligan, J. T., & Michelmore, M. C. (1997). Young Children’s Intuitive Models of Multiplication and Division. Journal for Research in Mathematical Education, 28, 309-330.

http://dx.doi.org/10.2307/749783

[19] 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 (PME 24), Hiroshima, Japan: Hiroshima University, 39-54.

[20] Polya, G. (1954). Mathematics and Plausible Reasoning (Volume II): Patterns of Plausible Inference. Princeton, NJ: Princeton University Press.

[21] Thurston, W. P. (1990). Mathematical Education. Notices of the American Mathematical Society, 37, 844-850.

[22] Yoshida, M. (2008). Exploring Ideas for a Mathematics Teacher Educator’s Contribution to Lesson Study. In D. Tirosh, & T. Wood (Eds.), Tools and Process in Mathematics Teacher Education (pp. 85-106). Rotterdam: Sense Publishers.

[1] Anghileri, J. (1989). An Investigation of Young Children’s Understanding of Multiplication. Educational Studies in Mathematics, 20, 367-385.

http://dx.doi.org/10.1007/BF00315607

[2] Baba, T. (2007). Japanese Education and Lesson Study: An Overview. In M. Isoda, M. Stephen, Y. Ohara & T. Miyakawa (Eds.). Japanese Lesson Study in Mathematics: Its Impact, Diversity and Potential for Educaional Improvement (pp. 2-7). Singapore: World Scientific Publishing.

http://dx.doi.org/10.1142/9789812707475_0001

[3] Ben-Zeev, T., & Star, J. (2001). Intuitive Mathematics: Theoretical and Educational Implications. In B. Torff & R. J. Sternberg (Eds.), Understanding and Teaching the Intuitive Mind: Student and Teacher Learning (pp. 29-56). Mahwah, NJ: Lawrence Erlbaum.

[4] Bruner, J. (1960). The Process of Education. London: Oxford University.

[5] Fischbein, E. (1987). Intuition in Science and Mathematics. Dordrecht: Reidel.

[6] Fischbein, E. (1994). The Interaction between the Formal, the Algorithmic, and the Intuitive Components in a Mathematical Activity. In R. Biehler, R. W. Scholz, R. Straber, & B. Winkelmann (Eds.), Didactics of Mathematics as a Scientific Discipline (pp. 231-245). Dordrecht: Kluwer Academic.

[7] Fischbein, E. (1999). Intuitions and Schema in Mathematical Reasoning. Educational Studies in Mathematics, 38, 11-50.

http://dx.doi.org/10.1023/A:1003488222875

[8] Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The Role of Implicit Models in Solving Verbal Problems in Multiplication and Division. Journal for Research in Mathematics Education, 16, 3-17.

http://dx.doi.org/10.2307/748969

[9] Gakkoh Tosho Co., Ltd. (2005). Study with Your Friends MATHEMATICS for Elementary School 2nd Grade. Tokyo: Gakkotosho.

[10] Gelman, R (1980). What Young Children Know about Numbers. Educational Psychologist, 15, 54-68.

http://dx.doi.org/10.1080/00461528009529216

[11] Gelman, R. (1982). Basic Numerical Abilities. In R. J. Sternberg (Ed.), Advances in the Psychology of Human Intelligence (pp. 181-205). Hillsdale, Lawrence Erlbaum Associates.

[12] Ikeda, T. (2010). Roots of the Open-Ended Approach: Introduction. Special Issue (EARCOME5) Mathematics Education Theories for Lesson Study: Problem Solving Approach and the Curriculum through Extension and Integration. Journal of Japan Society of Mathematical Education, 6-7.

[13] Inprasitha, M. (2003). Reforming of Mathematics Learning in School Focusing on Mathematical Process. Khonkhan. Khonkhan Publishing.

[14] Inprasitha, M., & Loipha, S. (2004). Innovative Teachers Professional Development to Promote Mathematics Learning. KKU Journal of Mathematics Education, 1, 18-28.

[15] Inprasitha, M. (2006). Open-Ended Approach and Teacher Education. Tsukuba Journal of Educational Study in Mathematics, 25, 169-178.

[16] Inprasitha, M. (2010). One Feature of Adaptive Lesson Study in Thailand: Designing Learning Unit. In C. S. Cho, S. G. Lee, & Y. H. Choe (Eds.). Proceedings of the 45th National Meeting of Mathematics Education, Korea: Dongkook University, Gyeongju, 193-206.

[17] Kilpatrick, J. (1992). A History of Research in Mathematics Education. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 3-38). New York: Macmillan.

[18] Mulligan, J. T., & Michelmore, M. C. (1997). Young Children’s Intuitive Models of Multiplication and Division. Journal for Research in Mathematical Education, 28, 309-330.

http://dx.doi.org/10.2307/749783

[19] 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 (PME 24), Hiroshima, Japan: Hiroshima University, 39-54.

[20] Polya, G. (1954). Mathematics and Plausible Reasoning (Volume II): Patterns of Plausible Inference. Princeton, NJ: Princeton University Press.

[21] Thurston, W. P. (1990). Mathematical Education. Notices of the American Mathematical Society, 37, 844-850.

[22] Yoshida, M. (2008). Exploring Ideas for a Mathematics Teacher Educator’s Contribution to Lesson Study. In D. Tirosh, & T. Wood (Eds.), Tools and Process in Mathematics Teacher Education (pp. 85-106). Rotterdam: Sense Publishers.