How Student Teachers Use Proportional Number Line to Teach Multiplication and Division of Fraction: Professional Learning in Context of Lesson Study and Open Approach

Affiliation(s)

Centre of Excellence in Mathematics, CHE, Bangkok, Thailand.

Programme in Mathematics Education, Faculty of Education, Chiang Mai University, Chiang Mai, Thai-land.

Centre of Excellence in Mathematics, CHE, Bangkok, Thailand.

Programme in Mathematics Education, Faculty of Education, Chiang Mai University, Chiang Mai, Thai-land.

ABSTRACT

The objective of this study is to examine how student teachers use proportional number line in teaching multiplication and division of fractions in context of lesson study and open approach. Teaching experiment was employed to conduct this case study qualitative research with two mathematics student teachers who participated in the study as case studies. This research was carried out in two sixth grade mathematics classrooms from two schools project innovated by lesson study and open approach in the second semester of 2012 academic year. Research data included lesson plans on multiplication and division of fractions, classroom observation with video tape recordings, students’ written works and interviewing with the student teachers. The results showed that the student teachers use proportional number line in three ways. Firstly, they use it for asking students to interpret the problems using proportional table aiming at writing equation of the problem correctly in the step of posing open-ended problem situation. Secondly, they use it as a tool for giving student think about how to calculate the answer by themselves. Thirdly, they use it for connecting and checking the various way of thinking about calculation of fractions. The student teachers conceived that learning to teach calculation of fraction with proportional number line is beneficial to their own professional learning in teaching through open approach and student learning and thinking proportionally thought to be the most complex of the elementary mathematics curriculum.

The objective of this study is to examine how student teachers use proportional number line in teaching multiplication and division of fractions in context of lesson study and open approach. Teaching experiment was employed to conduct this case study qualitative research with two mathematics student teachers who participated in the study as case studies. This research was carried out in two sixth grade mathematics classrooms from two schools project innovated by lesson study and open approach in the second semester of 2012 academic year. Research data included lesson plans on multiplication and division of fractions, classroom observation with video tape recordings, students’ written works and interviewing with the student teachers. The results showed that the student teachers use proportional number line in three ways. Firstly, they use it for asking students to interpret the problems using proportional table aiming at writing equation of the problem correctly in the step of posing open-ended problem situation. Secondly, they use it as a tool for giving student think about how to calculate the answer by themselves. Thirdly, they use it for connecting and checking the various way of thinking about calculation of fractions. The student teachers conceived that learning to teach calculation of fraction with proportional number line is beneficial to their own professional learning in teaching through open approach and student learning and thinking proportionally thought to be the most complex of the elementary mathematics curriculum.

KEYWORDS

Proportional Number Line; Multiplication and Division of Fraction; Lesson Study and Open Approach

Proportional Number Line; Multiplication and Division of Fraction; Lesson Study and Open Approach

Cite this paper

Noparit, T. & Saengpun, J. (2013). How Student Teachers Use Proportional Number Line to Teach Multiplication and Division of Fraction: Professional Learning in Context of Lesson Study and Open Approach.*Creative Education, 4,* 19-24. doi: 10.4236/ce.2013.48A005.

Noparit, T. & Saengpun, J. (2013). How Student Teachers Use Proportional Number Line to Teach Multiplication and Division of Fraction: Professional Learning in Context of Lesson Study and Open Approach.

References

[1] Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What make it special? Journal of Teacher Education, 59, 389-407. doi:10.1177/0022487108324554

[2] Cobb, P. & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14, 83-94. doi:10.2307/748576

[3] Crossley, J. N., & Henry, A. S. (1990). Thus, speak al-Khwarimi: A translation of text of Cambridge University Libery. Historia Math, 17, 103-131. doi:10.1016/0315-0860(90)90048-I

[4] Davis, G. E., Hunting, R. P., & Pearn, C. (1993). What might a fraction mean to a child and how would a teacher know? The Journal of Mathematical Behavior, 12, 63-76.

[5] Davis, G. E. (2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. Journal of Mathematical Behavior, 22, 107-111. doi:10.1016/S0732-3123(03)00016-6

[6] Gakkoh Tosho (2005). Study with your friends: Mathematics for elementary school 6th grade. Gakkho Taosho, Japan.

[7] Inprasitha, M. (2010). One feature of adaptive lesson study in Thailand-Designing learning unit. In Proceedings of the 45th Korean National Meeting of Mathematics Education, Dongkook University.

[8] Isoda, M. (2010). Japanese theories for lesson study in mathematics education: A case of problem solving approach. In Y. Shimizu, Y. Sekiguchi, & K. Hatano (Eds.), Proceedings of the 5th East Asia Regional Conference on Mathematics Education, Vol. 1 (pp. 176-181). Tokyo.

[9] Karplus, R., Pulos, S., & Stage, E. K. (1983). Proportional reasoning of early adolescents. In R. Lesh, & M. Landau (Eds.), Acquisition of Mathematics concepts and processes (pp. 45-90). New York.

[10] Kishimoto, T. (2010). Proportional number line. In M. Isoda, & T. Nakamura. (Eds.), Special issue (EARCOME5) mathematics education theories for lesson study: Problem solving approach and the curriculum through extension and integration (pp. 46-47). Tokyo: Bunshoudo Insatusho.

[11] Lo, J. J., & Watanabe, T. (1997). Developing ratio and proportion schemes: A story of a fifth grader. Journal for Research in Mathematics Education, 28, 216-236. doi:10.2307/749762

[12] Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers, understanding of fundamental mathematics in China and the United States, Erlbaum, Mahwah.

[13] Murray, F. B. (1996). Beyond natural teaching: The case for professional education. In F. B. Murray (Ed.), The teacher educator’s handbook: Building a knowledge base for the preparation of teachers (pp. 3-13).

[14] Pearn, C. & Stephens, M. (2004). Why do you have to probe to discover what Year8 students really think about fraction. In I. Putt, R. Faraghher, & M. McLean (Eds.), Mathematics education for the third millennium: Towards 2011. Proceedings of the 27thAnnual Conference of Mathematics education of the Mathematics Education Research Group of Australasia (pp. 430-437). Townsville, Melbourne.

[1] Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What make it special? Journal of Teacher Education, 59, 389-407. doi:10.1177/0022487108324554

[2] Cobb, P. & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14, 83-94. doi:10.2307/748576

[3] Crossley, J. N., & Henry, A. S. (1990). Thus, speak al-Khwarimi: A translation of text of Cambridge University Libery. Historia Math, 17, 103-131. doi:10.1016/0315-0860(90)90048-I

[4] Davis, G. E., Hunting, R. P., & Pearn, C. (1993). What might a fraction mean to a child and how would a teacher know? The Journal of Mathematical Behavior, 12, 63-76.

[5] Davis, G. E. (2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. Journal of Mathematical Behavior, 22, 107-111. doi:10.1016/S0732-3123(03)00016-6

[6] Gakkoh Tosho (2005). Study with your friends: Mathematics for elementary school 6th grade. Gakkho Taosho, Japan.

[7] Inprasitha, M. (2010). One feature of adaptive lesson study in Thailand-Designing learning unit. In Proceedings of the 45th Korean National Meeting of Mathematics Education, Dongkook University.

[8] Isoda, M. (2010). Japanese theories for lesson study in mathematics education: A case of problem solving approach. In Y. Shimizu, Y. Sekiguchi, & K. Hatano (Eds.), Proceedings of the 5th East Asia Regional Conference on Mathematics Education, Vol. 1 (pp. 176-181). Tokyo.

[9] Karplus, R., Pulos, S., & Stage, E. K. (1983). Proportional reasoning of early adolescents. In R. Lesh, & M. Landau (Eds.), Acquisition of Mathematics concepts and processes (pp. 45-90). New York.

[10] Kishimoto, T. (2010). Proportional number line. In M. Isoda, & T. Nakamura. (Eds.), Special issue (EARCOME5) mathematics education theories for lesson study: Problem solving approach and the curriculum through extension and integration (pp. 46-47). Tokyo: Bunshoudo Insatusho.

[11] Lo, J. J., & Watanabe, T. (1997). Developing ratio and proportion schemes: A story of a fifth grader. Journal for Research in Mathematics Education, 28, 216-236. doi:10.2307/749762

[12] Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers, understanding of fundamental mathematics in China and the United States, Erlbaum, Mahwah.

[13] Murray, F. B. (1996). Beyond natural teaching: The case for professional education. In F. B. Murray (Ed.), The teacher educator’s handbook: Building a knowledge base for the preparation of teachers (pp. 3-13).

[14] Pearn, C. & Stephens, M. (2004). Why do you have to probe to discover what Year8 students really think about fraction. In I. Putt, R. Faraghher, & M. McLean (Eds.), Mathematics education for the third millennium: Towards 2011. Proceedings of the 27thAnnual Conference of Mathematics education of the Mathematics Education Research Group of Australasia (pp. 430-437). Townsville, Melbourne.