Students’ Abstraction Process Based on Compression into Thinkable Concept from Blending Embodiment and Symbolism under Context Lesson Study and Open Approach

Affiliation(s)

Doctoral Program in Mathematics Education, Faculty of Education, Khon Kean University, Khon Kean, Thailand.

Center for Research in Mathematics Education, Faculty of Education, Khon Kean University, Khon Kean, Thailand.

Doctoral Program in Mathematics Education, Faculty of Education, Khon Kean University, Khon Kean, Thailand.

Center for Research in Mathematics Education, Faculty of Education, Khon Kean University, Khon Kean, Thailand.

ABSTRACT

The objective of mathematics learning and teaching was to develop students’ concept in content so that the persons as teachers, educators, and researchers would try to search for instruments, and know for comprehending the students’ existing concepts. The study abstraction process based on compression into thinkable concept was to be a major guideline in considering and findings answer in order to understand the students’ concept (Gray & Tall, 2007). In Thai classroom using Lesson Study and Open Approach produced the students’ mathematical thinking by using open-ended problems with designed material for supporting interaction of students and their problem solving arithmetic (Inprasitha, 1997). According to view of Tall (2007a) suggested a parallel construction of compression in the symbolism and embodiment to thinkable concept. This paper aim to analyze the students’ abstraction process based on compression into thinkable concept from blending embodiment and symbolism. The four first grader as targeted group at Kookham Pittayasan School, a project school with supported by CRME, Faculty of Education, Khon Kaen University, Thailand. For research design used ethnographic study and teaching experiment. The collected data were used video analysis, interviewing, and students’ task analysis. The research revealed that, the students’ thinking shift steadily from performing sequence of parallel compression from actions being linked together in increasingly sophisticated ways to thinkable concept in embodiment and symbol- ism. This research revealed that Lesson Study incorporated Open Approach as teaching approach pro- vided to students’ abstraction process from considering that they manipulated with designed materials for supporting and checking their various symbolic thinking before into same effect on arithmetic operation.

The objective of mathematics learning and teaching was to develop students’ concept in content so that the persons as teachers, educators, and researchers would try to search for instruments, and know for comprehending the students’ existing concepts. The study abstraction process based on compression into thinkable concept was to be a major guideline in considering and findings answer in order to understand the students’ concept (Gray & Tall, 2007). In Thai classroom using Lesson Study and Open Approach produced the students’ mathematical thinking by using open-ended problems with designed material for supporting interaction of students and their problem solving arithmetic (Inprasitha, 1997). According to view of Tall (2007a) suggested a parallel construction of compression in the symbolism and embodiment to thinkable concept. This paper aim to analyze the students’ abstraction process based on compression into thinkable concept from blending embodiment and symbolism. The four first grader as targeted group at Kookham Pittayasan School, a project school with supported by CRME, Faculty of Education, Khon Kaen University, Thailand. For research design used ethnographic study and teaching experiment. The collected data were used video analysis, interviewing, and students’ task analysis. The research revealed that, the students’ thinking shift steadily from performing sequence of parallel compression from actions being linked together in increasingly sophisticated ways to thinkable concept in embodiment and symbol- ism. This research revealed that Lesson Study incorporated Open Approach as teaching approach pro- vided to students’ abstraction process from considering that they manipulated with designed materials for supporting and checking their various symbolic thinking before into same effect on arithmetic operation.

Cite this paper

Suthisung, N. & Inprasitha, M. (2012). Students’ Abstraction Process Based on Compression into Thinkable Concept from Blending Embodiment and Symbolism under Context Lesson Study and Open Approach.*Psychology, 3,* 729-736. doi: 10.4236/psych.2012.39110.

Suthisung, N. & Inprasitha, M. (2012). Students’ Abstraction Process Based on Compression into Thinkable Concept from Blending Embodiment and Symbolism under Context Lesson Study and Open Approach.

References

[1] Howat, H. (2005). Participation in elementary mathematics: An analysis of engagement, attainment and intervention. Ph.D. Thesis, Coventry: University of Warwick.

[2] Gakkoh Tosho (2005). Study with your friends mathematics for elementary school 1st grade.

[3] Gray, E., & Tall, D. (1994). Duality, ambiguity and flexibility: A proceptual view of Simple arithmetic. Journal for Research in Mathematics Education, 25, 115-141. doi:10.2307/749505

[4] Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19, 23-40. doi:10.1007/BF03217454

[5] Inprasitha, M. (1997). Problem solving: A basis to reform math ematics instruction. Journal of the National Research Council of Thailand, 29, 221-259.

[6] Inprasitha, M., Pattanajak, A., & Thasarin, P. (2007). To prepare context for leading the teacher professional development of Japan to be called “Lesson Study” implemented in Thailand. Document Later National Academic Meeting Japanese Studies Network. Bangkok: Japanese Studies Network; Thailand: Thammasat University. 152- 163.

[7] Inprasitha, M. (2010). One feature of adaptive lesson study in Thailand: Designing a learning unit. Proceedings of the 45th Korean National Meeting of Mathematics Education, Gyeongju, 8-9 October 2010, 193-206.

[8] Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Hiladelphla: Research for Better School, Inc.

[9] Nohda, N. (1998). Mathematics teaching by “open-approach method” in Japanese classroom activities. Proceedings of ICMI-EARCOME 1, Cheongju, 17-21 August 1998, 185-192.

[10] Nohda, N. (2000). Teaching by approach method in Japanese mathematics classroom. Proceeding of the 24th Conference of the International Group for the Psychology of Mathematics Education, Hiroshima, 23-27 July 2000, 11-39.

[11] Poynter, A. (2004). Effect as a pivot between actions and symbols: The case of vector. Ph.D. Thesis, Coventry: University of Warwick.

[12] Shimada, S., & Becker, P. J. (1997). The open-ended approach: A new proposal for teaching mathematics. Reston: National Council of Teachers of Mathematics.

[13] Skemp, R. R (1971). The psychology of learning mathematics. London: Penguin.

[14] Skemp, R. R. (1987). The psychology of learning mathematics. Hove and London: Lawrence Erlbaum Associated, Inc., 9-21.

[15] Suthisung, N., & Sangaroon, K. (2011a). The steps up of compression to thinkable concept in action of the student’s abstraction process. The 16th Annual Meeting in Mathematics, Khon Kaen, 10-11 March 2011, 413-432.

[16] Sutisung, N., & Sangaroon, K. (2011b). “How to” in the students’ abstraction process through compression to thinkable concept. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Developing Mathematical Thinking), Ankara-Turkey, 10-15 July 2011, 1-398.

[17] Sutisung, N., & Sangaroon, K. (2011c). The students’ process of abstraction based on action in compression to thinkable concept of blending embodiment and symbolism under context using lesson study and open approach. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Developing Mathematical thinking), Ankara-Turkey, 10-15 July 2011, 1-505.

[18] Tall, D. (2004). The nature of mathematical growth. URL (last checked 2 January 2010). http://www.tallfamily.co.uk/davidmathematical-growth/

[19] Tall. D. (2006a). A Theory of mathematical growth through embodiment, symbolism and proof. Annales de Didactique et de Sciences Cognitives, IREM de Strasbourg, Vol. 11, 195-215.

[20] Tall, D. (2006b). Encouraging mathematical thinking that has both power and simplicity. Plenary Presented at the APEC-Tsukuba International Conference, Ichigaya, 3-7 December 2006, 1-15.

[21] Tall, D. (2007a). Developing a theory of mathematical growth. ZDM Mathematics Education, 39, 145-154. doi:10.1007/s11858-006-0010-3

[22] Tall, D. (2007b). Setting lesson study within a long-term framework of learning. Presented at APEC Conference on Lesson Study, Khon Kaen, 14 August 2007, 1-17.

[23] Tall, D. (2008). Using Japanese lesson study in teaching mathematics. Scottish Mathematical Council Journal, 38, 45-50.

[24] Tall, D., & Isoda, M. (2007). Long-term development of mathematical thinking and lesson study. Prepared as a Chapter for a Forthcoming Bookon Lesson Study, 1-34.

[1] Howat, H. (2005). Participation in elementary mathematics: An analysis of engagement, attainment and intervention. Ph.D. Thesis, Coventry: University of Warwick.

[2] Gakkoh Tosho (2005). Study with your friends mathematics for elementary school 1st grade.

[3] Gray, E., & Tall, D. (1994). Duality, ambiguity and flexibility: A proceptual view of Simple arithmetic. Journal for Research in Mathematics Education, 25, 115-141. doi:10.2307/749505

[4] Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19, 23-40. doi:10.1007/BF03217454

[5] Inprasitha, M. (1997). Problem solving: A basis to reform math ematics instruction. Journal of the National Research Council of Thailand, 29, 221-259.

[6] Inprasitha, M., Pattanajak, A., & Thasarin, P. (2007). To prepare context for leading the teacher professional development of Japan to be called “Lesson Study” implemented in Thailand. Document Later National Academic Meeting Japanese Studies Network. Bangkok: Japanese Studies Network; Thailand: Thammasat University. 152- 163.

[7] Inprasitha, M. (2010). One feature of adaptive lesson study in Thailand: Designing a learning unit. Proceedings of the 45th Korean National Meeting of Mathematics Education, Gyeongju, 8-9 October 2010, 193-206.

[8] Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Hiladelphla: Research for Better School, Inc.

[9] Nohda, N. (1998). Mathematics teaching by “open-approach method” in Japanese classroom activities. Proceedings of ICMI-EARCOME 1, Cheongju, 17-21 August 1998, 185-192.

[10] Nohda, N. (2000). Teaching by approach method in Japanese mathematics classroom. Proceeding of the 24th Conference of the International Group for the Psychology of Mathematics Education, Hiroshima, 23-27 July 2000, 11-39.

[11] Poynter, A. (2004). Effect as a pivot between actions and symbols: The case of vector. Ph.D. Thesis, Coventry: University of Warwick.

[12] Shimada, S., & Becker, P. J. (1997). The open-ended approach: A new proposal for teaching mathematics. Reston: National Council of Teachers of Mathematics.

[13] Skemp, R. R (1971). The psychology of learning mathematics. London: Penguin.

[14] Skemp, R. R. (1987). The psychology of learning mathematics. Hove and London: Lawrence Erlbaum Associated, Inc., 9-21.

[15] Suthisung, N., & Sangaroon, K. (2011a). The steps up of compression to thinkable concept in action of the student’s abstraction process. The 16th Annual Meeting in Mathematics, Khon Kaen, 10-11 March 2011, 413-432.

[16] Sutisung, N., & Sangaroon, K. (2011b). “How to” in the students’ abstraction process through compression to thinkable concept. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Developing Mathematical Thinking), Ankara-Turkey, 10-15 July 2011, 1-398.

[17] Sutisung, N., & Sangaroon, K. (2011c). The students’ process of abstraction based on action in compression to thinkable concept of blending embodiment and symbolism under context using lesson study and open approach. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Developing Mathematical thinking), Ankara-Turkey, 10-15 July 2011, 1-505.

[18] Tall, D. (2004). The nature of mathematical growth. URL (last checked 2 January 2010). http://www.tallfamily.co.uk/davidmathematical-growth/

[19] Tall. D. (2006a). A Theory of mathematical growth through embodiment, symbolism and proof. Annales de Didactique et de Sciences Cognitives, IREM de Strasbourg, Vol. 11, 195-215.

[20] Tall, D. (2006b). Encouraging mathematical thinking that has both power and simplicity. Plenary Presented at the APEC-Tsukuba International Conference, Ichigaya, 3-7 December 2006, 1-15.

[21] Tall, D. (2007a). Developing a theory of mathematical growth. ZDM Mathematics Education, 39, 145-154. doi:10.1007/s11858-006-0010-3

[22] Tall, D. (2007b). Setting lesson study within a long-term framework of learning. Presented at APEC Conference on Lesson Study, Khon Kaen, 14 August 2007, 1-17.

[23] Tall, D. (2008). Using Japanese lesson study in teaching mathematics. Scottish Mathematical Council Journal, 38, 45-50.

[24] Tall, D., & Isoda, M. (2007). Long-term development of mathematical thinking and lesson study. Prepared as a Chapter for a Forthcoming Bookon Lesson Study, 1-34.