Students’ Abstraction Process through Compression to Thinkable Concepts: Focusing on Using “How To” in Learning Units of Lesson Sequences to Provide a Tool in Conducting Students’ Concepts

Affiliation(s)

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

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

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

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

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

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

ABSTRACT

The purpose of this study is to analyze “how to” in the students’ abstraction process through compression to thinkable concept under classroom using Lesson Study and Open Approach. Data for this study were collected by using a teaching experiment, with the four of first graders as targeted. The research results revealed that in the students’ abstraction process, they compressed computable symbols and conducted 10 as “how to” in their thinking and thinkable concept at the same time. It is shift steadily from performing sequence of compression in students’ thinking from actions being linked together in increasingly sophisticated ways.

The purpose of this study is to analyze “how to” in the students’ abstraction process through compression to thinkable concept under classroom using Lesson Study and Open Approach. Data for this study were collected by using a teaching experiment, with the four of first graders as targeted. The research results revealed that in the students’ abstraction process, they compressed computable symbols and conducted 10 as “how to” in their thinking and thinkable concept at the same time. It is shift steadily from performing sequence of compression in students’ thinking from actions being linked together in increasingly sophisticated ways.

KEYWORDS

Lesson Study; Open Approach; Precept; Compression to Thinkable Concept; How to; Learning Unit

Lesson Study; Open Approach; Precept; Compression to Thinkable Concept; How to; Learning Unit

Cite this paper

Suthisung, N. , Inprasitha, M. & Sangaroon, K. (2012). Students’ Abstraction Process through Compression to Thinkable Concepts: Focusing on Using “How To” in Learning Units of Lesson Sequences to Provide a Tool in Conducting Students’ Concepts.*Creative Education, 3,* 1188-1196. doi: 10.4236/ce.2012.37177.

Suthisung, N. , Inprasitha, M. & Sangaroon, K. (2012). Students’ Abstraction Process through Compression to Thinkable Concepts: Focusing on Using “How To” in Learning Units of Lesson Sequences to Provide a Tool in Conducting Students’ Concepts.

References

[1] Biggs, J., & Collis, K. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.

[2] Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. Norwood, NJ: Ablex.

[3] Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Dorfrecht: Kluwer.

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

[5] Gakkotosho Co., Ltd. (2005). Study with your friends MATHEMATICS for elementary school 1st grade. Tokyo: Gakkotosho Co., LTD.

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

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

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

[9] 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. Bangkok: Thammasat University, 152-163.

[10] 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: Dongkook University, 8-9 October 2010, 193-206.

[11] Isoda, M. (2010). The principles for problem solving approach and open approach: As a product of lesson study. International Conference on Educational Research (ICER 2010), Learning Communities for Sustainable Development, 10-11 September 2011.

[12] Leslie, P. S., & Patrick, W. T. (2000). Teaching experiment methodology: Underlying principles and essential elements. Handbook of Research Design in Mathematics and Science Education (pp. 267-306). Mahwah: Lawrence Erlbaum Associate.

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

[14] 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, 11-39.

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

[16] Pegg, J., & Tall, D. O. (2005). The fundamental cycle of concept costruction underlying various theoretical framework. ZDM (Mathematics Education), 37, 468-475. doi:10.1007/BF02655855

[17] Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36. doi:10.1007/BF00302715

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

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

[20] Suthisung, N. and Sangaroon, K. (2011a). The steps up of compression to thinkable concept inaction of the student’s abstraction process. The 16th Annual Meeting in Mathematics (AMM 2011), 10-11 March, 2011.

[21] Suthisung, 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, 10-15 July 2011, 1-398.

[22] Tall, D. O. (2004). The nature of mathematical growth. URL (last checked 23 March 2010). http://www.tallfamily.co.uk/david/mathematical-growth

[23] Tall. D. O. (2006). A theory of mathematical growth through embodiment, symbolism and proof. Annales de Didactique et de Sciences Cognitives, 1, 195-215.

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

[25] Tall, D. O. (2007b). Setting lesson study within a long-term framework of learning. APEC Conference on Lesson Study in Thailand, 1-17.

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

[27] Tall, D. O., & Isoda, M. (2007). Long-term development of mathematical thinking and lesson study. Chapter for a Forthcoming Book on Lesson Study.

[28] Tall, D. O, Thomas, M., Davis, G., & Gray, E. (2000). What is the object of the encapsulation of a process? Journal of Mathematical Behavior, 18, 223-241. doi:10.1016/S0732-3123(99)00029-2

[1] Biggs, J., & Collis, K. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.

[2] Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. Norwood, NJ: Ablex.

[3] Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Dorfrecht: Kluwer.

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

[5] Gakkotosho Co., Ltd. (2005). Study with your friends MATHEMATICS for elementary school 1st grade. Tokyo: Gakkotosho Co., LTD.

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

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

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

[9] 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. Bangkok: Thammasat University, 152-163.

[10] 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: Dongkook University, 8-9 October 2010, 193-206.

[11] Isoda, M. (2010). The principles for problem solving approach and open approach: As a product of lesson study. International Conference on Educational Research (ICER 2010), Learning Communities for Sustainable Development, 10-11 September 2011.

[12] Leslie, P. S., & Patrick, W. T. (2000). Teaching experiment methodology: Underlying principles and essential elements. Handbook of Research Design in Mathematics and Science Education (pp. 267-306). Mahwah: Lawrence Erlbaum Associate.

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

[14] 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, 11-39.

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

[16] Pegg, J., & Tall, D. O. (2005). The fundamental cycle of concept costruction underlying various theoretical framework. ZDM (Mathematics Education), 37, 468-475. doi:10.1007/BF02655855

[17] Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36. doi:10.1007/BF00302715

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

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

[20] Suthisung, N. and Sangaroon, K. (2011a). The steps up of compression to thinkable concept inaction of the student’s abstraction process. The 16th Annual Meeting in Mathematics (AMM 2011), 10-11 March, 2011.

[21] Suthisung, 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, 10-15 July 2011, 1-398.

[22] Tall, D. O. (2004). The nature of mathematical growth. URL (last checked 23 March 2010). http://www.tallfamily.co.uk/david/mathematical-growth

[23] Tall. D. O. (2006). A theory of mathematical growth through embodiment, symbolism and proof. Annales de Didactique et de Sciences Cognitives, 1, 195-215.

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

[25] Tall, D. O. (2007b). Setting lesson study within a long-term framework of learning. APEC Conference on Lesson Study in Thailand, 1-17.

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

[27] Tall, D. O., & Isoda, M. (2007). Long-term development of mathematical thinking and lesson study. Chapter for a Forthcoming Book on Lesson Study.

[28] Tall, D. O, Thomas, M., Davis, G., & Gray, E. (2000). What is the object of the encapsulation of a process? Journal of Mathematical Behavior, 18, 223-241. doi:10.1016/S0732-3123(99)00029-2