N. SUTHISUNG, M. INPRASIT HA

Especially, the parallel compression to thinkable concepts in

embodiment and symbolism that is compression in embodiment

including action, multi-action, same effect, effect as prototype

and expanded to effect is used. Compression in symbolism in-

cluding procedure, multi-procedure, process, a thinkable con-

cept (procept) and expanded to revise thinkable concepts as in

solving mathematics problem. It is shifting steadily from per-

forming sequence of compression in students’ thinking from

actions being linked together increasingly sophisticated ways:

accumulation students’ way thinking in 1 - 3 steps to refine im-

portant ideas in step 4 and it is realized to extend useable

mathematical structure in step 5 also. It happened clearly by

compression of knowledge from step-by-step procedure, to the

possible choice of several different procedures, to seen the

overall effect as a general process that can be carried at in va-

rious ways, to compressing it as a thinkable concept.

The further study, my research will analyze the function of

students’ abstraction process as operation of compression to

thinkable concept from blending embodiment and symbolism,

which is micro scale in analyzing mechanism students’ mathe-

matical thinking.

Acknowledgements

This work was supported by the Higher Education Research

Promotion and National Research University Project of Thai-

land, Office of the Higher Education Commission, through the

Cluster of Research to Enhance the Quality of Basic Education

and Center for Research in Mathematics Education, Faculty of

Education, Khon Kaen University, Thailand.

REFERENCES

Howat, H. (2005). Participation in elementary mathematics: An analy-

sis of engagement, attainment and intervention. Ph.D. Thesis, Cov-

entry: University of Warwick.

Gakkoh, T. (2005). Study with your friends mathematics for elementary

school 1st grade.

Gray, E., & Tall, D. (1994). Duality, ambiguity and flexibility: A pro-

ceptual view of Simple arithmetic. Journal for Research in Mathe-

matics Education, 25, 115- 141. doi:10.2307/749505

Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental

compression. Mathematics Education Research Journal, 19, 23-40.

doi:10.1007/BF03217454

Inprasitha, M. (1997). Problem solving: A basis to reform math ematics

instruction. Journal of the National Research Council of Thailand,

29, 221-259.

Inprasitha, M., Pattanajak, A., & Thasarin, P. (2007). To prepare con-

text 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.

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.

Lewis, C. (2002). Lesson study: A handbook of teacher-led instruc-

tional change. Hiladelp h la: Research for Better School, Inc.

Nohda, N. (1998). Mathematics teaching by “open-approach method”

in Japanese classroom activities. Proceedings of ICMI-EARCOME 1,

Cheongju, 17-21 Aug ust 19 98, 185-192.

Nohda, N. (2000). Teaching by approach method in Japanese mathe-

mati cs c lass roo m. Proceeding of the 24th Conference of the Interna-

tional Group for the Psychology of Mathematics Education, Hi-

roshima, 23-27 July 2000, 11-39.

Poynter, A. (2004). Effect as a pivot between actions and symbols: The

case of vector. Ph.D. Thesis, Coventry: University of W arwick.

Shimada, S., & Becker, P. J. (1997). The open-ended approach: A new

proposal for teaching mathematics. Reston: National Council of Tea-

chers of Mathematics.

Skemp, R. R (1971). The psychology of learning mathematics. London:

Penguin.

Skemp, R. R. (1987). The psychology of learning mathematics. Hove

and London: Lawrence Erlbaum Associated, Inc., 9-21.

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.

Sutisung, N., & Sangaroon, K. (2011b). “How to” in the students’ ab-

straction process through compression to thinkable concept. Pro-

ceedings 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.

Sutisung, N., & Sangaroon, K. (2011c). The students’ process of ab-

straction 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.

Tall, D. (2004). The nature of mathematical growth. URL (last checked

2 January 2010).

http://www.tallfamily.co.uk/davidmathematical-growth/

Tall. D. (2006a). A Theory of mathematical growth through embodi-

ment, symbolism and proof. Annales de Didactique et de Sciences

Cognitives, IREM de Strasbourg, 11, 195-215.

Tall, D. (2006b). Encouraging mathematical thinking that has both

power and simplicity. Plenary Presented at the APEC-Tsukuba In-

ternational Conference, Ichigaya, 3-7 December 2006, 1-15.

Tall, D. (2007a). Developing a theory of mathematical growth. ZDM

Mathematics Education, 39, 145-154.

doi:10.1007/s11858-006-0010-3

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.

Tall, D. (2008). Using Japanese lesson study in teaching mathematics.

Scottish Mathematical Council Journal, 38, 45-50.

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.

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