Mathematical Communication by 5^{th} Grade Students’ Gestures in Lesson Study and Open Approach Context

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 this research was to explore the Mathematical Communication by 5th grade students’ gestures in Lesson Study and Open Approach context. This study was conducted at Nongtoom-nong- ngu-lerm School, and Ban-Beung-neum-beung-krai-noon School, Muang District, Khon Kaen Province in Project for Professional development of Mathematics teachers through Lesson Study and Open Approach, using qualitative research: Ethnographic Study, in-depth interview, Video Analysis supported by protocol analysis, and Descriptive Analysis. The research findings found that there were 7 kinds of students’ Mathematical Communication by students’ Gestures including 1) rigorousness by students’ beat gesture; 2) rigorousness by students’ metaphoric gesture; 3) economy by students’ deictic gesture; 4) economy by students’ iconic gestures; 5) freedom by students’ deictic gesture; 6) freedom by students’ iconic gesture; and 7) freedom by students’ deictic and iconic gestures in explaining students’ Mathematical Ideas, and the most commonly used economically by deictic gestures, and students’ self learning in Open Approach. Furthermore, the schools in Lesson Study and Open Approach context, the students had opportunity in learning based on their potentiality, being able to think, perform, and express. They preferred to express divergent think.

The objective of this research was to explore the Mathematical Communication by 5th grade students’ gestures in Lesson Study and Open Approach context. This study was conducted at Nongtoom-nong- ngu-lerm School, and Ban-Beung-neum-beung-krai-noon School, Muang District, Khon Kaen Province in Project for Professional development of Mathematics teachers through Lesson Study and Open Approach, using qualitative research: Ethnographic Study, in-depth interview, Video Analysis supported by protocol analysis, and Descriptive Analysis. The research findings found that there were 7 kinds of students’ Mathematical Communication by students’ Gestures including 1) rigorousness by students’ beat gesture; 2) rigorousness by students’ metaphoric gesture; 3) economy by students’ deictic gesture; 4) economy by students’ iconic gestures; 5) freedom by students’ deictic gesture; 6) freedom by students’ iconic gesture; and 7) freedom by students’ deictic and iconic gestures in explaining students’ Mathematical Ideas, and the most commonly used economically by deictic gestures, and students’ self learning in Open Approach. Furthermore, the schools in Lesson Study and Open Approach context, the students had opportunity in learning based on their potentiality, being able to think, perform, and express. They preferred to express divergent think.

Cite this paper

Kongthip, Y. , Inprasitha, M. , Pattanajak, A. & Inprasitha, N. (2012). Mathematical Communication by 5^{th} Grade Students’ Gestures in Lesson Study and Open Approach Context. *Psychology, 3,* 632-637. doi: 10.4236/psych.2012.38097.

Kongthip, Y. , Inprasitha, M. , Pattanajak, A. & Inprasitha, N. (2012). Mathematical Communication by 5

References

[1] Arzarello, F., & Edwards, L. (2005). Gesture and the construction of mathematical meaning. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 1, 123-127.

[2] Bjuland, R., Cestari, M. L., & Erik Borgersen, H. (2007). Pupils’ mathematical reasoning expressed through gesture and discourse: A case study from a sixth-grade lesson. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the 5th Conference of the European Society for Research in Mathematics Education, Larnaca, 2-26 February 2007, 1129-1139.

[3] Cooke, B., & Buchholz, D. (2005). Mathematical communication in the classroom: A teacher makes a difference. Early Childhood Education Journal, 32, 365-369. doi:10.1007/s10643-005-0007-5

[4] Edwards, L. D. (2005). The role of gestures in mathematical discourse: Remembering and problem solving. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 1, 135-138.

[5] Emori, H. (2005). The workshop and intensive lecture for young mathematics education in Thailand 2005. Khon Kaen: Khon Kaen University.

[6] Fernandez, C., & Yoshida, M. (2004). Lesson study: A Japanese approach to improving mathematics teaching and learning. Mahwah, NJ: Lawrence Erlbaum.

[7] Inprasitha, N., Inprasitha, M., & Pattanajak, A. (2008). Teacher’s worldview changes in process of teaching professional development by using lesson study. Khon Kaen: Khon Kaen University.

[8] Inprasitha, M. (2003). Reforming of the learning processes in school mathematics with emphasizing on mathematical process. Bangkok: National Research Council of Thailand.

[9] Inprasitha, M. (2006). Open-ended approach and teacher education. Tsukuba Journal of Educational Study in Mathematics, 25, 168-177.

[10] Inprasitha, M. (2010). One feature of adaptive lesson study in Thailand—Designing learning unit. Proceedings of the 45th Korean National Meeting of Mathematics Education, Gyeongju, 8-10 October 2010, 193-206.

[11] Inprasitha, M., & Loipha, S. (2007). Developing student’s mathematical thinking though lesson study in Thailand. Progress Report of the APEC Project: Collaborative Studies on Innovations for Teaching and Learning Mathematics in Different Cultures (II)—Lesson Study Focusing on Mathematical Thinking. Tsukuba: Center for Research on International Cooperation in Educational Development.

[12] Inprasitha, M., Loipha, S., & Silanoi, L. (2006). Development of effective lesson plan through lesson study approach: A Thai experience. In M. Isoda, S. Shimisu, T. Miyakawa, K. Aoyama, & K. Chino (Eds.), Tsukuba Journal of Educational Study in Mathematics, 25, 237-245.

[13] Isoda, M., Shimizu, S., & Ohtani, M. (2007). APEC—Tsukuba international conference III: Innovation of classroom teaching and learning through lesson study—Focusing on mathematical communication. Tsukuba: Center for Research on International Cooperation in Educational Development.

[14] Kendon, A. (1997). Gesture. Annual Review Anthropology, 26, 10-28.doi:10.1146/annurev.anthro.26.1.109

[15] Kendon, A. (2000). Language and gesture: Unity or duality? In D. McNeill (Ed.), Language and gesture (pp. 47-63). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511620850.004

[16] Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Philadelphia: Research for better schools..

[17] Lozano, S. C., & Tversky, B. (2006). Communicative gestures facilitate problem solving fro both communicators and recipients. Journal of Memory and Language, 55, 47-63. doi:10.1016/j.jml.2005.09.002

[18] National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.

[19] Nohda, N. (2000). Teaching by open-approach method in Japanese mathematics classroom. In T. Nakahara, & M. Koyama (Eds.), Proceedings 24th of the conference of the International Group for the Psychology of Mathematics Education, 1, 39-53.

[20] Nú?ez, R. (2004). Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. Embodied Artificial Intelligence, LNAI3139, 54-73.

[21] Office of National Education Commission (1999). National Education Act 1999. Bangkok: Kurusapa Ladprao Printing.

[22] Pasjuso, S., Thinwiangthong, S., & Kongthip, Y. (2010). Comparative study of gesture in mathematical communication in Thai traditional and innovation classroom. In Y. Shimizu, Y. Sekiguchi, & K. Hino (Eds.), Proceeding of the 5th East Asia Regional Conference on Mathematics Education, 1, 230.

[23] Rasmussen, C., Stephan, M., & Allen, K. (2004). Classroom mathematical practices and gesturing. Journal of Mathematical Behaviour, 23, 301-323. doi:10.1016/j.jmathb.2004.06.003

[24] Scherr, R. E. (2008). Gesture analysis for physics education researchers. Physical Review Special Topics—Physics Education Research, 4, 1- 9. doi:10.1103/PhysRevSTPER.4.010101

[25] Sierpinska, A. (1998). Three epistemologies, three views of classroom communication: Constructivism, sociocultural approachers, interactionism. In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 30-62). Virginia: National Council of Teachers of Mathematics.

[26] So, W. C., Kita, S., & Goldin-Meadow, S. (2009). Using the hands to identify who does what to whom: Gesture and speech go hand- in-hand. Cognitive Science, 33, 115-125.doi:10.1111/j.1551-67.2008.01006.x

[27] Thurston, W. P. (1994). On proof and progress in mathematics. Appeared in Bulletin of the American Mathematical Society, 30, 161- 177. doi:10.1090/S0273-0979-1994-00502-6

[28] Wood, T. (1998). Alternative patterns of communication in mathematics classroom: Funneling or focussing? In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167-178). Virginia: National Council of Teachers of Mathematics.

[29] Wu, Y. C., & Coulson, S. (2007). How iconic gestures enhance communication: An ERP study. Brain and Language, 101, 234-245. doi:10.1016/j.bandl.2006.12.003

[1] Arzarello, F., & Edwards, L. (2005). Gesture and the construction of mathematical meaning. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 1, 123-127.

[2] Bjuland, R., Cestari, M. L., & Erik Borgersen, H. (2007). Pupils’ mathematical reasoning expressed through gesture and discourse: A case study from a sixth-grade lesson. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the 5th Conference of the European Society for Research in Mathematics Education, Larnaca, 2-26 February 2007, 1129-1139.

[3] Cooke, B., & Buchholz, D. (2005). Mathematical communication in the classroom: A teacher makes a difference. Early Childhood Education Journal, 32, 365-369. doi:10.1007/s10643-005-0007-5

[4] Edwards, L. D. (2005). The role of gestures in mathematical discourse: Remembering and problem solving. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 1, 135-138.

[5] Emori, H. (2005). The workshop and intensive lecture for young mathematics education in Thailand 2005. Khon Kaen: Khon Kaen University.

[6] Fernandez, C., & Yoshida, M. (2004). Lesson study: A Japanese approach to improving mathematics teaching and learning. Mahwah, NJ: Lawrence Erlbaum.

[7] Inprasitha, N., Inprasitha, M., & Pattanajak, A. (2008). Teacher’s worldview changes in process of teaching professional development by using lesson study. Khon Kaen: Khon Kaen University.

[8] Inprasitha, M. (2003). Reforming of the learning processes in school mathematics with emphasizing on mathematical process. Bangkok: National Research Council of Thailand.

[9] Inprasitha, M. (2006). Open-ended approach and teacher education. Tsukuba Journal of Educational Study in Mathematics, 25, 168-177.

[10] Inprasitha, M. (2010). One feature of adaptive lesson study in Thailand—Designing learning unit. Proceedings of the 45th Korean National Meeting of Mathematics Education, Gyeongju, 8-10 October 2010, 193-206.

[11] Inprasitha, M., & Loipha, S. (2007). Developing student’s mathematical thinking though lesson study in Thailand. Progress Report of the APEC Project: Collaborative Studies on Innovations for Teaching and Learning Mathematics in Different Cultures (II)—Lesson Study Focusing on Mathematical Thinking. Tsukuba: Center for Research on International Cooperation in Educational Development.

[12] Inprasitha, M., Loipha, S., & Silanoi, L. (2006). Development of effective lesson plan through lesson study approach: A Thai experience. In M. Isoda, S. Shimisu, T. Miyakawa, K. Aoyama, & K. Chino (Eds.), Tsukuba Journal of Educational Study in Mathematics, 25, 237-245.

[13] Isoda, M., Shimizu, S., & Ohtani, M. (2007). APEC—Tsukuba international conference III: Innovation of classroom teaching and learning through lesson study—Focusing on mathematical communication. Tsukuba: Center for Research on International Cooperation in Educational Development.

[14] Kendon, A. (1997). Gesture. Annual Review Anthropology, 26, 10-28.doi:10.1146/annurev.anthro.26.1.109

[15] Kendon, A. (2000). Language and gesture: Unity or duality? In D. McNeill (Ed.), Language and gesture (pp. 47-63). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511620850.004

[16] Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Philadelphia: Research for better schools..

[17] Lozano, S. C., & Tversky, B. (2006). Communicative gestures facilitate problem solving fro both communicators and recipients. Journal of Memory and Language, 55, 47-63. doi:10.1016/j.jml.2005.09.002

[18] National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.

[19] Nohda, N. (2000). Teaching by open-approach method in Japanese mathematics classroom. In T. Nakahara, & M. Koyama (Eds.), Proceedings 24th of the conference of the International Group for the Psychology of Mathematics Education, 1, 39-53.

[20] Nú?ez, R. (2004). Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. Embodied Artificial Intelligence, LNAI3139, 54-73.

[21] Office of National Education Commission (1999). National Education Act 1999. Bangkok: Kurusapa Ladprao Printing.

[22] Pasjuso, S., Thinwiangthong, S., & Kongthip, Y. (2010). Comparative study of gesture in mathematical communication in Thai traditional and innovation classroom. In Y. Shimizu, Y. Sekiguchi, & K. Hino (Eds.), Proceeding of the 5th East Asia Regional Conference on Mathematics Education, 1, 230.

[23] Rasmussen, C., Stephan, M., & Allen, K. (2004). Classroom mathematical practices and gesturing. Journal of Mathematical Behaviour, 23, 301-323. doi:10.1016/j.jmathb.2004.06.003

[24] Scherr, R. E. (2008). Gesture analysis for physics education researchers. Physical Review Special Topics—Physics Education Research, 4, 1- 9. doi:10.1103/PhysRevSTPER.4.010101

[25] Sierpinska, A. (1998). Three epistemologies, three views of classroom communication: Constructivism, sociocultural approachers, interactionism. In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 30-62). Virginia: National Council of Teachers of Mathematics.

[26] So, W. C., Kita, S., & Goldin-Meadow, S. (2009). Using the hands to identify who does what to whom: Gesture and speech go hand- in-hand. Cognitive Science, 33, 115-125.doi:10.1111/j.1551-67.2008.01006.x

[27] Thurston, W. P. (1994). On proof and progress in mathematics. Appeared in Bulletin of the American Mathematical Society, 30, 161- 177. doi:10.1090/S0273-0979-1994-00502-6

[28] Wood, T. (1998). Alternative patterns of communication in mathematics classroom: Funneling or focussing? In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167-178). Virginia: National Council of Teachers of Mathematics.

[29] Wu, Y. C., & Coulson, S. (2007). How iconic gestures enhance communication: An ERP study. Brain and Language, 101, 234-245. doi:10.1016/j.bandl.2006.12.003