Exploring Teaching Performance and Students’ Learning Effects by Two Elementary Indigenous Teachers Implementing Culture-Based Mathematics Instruction

Affiliation(s)

Graduate Institute of Mathematics and Science Education, National Pingtung University of Education, Pingtung, Taiwan, China.

Department of Computer Science, National Pingtung University of Education, Pingtung, Taiwan, China.

Graduate Institute of Mathematics and Science Education, National Pingtung University of Education, Pingtung, Taiwan, China.

Department of Computer Science, National Pingtung University of Education, Pingtung, Taiwan, China.

ABSTRACT

This study aims to probe into the teaching performance and the effects of implementation of culture-based mathematics instruction by two indigenous teachers. By case study, this study treats two Paiwan elementary school teachers as the subjects and collects data by the design of teaching plans, instructional observations, video recordings, and mathematical cognitive tests. The researcher thus explores their culture-based curriculum design, instructional implementation, and the effect on Grade 5 and Grade 6 Paiwan students’ learning performance of mathematics. The findings demonstrate that prior to implementation of culturebased mathematics instruction, mathematics learning performance of the students of the two teachers was behind those of other counties, cities, and schools. The two teachers adopt three types of instructional design, namely, Paiwan culture and festivals, stories and traditional art, and practice mathematics questions upon cultural situations by teacher demonstration, individual problem-solving, and group discussion. After the teachers practice 23 and 31 units of culture-based mathematics instruction, the researcher finds that the gap of learning performance between Paiwan students and those in other cities, counties, and schools is reduced, which demonstrates that culture-based mathematics instruction can enhance Paiwan students’ learning performance of mathematics.

This study aims to probe into the teaching performance and the effects of implementation of culture-based mathematics instruction by two indigenous teachers. By case study, this study treats two Paiwan elementary school teachers as the subjects and collects data by the design of teaching plans, instructional observations, video recordings, and mathematical cognitive tests. The researcher thus explores their culture-based curriculum design, instructional implementation, and the effect on Grade 5 and Grade 6 Paiwan students’ learning performance of mathematics. The findings demonstrate that prior to implementation of culturebased mathematics instruction, mathematics learning performance of the students of the two teachers was behind those of other counties, cities, and schools. The two teachers adopt three types of instructional design, namely, Paiwan culture and festivals, stories and traditional art, and practice mathematics questions upon cultural situations by teacher demonstration, individual problem-solving, and group discussion. After the teachers practice 23 and 31 units of culture-based mathematics instruction, the researcher finds that the gap of learning performance between Paiwan students and those in other cities, counties, and schools is reduced, which demonstrates that culture-based mathematics instruction can enhance Paiwan students’ learning performance of mathematics.

Cite this paper

Hsu, W. , Lin, C. & Kao, H. (2013). Exploring Teaching Performance and Students’ Learning Effects by Two Elementary Indigenous Teachers Implementing Culture-Based Mathematics Instruction.*Creative Education, 4,* 663-672. doi: 10.4236/ce.2013.410095.

Hsu, W. , Lin, C. & Kao, H. (2013). Exploring Teaching Performance and Students’ Learning Effects by Two Elementary Indigenous Teachers Implementing Culture-Based Mathematics Instruction.

References

[1] Anderson, C. W. (2003). How can schools support teaching for understanding in mathematics and science? In G. Adam et al. (Eds.), Transforming: How schools and districts can support change (pp. 1-21). New York: Teacher College.

[2] Artzt, A., & Armour-Thomas, E. (2002). Becoming a reflective mathematics teacher: A guide for observations and self-assessment. Mahwah, NJ: Lawrence Erlbaum.

[3] Barnes, M. B., & Barnes, L. W. (2005). Using inquiry processes to investigate knowledge, skills, and perceptions of diverse learners: An approach to working with prospective and current science teachers. In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 61-86). Mahwah, NJ: Laurence Erlbaum.

[4] Barton, B. (2009). The language of mathematics: Telling mathematical tales. New York: Springer.

[5] Bishop, A. J. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19, 179-191. http://dx.doi.org/10.1007/BF00751231

[6] Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teacher College Record, 110, 608-645.

[7] Chi, H. Y. (2001). The Ethnography of a Mathematics Classroom in an Atayal Native Elementary School. Unpublished Doctoral Dissertation, Taipei: National Taiwan Normal University.

[8] Chien, S. C. (1998). Cultural features and math learning: A case of Yami people in the orchid island. Journal of National Taitung Teachers College, 9, 283-306.

[9] Cummins, J. (1986). Empowering minority students: A framework for intervention. Harvard Educational Review, 56, 18-36.

[10] D’Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5, 44-48.

[11] Ensign, J. (2005). Helping teachers use students’ home cultures in mathematics lessons: Developmental stages of becoming effective teachers of diverse students. In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and Science Teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 225-242). Mahwah, NJ: Laurence Erlbaum.

[12] Ernest, P. (1998). A postmodern perspective on research in mathematics education. In A. Sierpinska, & J. Kilpatrick (Ed.), Mathematics education as a research domain: A search for identify (pp. 71-85). Dordrecht: Kluwer Academic.

[13] Fauvel, J., & Van Maanen, J. (2000). History in mathematical education: The ICMI study. Dordrecht: Kluwer Academic.

[14] Feldman, A. (2003). Mathematics instruction: Cognitive, affective, and existential perspectives. In J. M. Royer (Ed.), Mathematical cognition. Greenwich, CT: Information Age.

[15] Fuson, K. C. et al. (2000). Blending the best of the twentieth century to achieve a mathematics equity pedagogy in the twenty-first century. In M. J. Burke, & F. R. Curcio (Eds.), Learning mathematics for a new century (pp. 197-212). Reston, VA: NCTM.

[16] Gerdes, P. (1996). Ethnomathematics and mathematics education. In A. J. Bishop, et al. (Eds.), International handbook of mathematics education (pp. 909-943). Dordrecht: Kluwer Academic. http://dx.doi.org/10.1007/978-94-009-1465-0_28

[17] Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban Latino school. Journal for Research in Mathematics Education, 34, 37-73. http://dx.doi.org/10.2307/30034699

[18] Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhabit highlevel mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524-549. http://dx.doi.org/10.2307/749690

[19] Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Charlotte, NC: Information Age.

[20] Hsu, W. M., & Yang, Y. C. (2009). What factors influence aboriginal students’ mathematics learning: An action research in a tribal elementary school of Pingtung County. Journal of National Taichung University: Education, 23, 129-152.

[21] Hsu, W. M. (2011). A case study: How did an experienced teacher implement mathematics curriculum in her classroom? Chinese Journal of Science Education, 19, 101-122.

[22] Huang, C. H. (2006). Investigating the mathematical teaching module of Taiwanese Tayal junior high students: The dialectic and practice of activity theory. Unpublished Doctoral Dissertation, Taipei: National Taiwan Normal University.

[23] Huang, C. W. (2002). Impact of multiple cultures on mathematics curriculum: Deprivation and return of ethno-mathematics. The Educator Monthly, 415, 38-41.

[24] Hudson, P., & Miller, S. P. (2006). Designing and implementing mathematics instruction for students with diverse learning need. Boston, MA: Allyn and Bacon.

[25] Leonard, J., & Dantley, S. J. (2005). Breaking through the ice: Dealing with issues of diversity in mathematic and science education course. In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 87-117). Mahwah, NJ: Laurence Erlbaum.

[26] Li, H. C. (2006). An exploration of models of mathematics academic achievement of different ethnical schoolchildren in Taitung County. Taiwan Journal of Sociology of Education, 6, 1-41.

[27] Lloyd, G. (2008). Curriculum use while learning to teach: One student teacher’s appropriation of mathematics curriculum materials. Journal for Research in Mathematics Education, 39, 63-94.

[28] Ministry of Education (2003). The learning domain of mathematics of grade 1-9 curriculum guidelines. Taipei: Ministry of Education in Taiwan.

[29] National Council of Teacher of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

[30] Rodriguez, A. J. (2005). Teachers’ resistance to ideological and pedagogical change: In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 1-16). Mahwah, NJ: Lawrence Erlbaum.

[31] Stein, M., Remillard, J., & Smith M. (2007). How curriculum influences student learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Gweenwich, CT: Information Age.

[32] Stuart, C., & Thrulow, D. (2000). Making it their own: Preservice teachers’ experiences, beliefs, and classroom practices. Journal of Teacher Education, 51, 113-121.

http://dx.doi.org/10.1177/002248710005100205

[33] Tan, G. D., & Lin, M. F. (2002). Traits of learning styles of aboriginal children: A study on Atayal children in Hualien County. Bulletin of Educational Research, 48, 233-261.

[34] White, P., & Mitchelmore, M. C. (2010). Teaching for Abstraction: A Model. Mathematical Thinking and Learning, 12, 205-226. http://dx.doi.org/10.1080/10986061003717476

[35] Wiske, M. S., Franz, K. R., & Breit, L. (2005). Teaching for understanding with technology. San Francisco, CA: Jossey-Bass.

[1] Anderson, C. W. (2003). How can schools support teaching for understanding in mathematics and science? In G. Adam et al. (Eds.), Transforming: How schools and districts can support change (pp. 1-21). New York: Teacher College.

[2] Artzt, A., & Armour-Thomas, E. (2002). Becoming a reflective mathematics teacher: A guide for observations and self-assessment. Mahwah, NJ: Lawrence Erlbaum.

[3] Barnes, M. B., & Barnes, L. W. (2005). Using inquiry processes to investigate knowledge, skills, and perceptions of diverse learners: An approach to working with prospective and current science teachers. In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 61-86). Mahwah, NJ: Laurence Erlbaum.

[4] Barton, B. (2009). The language of mathematics: Telling mathematical tales. New York: Springer.

[5] Bishop, A. J. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19, 179-191. http://dx.doi.org/10.1007/BF00751231

[6] Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teacher College Record, 110, 608-645.

[7] Chi, H. Y. (2001). The Ethnography of a Mathematics Classroom in an Atayal Native Elementary School. Unpublished Doctoral Dissertation, Taipei: National Taiwan Normal University.

[8] Chien, S. C. (1998). Cultural features and math learning: A case of Yami people in the orchid island. Journal of National Taitung Teachers College, 9, 283-306.

[9] Cummins, J. (1986). Empowering minority students: A framework for intervention. Harvard Educational Review, 56, 18-36.

[10] D’Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5, 44-48.

[11] Ensign, J. (2005). Helping teachers use students’ home cultures in mathematics lessons: Developmental stages of becoming effective teachers of diverse students. In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and Science Teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 225-242). Mahwah, NJ: Laurence Erlbaum.

[12] Ernest, P. (1998). A postmodern perspective on research in mathematics education. In A. Sierpinska, & J. Kilpatrick (Ed.), Mathematics education as a research domain: A search for identify (pp. 71-85). Dordrecht: Kluwer Academic.

[13] Fauvel, J., & Van Maanen, J. (2000). History in mathematical education: The ICMI study. Dordrecht: Kluwer Academic.

[14] Feldman, A. (2003). Mathematics instruction: Cognitive, affective, and existential perspectives. In J. M. Royer (Ed.), Mathematical cognition. Greenwich, CT: Information Age.

[15] Fuson, K. C. et al. (2000). Blending the best of the twentieth century to achieve a mathematics equity pedagogy in the twenty-first century. In M. J. Burke, & F. R. Curcio (Eds.), Learning mathematics for a new century (pp. 197-212). Reston, VA: NCTM.

[16] Gerdes, P. (1996). Ethnomathematics and mathematics education. In A. J. Bishop, et al. (Eds.), International handbook of mathematics education (pp. 909-943). Dordrecht: Kluwer Academic. http://dx.doi.org/10.1007/978-94-009-1465-0_28

[17] Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban Latino school. Journal for Research in Mathematics Education, 34, 37-73. http://dx.doi.org/10.2307/30034699

[18] Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhabit highlevel mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524-549. http://dx.doi.org/10.2307/749690

[19] Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Charlotte, NC: Information Age.

[20] Hsu, W. M., & Yang, Y. C. (2009). What factors influence aboriginal students’ mathematics learning: An action research in a tribal elementary school of Pingtung County. Journal of National Taichung University: Education, 23, 129-152.

[21] Hsu, W. M. (2011). A case study: How did an experienced teacher implement mathematics curriculum in her classroom? Chinese Journal of Science Education, 19, 101-122.

[22] Huang, C. H. (2006). Investigating the mathematical teaching module of Taiwanese Tayal junior high students: The dialectic and practice of activity theory. Unpublished Doctoral Dissertation, Taipei: National Taiwan Normal University.

[23] Huang, C. W. (2002). Impact of multiple cultures on mathematics curriculum: Deprivation and return of ethno-mathematics. The Educator Monthly, 415, 38-41.

[24] Hudson, P., & Miller, S. P. (2006). Designing and implementing mathematics instruction for students with diverse learning need. Boston, MA: Allyn and Bacon.

[25] Leonard, J., & Dantley, S. J. (2005). Breaking through the ice: Dealing with issues of diversity in mathematic and science education course. In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 87-117). Mahwah, NJ: Laurence Erlbaum.

[26] Li, H. C. (2006). An exploration of models of mathematics academic achievement of different ethnical schoolchildren in Taitung County. Taiwan Journal of Sociology of Education, 6, 1-41.

[27] Lloyd, G. (2008). Curriculum use while learning to teach: One student teacher’s appropriation of mathematics curriculum materials. Journal for Research in Mathematics Education, 39, 63-94.

[28] Ministry of Education (2003). The learning domain of mathematics of grade 1-9 curriculum guidelines. Taipei: Ministry of Education in Taiwan.

[29] National Council of Teacher of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

[30] Rodriguez, A. J. (2005). Teachers’ resistance to ideological and pedagogical change: In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 1-16). Mahwah, NJ: Lawrence Erlbaum.

[31] Stein, M., Remillard, J., & Smith M. (2007). How curriculum influences student learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Gweenwich, CT: Information Age.

[32] Stuart, C., & Thrulow, D. (2000). Making it their own: Preservice teachers’ experiences, beliefs, and classroom practices. Journal of Teacher Education, 51, 113-121.

http://dx.doi.org/10.1177/002248710005100205

[33] Tan, G. D., & Lin, M. F. (2002). Traits of learning styles of aboriginal children: A study on Atayal children in Hualien County. Bulletin of Educational Research, 48, 233-261.

[34] White, P., & Mitchelmore, M. C. (2010). Teaching for Abstraction: A Model. Mathematical Thinking and Learning, 12, 205-226. http://dx.doi.org/10.1080/10986061003717476

[35] Wiske, M. S., Franz, K. R., & Breit, L. (2005). Teaching for understanding with technology. San Francisco, CA: Jossey-Bass.