School Mathematics (대한수학교육학회지:학교수학)

The Korea Society of Educational Studies in Mathematics (대한수학교육학회)
권호 표지

Effects of Professional Development for Equity: Focusing on High School Students' Attitudes toward Mathematics

교육 형평성을 위한 고등학교 수학 교사 교육 시행 효과: 학생들의 수학 정의적 영역을 중심으로

  • Received : 2017.11.10
  • Accepted : 2017.12.21
  • Published : 2017.12.29
Download PDF
⟨ Previous Next ⟩

Abstract

Having mathematics for everyone in terms of students' mathematics achievement and attitudes toward mathematics is challenging in high school in South Korea. To gain such purpose, teachers are supposed to have a considerable amount of knowledge and develop mathematical and pedagogical reasoning and insight because equity can be fulfilled in mathematics classroom when any student share their ideas and have mathematical discussions. As a part of a large project aimed to develop and enact professional development for equity and examine its effects and, finally, to propose the direction of professional development to help students cognitively and affectively balanced grow in mathematics, the current study briefly introduces how such professional development was designed and implemented. This study reports its effect based on the statistical analysis of students' responses for the three different surveys, which are parts of the National Assessment of Educational Achievement study, TIMSS Advanced, and the survey about classroom interaction. The data collected in all students in school whose three mathematics teachers had participated in the professional development for two years. The findings consistently indicate the strong and impressive growths in students' attitudes toward mathematics, which are statistically significant. Furthermore, their attitudes toward mathematics are also related to interactions in a mathematics classroom. Based on such results, this study claims expansion of professional development for equity.

모든 학생의 전인적 성장을 지원할 수 있는 수학 교사들의 능력을 신장시키기 위하여, 본 연구는 교육 형평성의 관점에 기반을 둔 교사 교육을 읍면지역에 위치한 고등학교에 재직 중인 세 명의 수학교사를 대상으로 실행하였다. 학생들이 수업시간에 자신의 수학적 아이디어를 공유하고 토론하는 기회를 제공하는 것이 교육 형평성을 실현하는 가장 근본적인 방법인데, 이를 위해서는 상당한 양과 질의 지식과 판단력이 필요하다. 이러한 교사 교육을 두 해 동안 받은 교사들이 가르치는 수학 수업을 받은 고등학생들을 대상으로 사전 사후 설문조사를 시행하였고, 학생들의 수학 교과에 대한 정의적 특성이 인상적으로 성장하였음을 본 연구는 보고한다. 그러한 변화는 수학 교실에서 상당히 자유로운 의사소통과 관련이 있었다. 학생들의 수학과에 대한 정의적 영역의 신장을 위해 교육 형평성에 기반을 둔 수학 교사 교육의 장기간 실행에 논의한다.

Keywords

Acknowledgement

Supported by : 한국연구재단

References

  1. 고은성(2012). 일반학급 내에서 수학영재아 지도에 대한 교사들의 인식 조사. 교원교육, 28(3), 229-247.
  2. 교육부(2014). 사교육 경감 및 공교육 정상화 대책. 세종: 교육부.
  3. 교육부(2015). 교육부 고시 제2015-74호 [별책 8] 수학과 교육과정. 서울: 교육부.
  4. 김연(2017). 학생의 수학 성취도와 학교의 연대책임: 다수준 분석 방법의 적용. East Asian Mathematical Journal, 33(4), 333-351. https://doi.org/10.7858/eamj.2017.026
  5. 나귀수(2010). 초등학교 수학 수업 학습공동체 활동에 대한 연구. 수학교육학연구, 20(3), 373-395.
  6. 노현정(2008). 평가유형과 피드백 유형이 초등학교 학업 성취와 학습 동기에 미치는 영향. 서강대학교 교육대학원 석사학위논문.
  7. 박강원(2009). 수학학습의 누적 피드백이 초등학교 저학년의 수학 학습태도 및 수학 자기효능감에 미치는 영향. 부경대학교 교육대학원 석사학위논문.
  8. 방정숙.선우진(2014). 수학 교사교육에 관한 국내 연구의 동향 분석: 대한수학교육학회의 학술지를 중심으로. 학교수학, 16(2), 335-353.
  9. 오영열(2006). 수업개선 관행공동체를 통한 교사의 변화 탐색. 수학교육학연구, 16(3), 251-272.
  10. 오택근(2016). 수학 수업의 성찰적 실천을 위하여: 학교 안 수학교사 학습공동체 운영 사례 연구. 학교수학, 18(1), 101-126.
  11. 이경화.강현영.고은성.권석일.김동원.김선희,... 류경민(2017). 수학교육 현장지원단 운영. 서울: 교육부.
  12. 이광상.임해미.박인용.서민희.김부미(2016). 국가수준 학업성취도 평가의 수학과 정의적 영역 설문 문항 개선 방안. 서울: 한국교육과정평가원.
  13. 이광상.임해미.서민희.김부미.전경희(2016). 국가수준 학업성취도 평가의 수학과 정의적 영역 규준 및 지표 산출 방안. 서울: 한국교육과정평가원.
  14. 최승현.황혜정(2014). 수학 교과에서의 정의적 특성 요인의 의미 및 지도 방안 탐색. 수학교육 논문집, 28(1), 19-44.
  15. Antil, L., Jenkins, J., Wayne, S., & Vadasy, P. (1998). Cooperative learning: Prevalence, conceptualizations, and the relation between research and practice. American Educational Research Journal, 35(3), 419-454. https://doi.org/10.3102/00028312035003419
  16. Azmitia, M. (1988). Peer interaction and problem solving: When are two heads better than one? Child Development, 59(1), 87-96. https://doi.org/10.2307/1130391
  17. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  18. Ball, S. J. (1993). Education, majorism, and the "curriculum of the dead" Curriculum Studies, 1, 195-214. https://doi.org/10.1080/0965975930010202
  19. Barkatsas, A. N. (2012). Students' attitudes, engagement and confidence in mathematics and statistics learning: ICT, Gender, and equity dimensions. In H. Forgasz & F. Rivera (Eds.), Towards equity in mathematics education. Advances in Mathematics Education. Berlin: Springer.
  20. Boaler, J. (2002a). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. Mahwah, New Jersey: Lawrence Erlbaum Associates.
  21. Boaler, J. (2002b). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal of Research in Mathematics Education, 33(4), 239-258. https://doi.org/10.2307/749740
  22. Boaler, J. (2010). The elephant in the classroom: helping children learn and love maths. London: Souvenir Press Limited (신준식 외 역, 수학다운 수학 가르치고 배우기. 서울: 경문사)
  23. Boaler, J., & Selling, S. K. (2017). Psychological imprisonment or intellectual freedom? A longitudinal study of contrasting school mathematics approaches and their impact on adults' lives. Journal for Research in Mathematics Education, 48(1), 78-105. https://doi.org/10.5951/jresematheduc.48.1.0078
  24. Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers College Record, 110(3), 608-645.
  25. Brenner, M. (1998). Adding cognition to the formula for culturally relevant instruction in mathematics. Anthropology and Education Quarterly, 29(2), 214-244. https://doi.org/10.1525/aeq.1998.29.2.214
  26. Brown, C. A., Stein, M. K., & Forman, E. A. (1996). Assisting teachers and students to reform their mathematics classroom. Educational Studies in Mathematics, 31, 63-93. https://doi.org/10.1007/BF00143927
  27. Buchs, C., Butera, F., Mugny, G., & Darnon, C. (2004). Conflict elaboration and cognitive outcomes. Theory into Practice, 43(1), 23-30. https://doi.org/10.1207/s15430421tip4301_4
  28. Chizhik, A., Alexander, M., Chizhik, E., & Goodman, J. (2003). The rise and fall of power and prestige orders: Influence of task structure. Social Psychology Quarterly, 66(3), 303-317. https://doi.org/10.2307/1519828
  29. Chizhik, A. W. (2001). Equity and status in group collaboration: Learning through explanations depends on task characteristics. Social Psychology of Education, 5, 179-200. https://doi.org/10.1023/A:1014405118351
  30. Civil, M., Planas, N., & Quintos, B. (2012). Immigrant Parents' Perspectives on Their Children's Mathematics Education. In H. Forgasz & F. Rivera (Eds.), Towards Equity in Mathematics Education: Gender, Culture, and Diversity (pp. 267-282). Berlin, Heidelberg: Springer Berlin Heidelberg.
  31. Cochran-Smith, M., & Lytle, S. L. (1992). Interrogating cultural diversity: Inquiry and action. A paper presented at the annual meeting of the American Educational Research Association, San Francisco.
  32. Cohen, D. K. (2011). Teaching and its predicaments. Cambridge, MA: Harvard University Press.
  33. Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119-142. https://doi.org/10.3102/01623737025002119
  34. Cone, J. K. (1992). Untracking advanced placement English: Creating opportunity is not enough. Phi Delta Kappan, 73(9), 712-717.
  35. Esmonde, I. (2009). Ideas and identities: Supporting equity in cooperative mathematics learning. Review of Educational Research, 79(2), 1008-1043. https://doi.org/10.3102/0034654309332562
  36. Esmonde, I. (2012). Mathematics learning in groups: Analysing equity within an activity structure. In B. Herbel-Eisenmann, J. M. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in discourse for mathematics education: theories, practices, and policies (pp. 51-67). Dordrecht: Springer.
  37. Fawcett, L. M., & Garton, A. F. (2005). The effect of peer collaboration on children's problem-solving ability. British Journal of Educational Psychology, 75, 157-169. https://doi.org/10.1348/000709904X23411
  38. Forgasz, H. J., & Mittelberg, D. (2008). Israeli Jewish and Arab students' gendering of mathematics. ZDM, 40(4), 545-558. https://doi.org/10.1007/s11858-008-0139-3
  39. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: D. Reidel Publish Company.
  40. Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What Makes Professional Development Effective? Results from a National Sample of Teachers. American Educational Research Journal, 38(4), 915-945. https://doi.org/10.3102/00028312038004915
  41. Gutierrez, R. (2012). Context matters: How should we conceptualize equity in mathematics education? In Choppin, J., Herbel-Eisenmann, B., & Wagner, D., (eds.), Equity in discourse for mathematics education: Theories, practices, and policies, pp. 17-33. New York: Springer.
  42. Herbel-Eisenmann, B., Choppin, J., Wagner, D., & Pimm, D. (Eds.). (2011). Equity in discourse for mathematics education: Theories, practices, and policies (Vol. 55). Dordrecht, The Netherlands: Springer.
  43. Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. https://doi.org/10.1080/07370000802177235
  44. Kaiser, G., Hoffstall, M., & Orschulik, A. B. (2012). Gender role stereotypes in the perception of mathematics: An empirical study with secondary students in Germany. In H. Forgasz & F. Rivera (Eds.), Towards equity in mathematics education: Gender, culture, and diversity (pp. 115-140). Berlin: Springer.
  45. Kang, W. (1990). Didactic transposition of mathematical knowledge in textbooks. Unpublished doctoral dissertation, University of Georgia, Athens.
  46. Kim, Y. (2013). A decomposition of the work of leading mathematical discussions with single case questions. Journal of Educational Research in Mathematics, 23(4), 449-266.
  47. King, A. (1991). Effects of training in strategic questioning on children's problemsolving performance. Journal of Educational Psychology, 83(3), 307-317. https://doi.org/10.1037/0022-0663.83.3.307
  48. Kitchen, R. (2005). Making equity and multiculturalism explicit to transform mathematics education. In A. Rodriguez & R. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 33-60). Mahwah, NJ: Lawrence Erlbaum.
  49. Koellner, K., Jacobs, J., Borko, H., Schneider, C., Pittman, M. E., Eiteljorg, E., . . . Frykholm, J. (2007). The problem-solving cycle: A model to support the development of teachers' professional knowledge. Mathematical Thinking and Learning, 9(3), 273-303. https://doi.org/10.1080/10986060701360944
  50. Kridel, C., & Bullough, J., R. V. (2012). Stories of the eight-year study: Reexamining secondary education in America. Albany, NY: SUNY Press.
  51. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, UK: Cambridge University Press.
  52. Lee, C. (2009). Historical evolution of risk and equity: Interdisciplinary issues and critiques. Review of Research in Education, 33(1), 63-100. https://doi.org/10.3102/0091732X08328244
  53. Lee, V. E., & Smith, J. B. (1996). Collective responsibility for learning and its effects on gains in achievement for early secondary school students. American Journal of Education, 104(2), 103-147. https://doi.org/10.1086/444122
  54. Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructional improvement? The case of lesson study. Educational Researcher, 35(3), 3-14. https://doi.org/10.3102/0013189X035003003
  55. Lim, J. H. (2008). Adolescent girls' construction of moral discourses and appropriation of primary identity in a mathematics classroom. ZDM, 40(4), 617-631. https://doi.org/10.1007/s11858-008-0119-7
  56. Lortie, D. C. (1975). Schoolteacher: A sociological study. Chicago: University of Chicago Press.
  57. Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS Advanced 2015 International Results in Advanced Mathematics and Physics. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/internationalresults/advanced/.
  58. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  59. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.
  60. OECD. (2013a). Education at a glance 2013: OECD indicators. Paris, France: OECD Publishing.
  61. OECD. (2013b). PISA 2012 Results: Ready to learn: Students' engagement, drive and selfbeliefs (Volume III). PISA, OECD Publishing.
  62. Rogoff, B. (2003). The cultural nature of human development. Oxford, UK: Oxford University Press.
  63. Ruane, F. S., & deTar, J. (1995). Conflict and consensus in teacher candidates' discussion of ethnic autobiography. English Education, 27, 11-39.
  64. Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25. https://doi.org/10.3102/0013189X031001013
  65. Schwab, K. (2016). The fourth industrial revolution. doi: https://www.weforum.org/pages/the-fourth-industri al-revolutionby-klaus-schwab/
  66. Silver, E. A., Clark, L. M., Ghousseini, H. N., Charalambous, C. Y., & Sealy, J. T. (2007). Where is the mathematics? Examining teachers' mathematical learning opportunities in practice-based professional learning tasks. Journal of Mathematics Teacher Education, 10(4-6), 261-277. https://doi.org/10.1007/s10857-007-9039-7
  67. Silver, E. A., & Stein, M. K. (1996). The QUASAR project: The "revolution of the possible" in mathematics instructional reform in urban middle schools. Urban Education, 30(4), 476-521. https://doi.org/10.1177/0042085996030004006
  68. Sleeter, C. E. (2001). Preparing teachers for culturally diverse schoos: Ther overwhelming presence of whiteness. Journal of Teacher Education, 52(2), 94-106. https://doi.org/10.1177/0022487101052002002
  69. Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics (방정숙 역, 효과적인 수학적 논의를 위해 교사가 알아야 할 5가지 관행. 서울: 경문사.).
  70. Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Charlotte, NC: Information Age Publishing.
  71. Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. New York: Free Press.
  72. Webb, N. M. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal for Research in Mathematics Education, 22(5), 366-389. https://doi.org/10.2307/749186
  73. Willis, P. (1977). Learning to labor: How working class kids get working class jobs. New York: Columbia University Press.