Investigating the Alignment of Bhutanese Mathematics Teachers’ Planned Approaches Within the Context of a Reformed Curriculum
Tóm tắt
Reform of mathematics education has been in focus in many countries including those in major economic transition. This paper reports a segment of a study which was conducted in Bhutan, where a reformed elementary mathematics curriculum has been recently introduced. The reformed curriculum is based on social constructivism and its design has been influenced by the USA’s National Council of Teachers of Mathematics (NCTM) standards. This paper reports upon the planned teaching of a sample of elementary (primary) teachers in their implementation of the reformed curriculum. The data for this part of the investigation were aggregated from a qualitative survey of randomly selected elementary school teachers (N = 72) from 40 schools across the country. A set of 3 analytical rubrics, based on intentions embedded in the curriculum, was developed to analyse the alignment of teachers’ planned sample learning activities with the intentions of the curriculum. Our conclusions are that while the curriculum’s intentions might be meaningfully stated in the curriculum documents, implementation remains problematic because there appears to be a mis-alignment between curriculum intentions and classroom practices. For instance, teachers by not adopting evidence-based approaches recommended in the curriculum document and are continuing to deny students opportunities to achieve deep understanding in achieving national priorities. This paper also argues that the proposed analytical rubrics may be of value for Bhutanese mathematics educators and, with minor modification, educators in other contexts, as they critique planned and actual practices.
Tài liệu tham khảo
Aguirre, J. & Speer, N. M. (2000). Examining the relationship between beliefs and goals in teacher practice. Journal of Mathematical Behaviour, 18(3), 327–356.
Alba, J. A. (2001). An analysis of secondary mathematics teachers’ beliefs and classroom practices in relationship to the NCTM standards (Doctoral Dissertation). Retrieved from DigitalCommons@UConn. (AAI3037987)
Ambrose, R. (2004). Initiating change in prospective elementary school teachers’ orientations to mathematics teaching by building beliefs. Journal of Mathematics Teacher Education, 7(2), 91–119.
An, S. A., Ma, T. & Capraro, M. M. (2011). Preservice teachers’ beliefs and attitude about teaching and learning mathematics through music: An intervention study. School Science & Mathematics, 111(5), 236–248. doi:10.1111/j.1949-8594.2011.00082.x.
Diezmann, C. M & Watters, J. J. (2001). The collaboration of mathematically gifted students on challenging tasks. Journal for the Education of the Gifted, 25(1), 7–31.
Barnes, H. (2005). The theory of realistic mathematics education as a theoretical framework for teaching low attainers in mathematics. Pythagoras, 33(3), 42–57.
Bickmore-Brand, J. (1998). Whose questions are being answered in the maths classrooms? Australian Primary Mathematics Classroom, 3(1), 4–8.
Bishop, A. J. (1994). Cultural conflicts in mathematics education: Developing a research agenda. For the Learning of Mathematics, 14(2), 15–18.
Blömeke, S. & Delaney, S. (2014). Assessment of teacher knowledge across countries: A review of the state of research. In S. Blömeke, F.-J. Hsieh, G. Kaiser & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 541–585). Dordrecht, The Netherlands: Springer.
Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, UK: Harvard University Press.
Charalambous, C. & Philippou, G. (2010). Teachers’ concerns and efficacy beliefs about implementing a mathematics curriculum reform: Integrating two lines of inquiry. Educational Studies in Mathematics, 75(1), 1–21. doi:10.1007/s10649-010-9238-5.
Clement, D. H. & Battista, M. T. (1990). Constructivist learning and teaching. Arithmetic Teacher, 38(1), 34–35.
Cuban, L. (1993). The lure of curricular reform and its pitiful history (Vol. 75). Bloomington, IN: Phi Delta Kappan.
Curriculum and Professional Support Division (2008). Understanding mathematics, textbook for class V. Thimphu, Bhutan: Author.
Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teachers: A model. Journal of Education for Teaching, 15(1), 13–33. doi:10.1080/0260747890150102.
Foster, C. (2014). Exploiting unexpected situations in the mathematics classroom. International Journal of Science and Mathematics Education, 13(5), 1065–1088. doi:10.1007/s10763-014-9515-3.
Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: Reidel Company.
Freudenthal, H. (2002). Revisiting mathematics education. Dordrecht, The Netherlands: Kluwer.
Goodrum, D., Hackling, M. & Rennie, L. (2001). The status and quality of teaching and learning in science in Australian schools. Canberra, Australia: Training and Youth Affairs.
Handal, B. & Herrington, A. (2003). Mathematics teachers’ beliefs and curriculum. Mathematics Education Research Journal, 15(1), 59–69. doi:10.1007/BF03217369.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L. & Ball, D. L. M. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511. doi:10.1080/07370000802177235.
Hill, H. C., Schilling, S. G. & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11–30. doi:10.1086/428763.
Hurst, C. (2011). Engaging and connection in mathematical learning. Prime Number, 26(3), 3–6.
Irez, S. (2007). Reflection-oriented qualitative approach in beliefs research. Eurasia Journal of Mathematics, Science & Technology Education, 3(1), 17–27.
Kellman, S. D. (1996). The relationship between teacher qualification, years of teaching, in-service training, and student achievement on the common entrance examination in Barbados (Doctoral Dissertation). Retrieved from University of Cincinnati Database. (9718263).
Lazim, M. A., Abu, O. M. T. & Wan, S. W. A. (2004). The statistical evidence in describing the students’ beliefs about mathematics. International Journal for Teaching and Learning of Mathematics, 6(1), 1–12.
Leatham, K. R. (2006). Viewing mathematics teachers’ beliefs as sensible system. Journal of Mathematics Teacher Education, 9(1), 91–102. doi:10.1007/s10857-006-9006-8.
Lowrie, T. (2004). Authentic artefacts: Influencing practice and supporting problem solving in the mathematics classroom. Paper presented at the Mathematics Education Research Group of Australasia, Townsville, QLD, Australia.
Lowrie, T. & Jorgensen, R. (2011). Gender differences in students’ mathematics game playing. Computers and Education, 57(4), 2244–2248. doi:10.1016/j.compedu.2011.06.010.
Mansour, N. (2013). Consistencies and inconsistencies between science teachers’ beliefs and practices. International Journal of Science Education, 35(7), 1230–1275. doi:10.1080/09500693.2012.743196.
Maslow, A. H. (1970). Motivation and personality (3rd ed.). New York, NY: Addison-Wesley Longman.
Mayer, R. E. (2004). Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction. American Psychologist, 59(1), 14–19. doi:10.1037/0003-066X.59.1.14.
Ministry of Education (2002). Purpose of school education for Bhutanese schools PP-VIII. Thimphu, Bhutan: KMT.
Ministry of Education (2013). Annual education statistics 2013. Thimphu, Bhutan: Policy and Planning Division, Ministry of Education. Retrieved from www.education.gov.bt.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, NY: National Council of Teachers of Mathematics.
Perrin, J. R. (2008). A study of the beliefs and reported practices of seventh and eighth grade mathematics teachers in relation to NCTM’s vision of school mathematics (Doctoral Dissertation). Retrieved from ProQuest. (3339136)
Powell, J. & Anderson, R. D. (2002). Changing teachers’ practice: Curriculum materials and science education reform in the USA. Studies in Science Education, 37(1), 107–135. doi:10.1080/03057260208560179.
Putnam, R. T., Lampert, M. & Peterson, P. L. (1990). Alternative perspectives on knowing mathematics in elementary schools. Review of Research in Education, 16, 57–149.
Roche, A., Clark, D. M. & Clarke, D. J. (2014). Primary teachers’ written plans in mathematics and their perceptions of essentials elements. Mathematics Education Research Journal, 26(4), 853–870. doi:10.1007/s13394-014-0130-y.
Roehrig, G. H. & Kruse, R. A. (2005). The role of teachers’ beliefs and knowledge in the adoption of a reform-based curriculum. School Science and Mathematics, 105(8), 412–422.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(20), 20–26.
Subba, T. B. (2006). Learning of mathematics by Bhutanese children. RABSEL, 8, 16–26.
Sweller, J., Kirschner, P. A. & Clark, R. E. (2007). Why minimally guided teaching techniques do not work: A reply to commentaries. Educational Psychologist, 42(2), 115–121. doi:10.1080/00461520701263426.
Treffers, A. (1987). Three dimensions. A model of goal and theory descriptions in mathematics instructions. Dordrecht, Netherlands: Reidel.
Vace, N. B. & Bright, G. M. (1999). Elementary preservice teachers’ changing beliefs and instructional use of children’s mathematical thinking. Journal for Research in Mathematics Education, 30(1), 89–110. doi:10.2307/749631.
Van de Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NY: Pearson Higher Education.
VanBalkom, W. D. & Sherman, A. (2010). Teacher education in Bhutan: Highlights and challenges for reform. Asia Pacific Journal of Education, 30(1), 43–55. doi:10.1080/02188790903503585.
Vidic, A. D. (2015). First-year students’ beliefs about context problems in mathematics in university science programmes. International Journal of Science and Mathematics Educational, 13(5), 1161–1187. doi:10.1007/s10763-014-9533-1.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University, The President and Fellows of Harvard College Press.
Yackel, E. (2001). Explanation, justification and argumentation mathematics classrooms. Paper presented at the International Group for the Psychology of Mathematics Education, Utrecht, Netherlands.
Yin, R. K. (2013). Case study research: Design and methods (5th ed.). Thousand Oaks, CA: Sage.