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Making things explicit using instructional materials: a case study of a Singapore teacher’s practice

  • Yew Hoong Leong
  • Lu Pien Cheng
  • Wei Yeng Karen Toh
  • Berinderjeet Kaur
  • Tin Lam Toh
Original Article

Abstract

The phrase ‘make it explicit’ is a common advice given to teachers. It is, however, not clear to us what this actually means when translated into classroom practice. Our review found that we are not alone: “explicit” is used in different ways in the education literature. This paper explores, through a case study of a teacher who stated “making things explicit” as an ostensible goal of his instructional practice, how the explicitation is realised in teaching mathematics. In particular, we examine how he used the instructional materials that he crafted to fulfil his goal of explicitation. We were able to uncover three strategies he used: explicit-from, explicit-within, and explicit-to.

Keywords

Instructional materials Explicit Teaching mathematics 

Notes

Acknowledgements

The investigation reported in this paper is part of a larger research project known as “A study of the enacted school mathematics curriculum (secondary).” (Grant number: OER 31/15 BK) funded by the Office of Education Research, National Institute of Education, Nanyang Technological University, Singapore.

References

  1. Arop, B. A., Umanah, F. I., & Effiong, O. E. (2015). Effect of instructional materials on the teaching and learning of basic science in junior secondary schools in Cross River state, Nigeria. Global Journal of Educational Research, 14(2015), 67–73.Google Scholar
  2. Authors. (2015).Google Scholar
  3. Ball, D. L., & Bass, H. (2003). Towards a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 annual meeting of the Canadian Mathematics Education Study Group (pp. 3–14). Edmonton: CMESG/GCEDM.Google Scholar
  4. 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.CrossRefGoogle Scholar
  5. Brophy, J. (1988). Research linking teacher behavior to student achievement: Potential implications for instruction of Chapter 1 students. Educational Psychologist, 23(3).Google Scholar
  6. Brophy, J., & Good, T. L. (1986). Teacher behavior and student achievement. In M. L. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 328–375). New York: Macmillan.Google Scholar
  7. Brown, R. M. (2000). Curriculum and teaching in introduction to method of teaching. Ibadan: Macmillan Press.Google Scholar
  8. Brown, M. W. (2009). The teacher-tool relationship: Theorizing the design and use of curriculum materials. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 17–36). New York: Routledge.Google Scholar
  9. Chow, W. K., Lui, A. Y. L., & Ling, S. (2016). Discovering mathematics. Singapore: Star Publishing Pte Ltd.Google Scholar
  10. Christenson, S. L., Ysseldyke, J. E., & Thurlow, M. L. (1989). Critical instructional factors for students with mild handicaps: An integrative review. Remedial and Special Education, 10(5), 21–31.Google Scholar
  11. Clark-Wilson, A., Aldon, G., Cusi, A., Goss, M., Haspekian, M., Robutti, O., & Thomas, M. (2014). The challenges of teaching mathematics with digital technologies—the evolving role of the teacher. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 1, pp. 87–116). Vancouver: PME.Google Scholar
  12. Doabler, C. T., Baker, S. K., Kosty, D. B., Smolkowski, K., Clarke, B., Miller, S. J., & Fien, H. (2015). Examining the association between explicit mathematics instruction and student mathematics achievement. The Elementary School Journal, 115(3), 303–333.CrossRefGoogle Scholar
  13. Gersten, R., & Carnine, D. (1984). Direct instruction mathematics: A longitudinal evaluation of low-income elementary school students. Elementary School Journal, 84(4), 395–407.Google Scholar
  14. Gersten, R., Schiller, E. P., & Vaughn, S. R. (2000). Contemporary special education research: Syntheses of the knowledge base on critical instructional issues. Abingdon: Routledge.Google Scholar
  15. Goeke, J. L. (2009). Explicit instruction: A framework for meaningful direct teaching (V. Lanigan Ed.). Upper Saddle River: Pearson Education, Inc.Google Scholar
  16. Grossman, P., & Thompson, C. (2008). Learning from curriculum materials: Scaffolds for new teachers? Teacher and Teacher Education, 24(2008), 2014–2026.Google Scholar
  17. Gueudet, G., Pepin, B., & Trouche, L. (2013). Collective work with resources: An essential dimension for teacher documentation. ZDM Mathematics Education, 45(7), 1003–1016.Google Scholar
  18. Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218.CrossRefGoogle Scholar
  19. 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.Google Scholar
  20. Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematics interventions for children with special needs: A meta-analysis. Remedial and Special Education, 24, 97–114.Google Scholar
  21. Leong, Y.H., Ho, W.K., Cheng, L.P. (2015). Concrete-Pictorial-Abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1–18.Google Scholar
  22. Marchand-Martella, N., Slocum, T. A., & Martella, R. (2004). Introduction to direct instruction. Boston: Allyn-Bacon.Google Scholar
  23. Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah: Lawrence Erlbaum.Google Scholar
  24. Ministry of Education. (2012). Mathematics syllabus: Secondary one to four. Express course. Normal (Academic) Course. Singapore.Google Scholar
  25. Moyer-Packenham, P. S. (2016). International perspectives on teaching and learning mathematics with virtual manipulatives. Switzerland: Springer.CrossRefGoogle Scholar
  26. Remillard, J. T. (2000). Can curriculum materials support teachers’ learning? Two fourth-grade teachers’ use of a new mathematics text. The Elementary School Journal, 100(4), 331–350.CrossRefGoogle Scholar
  27. Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246.CrossRefGoogle Scholar
  28. Rosenshine, B. (1997). The case for explicit, teacher-led, cognitive strategy instruction. MF Graves (Chair), What sort of comprehension strategy instruction should schools provide.Google Scholar
  29. Rosenshine, B., & Stevens, R. (1986). Teaching functions. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 376–391). New York: Macmillan.Google Scholar
  30. Selling, S. K. (2016). Making mathematics practices explicit in urban middle and high school mathematics classrooms. Journal for Research in Mathematics Education, 47(5), 505–551.CrossRefGoogle Scholar
  31. Simmons, D. C., Fuchs, L. S., Fuchs, D., Mathes, P., & Hodge, J. P. (1995). Effects of explicit teaching and peer tutoring on the reading achievement of learning-disabled and low-performing students in regular classrooms. The Elementary School Journal, 95(5), 387–408.CrossRefGoogle Scholar
  32. Swanson, H. L. (2001). Searching for the best model for instructing students with learning disabilities. Focus on Exceptional Children, 34(2), 1–15.Google Scholar
  33. Watson, A., & Mason, J. (2006). Seeing an exercise as a single mathematical object: Using variation to structure sense-making. Mathematical Thinking and Learning, 8(2), 91–111.Google Scholar
  34. White, B. Y., & Frederiksen, J. R. (1998). Inquiry, modeling, and metacognition: Making science accessible to all students. Cognition and Instruction, 16(1), 3–118.Google Scholar
  35. Zohar, A., & Peled, B. (2008). The effects of explicit teaching of metastrategic knowledge on low-and high-achieving students. Learning and Instruction, 18(4), 337–335.CrossRefGoogle Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2018

Authors and Affiliations

  1. 1.National Institute of EducationNanyang Technological UniversitySingaporeSingapore

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