Developing Namibian Grade 8 Learners’ Conceptions of Fractions Using Visual Models

References

• Bertram, C., & Christiansen, I. (2014). Understanding research: An introduction to reading research. Pretoria: Van Schaik Publishers.
   Google Scholar
• Brown, B. (2015). The relational nature of rational numbers. Pythagoras, 36(1), Art. #273, 8 pages. doi:10.4102/pythagoras.v36i1.273.
   Web of Science ®Google Scholar
• Clarke, D., Roche, A., & Mitchell, A. (2011). One-to-one student interviews provide powerful insights and clear focus for the teaching of fractions in the middle years. In Fractions: Teaching for understanding (pp. 23–41). Adelaide, SA: The Australian Association of Mathematics Teachers (AAMT) Inc.
   Google Scholar
• Cortina, J. L., Visnovska, J., & Zuniga, C. (2015). An alternative starting point for fraction instruction. International Journal for Mathematics Teaching and Learning, 26(1), 79–99.
   Google Scholar
• Cramer, K., Wyberg, T., & Leavitt, S. (2008, April). The role of representations in fraction addition and subtraction. Mathematics Teaching in the Middle School, 13(8), 490–496. http://www.jstor.org/stable/41182601.
   Google Scholar
• Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, The Netherlands: Kluwer.
   Google Scholar
• Gray, P. (2014). Instructional strategies that build mathematical proficiency. New York: Common Core Coach. Retrieved from http://www.triumphlearning.com/assets/ … /001M13_C3_Math_White_Paper.pdf
   Google Scholar
• Hamdan, N., & Gunderson, E. A. (2017). The number line is a critical spatial-numerical representation: Evidence from a fraction intervention. Developmental Psychology, 53(3), 587–596. doi: 10.1037/dev0000252
   PubMed Web of Science ®Google Scholar
• Harvey, R. (2011). Challenging and extending a student teacher’s concepts of fractions using an elastic strip. In Mathematics: Traditions and [new] practices (pp. 333–339). AAMT and MERGA. Retrieved from http://www.victoria.ac.nz/research/research … /research-publications-2011.pdf
   Google Scholar
• Kerslake, D. (1986). Fractions: Children’s strategies and errors. A report of the strategies and errors in secondary mathematics project. England: NFER-NELSON Publishing Company, Ltd.
   Google Scholar
• Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
   Google Scholar
• Larson, C. N. (1987, July). Regions, number lines, and rulers as models for fractions. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the eleventh annual meeting of the international group for the psychology of mathematics education (Vol. 1, pp. 398–404). Montreal: PME. Retrieved from http://www.files.eric.ed.gov/fulltext/ED383532.pdf
   Google Scholar
• Maree, K. (Ed.). (2015). First steps in research. Van Schaik: Pretoria.
   Google Scholar
• McMullen, J., Laakkonen, E., Hannula-Sormunen, M., & Lehtinen, E. (2015). Modeling the developmental trajectories of rational number concept(s). Learning and Instruction, 37, 14–20. doi: 10.1016/j.learninstruc.2013.12.004
   Web of Science ®Google Scholar
• Mitchell, A., & Horne, M. (2011). Listening to children’s explanations of fraction pair tasks: When more than an answer and an initial explanation are needed. In J. Clark, B. Kissane, & J. Mousley (Eds.), Mathematics: Traditions and new practices. Proceedings of the 2011 AAMT-MERGA conference (pp. 515–522). Australia: AAMT and MERGA.
   Google Scholar
• Namibia. Ministry of Education. (2010a). Mathematics syllabus grades 8–10: Junior secondary phase. Okahandja: NIED.
   Google Scholar
• Namibia. Ministry of Education. (2010b). National curriculum for basic education. Okahandja: NIED.
   Google Scholar
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
   Google Scholar
• National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, DC: US Dept of Education.
   Google Scholar
• Pantziara, M., & Philippou, G. (2012). Levels of students’ “conception” of fractions. Educational Studies in Mathematics, 79(1), 61–83. doi: 10.1007/s10649-011-9338-x
   Web of Science ®Google Scholar
• Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19. doi: 10.1016/j.tics.2012.11.004
   PubMed Web of Science ®Google Scholar
• Simon, M. A., Placa, N., Avitzur, A., & Kara, M. (2018). Promoting a concept of fraction-as-measure: A study of the learning through activity research program. The Journal of Mathematical Behavior, 52, 122–133. doi: 10.1016/j.jmathb.2018.03.004
   Web of Science ®Google Scholar
• Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M., & Wray, J. (2019). Developing fraction concepts. In J. A. Van de Walle, K. S. Karp, J. M. Bay-Williams, & J. Wray (Eds.), Elementary and middle school mathematics: Teaching developmentally. (10th Ed.) (pp. 337–372). Boston: Pearson.
   Google Scholar
• Vatilifa, N. (2012). An investigation into understanding the experiences of the level 5-7 student teachers when teaching fractions in primary schools in Namibia: A case study (Unpublished master’s thesis). Rhodes University, Grahamstown.
   Google Scholar
• Watanabe, T. (2002, April). Representations in teaching and learning fractions. Teaching Children Mathematics, 8(8), 457–463. Reston: The National Council of Teachers of Mathematics. Retrieved from http://www.lesage.blogs.uoit.ca/wp … /Representing-Fractions-NCTM-April-2002.pdf
   Google Scholar