References
Bartelet, D., Ansari, D., Vaessen A., Blomert, A. (2014) Cognitive subtypes of mathematics learning difficulties in primary education. Research in Developmental Disabilities 35 (2014) 657–670
Baroody, A. J., & Hume, J. (1991). Meaningful mathematics instruction: The case of fractions. Remedial and Special Education, 12(3), 54-68.
Behr, M., Lesh, R., Post, T., & Silver, E. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91–125). New York, NY: Academic Press.
Bogdan, R. C., & Biklen, S. K. (2003). Qualitative research for education: An introduction to theories and methods (4th ed.). Boston: Allyn and Bacon.
Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625.
Bulgar, S. (2003) Children’s’ sense-making of division of fractions. Journal of Mathematical Behavior, 22(3), 319–334.
Byrnes, J. P., & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27(5), 777–786.
Charalambous, C. Y. & Pitta-Pantazi, D. (2007) Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293–316.
Creswell, W. J. (2003). Research design: Qualitative, quantitative and mixed methods approaches (2nd ed.). London: Sage Publications.
D'Ambrosio, B. S., & Spangler Mewborn, D. (1994) Children's constructions of fractions and their implications for classroom instruction. Journal of Research in Childhood Education, 8(2), 150-161.
DeWolf , M., Rapp, M., Bassok, M. and Holyoak, K. J. (2014) Semantic alignment of fractions and decimals with discrete versus continuous entities: A textbook analysis. Proceedings of the Annual Meeting of the Cognitive Science Society, 36, 2133- 2138.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.
Gabriel, F., Coché, F., Szucs, D., Carette, V., Rey, B., & Content, A. (2013). A componential view of children’s difficulties in learning fractions. Frontiers in Psychology, 4, 715.
Goldin, G. A. (2000). A scientific perspective on structure: task-based interviews in mathematics education research. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517-546). Mahwah, NJ: Lawrence Erlbaum Associates.
Hallett, D., Nunes, T., & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal Of Educational Psychology, 102(2), 395-406.
Halliday, M. A. K. (1975). Learning how to mean: Explorations in the development of language. London: Edward Arnold.
Halliday, M. A. K. (1993). Towards a language-based theory of learning. Linguistics and Education, 5(2), 93–116.
Halliday, M. A. K., McIntosh, A., & Strevens, P. (1964). The linguistic sciences and language teaching. London: Longmans.
Hyde, D. C., Khanum, S., & Spelke, E. S. (2014). Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 131, 92–107.
Inglis, M., & Gilmore, C. (2013). Sampling from the mental number line: How are approximate number system representations formed? Cognition, 129, 63–69.
Iuculano, T. & Butterworth, B. (2011). Rapid communication Understanding the real value of fractions and decimals. The Quarterly Journal of Experimental Psychology, 64 (11), 2088–2098.
Jacob, S. N., & Nieder, A. (2009). Notation-independent representation of fractions in the human parietal cortex. The Journal of Neuroscience, 29(14), 4652–4657.
Kallai, A.Y., & Tzelgov, J. (2009). A generalized fraction: An entity smaller than one of the mental number line. Journal of Experimental Psychology: Human Perception and Performance, 35(6), 1845–1864.
Kaput, J. J. (1987a). Representation systems and mathematics. In C. Janvier (Ed.), Problems of representation in teaching and learning mathematics (pp. 19–26). Hillsdale, NJ: Erlbaum.
Kaput, J. J. (1987b). Toward a theory of symbol use in mathematics. In C. Janvier (Ed.), Problems of representation in mathematics learning and problem solving (pp. 159-195). Hillsdale, NJ: Erlbaum.
Kerslake, D. (1986). Fractions: Children’s strategies and errors. A report of the strategies and errors in secondary mathematics project. Windsor, England: NFER-Nelson.
Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. A. Lesh & D. A. Bradbard (Eds.), Number and Measurement. Papers from a Research Workshop (pp. 101–144). Columbus, OH: ERIC
Kolkman, M.E., Kroesbergen, E.H., & Leseman, P.P.M. (2013). Early numerical development and the role of non-symbolic and symbolic skills. Learning and Instruction, 25, 95.
Leibovich, T. and Ansari, D. (2016). The symbol-grounding problem in numerical cognition: A review of theory, evidence, and outstanding questions. Canadian Journal of Experimental Psychology, 1196-1961.
Lyons, I. M., Price, G. R., Vaessen, A, Blomert, L., & Ansari, A. (2014). Numerical predictors of arithmetic success in grades 1–6. Developmental Science, X, pp 1–11.
Meert, G., Grégoire, J., & Noël, M.-P. (2009). Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. The Quarterly Journal of Experimental Psychology, 62(8), 1598–1616.
Miles, M. B. & Huberman, M. N. (1994). Qualitative data analysis: an expanded sourcebook. Thousand Oaks, CA: Sage.
Murray, H., Olivier, A., & Human, P. (1996). Young students’ informal knowledge of fractions. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the Twentieth Conference of the International Group for the Psychology of Mathematics Education, 4, 43 – 50. Valencia, Spain.
Newstead, K. and Murray, H. (1998). Young students' constructions of fractions. In A. Olivier & K. Newstead (Eds.), Proceedings of the Twenty-second International Conference for the Psychology of Mathematics Education: Vol. 3. (pp. 295-302). Stellenbosch, South Africa.
Opfer, J. E., & DeVries, J. M. (2008). Representational change and magnitude estimation: Why young children can make more accurate salary comparisons than adults. Cognition, 108, 843–849.
Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24, 2013– 2019.
Park, J., & Brannon, E. M. (2014). Improving arithmetic performance with number sense training: An investigation of underlying mechanism. Cognition, 133, 188–200.
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346 –362.
Sasanguie, D., Gobel, S.M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement? Journal of Experimental Child Psychology, 114 (3), 418–431.
Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139–159.
Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36, 1227–1238.
Schulze, J. M. (2016). Understanding the developing persuasive writing practices of an adolescent emergent bilingual through systemic functional linguistics: A case study. International Journal of Learning, Teaching and Educational Research, 15(10), 163–179.
Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M.,... Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(10), 691– 697.
Siegler, R. S., Thompson, C. & Schneider, M. (2011) An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273–296.
Stafylidou, S. & Vosniadou, S. (2004) The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503–518.
Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Springer Science & Business Media.
Strauss, A., & Corbin, J. (1990). Basics of qualitative research. London: Sage Publications Ltd.
Thwaite, A. (2015). Pre-service teachers linking their metalinguistic knowledge to their practice: A functional approach. Functional Linguistics, 2(1), 1–17.
Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: the case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25.
Turkan, S., de Oliveira, L. C., Lee, O., & Phelps, G. (2014). Proposing a knowledge base for teaching academic content to English language learners: Disciplinary linguistic knowledge. Teachers College Record, 116(3), 1–30.
van Lier, L., & Walqui, A. (2012). Language and the Common Core State Standards. Commissioned paper by the Understanding Language Initiative. Stanford, CA: Stanford University. Retrieved from http://ell.stanford.edu/papers/language
Van Steenbrugge, H., Lesage, E., Valcke, M., & Desoete, A. (2014). Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?. Journal of Curriculum Studies, 46(1), 138-161.
Wodak, R. & Meyer, M. (2009). Methods for critical discourse analysis. SAGE