References

Ball, D. L. (1993). Halves, pieces, and twoths: Constructing representational contexts in teaching fractions. In T. P. Carpenter, E. Fennema, & T. Romberg (Eds.), Rational numbers: An integration of research pp. 157–196. Hillsdale, NJ: Erlbaum.

Behr, M. J., Post T., Silver E., Mierkiewicz D., (1980). Theoretical foundations for instructional research on rational numbers. Proceedings PME 1 pp. 60-67.

Behr, M.J., Wachsmuth I., Post T., (1985). Construct a sum: a measure of children’s understanding of fraction size. Journal for research in mathematics education, 16, p p. 120-131.

Davis, B., and Simmt, E., (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34, pp.137–167.

Ellerbruch, L. W., and Payne, J. N. (1978). A teaching sequence for intial fraction concepts through the addition of unlike fractions. In Suydam, M. (Ed) Developing computational Skills. Reston. Virgina. National Council of Teachers of Mathematics.

Gabriel, F., Coché, F., Szucs, D., Carette, V., Rey, B. and Content, A., (2013). A componential view of children's difficulties in learning fractions. Frontiers in psychology, 4, p.715.

Kieren, T. E. (1988). Personal knowledge of rational numbers: Its intuitive and formal development. In Hiebert, J. and Behr, M. (Eds.), Number concepts and operation in the middle grades. Reston, VA: National Council of Teachers of Mathematics. pp. 53-92.

Kotsopoulos, D. (2007). Mathematics Discourse It's like hearing a foreign Language, NCTM, 4, pp. 301-305.

Moyer, P. (2001) Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics 47, pp. 175-197. Netherlands: Kluwer.

Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), pp. 1080–1110.

Novillis-Larson, C. (1980). Locating proper fractions on number lines: Effect of length and equivalence. School Science and Mathematics, 80 (5), pp. 423-428.

Olanoff, D., Lo, J.J. and Tobias, J., (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on fractions. The Mathematics Enthusiast, 11(2), pp.267-310.

Owens, D. T. (1980). Study of the relationship of area concept and learning concepts by children in grades three and four. In T. E. Kieren (Ed.), Recent research on number concepts. Columbus, Ohio: ERIC/SMEAC.

Pimm, D. (1987). Speaking Mathematically: Communication in Mathematics Classrooms. Routledge. London.

Siegler, R.S. and Lortie-Forgues, H., (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), p.909.

Yang, D.-C., Reys, R. E., & Reys, B. J., (2008). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education, 7, pp. 383–403.