Vlassis, Joëlle ; University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > Department of Education and Social Work (DESW)
Banerjee, R., & Subramaniam, K. (2012). Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics, 80(3), 351–367. 10.1007/s10649-011-9353-y DOI: 10.1007/s10649-011-9353-y
Bishop, J., Lamb, L., Philipp, R., Whitacre, I., Schappelle, B., & Lewis, M. (2014). Obstacles and affordances for integer reasoning: An analysis of children’s thinking and the history of mathematics. Journal for Research in Mathematics Education, 45(1), 19–61. 10.5951/jresematheduc.45.1.0019 DOI: 10.5951/jresematheduc.45.1.0019
Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Gardiner, A. M. (2019). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics, 102(2), 193–219. 10.1007/s10649-019-09894-7 DOI: 10.1007/s10649-019-09894-7
Bofferding, L. (2014). Negative integer understanding: Characterizing first graders’ mental models. Journal for Research in Mathematics Education, 45(2), 194–245. 10.5951/jresematheduc.45.2.0194 DOI: 10.5951/jresematheduc.45.2.0194
Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics education, 37(2), 87–115. https://doi.org/10.2307/30034843
Gallardo, A. (2002). The extension of the natural-number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49(2), 171–192. http://www.jstor.org/stable/3483074.
Herscovics, N., & Linchevski, L. (1991). Pre-algebraic thinking: Range of equations and informal solution processes used by seventh graders prior to any instruction. In F. Furinghetti (Ed.), Proceedings of the Fifteenth International Conference for the Psychology of Mathematics Education (pp. 173–180). Assissi, Italy.
Hickendorff, M. (2018). Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems. European Journal of Psychology of Education, 33(4), 577–594. 10.1007/s10212-017-0357-6 DOI: 10.1007/s10212-017-0357-6
Irwin, K., & Britt, M. (2005). The algebraic nature of students’ numerical manipulation in the New Zealand Numeracy Project. Educational Studies in Mathematics, 58(2), 169–188. http://www.jstor.org/stable/25047145.
Kaput, J. J. (2008). What is algebra? What is algebraic reasoning. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Lawrence Erlbaum.
Kieran C. (2018). Seeking, using, and expressing structure in numbers and numerical operations: A fundamental path to developing early algebraic thinking. In C. Kieran (Ed.) Teaching and learning algebraic thinking with 5- to 12-year-olds. ICME-13 Monographs (pp. 79–105). Cham: Springer. https://doi.org/10.1007/978-3-319-68351-5_4
Kieran, C., Pang, J., Schifter, D., & Ng, S. F. (2016). Early algebra: Research into its nature, its learning, its teaching. Springer Nature. 10.1007/978-3-319-32258-2 DOI: 10.1007/978-3-319-32258-2
Kiziltoprak, A., & Köse, N. (2017). Relational thinking: The bridge between arithmetic and algebra. International Electronic Journal of Elementary Education, 10(1), 131–145. https://www.iejee.com/index.php/IEJEE/article/view/305.
Kumar, R. S., Subramaniam, K., & Naik, S. S. (2017). Teachers’ construction of meanings of signed quantities and integer operation. Journal of Mathematics Teacher Education, 20(6), 557–590. 10.1007/s10857-015-9340-9 DOI: 10.1007/s10857-015-9340-9
Lamb, L., Bishop, J., Philipp, R., Whitacre, I., & Schappelle, B. (2016). The relationship between flexibility and student performance on open number sentences with integers. In M. Wood, E. Turner, M. Civile, & J. Eli (Eds.), Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education. North American Chapter (pp. 171–178). Tucson, Arizona.
Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40(2), 173–196. 10.1023/A:1003606308064 DOI: 10.1023/A:1003606308064
Livneh, D., & Linchevski, L. (2007). Algebrification of arithmetic: Developing algebraic structure sense in the context of arithmetic. In J. H. Woo, H.C. Lew, K.S. Park, & D.Y. Seo (Eds.), Proceedings of the 31st Conference of the Psychology of Mathematics Education (pp. 217–225). Seoul, Korea.
McGowen, M. A., & Tall, D. O. (2013). Flexible thinking and met-befores: Impact on learning mathematics. The Journal of Mathematical Behavior, 32(3), 527–537. 10.1016/j.jmathb.2013.06.004 DOI: 10.1016/j.jmathb.2013.06.004
MEN, Ministère de l'Éducation Nationale et de la Formation professionnelle. (2011). Plan d'études de l’école fondamentale. Luxembourg: Ministère de l'Éducation nationale et de la Formation professionnelle.
Molina, M., & Castro, E. (2021). Third grade students’ use of relational thinking. Mathematics, 9(2), 187. http://hdl.handle.net/10481/66574.
Pang, J., & Kim, J. (2018). Characteristics of Korean students’ early algebraic thinking: A generalized arithmetic perspective. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5 - to 12-year-olds. ICME-13 Monographs (pp. 141–65). Cham: Springer. https://doi.org/10.1007/978-3-319-68351-5_6.
Peled, I., Mukhopadhyay, S., & Resnick, L. (1989). Formal and informal sources of mental models for negative numbers. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 106–110). Paris, France.
Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds. ICME-13 Monographs (pp. 3–25). Cham: Springer. https://doi.org/10.1007/978-3-319-68351-5_1.
Selter, C., Prediger, S., Nührenbörger, M., & Hußmann, S. (2012). Taking away and determining the difference—a longitudinal perspective on two models of subtraction and the inverse relation to addition. Educational Studies in Mathematics, 79(3), 389–408. 10.1007/s10649-011-9305-6 DOI: 10.1007/s10649-011-9305-6
Stephens, A. (2008). What ‘counts’ as algebra in the eyes of preservice elementary teachers? The Journal of Mathematical Behavior, 27(1), 33–47. 10.1016/j.jmathb.2007.12.002 DOI: 10.1016/j.jmathb.2007.12.002
Subramaniam, K. (2019). Representational coherence in instruction as a means of enhancing students’ access to mathematics’. In M. Graven, H. Venkat, A. Essien, & P. Vale (Eds.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (pp. 33–52). Pretoria, South Africa.
Thompson, P., & Dreyfus, T. (1988). Integers as transformations. Journal for Research in Mathematics Education, 19(2), 115–133. 10.5951/jresematheduc.19.2.0115 DOI: 10.5951/jresematheduc.19.2.0115
Vergnaud, G. (1982). Cognitive and developmental psychology and research in mathematics education: Some theoretical and methodological issues. For the Learning of Mathematics, 3(2), 31–41. https://www.jstor.org/stable/40248130.
Vlassis, J. (2009). What do students say about the role of the minus sign in polynominals?. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (pp. 289–296). Thessaloniki, Greece.
Vlassis, J. (2004). Making sense of the minus sign or becoming flexible in ‘negativity.’ Learning and Instruction, 14(5), 469–484. 10.1016/j.learninstruc.2004.06.012 DOI: 10.1016/j.learninstruc.2004.06.012
Vlassis, J. (2008). The role of mathematical symbols in the development of number conceptualization: The case of the minus sign. Philosophical Psychology, 21(4), 555–570. 10.1080/09515080802285552 DOI: 10.1080/09515080802285552
Warren, E., & Cooper, T. J. (2009). Developing mathematics understanding and abstraction: The case of equivalence in the elementary years. Mathematics Education Research Journal, 21(2), 76–95. 10.1007/BF03217546 DOI: 10.1007/BF03217546
Whitacre, I., Pierson Bishop, J., Lamb, L. L., Philipp, R. A., Bagley, S., & Schappelle, B. P. (2015). ‘Negative of my money, positive of her money’: Secondary students’ ways of relating equations to a debt context. International Journal of Mathematical Education in Science and Technology, 46(2), 234–249. 10.1080/0020739X.2014.956822 DOI: 10.1080/0020739X.2014.956822
Young, L., & Booth, J. (2020). Don’t eliminate the negative: Influences of negative number magnitude knowledge on algebra performance and learning. Journal of Educational Psychology, 112(2), 384–396. 10.1037/edu0000371 DOI: 10.1037/edu0000371
