Abstract
The crucial role of teachers in introducing integers to children is highlighted in chapters 8–10, comprising this section. The three chapters discuss (prospective) teachers’ conceptions of integer equations, of children’s thinking about integer expressions, and of the role of some didactical models used in teaching integer addition and subtraction. These different aspects of teacher knowledge and conceptions draw an important picture of characteristics and issues that should be taken into account by teacher educators in preparing teachers for teaching integers. In the first part of our commentary we highlight the main contributions of each of the chapters, focusing on the central findings and on important issues brought up by each chapter. The second part offers a meta-perspective of some of the issues by discussing more general educational implications. In this part we also take the opportunity to express our own insights emerging and associated with the ideas presented in the three chapters.
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References
Almeida, R., & Bruno, A. (2014). Strategies of pre-service primary school teachers for solving addition problems with negative numbers. International Journal of Mathematical Education in Science and Technology, 45(5), 719–737. https://doi.org/10.1080/002073999287482
Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373–397. https://doi.org/10.1086/461730
Carpenter, T. P., Lindquist, M. M., Matthews, W., & Silver, E. A. (1983). Results of the third NAEP mathematics assessment. Secondary school. Mathematics Teacher, 76, 652–659. http://www.jstor.org/stable/27963780
Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155–177. https://doi.org/10.1207/s15327833mtl0102_4
Hatano, G., & Inagaki, K. (1998). Cultural contexts of schooling revisited: A review of the learning gap from a cultural psychology perspective. In S. G. Paris & H. M. Wellman (Eds.), Global prospects for education: Development, culture, and schooling (pp. 79–104). Washington, DC: American Psychological Association. https://doi.org/10.1037/10294-003
Kieren, T. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101–144). Columbus, OH: ERIC/SMEAC.
Linchevski, L., & Williams, J. (1999). Using intuition from everyday life in ‘filling’ the gap in children’s extension of their number concept to include the negative numbers. Educational Studies in Mathematics, 39, 131–147. https://doi.org/10.1023/A:1003726317920
Nesher, P. (1980). The stereotyped nature of school word problems. For the Learning of Mathematics, 1(1), 41–48. http://www.jstor.org/stable/40247701
Peled, I., & Carraher, D. (2008). Signed numbers and algebraic thinking. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 303–328). Mahwah, NJ: NCTM: Lawrence Erlbaum Associates.
Peled, I., & Segalis, B. (2005). It’s not too late to conceptualize: Constructing a generalized subtraction schema by abstracting and connecting procedures. Mathematical Thinking and Learning, 7, 207–230. https://doi.org/10.1207/s15327833mtl0703_2
Peled, I., & Zaslavsky, O. (2008). Beyond local conceptual connections: Meta-knowledge about procedures. For the Learning of Mathematics, 28(3), 28–35. http://www.jstor.org/stable/40248626
Schoenfeld, H. A. (1987). What’s all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189–215). Hillsdale, NJ: Erlbaum.
Thompson, P. W. (2002). Didactic objects and didactic models in radical constructivism. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling, and tool use in mathematics education (pp. 197–220). Dordrecht, The Netherlands: Kluwer. https://doi.org/10.1007/978-94-017-3194-2_12
Verschaffel, L. (1994). Using retelling data to study elementary school children’s representations and solutions of compare problems. Journal for Research in Mathematics Education, 25(2), 141–165. https://doi.org/10.2307/749506
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Peled, I., Klemer, A. (2018). Commentary on Chapters 8 to 10: Teachers’ Knowledge and Flexibility—Understanding the Roles of Didactical Models and Word Problems in Teaching Integer Operations. In: Bofferding, L., Wessman-Enzinger, N. (eds) Exploring the Integer Addition and Subtraction Landscape. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-90692-8_13
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