Mathematical problem solving in textbooks from twelve countries

References

• Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71–80. doi: 10.1016/j.ijer.2013.06.005
   Web of Science ®Google Scholar
• Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41–62. doi: 10.2307/749717
   Web of Science ®Google Scholar
• Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., Palmberg, B., et al. (2014). Developing mathematical competence: From the intended to the enacted curriculum. The Journal of Mathematical Behavior, 33(1), 72–87. doi: 10.1016/j.jmathb.2013.10.001
   Google Scholar
• Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75(1), 89–105. doi: 10.1007/s10649-010-9242-9
   Web of Science ®Google Scholar
• Brehmer, D., Ryve, A., & Van Steenbrugge, H. (2016). Problem solving in Swedish mathematics textbooks for upper secondary school. Scandinavian Journal of Educational Research, 60(6), 577–593. doi: 10.1080/00313831.2015.1066427
   Web of Science ®Google Scholar
• Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht, Netherlands: Kluwer Academic Publishers.
   Google Scholar
• Davis, J. D., Smith, D. O., Roy, A. R., & Bilgic, Y. K. (2014). Reasoning-and-proving in algebra: The case of two reform-oriented U.S. Textbooks. International Journal of Educational Research, 64, 92–106. doi: 10.1016/j.ijer.2013.06.012
   Web of Science ®Google Scholar
• Department of Education, Republic of South Africa. (2008). National Curriculum Statement, Grades 10–12 (General): Learning programme guidelines, Mathematical Literacy.
   Google Scholar
• Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159–199. doi: 10.3102/00346543053002159
   Web of Science ®Google Scholar
• Fan, L., & Bokhove, C. (2014). Rethinking the role of algorithms in school mathematics: A conceptual model with focus on cognitive development. ZDM, 46(3), 481–492. doi: 10.1007/s11858-014-0590-2
   Google Scholar
• Floden, R. E. (2002). The measurement of opportunity to learn. In A. C. Porter, & A. Gamoran (Eds.), Methodological advances in cross-national surveys of educational achievement (pp. 231–266). Washington, DC: National Academies Press.
   Google Scholar
• Gresalfi, M. S. (2009). Taking up opportunities to learn: Constructing dispositions in mathematics classrooms. Journal of the Learning Sciences, 18(3), 327–369. doi: 10.1080/10508400903013470
   Web of Science ®Google Scholar
• Halldén, O., Scheja, M., & Haglund, L. (2008). The contextuality of knowledge: An intentional approach to meaning making and conceptual change. In S. Vosniadou (Ed.), International handbook of research on conceptual change (pp. 509–532). New York, NY: Routledge.
   Google Scholar
• Henderson, S. (2012). Why the journey to mathematical excellence may be long in Scotland's primary schools. Scott Educ Rev, 44(1), 46–56.
   Google Scholar
• Hiebert, J. (2003). What research says about the NCTM standards. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research companion to the principles and standards for school mathematics (pp. 5–23). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 371–404). Charlotte, NC: Information Age Pub.
   Google Scholar
• Jäder, J., Sidenvall, J., & Sumpter, L. (2017). Students’ mathematical reasoning and beliefs in non-routine task solving. International Journal of Science and Mathematics Education, 15(4), 759–776. doi: 10.1007/s10763-016-9712-3
   Web of Science ®Google Scholar
• Johansson, M. (2006). Teaching mathematics with textbooks: A classroom and curricular perspective [dissertation]. Luleå, Sweden: Luleå University of Technology, Department of Mathematics.
   Google Scholar
• Kaur, B. (2010). A study of mathematical tasks from three classrooms in Singapore. In Y. Shimizu, B. Kaur, R. Huang, & D. Clarke (Eds.), Mathematical tasks in classrooms around the world (pp. 15–33). Rotterdam, the Netherlands: Sense Publishers.
   Google Scholar
• Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
   Google Scholar
• Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234–241. doi: 10.2307/749754
   Web of Science ®Google Scholar
• Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52(1), 29–55. doi: 10.1023/A:1023683716659
   Google Scholar
• Lithner, J. (2004). Mathematical reasoning in calculus textbook exercises. The Journal of Mathematical Behavior, 23(4), 405–427. doi: 10.1016/j.jmathb.2004.09.003
   Google Scholar
• Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276. doi: 10.1007/s10649-007-9104-2
   Google Scholar
• Ministry of Education, Ontario. (2005). The Ontario Curriculum, Grades 9 and 10. Mathematics.
   Google Scholar
• Mullis, I. V. S., Martin, M. O., Foy, P., et al. (2008). TIMSS 2007 international mathematics Report: Findings from IEA’s trends in international mathematics and science study at the fourth and eighth grades. Chestnut Hill, MA: Boston College, TIMSS & PIRLS International Study Center.
   Google Scholar
• Mullis, I. V. S., Martin, M. O., Foy, P., et al. (2012). TIMSS 2011 international results in mathematics. Chestnut Hill, MA: Boston College, TIMSS & PIRLS International Study Center.
   Google Scholar
• Mullis, I. V. S., Martin, M. O., Ruddock, G. J., et al. (2009). TIMSS 2011 assessment frameworks. Chestnut Hill, MA: Boston College, TIMSS & PIRLS International Study Center.
   Google Scholar
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Newton, D. P., & Newton, L. D. (2007). Could elementary mathematics textbooks help give attention to reasons in the classroom? Educational Studies in Mathematics, 64(1), 69–84. doi: 10.1007/s10649-005-9015-z
   Google Scholar
• Niss, M. (2003). The mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagatsis, & S. Papastavridis (Eds.), Proceedings of the 3rd Mediterranean Conference on mathematics education; 2003 Jan 3–5; Athens (pp. 115–124). Athens, Greece: Hellenic Mathematical Society.
   Google Scholar
• Norqvist, M. (2017). The effect of explanations on mathematical reasoning tasks. International Journal of Mathematical Education in Science and Technology, 49(1), 15–30. doi: 10.1080/0020739X.2017.1340679
   Web of Science ®Google Scholar
• OECD. (2014). PISA 2012 results in focus: What 15-year-olds know and what they can do with what they know. Paris, France: OECD Publishing.
   Google Scholar
• Palm, T., Boesen, J., & Lithner, J. (2011). Mathematical reasoning requirements in Swedish upper secondary level assessments. Mathematical Thinking and Learning, 13(3), 221–246. doi: 10.1080/10986065.2011.564994
   Web of Science ®Google Scholar
• Pehkonen, L. (2004). The magic circle of the textbook: An option or an obstacle for teacher change. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for the Psychology of mathematics education: Vol 3; 2004 July 14–18; Bergen (pp. 513–520). Bergen, Norway: Bergen University College.
   Google Scholar
• Pepin, B. E., & Haggarty, L. (2001). Mathematics textbooks and their use in English, French and German classrooms: A way to understand teaching and learning cultures. ZDM, 33(5), 158–175.
   Google Scholar
• Rezat, S., & Strässer, R. (2014). Mathematics textbooks and how they are used. In P. Andrews, & T. Rowland (Eds.), Master class in mathematics education: International perspectives on teaching and learning (pp. 51–62). New York (NY: Bloomsbury.
   Google Scholar
• Schmidt, W., Gueudet, G., Pepin, B., & Trouche, L. (2012). Measuring content through textbooks: The cumulative effect of middle-school tracking. In From text to ‘lived’ resources: Mathematics curriculum materials and teacher development (pp. 143–160). Dordrecht, Netherlands: Springer Science & Business Media B.V.
   Google Scholar
• Schmidt, W. H., McKnight, C. C., Houang, R. T., et al. (2001). Why schools matter: A cross-national comparison of curriculum and learning. The Jossey-Bass education series. San Francisco, CA: Jossey-Bass.
   Google Scholar
• Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
   Google Scholar
• Schoenfeld, A. H. (2012). Problematizing the didactic triangle. ZDM, 44(5), 587–599. doi: 10.1007/s11858-012-0395-0
   Google Scholar
• Shield, M., & Dole, S. (2013). Assessing the potential of mathematics textbooks to promote deep learning. Educational Studies in Mathematics, 82(2), 183–199. doi: 10.1007/s10649-012-9415-9
   Web of Science ®Google Scholar
• Sidenvall, J., Lithner, J., & Jäder, J. (2015). Students’ reasoning in mathematics textbooks task-solving. International Journal of Mathematical Education in Science and Technology, 46(4), 533–552. doi: 10.1080/0020739X.2014.992986
   Web of Science ®Google Scholar
• Silver, E. A. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 181–198). Hillsdale, NJ: Erlbaum.
   Google Scholar
• Stacey, K., & Vincent, J. (2009). Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks. Educational Studies in Mathematics, 72(3), 271–288. doi: 10.1007/s10649-009-9193-1
   Web of Science ®Google Scholar
• Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369). Charlotte, NC: National Council of Teachers of Mathematics; Information Age Pub.
   Google Scholar
• Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258–288. doi: 10.1080/10986060903253954
   Web of Science ®Google Scholar
• Thompson, D. R., Senk, S. L., & Johnson, G. J. (2012). Opportunities to learn reasoning and proof in high school mathematics textbooks. Journal for Research in Mathematics Education, 43(3), 253–295. doi: 10.5951/jresematheduc.43.3.0253
   Web of Science ®Google Scholar
• Valverde, G. A., Bianchi, L. J., Wolfe, R. G., et al. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht, the Netherlands: Kluwer Academic Publishers.
   Google Scholar
• Vincent, J., & Stacey, K. (2008). Do mathematics textbooks cultivate shallow teaching?: Applying the TIMSS video study criteria to Australian eighth-grade mathematics textbooks. Mathematics Education Research Journal, 20(1), 82–107. doi: 10.1007/BF03217470
   Google Scholar