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Abstract

This chapter focuses on the design of text-based tasks in textbooks, downloadable materials, and other forms of text-based communication. Tasks may be freestanding or may form part of a task collection with a prepared order, such as in a textbook series or as a resource from which teachers or students may choose. The chapter looks at content decisions, the implications of author intentions for design and learning, and visual aspects of prepared text-based tasks. An international range of text-based tasks is used to illustrate differences in how conceptual coherence and mathematical challenge are intended to be achieved and the different views of the nature of mathematics that might be developed.

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References

  • Amit, B., & Movshovitz-Hadar, N. (2011). Design and high-school implementation of mathematical-news-snapshots - An action-research into ‘Today’s news is tomorrow’s history’. In E. Barbin, M. Krongellner, & C. Tzanakis (Eds.), History and epistemology in mathematics education: Proceedings of the Sixth European Summer University (pp. 171–184). Austria: Verlag Holzhausen GmbH/Holzhausen Publishing Ltd. Based upon a workshop given at ESU 6, Vienna, July, 2010.

    Google Scholar 

  • Anderson, J. R., & Schunn, C. D. (2000). Implications of the ACT-R learning theory: No magic bullets. In R. Glaser (Ed.), Advances in instructional psychology: Educational design and cognitive science (Vol. 5, pp. 1–34). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Baker, W., & Bourne, A. (1937). Elementary algebra. London: G. Bell and Sons.

    Google Scholar 

  • Barabash, M., & Guberman, R. (2013). Developing young students’ geometric insight based on multiple informal classifications as a central principle in the task design. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 293–302). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Barzel, B., Leuders, T., Prediger, S., & Huβmann, S. (2013). Designing tasks for engaging students in active knowledge organization. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 283–292). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Bell, A. W. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7(1), 23–40.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics 1970–1990. Translation from French: M. Cooper, N. Balacheff, R. Sutherland, & V. Warfield. Dordrecht, The Netherlands: Kluwer Academic (1998, French version: Théorie des situations didactiques. Grenoble, France: La Pensée Sauvage).

    Google Scholar 

  • Burns, R. P. (1982). A pathway into number theory. Cambridge, England: Cambridge University Press.

    Google Scholar 

  • Byrne, O. (1847). The first six books of Euclid. London: William Pickering. Available from http://www.math.ubc.ca/~cass/Euclid/byrne.html.

    Google Scholar 

  • Chang, Y., Lin, F., & Reiss, K. (2013). How do students learn mathematical proof? A comparison of geometry designs in German and Taiwanese textbooks. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 303–312). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Chesné, J.-F., Le Yaouanq, M.-H., Coulange, L., & Grapin, N. (2009). Hélice 6e. Paris: Didier.

    Google Scholar 

  • Common Problem Solving Strategies as links between Mathematics and Science (COMPASS). (2013). Retrieved from: http://www.compass-project.eu

  • Corcoran, D., & Moffett, P. (2011). Fractions in context: The use of ratio tables to develop understanding of fractions in two different school systems. In C. Smith (Ed.), Proceedings of the British Society for Research into Learning Mathematics, 31(3), 23–28. Available from http://www.bsrlm.org.uk/IPs/ip31-3/BSRLM-IP-31-3-05.pdf

  • Crisp, R., Inglis, M., Mason, J., & Watson, A. (2011). Individual differences in generalization strategies. In C. Smith (Ed.), Proceedings of the British Society for Research into Learning Mathematics, 31(3), 35–40.

    Google Scholar 

  • Cuoco, A. (2001). Mathematics for teaching. Notices of the AMS, 48(2), 168–174.

    Google Scholar 

  • Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375–402.

    Google Scholar 

  • Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18, 382–393.

    Google Scholar 

  • Davis, B. (2008). Is 1 a prime number? Developing teacher knowledge through concept study. Mathematics Teaching in the Middle School, 14(2), 86–91.

    Google Scholar 

  • Dickinson, P., & Hough, S. (2012). Using realistic mathematics education in UK classrooms. MEI. http://www.mei.org.uk/files/pdf/rme_impact_booklet.pdf. Retrieved November 20, 2014.

  • Dindyal, J., Tay, E. G., Quek, K. S., Leong, Y. H., Toh, T. L., Toh, P. C., et al. (2013). Designing the practical worksheet for problem solving tasks. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 313–324). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Dole, S., & Shield, M. (2008). The capacity of two Australian eighth-grade textbooks for promoting proportional reasoning. Research in Mathematics Education, 10(1), 19–35.

    Google Scholar 

  • Dörfler, W. (2005). Diagrammatic thinking: Affordances and constraints. In M. H. Hoffman, J. Lenhard, & F. Seeger (Eds.), Activity and sign: Grounding mathematics education (pp. 57–66). Berlin/New York: Springer.

    Google Scholar 

  • Drake, C., & Sherin, M. G. (2009). Developing curriculum vision and trust: Changes in teachers’ curriculum strategies. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 321–337). New York: Routledge.

    Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.

    Google Scholar 

  • Even, R., & Olsher, S. (2012). The integrated mathematics wiki-book project. Available from http://www.openu.ac.il/innovation/chais2012/downloads/e-Even-Olsher-61_eng.pdf

  • Fan, L. (2013). A study on the development of teachers’ pedagogical knowledge (2nd ed.). Shanghai: East China Normal University Press.

    Google Scholar 

  • Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education, development status and directions. ZDM: The International Journal on Mathematics Education, 45, 633–646.

    Google Scholar 

  • Fujii, T. (2015). The critical role of task design in lesson study. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education: An ICMI Study 22. New York: Springer.

    Google Scholar 

  • Godfrey, C., & Siddons, A. (1915). Elementary algebra, Part 1C. Cambridge, England: Cambridge University Press.

    Google Scholar 

  • Gregório, M., Valente, N. M., & Calafate, R. (2010). Segredos dos Números 1 - Manual -Matemática/1.° ano do Ensino Básico. Lisboa: Lisboa Editora.

    Google Scholar 

  • Gueudet, G., Pepin, B., & Trouche, L. (2013). Textbooks’ design and digital resources. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 325–336). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Harel, G. (2009). A review of four high school mathematics programs. Retrieved from http://www.math.jhu.edu/~wsw/ED/harelhsreview2.pdf

  • Hart, E. W. (2013). Pedagogical content analysis of mathematics as a framework for task design. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 337–346). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Herbart, J. F. (1904a). Outlines of educational doctrine. New York: Macmillan.

    Google Scholar 

  • Herbart, J. F. (1904b). The science of education. London: Sonnenschein.

    Google Scholar 

  • Herbel-Eisenmann, B. A. (2009). Negotiating the “presence of the text”: How might teachers’ language choices influence the positioning of the textbook? In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 134–151). New York: Routledge.

    Google Scholar 

  • Hirsch, C. R. (Ed.). (2007). Perspectives on the design and development of school mathematics curricula. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Hoven, J., & Garelick, B. (2007). Singapore math: Simple or complex? Educational Leadership, 65(3), 28–31.

    Google Scholar 

  • Hußmann, S., Leuders, T., Prediger, S., & Barzel, B. (2011a) Mathewerkstatt 5. Cornelsen.

    Google Scholar 

  • Hußmann, S., Leuders, T., Prediger, S., & Barzel, B. (2011b). Kontexte für sinnstiftendes Mathematiklernen (KOSIMA) – ein fachdidaktisches Forschungs-und Entwicklungsprojekt. Beiträge zum Mathematikunterricht, pp. 419422.

    Google Scholar 

  • Huntley, M. A., & Terrell, M. S. (2014). One-step and multi-step linear equations: A content analysis of five textbook series. ZDM: The International Journal on Mathematics Education, 46(5), 751–766.

    Google Scholar 

  • Kress, G. R., & Van Leeuwen, T. (1996). Reading images: The grammar of visual design. New York: Psychology Press.

    Google Scholar 

  • Lee, K., Lee, E., & Park, M. (2013). Task modification and knowledge utilization by Korean prospective mathematics teachers. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 347–356). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Li, Y., Zhang, J., & Ma, T. (2009). Approaches and practices in developing school mathematics textbooks in China. ZDM: The International Journal on Mathematics Education, 41(6), 733–748.

    Google Scholar 

  • Llinares, S., Krainer, K., & Brown, L. (2014). Mathematics, teachers and curricula. In S. Lerman (Ed.), Encyclopaedia of mathematics education (pp. 438–441). New York: Springer.

    Google Scholar 

  • Love, E., & Pimm, D. (1996). “This is so”: A text on texts. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 371–409). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Lundberg, A. L. V., & Kilhamn, C. (2013). The lemon squash task. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 357–366). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Maaβ, K., Garcia, F. J., Mousouides, N., & Wake, G. (2013). Designing interdisciplinary tasks in an international design community. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 367–376). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • MARS (Mathematics Assessment Resource Service) (2014). Summative assessment. Available from: http://map.mathshell.org.uk/materials/background.php?subpage=summative

  • Marton, F. (2014). Necessary conditions of learning. London: Routledge.

    Google Scholar 

  • Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). Harlow, England: Prentice Hall.

    Google Scholar 

  • Mathematics Textbook Developer Group for Elementary School. (2005). Mathematics. [in Chinese]. Beijing: People’s Education Press.

    Google Scholar 

  • Mayer, R. E., Sims, V., & Tajika, H. (1995). A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32, 443–460.

    Google Scholar 

  • Movshovitz-Hadar, N., & Edri, Y. (2013). Enabling education for values with mathematics teaching. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 377–388). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Movshovitz-Hadar, N., & Webb, J. (2013). One equals zero and other mathematical surprises. Reston, VA: National Council of Teachers of Mathematics. http://www.nctm.org/catalog/product.aspx?id=14553

  • National Academy for Educational Research. (2009). Mathematics, grade 8 (Vol. 4). Retrieved from http://www.naer.edu.tw/bookelem/u_booklist_v1.asp?id=267&bekid=2&bemkind=1. Accessed on February 07, 2010.

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Nicely, R. F., Jr. (1985). Higher order thinking in mathematics textbooks. Educational Leadership, 42, 26–30.

    Google Scholar 

  • Nicely, R., Jr., Fiber, H., & Bobango, J. (1986). The cognitive content of elementary school mathematics textbooks. Arithmetic Teacher, 34(2), 60–61.

    Google Scholar 

  • Nikitina, S. (2006). Three strategies for interdisciplinary teaching: Contextualising, conceptualizing, and problem-centring. Journal of Curriculum Studies, 38(3), 251–271.

    Google Scholar 

  • Paas, F., Renkl, A., & Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational Psychologist, 38(1), 1–4.

    Google Scholar 

  • Pepin, B., & Haggarty, L. (2001). Mathematics textbooks and their use in English, French, and German classrooms: A way to understand teaching and learning cultures. ZDM: The International Journal on Mathematics Education, 33(5), 158–175.

    Google Scholar 

  • Prestage, S., & Perks, P. (2007). Developing teacher knowledge using a tool for creating tasks for the classroom. Journal of Mathematics Teacher Education, 10, 381–390.

    Google Scholar 

  • Puphaiboon, K., Woodcock, A., & Scrivener, S. (2005, March 25). Design method for developing mathematical diagrams. In P. D. Bust & P. T. McCabe (Eds.), Contemporary ergonomics: 2005 Proceedings of the International Conference on Contemporary Ergonomics (CE2005). New York: Taylor & Francis.

    Google Scholar 

  • Radford, L. (2008). Diagrammatic thinking: Notes on Peirce’s semiotics and epistemology. PNA, 3(1), 1–18.

    Google Scholar 

  • Remillard, J. T., Herbel-Eisenmann, B. A., & Lloyd, G. M. (Eds.). (2009). Mathematics teachers at work: Connecting curriculum materials and classroom instruction. New York: Routledge.

    Google Scholar 

  • Rezat, S. (2006). A model of textbook use. In J. Novotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 409–416). Prague: Psychology of Mathematics Education.

    Google Scholar 

  • RLDU, Resources for Learning and Development Unit (n.d.). Available from www.nationalstemcentre.org.uk/elibrary/maths/resource/6910/an-addendum-to-cockcroft

  • Rotman, B. (1988). Toward a semiotics of mathematics. Semiotica, 72(1/2), 1–35.

    Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic.

    Google Scholar 

  • Sesamath. (2009). Le manuel Sésamath 6e. Chambéry: Génération 5.

    Google Scholar 

  • Shuard, H., & Rothery, A. (1984). Children reading mathematics. London: John Murray.

    Google Scholar 

  • Small, M., Connelly, R., Hamilton, D., Sterenberg, G. & Wagner, D. (2008). Understanding mathematics: Textbook for Class VII. Thimpu, Bhutan Curriculum and Professional Support Division, Department of School Education.

    Google Scholar 

  • SMILE. (n.d.). Available from http://www.nationalstemcentre.org.uk/elibrary/resource/675/smile-wealth-of-worksheets

  • Smith, G., Wood, L., Coupland, M., Stephenson, B., Crawford, K., & Ball, G. (1996). Constructing mathematical examinations to assess a range of knowledge and skills. International Journal of Mathematical Education in Science and Technology, 27(1), 65–77.

    Google Scholar 

  • Staats, S., & Johnson, J. (2013). Designing interdisciplinary curriculum for college algebra. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 389–400). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Stacey, K., & Vincent, J. (2009). Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks. Educational Studies in Mathematics, 72(3), 271–288.

    Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.

    Google Scholar 

  • Stigler, J. W., Fuson, K. C., Ham, M., & Kim, M. S. (1986). An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction, 3, 153–171.

    Google Scholar 

  • Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11, 258–288.

    Google Scholar 

  • Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges. International Journal of Educational Research, 64, 63–70.

    Google Scholar 

  • Sun, X., Neto, T., & Ordóñez, L. E. (2013). Different features of task design associated with goals and pedagogies in Chinese and Portuguese textbooks: The case of addition and subtraction. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 409–418). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Sun, X. (2011). “Variation problems” and their roles in the topic of fraction division in Chinese mathematics textbook examples. Educational Studies in Mathematics, 76(1), 65–85.

    Google Scholar 

  • Swan, M. (2006). Collaborative learning in mathematics: A challenge to our beliefs and practices. London: National Institute for Advanced and Continuing Education.

    Google Scholar 

  • Takahashi, A. (2011). The Japanese approach to developing expertise in using the textbook to teach mathematics. In Y. Li & G. Kaiser (Eds.), Expertise in mathematics instruction: An international perspective (pp. 197–220). Dordrecht: Springer.

    Google Scholar 

  • Thompson, D. R., Hunsader, P. D., & Zorin, B. (2013). Assessments accompanying published curriculum materials: Issues for curriculum designers, researchers, and classroom teachers. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 401–408). Oxford, UK. Available from http://hal.archives-ouvertes.fr/hal-00834054

  • Thompson, D. R., & Senk, S. L. (2010). Myths about curriculum implementation. In B. J. Reys, R. E. Reys, & R. Rubenstein (Eds.), Mathematics curriculum: Issues, trends, and future directions (pp. 249–263). Reston, VA: National Council of Teachers of Mathematics.

    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.

    Google Scholar 

  • Thompson, D. R., & Usiskin, Z. (2014). Enacted mathematics curriculum: A conceptual model and research needs. Charlotte, NC: Information Age.

    Google Scholar 

  • Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics education: The Wiskobas project. Dordrecht: Kluwer Academic.

    Google Scholar 

  • Tufte, E. (1997). Visual explanations: Images and quantities, evidence and narrative. Cheshire, CT: Graphics Press.

    Google Scholar 

  • Tzur, R., Zaslavsky, O., & Sullivan, P. (2008). Examining teachers’ use of (non-routine) mathematical tasks in classrooms from three complementary perspectives: Teacher, teacher educator, researcher. In Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education, and the 30th North American Chapter (Vol. 1, pp. 133–137).

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9–35.

    Google Scholar 

  • Wagner, D. (2012). Opening mathematics texts: Resisting the seduction. Educational Studies in Mathematics, 80(1–2), 153–169.

    Google Scholar 

  • Watson, A., & Mason, J. (1998). Questions and prompts for mathematical thinking. Derby, UK: Association of Teachers of Mathematics.

    Google Scholar 

  • Watson, A., & Mason, J. (2006). Seeing an exercise as a single mathematical object: Using variation to structure sense-making. Mathematical Thinking and Learning, 8(2), 91–111.

    Google Scholar 

  • Wittmann, E. C. (1995). Mathematics education as a ‘design science’. Educational Studies in Mathematics, 29(4), 355–374.

    Google Scholar 

  • Xin, Y. P. (2008). The effects of schema-based instruction in solving mathematics word problems: An emphasis on prealgebraic conceptualization of multiplicative relations. Journal for Research in Mathematics Education, 39, 526–551.

    Google Scholar 

  • Yerushalmy, M. (2015). E-textbooks for mathematical guided inquiry: Design of tasks and task sequences. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education: An ICMI Study 22. New York: Springer.

    Google Scholar 

  • Zorin, B., Hunsader, P. D., & Thompson, D. R. (2013). Assessments: Numbers, context, graphics, and assumptions. Teaching Children Mathematics, 19(8), 480–488.

    Google Scholar 

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Watson, A., Thompson, D.R. (2015). Design Issues Related to Text-Based Tasks. In: Watson, A., Ohtani, M. (eds) Task Design In Mathematics Education. New ICMI Study Series. Springer, Cham. https://doi.org/10.1007/978-3-319-09629-2_5

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