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.
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.
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.
Baker, W., & Bourne, A. (1937). Elementary algebra. London: G. Bell and Sons.
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.
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).
Burns, R. P. (1982). A pathway into number theory. Cambridge, England: Cambridge University Press.
Byrne, O. (1847). The first six books of Euclid. London: William Pickering. Available from http://www.math.ubc.ca/~cass/Euclid/byrne.html.
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.
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.
Cuoco, A. (2001). Mathematics for teaching. Notices of the AMS, 48(2), 168–174.
Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375–402.
Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18, 382–393.
Davis, B. (2008). Is 1 a prime number? Developing teacher knowledge through concept study. Mathematics Teaching in the Middle School, 14(2), 86–91.
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.
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.
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.
Duval, R. (2006). A cognitive analysis of problems of comprehension in learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.
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.
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.
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.
Godfrey, C., & Siddons, A. (1915). Elementary algebra, Part 1C. Cambridge, England: Cambridge University Press.
Gregório, M., Valente, N. M., & Calafate, R. (2010). Segredos dos Números 1 - Manual -Matemática/1.° ano do Ensino Básico. Lisboa: Lisboa Editora.
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.
Herbart, J. F. (1904b). The science of education. London: Sonnenschein.
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.
Hirsch, C. R. (Ed.). (2007). Perspectives on the design and development of school mathematics curricula. Reston, VA: National Council of Teachers of Mathematics.
Hoven, J., & Garelick, B. (2007). Singapore math: Simple or complex? Educational Leadership, 65(3), 28–31.
Hußmann, S., Leuders, T., Prediger, S., & Barzel, B. (2011a) Mathewerkstatt 5. Cornelsen.
Hußmann, S., Leuders, T., Prediger, S., & Barzel, B. (2011b). Kontexte für sinnstiftendes Mathematiklernen (KOSIMA) – ein fachdidaktisches Forschungs-und Entwicklungsprojekt. Beiträge zum Mathematikunterricht, pp. 419–422.
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.
Kress, G. R., & Van Leeuwen, T. (1996). Reading images: The grammar of visual design. New York: Psychology Press.
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.
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.
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.
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.
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.
Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). Harlow, England: Prentice Hall.
Mathematics Textbook Developer Group for Elementary School. (2005). Mathematics. [in Chinese]. Beijing: People’s Education Press.
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.
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.
Nicely, R. F., Jr. (1985). Higher order thinking in mathematics textbooks. Educational Leadership, 42, 26–30.
Nicely, R., Jr., Fiber, H., & Bobango, J. (1986). The cognitive content of elementary school mathematics textbooks. Arithmetic Teacher, 34(2), 60–61.
Nikitina, S. (2006). Three strategies for interdisciplinary teaching: Contextualising, conceptualizing, and problem-centring. Journal of Curriculum Studies, 38(3), 251–271.
Paas, F., Renkl, A., & Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational Psychologist, 38(1), 1–4.
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.
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.
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.
Radford, L. (2008). Diagrammatic thinking: Notes on Peirce’s semiotics and epistemology. PNA, 3(1), 1–18.
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.
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.
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.
Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic.
Sesamath. (2009). Le manuel Sésamath 6e. Chambéry: Génération 5.
Shuard, H., & Rothery, A. (1984). Children reading mathematics. London: John Murray.
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.
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.
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.
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.
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.
Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11, 258–288.
Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges. International Journal of Educational Research, 64, 63–70.
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.
Swan, M. (2006). Collaborative learning in mathematics: A challenge to our beliefs and practices. London: National Institute for Advanced and Continuing Education.
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.
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.
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.
Thompson, D. R., & Usiskin, Z. (2014). Enacted mathematics curriculum: A conceptual model and research needs. Charlotte, NC: Information Age.
Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics education: The Wiskobas project. Dordrecht: Kluwer Academic.
Tufte, E. (1997). Visual explanations: Images and quantities, evidence and narrative. Cheshire, CT: Graphics Press.
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).
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.
Wagner, D. (2012). Opening mathematics texts: Resisting the seduction. Educational Studies in Mathematics, 80(1–2), 153–169.
Watson, A., & Mason, J. (1998). Questions and prompts for mathematical thinking. Derby, UK: Association of Teachers of Mathematics.
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.
Wittmann, E. C. (1995). Mathematics education as a ‘design science’. Educational Studies in Mathematics, 29(4), 355–374.
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.
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.
Zorin, B., Hunsader, P. D., & Thompson, D. R. (2013). Assessments: Numbers, context, graphics, and assumptions. Teaching Children Mathematics, 19(8), 480–488.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Open Access This book was originally published with exclusive rights reserved by the Publisher in 2015 and was licensed as an open access publication in March 2021 under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made.
The images or other third party material in this book may be included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material or in the Correction Note appended to the book. For details on rights and licenses please read the Correction https://doi.org/10.1007/978-3-319-09629-2_13. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2015 The Author(s)
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-09629-2_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09628-5
Online ISBN: 978-3-319-09629-2
eBook Packages: Humanities, Social Sciences and LawEducation (R0)