Skip to main content
SpringerLink
Log in
Book cover

Transforming Mathematics Instruction pp 153–172Cite as

Transforming Mathematics Education: The Role of Textbooks and Teachers

  • Chapter
  • First Online:

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

In this chapter, we discuss the question of how we can encourage mathematics education to shift towards more inquiry-oriented practices in schools and what role textbooks and teachers play in such a reform. The stage is set by an exposition on the need for curriculum innovation in light of the demands of the twenty-first century. This points to a need to address goals in the area of critical thinking, problem solving, collaborating, and communicating. However, previous efforts to effectuate a change in mathematics education in that direction have not been very successful. This is illustrated by experiences in the Netherlands. In relation to this, the limitations of transforming education using textbooks and problems with up-scaling are discussed. To find ways to address these problems, an inventory is made of what can be learned from decades of experimenting with reform mathematics education while trying to achieve the very goals that are discerned as crucial for the twenty-first century. On the basis of this inventory, suggestions are made for shaping textbooks in such a manner that they may better support this kind of transformation. At the same time it is pointed out that the latter requires a complementary effort in teacher professionalization and a well-considered alignment of both efforts.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    This concerned: the “Partnership for 21st century skills” (Partnership for 21st Century Skills 2008), “EnGauge” (North Central Regional Educational Laboratory and the Metiri Group 2003), “Assessment and Teaching of 21st Century Skills” (ATCS) (Binkley et al. 2010), “National Educational Technology Standards” (NETS) (Roblyer 2000), and “Technological Literacy for the 2012 National Assessment of Educational Progress” (NAEP).

  2. 2.

    In a similar feign, Stein et al. (2008) discern practices for promoting productive disciplinary engagement, which are related to identifying, framing, and discussing mathematical issues. Although a difference may be that Stein et al. (2008) seem to try to address both mathematical ideas and the solution strategies of the students, Cobb (1997) emphasizes the mathematical issues that underlie student solutions and tries to steer away from a focus on solution strategies as such.

  3. 3.

    In relation to this we may point to a study by Tarr et al. (2008), which showed that NCTM Standards-based learning environments positively impact achievement on performance assessments tests that measure mathematical reasoning, problem solving, and communication, as well as proficiency in skills and procedures, but only when coupled with a curriculum that is designed to embody this pedagogical orientation. In particular, when teachers of NSF-funded curricula were enacting the curriculum as intended by the authors, student achievement was compelling.

References

  • Akkerman, S., & Bakker, A. (2011, June). Boundary crossing and boundary objects. Review of Educational Research, 81(2), 132–169.

    Google Scholar 

  • Autor, D., Levy, F., & Murnane, R. (2003). The skill content of recent technological change: An empirical exploration. Quarterly Journal of Economics, 118(4), 1279–1333.

    Article  Google Scholar 

  • Bereiter, C. (1985). Towards a solution of the learning paradox. Review of Educational Research, 55(2), 201–226.

    Article  Google Scholar 

  • Binkley, M., Erstad, O., Herman, J., Raizen, S., Ripley, M., & Rumble, M. (2010). Defining 21st century skills. Retrieved from http://atc21s.org/wp-content/uploads/2011/11/1-Defining-21st-Century-Skills.pdf

  • Brousseau, G. (1988). Le contrat didactique: le milieu. Recherche en didactique des mathématiques, 9(3), 33–115.

    Google Scholar 

  • Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. Journal of the Learning Sciences, 2(2), 141–178.

    Article  Google Scholar 

  • Bruin-Muurling, G. (2010). The development of proficiency in the fraction domain. Affordances and constraints in the curriculum. Ph.D. thesis, Eindhoven School of Education, Eindhoven University of Technology, Eindhoven.

    Google Scholar 

  • Clements, D., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89.

    Article  Google Scholar 

  • Cobb, P. (1997). Instructional design and reform: Locating developmental research in context. In M. Beishuizen, K. P. E. Gravemeijer, & E. C. D. M. van Lieshout (Eds.), The role of contexts and models in the development of mathematical strategies and procedures. Utrecht: Cdß Press.

    Google Scholar 

  • Cobb, P., & Jackson, K. (2011). Towards an empirically grounded theory of action for improving the quality of mathematics teaching at scale. Mathematics Teacher Education and Development, 13(1), 6–33.

    Google Scholar 

  • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 175–190.

    Article  Google Scholar 

  • Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while doing mathematical problem solving. In D. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 117–148). New York: Springer.

    Chapter  Google Scholar 

  • Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23(1), 2–33.

    Article  Google Scholar 

  • Confrey, J., Maloney, A. P., Nguyen, K. H., Mojica, G., & Myers, M. (2009). Equipartitioning/splitting as a foundation of rational number reasoning using learning trajectories. Paper presented at the Exploratory Seminar: Measurement Challenges Within the Race to the Top Agenda Center for K – 12 Assessment & Performance Management. 33rd conference of the International Group for the Psychology of Mathematics Education, Thessaloniki, Greece.

    Google Scholar 

  • Cuban, L. (1984). How teachers taught: Constancy and change in American classrooms, 1890–1980. New York: Longman.

    Google Scholar 

  • Cuban, L. (1990). Reforming again, again and again. Educational Researcher, 13, 3–13.

    Article  Google Scholar 

  • Daro, P., Mosher, F., & Corcoran, T. (2011). Learning trajectories in mathematics (Research report No. 68). Madison: Consortium for Policy Research in Education.

    Google Scholar 

  • Desforges, C., & Cockburn, A. (1987). Understanding the mathematics teacher, a study of practice in first school. London: The Falmer Press.

    Google Scholar 

  • Dewey, J. (1901). The situation as regards the course of study. Journal of Proceedings and Addresses of the Fortieth Annual Meeting of the National Education Association, 332–348.

    Google Scholar 

  • Fosnot, C. T. (2003, June). Teaching and learning in the 21st century. Plenary address, AMESA conference, Capetown, South Africa.

    Google Scholar 

  • Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Riedel.

    Google Scholar 

  • Friedman, T. L. (2005). The world is flat (pp. 5–12). London: Penguin Books.

    Google Scholar 

  • Fullan, M. (2006, November). Leading professional learning, The School Administrator, 63(10), 10–14. http://www.michaelfullan.ca/Articles_06/Articles_06b.pdf

  • Gravemeijer, K. (2004). Learning trajectories and local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128.

    Article  Google Scholar 

  • Gravemeijer, K. (2008). RME theory and mathematics teacher education. In D. Tirosh & T. Wood (Eds.), International handbook of mathematics teacher education: Vol.1. Knowledge and beliefs in mathematics teaching and teaching development (pp. 283–302). Rotterdam: Sense Publishers.

    Google Scholar 

  • Gravemeijer, K. (2010). Mathematics education and the information society. In A. Araújo, A. Fernandes, A. Azevedo, & J. F. Rodrigues (Eds.), Educational interfaces between mathematics and industry, conference proceedings (pp. 243–252). Bedford: Comap, Inc.

    Google Scholar 

  • Gravemeijer, K. (2012). Aiming for 21st century skills. In S. Kafoussi, C. Skoumpourdi, & F. Kalavassis (Eds.), Proceedings of the Commission Internationale pour l’´Etude et L’Am´elioration de l’Enseignement des Math´ematiques (CIEAEM 64): Mathematics education and democracy: Learning and teaching practices (pp. 30–43). Greece: Rhodes.

    Google Scholar 

  • Gravemeijer, K., & Van Eerde, D. (2009). Design research as a means for building a knowledge base for teachers and teaching in mathematics education. Elementary School Journal, 109(5), 510–524.

    Article  Google Scholar 

  • Gravemeijer, K., van Heuvel-Panhuizen, M., van den Donselaar, G., Ruesink, N., Streefland, L., Vermeulen, W., te Woerd, E., & van der Ploeg, D. (1991). Methoden in het reken-wiskundeonderwijs, een rijke context voor vergelijkend onderzoek. Utrecht: OW&OC/ISOR.

    Google Scholar 

  • Hiebert, J., Gallimore, R., & Stigler, J. W. (2002). A knowledge base for the teaching profession: What would it look like and how can we get one? Educational Researcher, 31(5), 3–15.

    Article  Google Scholar 

  • Hoek, D., & Gravemeijer, K. (2011). Changes of interaction during the development of a mathematical learning environment. Journal of Mathematics Teacher Education, 14, 393–411.

    Article  Google Scholar 

  • Hoyles, C., Noss, R., Kent, P., & Bakker, A. (2010). Improving mathematics at work, the need for techno-mathematical literacies (TLRP’s Improving learning series). New York: Routledge.

    Google Scholar 

  • Jagacinski, C. M., & Nicholls, J. G. (1984). Conceptions of ability and related affects in task involvement and ego involvement. Journal of Educational Psychology, 76(5), 909–919.

    Article  Google Scholar 

  • Janssen, J., van der Schoot, F., & Hemker, B. (2005). Balans van het reken- wiskundeonderwijs aan het einde van de basisschool 4. Arnhem: Cito.

    Google Scholar 

  • Kamii, C., Lewis, B. A., & Livingstone Jones, S. (1993). Primary arithmetic: Children inventing their own procedures. Arithmetic Teacher, 41(4), 200–203, Columbia: Teacher College Press.

    Google Scholar 

  • Kraemer, J.-M. (2011). Oplossingsmethoden voor aftrekken tot 100. Ph.D. thesis, Eindhoven School of Education, Eindhoven University of Technology, Eindhoven.

    Google Scholar 

  • Labinowics, E. (1985). Learning from children. Amsterdam: Addison-Wesley.

    Google Scholar 

  • Levy, F., & Murnane, R. J. (2006). How computerized work and globalization shape human skill demands. Downloaded November 2, 2006, from http://web.mit.edu/flevy/www/

  • Magidson, S. (2005). Building bridges within mathematics education: Teaching, research, and instructional design. Journal of Mathematical Behavior, 24, 135–169.

    Article  Google Scholar 

  • Meira, L. (1995). The microevolution of mathematical representations in children’s activities. Cognition and Instruction, 13(2), 269–313.

    Article  Google Scholar 

  • Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). TIMSS 2003 international mathematics report: Findings from IEA’s Trends in International Mathematics and Science Study at the fourth and eighth grades. Boston: Boston College, International Study Center.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1980). An Agenda for action: Recommendations for school mathematics of the 1980s. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • North Central Regional Educational Laboratory and the Metiri Group. (2003). enGauge, 21st century skills: Literacy in the digital age. Naperville: NCREL.

    Google Scholar 

  • OECD. (2010). PISA 2009 results: What students know and can do – Student performance in reading, mathematics and science (Vol. 1). Paris: PISA, OECD Publishing.

    Google Scholar 

  • Partnership for 21st Century Skills. (2008). 21st century skills education & competitiveness. A resource and policy guide. Downloaded October 19, 2010, from http://www.p21.org/documents/21st_century_skills_education_and_competitiveness_guide.pdf

  • Ravitch, D. (2010). Death and life of the Great American school system. How testing and choice are undermining education. New York: Basic Books, 283 blz. € 24,95.

    Google Scholar 

  • Roblyer, M. D. (2000). The National Educational Technology Standards (NETS): A review of definitions, implications, and strategies for integrating NETS into K-12 curriculum. International Journal of Instructional Media, 27(2), 133–146.

    Google Scholar 

  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.

    Article  Google Scholar 

  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1–22.

    Google Scholar 

  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.

    Article  Google Scholar 

  • Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and learning, 10, 313–340.

    Article  Google Scholar 

  • Stephan, M., Underwood-Gregg, D., & Yackel, E. (2014). Guided reinvention: What is it and how do teachers learn this teaching approach? In Y. Li (Ed.), Transforming mathematics instruction: Multiple approaches and practices. Cham, Switzerland: Springer.

    Google Scholar 

  • Tarr, J. E., Reys, R. E., Reys, B. J., Chávez, O., Shih, J., & Osterlind, S. J. (2008). The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39(3), 247–280.

    Google Scholar 

  • Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105–127.

    Article  Google Scholar 

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

    Google Scholar 

  • Tzur, R., & Simon, M. (2004). Distinguishing two stages of mathematics conceptual learning. International Journal of Science and Mathematics Education, 2(2), 287–304.

    Article  Google Scholar 

  • van den Heuvel-Panhuizen, M. (2010). Reform under attack – Forty years of working on better mathematics education thrown on the scrapheap? No way! In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (pp. 1–25). Fremantle: MERGA.

    Google Scholar 

  • van den Heuvel-Panhuizen, M., & de Goeij, E. (2007). Offering primary school teachers a multi-approach experience-based learning setting to become a mathematics coordinator in their school [CD-ROM]. In Proceedings of the 15th ICMI study, The Professional Education and Development of Teachers of Mathematics, Águas de Lindóia, Brazil, 15–21 May 2005. Unesp.

    Google Scholar 

  • van Stiphout, I. (2011). The development of algebraic proficiency in Dutch secondary education. Ph.D. thesis, Eindhoven School of Education, Eindhoven University of Technology, Eindhoven.

    Google Scholar 

  • Voogt, J., & Pareja Roblin, N. (2010). 21st century skills – Discussion paper. Enschede: University of Twente.

    Google Scholar 

  • Wagner, T. (2008). The global achievement gap, why even our best schools don’t teach the survival skills our children need – And what we can do about it. New York: Basic Books.

    Google Scholar 

  • Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Westbury, I. (1983). How can curriculum guides guide teaching? Introduction to the symposium. Journal of Curriculum Studies, 1(1), 1–3.

    Article  Google Scholar 

  • Whitson, J. A. (1997). Cognition as a semiotic process: From situated mediation to critical reflective transcendence. In D. Kirschner & J. A. Whitson (Eds.), Situated cognition theory: Social, semiotic, and neurological perspectives (pp. 97–150). Hillsdale: Erlbaum.

    Google Scholar 

  • Yackel, E. (1992). The evolution of second grade children’s understanding of what constitutes an explanation in a mathematics class. Paper presented at the Seventh International Congress of Mathematics Education, Quebec City.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Eindhoven School of Education, Eindhoven University of Technology, Rijnsburgerweg 47, 2334BG, Leiden, The Netherlands

    Koeno P. E. Gravemeijer

Authors
  1. Koeno P. E. Gravemeijer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Koeno P. E. Gravemeijer .

Editor information

Editors and Affiliations

  1. Department of Teaching, Learning and Culture, Texas A&M University, College Station, Texas, USA

    Yeping Li

  2. School of Education, University of Michigan, Ann Arbor, Michigan, USA

    Edward A. Silver

  3. Dept. of Mathematics, East China Normal University, Putuo, China

    Shiqi Li

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Gravemeijer, K.P.E. (2014). Transforming Mathematics Education: The Role of Textbooks and Teachers. In: Li, Y., Silver, E., Li, S. (eds) Transforming Mathematics Instruction. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-04993-9_10

Download citation

Publish with us

Policies and ethics

Search

Navigation