Abstract
The aim of this chapter is to present and discuss the theoretical framework “Personalized Mathematics and Mathematics Inquiry” (PMMI) which supported the design and development of the Cyprus Mathematics Textbooks. The PMMI framework involves a set of Personalized Mathematics practices in which students actively set mathematics goals, engage, reason, discuss, create, make connections, solve problems, and reflect on mathematical content. Mathematics instruction, within this framework, seeks to actively involve students in authentic and personally relevant learning experiences. Mathematics Inquiry is at the core of the PMMI framework and evolves in three learning phases, “romance,” “precision,” and “generalization.” Mathematics Inquiry consists of challenging problems, namely explorations and investigations, which capture students’ curiosity and invite them to make hypotheses and pursue their hunches. The goal of an exploration, at the beginning of each chapter, is to elicit motivation, which will ignite students’ personal inquiry. Inevitably, students bring their own experiences in these explorations, and thus, differentiation and personal learning are facilitated. Each exploration is followed by an investigation. Investigations, however, are more closed and guided than explorations. To respond to these investigations, students often need to analyze, form hypotheses, and work systematically with various strategies, using different mathematical tools, manipulatives, and applets. During these investigations, the teachers’ role is to facilitate students to control their own learning. At this stage, new mathematical concepts and vocabulary are introduced. The application of the PMMI framework is exemplified through examples taken from the mathematics textbooks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abrantes, P., Ponte, J. P., Fonseca, H., & Brunheira, L. (Eds.). (1999). Investigações matemáticas na aula e no currículo. APM e Projecto MPT.
Alberta Learning: Special Programs Branch. (2004). Standards for special education. Alberta.
Alfieri, L., Brooks, P., Aldrich, N., & Tenenbaum, H. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103, 1–18. https://doi.org/10.1037/a0021017
Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245–274.
Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM - Mathematics Education, 45, 797–810.
Battista, M. T. (1994). Teacher beliefs and the reform movement in mathematics education. Phi Delta Kappan, 75(6), 462–462.
Blair, A., & Hindle, H. (2019). Models for teaching mathematics. Mathematics Teaching, 268, 37–40.
Boaler, J. (2008). Promoting ‘relational equity’ and high mathematics achievement through an innovative mixed ability approach. British Educational Research Journal, 34(2), 167–194.
Bos, R., Doorman, M., & Piroi, M. (2020). Emergent models in a reinvention activity for learning the slope of a curve. The Journal of Mathematical Behavior, 59, 100773. https://doi.org/10.1016/j.jmathb.2020.100773
Casey, L. (2013). Learning beyond competence to participation. International Journal of Progressive Education, 9(2), 45–60.
Cyprus Ministry of Education and Culture. (2016a). Cypriot mathematics national curriculum (2nd ed.).
Cyprus Ministry of Education and Culture. (2016b). Grade 8 mathematics textbook (3rd ed., Vols. 1–2).
Cyprus Ministry of Education and Culture. (2016c). Grade 7 mathematics textbook (3rd ed., Vols. 1–2).
Cyprus Ministry of Education and Culture. (2019). Grade 4 mathematics textbook (2nd ed., Vols. 1–6).
da Ponte, J. P. (2007). Investigations and explorations in the mathematics classroom. ZDM Mathematics Education, 39, 419–430. https://doi.org/10.1007/s11858-007-0054-z
Dorier, J., & Garcia, F. J. (2013). Challenges and opportunities for the implementation of inquiry-based learning in day-to-day teaching. ZDM—The International Journal on Mathematics Education, 45(6), 837–839.
Dorier, J. L., & Maass, K. (2020). Inquiry-based mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 384–388). Springer. https://doi.org/10.1007/978-3-030-15789-0_176
Drijvers, P. (2020). Digital tools in Dutch mathematics education: A dialectic relationship. In M. Van den Heuvel-Panhuizen (Ed.), National reflections on the Netherlands didactics of mathematics. ICME-13 Monographs (pp. 177–198). Springer.
Gruber, M. J., Gelman, B. D., & Ranganath, C. (2014). States of curiosity modulate hippocampus-dependent learning via the dopaminergic circuit. Neuron, 84(2), 486–496. https://doi.org/10.1016/j.neuron.2014.08.060
Harris, J., & Hofer, M. (2009). Instructional planning activity types as vehicles for curriculumbased TPACK development. In C. D. Maddux (Ed.), Research highlights in technology and teacher education (pp. 99–108) AACE.
Hegedus, S., & Moreno-Armella, L. (2014). Information and communication technology (ICT) affordances in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education SE—78 (pp. 295–299). Springer.
Kang, M. J., et al. (2009). The wick in the candle of learning: Epistemic curiosity activates reward circuitry and enhances memory. Psychological Science, 20, 963–973. https://doi.org/10.1111/j.1467-9280.2009.02402.x
Kaufman, J. C., & Beghetto, R. A. (2009). Beyond big and little: The four c model of creativity. Review of General Psychology, 13, 1. https://doi.org/10.1037/a0013688
Knuth, E. J. (2002). Fostering mathematical curiosity. The Mathematics Teacher, 95(2), 126–130. https://doi.org/10.5951/MT.95.2.0126
Koutselini, M. (2012). Textbooks as mechanisms for teacher’s sociopolitical and pedagogical alienation. In H. Hickman & B. J. Profilio (Eds.), The new politics of the textbook: Problematizing the portrayal of marginalized groups in textbooks (pp. 1–16). Sense Publishers.
Laursen, S. L., & Rasmussen, C. (2019). I on the prize: Inquiry approaches in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education, 5, 129–146. https://doi.org/10.1007/s40753-019-00085-6
Lazonder, A. W., & Harmsen, R. (2016). Meta-analysis of inquiry-based learning: Effects of guidance. Review of Educational Research, 86(3), 681–718.
Leikin, R. (2014). Challenging mathematics with multiple solution tasks and mathematical investigations in geometry. In Y. Li, E. Silver, & S. Li (Eds.), Transforming mathematics instruction. Advances in mathematics education. Springer. https://doi.org/10.1007/978-3-319-04993-9_5
Marshman, M., Pendergast, D., & Brimmer, F. (2011). Engaging the middle years in mathematics. In Mathematics: Traditions and [new] practices (Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia). MERGA.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Author.
NCTM. (2015). NCTM position statements. Online https://www.nctm.org/Standards-and-Positions/NCTM-Position-Statements/. Retrieved August 8, 2020.
Pepin, B., Gueudet, G., & Trouche, L. (2013). Investigating textbooks as crucial interfaces between culture, policy and teacher curricular practice: Two contrasted case studies in France and Norway. ZDM- Mathematics Education, 45(5), 685–698.
Peterson, E. G., & Cohen, J. (2019). A case for domain-specific curiosity in mathematics. Educational Psychology Review, 31, 807. https://doi.org/10.1007/s10648-019-09501-4
Pink, D. (2009). Drive: The surprising truth about what motivates us. Riverhead Books.
Reilly, E., Vartabedian, V., Felt, L., & Jenkins, H. (2012). Play: Participatory learning and you! Bill & Melinda Gates Foundation.
Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why mathematics textbooks matter. Educational Leadership, 61(5), 61–66.
Rezat, S. (2006). A model of textbook use. In J. Novotná, H. Moraová, M. Krátká, & N. A. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 409–416). Charles University.
Sievert, H., van den Ham, A.-K., Niedermeyer, I., & Heinze, A. (2019). Effects of mathematics textbooks on the development of primary school children’s adaptive expertise in arithmetic. Learning and Individual Differences, 74, 1–13. https://doi.org/10.1016/j.lindif.2019.02.006
Supovitz, J. A., & Turner, H. M. (2000). The effects of professional development on science teaching practices and classroom culture. Journal of Research in Science Teaching, 37(9), 963–980.
Swan, M. (2009). Improving learning in mathematics: Dean’s lecture series [Pamphlet]. University of Melbourne.
Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement studies. Studies in Educational Evaluation, 31, 315–327.
Thompson, D. & Watson A. (2013). Design and use of text-based resources. In C. Margolinas (Ed.), Task Design in Mathematics Education, Proceedings of ICMI Study 22, (pp. 279–282).
Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houng, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Kluwer Academic Publishers.
Whitehead, A. N. (1929). Aims of education and other essays. The Macmillan Co.
Wigley, A. (1992). Models for teaching mathematics. Mathematics Teaching, 141(4), 7.
Zhao, Y. (2012). Flunking innovation and creativity. The Phi Delta Kappan, 94(1), 56–61. https://doi.org/10.1177/003172171209400111
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Christou, C., Pitta-Pantazi, D., Pittalis, M., Demosthenous, E., Chimoni, M. (2023). Personalized Mathematics and Mathematics Inquiry: A Design Framework for Mathematics Textbooks. In: Leikin, R. (eds) Mathematical Challenges For All . Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-18868-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-031-18868-8_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-18867-1
Online ISBN: 978-3-031-18868-8
eBook Packages: EducationEducation (R0)