Skip to main content
SpringerLink
Log in

On the instructional model of a blended learning program for developing mathematical knowledge for teaching

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

Blended learning, which combines face-to-face workshops with self-directed online learning, is becoming a good alternative in designing and deploying professional development programs. The online component adapts to teachers’ time constraints, requires fewer trained professionals for its implementation, and enhances participants’ opportunities to engage in the exploration and visualization of mathematical concepts and ideas. Also, the face-to-face component of this instruction modality allows spontaneous communication and collaborative construction of knowledge in real settings. This paper describes the instructional model of Suma y Sigue, a b-learning professional development program for primary and middle school teachers, which has been designed and implemented in Chile since 2015, aimed at developing mathematical knowledge for teaching. A particular feature of the program is its high-degree of self-directed autonomous online learning. We discuss how contextualized situations are articulated to create a learning environment in which teachers get involved in a progressive construction of multiple components of this knowledge. We also describe the implementation of the program, discussing the effects of scaling in teachers’ experiences, and also how the information gathered upon implementation has led to changes in the training of instructors and in the program’s instructional design.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.

    Google Scholar 

  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14–17, 20–22, 43–46.

    Google Scholar 

  • Blömeke, S., Suhl, U., & Döhrmann, M. (2013). Assessing strengths and weaknesses of teacher knowledge in Asia, Eastern Europe, and Western countries: Differential item functioning in TEDS-M. International Journal of Science and Mathematics Education, 11(4), 795–817.

    Google Scholar 

  • Borba, M., Askar, P., Engelbrecht, J., Gadanidis, G., Llinares, S., & Aguilar, M. S. (2016). Blended learning, e-learning and mobile learning in mathematics education. ZDM Mathematics Education, 48(5), 589–610.

    Google Scholar 

  • Borba, M., & Llinares, S. (2012). Online mathematics teacher education: An overview of an emergent field of research. ZDM – The International Journal on Mathematics Education, 44(6), 697–704.

    Google Scholar 

  • Carney, M. B., Brendefur, J. L., Hughes, G., Thiede, K., Crawford, A. R., Jesse, D., et al. (2019). Scaling professional development for mathematics teacher educators. Teaching and Teacher Education, 80, 205–217.

    Google Scholar 

  • Cartier, J., Smith, M., Stein, M., & Ross, D. (2013). Practices for orchestrating task-based discussions in science. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Chapin, S., O’Connor, C., & Anderson, N. (2003). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions Publications.

    Google Scholar 

  • Darling-Hammond, L., Hyler, M. E., & Gardner, M. (2017). Effective teacher professional development. Palo Alto, CA: Learning Policy Institute.

    Google Scholar 

  • Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers’ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26, 152–160.

    Google Scholar 

  • Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–25.

    Google Scholar 

  • Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181–199.

    Google Scholar 

  • Ernest, P. (1996). Varieties of constructivism: A framework for comparison. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Flick, U. (2002). An introduction to qualitative research. London: SAGE.

    Google Scholar 

  • Francescato, D., Porcelli, R., Mebane, M., Cuddetta, M., Klobas, J., & Renzi, P. (2006). Evaluation of the efficacy of collaborative learning in face-to-face and computer-supported university contexts. Computers in Human Behavior, 22(2), 163–176.

    Google Scholar 

  • Freudenthal, H. (2012). Mathematics as an educational task. Dordrecht: Springer.

    Google Scholar 

  • Garet, M. S., Yoon, K. S., & Porter, A. P. (2005). Measuring differences in the quality of professional development. Paper presented at the annual meeting of the American Educational Research Association, Montréal, Canada.

  • Goos, M., & Geiger, V. (2012). Connecting social perspectives on mathematics teacher education in online environments. ZDM – The International Journal on Mathematics Education, 44(6), 705–715.

    Google Scholar 

  • Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1–3), 111–129.

    Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Education Research Journal, 42(2), 371–406.

    Google Scholar 

  • Ingvarson, L., Schwille, J., Tatto, M. T., Rowley, G., Peck, R., & Senk, S. L. (2013). An analysis of teacher education context, structure, and quality-assurance arrangements in TEDS-M countries. Amsterdam: International Association for the Evaluation of Educational Achievement.

    Google Scholar 

  • Jackson, K., Cobb, P., Wilson, J., Webster, M., Dunlap, C., & Appelgate, M. (2015). Investigating the development of mathematics leaders’ capacity to support teachers’ learning on a large scale. ZDM Mathematics Education, 47(1), 93–104.

    Google Scholar 

  • Jonassen, D. H. (1999). Designing constructivist learning environments. Instructional design theories and models: A new paradigm of instructional theory. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Kynigos, C., & Kalogeria, E. (2012). Boundary crossing through in-service online mathematics teacher education: The case of scenarios and half-baked microworlds. ZDM – The International Journal on Mathematics Education, 44(6), 733–745.

    Google Scholar 

  • Leron, U., & Zaslavsky, O. (2009). Generic proving: Unpacking the main ideas of a proof. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd conference of the international group for the psychology of mathematics education (Vol. 1, p. 297). Thessaloniki: PME.

    Google Scholar 

  • Lin, F. L., & Rowland, T. (2016). Pre-service and in-service mathematics teachers’ knowledge and professional development. In A. Gutiérrez, G. Leder, & P. Boero (Eds.), The second handbook in the psychology of mathematics education (pp. 483–520). Rotterdam: Sense.

    Google Scholar 

  • Loucks-Horsley, S., Stiles, K. E., Mundry, S., Love, N., & Hewson, P. W. (2009). Designing professional development for teachers of science and mathematics. Newbury Park, CA: Corwin Press.

    Google Scholar 

  • Marrongelle, K., Sztajn, P., & Smith, M. (2013). Providing professional development at scale: Recommendations from research to practice. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th conference of the international group for the psychology of mathematics education “mathematics learning across the life span” (Vol. 3). Kiel: IPN–Leibniz Institute for Science and Mathematics Education at the University of Kiel.

    Google Scholar 

  • Naaj, M. A., Nachouki, M., & Ankit, A. (2012). Evaluating student satisfaction with blended learning in a gender-segregated environment. Journal of Information Technology Education: Research, 11(1), 185–200.

    Google Scholar 

  • OECD. (2009). Revisión de Políticas Nacionales de Educación: La Educación Superior en Chile. Chile: Organización para el Desarrollo y la Cooperación Económica y el BIRD/Banco Mundial.

    Google Scholar 

  • OECD. (2014). TALIS 2013: An international perspective on teaching and learning. Paris: OECD Publishing.

    Google Scholar 

  • Owens, D. C., Sadler, T. D., Murakami, C. D., & Tsai, C. L. (2018). Teachers’ views on and preferences for meeting their professional development needs in STEM. School Science and Mathematics, 118(8), 370–384.

    Google Scholar 

  • Peled, I., & Balacheff, N. (2011). Beyond realistic considerations: Modeling conceptions and controls in task examples with simple word problems. ZDM – The International Journal on Mathematics Education, 43(2), 307–315.

    Google Scholar 

  • Pituch, K. A., & Lee, Y. (2006). The influence of system characteristics on e-learning use. Computers & Education, 47(2), 222–244.

    Google Scholar 

  • Putnam, R., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Research, 29(1), 4–15.

    Google Scholar 

  • Radovic, D., & Preiss, D. (2010). Patrones de discurso observados en el aula de matemática de 2° ciclo básico. Psykhe, 19(2), 65–79.

    Google Scholar 

  • Roesken-Winter, B., Hoyles, C., & Blömeke, S. (2015). Evidence-based CPD: Scaling up sustainable interventions. ZDM Mathematics Education, 47(1), 1–12.

    Google Scholar 

  • Ruiz, A. (2013). Reforma de la Educación Matemática en Costa Rica. Cuadernos de Investigación y Formación en Educación Matemática. Special Issue. Centro de Investigaciones Matemáticas y Metamatemáticas, Universidad de Costa Rica.

  • Santhanam, R., Sasidharan, S., & Webster, J. (2008). Using self-regulatory learning to enhance e-learning-based information technology training. Information Systems Research, 19(1), 26–47.

    Google Scholar 

  • Slavin, R. (2008). Perspectives on evidence-based research in education—What works? Issues in synthesizing educational program evaluations. Educational Researcher, 37, 5–14.

    Google Scholar 

  • So, H. J., & Brush, T. A. (2008). Student perceptions of collaborative learning, social presence and satisfaction in a blended learning environment: Relationships and critical factors. Computers & Education, 51(1), 318–336.

    Google Scholar 

  • Suzuka, K., Sleep, L., Ball, D. L., Bass, H., Lewis, J., & Thames, M. (2009). Designing and using tasks to teach mathematical knowledge for teaching. In D. S. Mewborn & H. S. Lee (Eds.), AMTE Monograph Series, 6. Scholarly practices and inquiry in the preparation of mathematics teachers (pp. 7–24). San Diego, CA: Association of Mathematics Teacher Educators.

    Google Scholar 

  • Thompson, P. W. (2014). Constructivism in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 96–102). Dordrecht: Springer.

    Google Scholar 

  • UNESCO. (2005). Formación Docentes y las TIC: Logros, tensiones y desafíos. Estudios realizados en Bolivia, Chile, Colombia, Ecuador, México, Panamá, Paraguay y Perú. OREALC/UNESCO, Santiago. Chile. http://unesdoc.unesco.org/images/0014/001410/141010s.pdf. Accessed 6 Jan 2020.

  • Wei, R. C., Darling-Hammond, L., Andree, A., Richardson, N., & Orphanos, S. (2009). Professional learning in the learning profession: A status report on teacher development in the United States and abroad (Technical Report). Dallas, TX: National Staff Development Council.

    Google Scholar 

  • Wu, J. H., Tennyson, R. D., & Hsia, T. L. (2010). A study of student satisfaction in a blended e-learning system environment. Computers & Education, 55(1), 155–164.

    Google Scholar 

  • Zaslavsky, O., & Sullivan, P. (Eds.). (2011). Constructing knowledge for teaching secondary mathematics: Tasks to enhance prospective and practicing teacher learning (Vol. 6). Dordrecht: Springer.

    Google Scholar 

Download references

Acknowledgements

Center for Mathematical Modeling, Grant PIA AFB-170001, Colaboración Ministerio de Educación—CMM 2014–2018 and UNESCO-Hamdan Award.

Author information

Authors and Affiliations

  1. Centro de Modelamiento Matemático, UMI 2807 CNRS-UChile, Universidad de Chile, Santiago, Chile

    Salomé Martínez, Flavio Guíñez, Raúl Zamora, Sofía Bustos & Becky Rodríguez

Authors
  1. Salomé Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Flavio Guíñez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raúl Zamora
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sofía Bustos
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Becky Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Salomé Martínez.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Martínez, S., Guíñez, F., Zamora, R. et al. On the instructional model of a blended learning program for developing mathematical knowledge for teaching. ZDM Mathematics Education 52, 877–891 (2020). https://doi.org/10.1007/s11858-020-01152-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-020-01152-y

Keywords

Search

Navigation