Mathematical Modelling in Upper Primary School: Finding Relevance and Value for Others Outside School

Frode Olav Haara 1 *
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1 Faculty of Education, Arts and Sports, Western Norway University of Applied Sciences, Sogndal, NORWAY
* Corresponding Author
EUR J SCI MATH ED, Volume 10, Issue 4, pp. 555-569.
Published: 26 August 2022
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This article reports on how a pedagogical entrepreneurship approach combined with fundamental elements of mathematical modelling may be used to strengthen students’ development of mathematical literacy in upper primary school. This is done first through a review of the relationship between pedagogical entrepreneurship in mathematics, mathematical modelling, and mathematical literacy, and then through presentation of a best-practice example where the pedagogical entrepreneurship approach and mathematical modelling have been the foundation for an assignment given to teacher education students. An action-research perspective influenced by self-study methodology has been used in identification and presentation of the best-practice example. The example shows that through emphasis on mathematical modelling and a scientific approach based on pedagogical entrepreneurship, we may have expectations towards increase of upper primary school students’ development of mathematical literacy. In conclusion, key elements in pedagogical entrepreneurship like authenticity, relevance, and value for others enrich the mathematical modelling process, and provide valuable stepping-stones for the upper primary school students’ development of mathematical literacy.


Haara, F. O. (2022). Mathematical Modelling in Upper Primary School: Finding Relevance and Value for Others Outside School. European Journal of Science and Mathematics Education, 10(4), 555-569.


  • Anderson, T., & Shattuck, J. (2012). Design-based research: A decade of progress in education research? Educational Researcher, 41(1), 16-25.
  • Blum, W. (2002). ICME study 14: Applications and modelling in mathematics education–Discussion document. Educational Studies in Mathematics, 51(1-2), 149-171.
  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In Proceedings of the 12th International Congress on Mathematical Education (pp. 73-96). Springer.
  • Bocconi, S., Chioccariello, A., & Earp, J. (2018). The Nordic approach to introducing computational thinking and programming in compulsory education. Nordic@BETT2018 Steering Group.
  • Bolstad, O. H. (2020). Teaching and learning for mathematical literacy [PhD thesis, University of Agder].
  • Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in school. British Journal of Developmental Psychology, 3(1), 21-29.
  • Chowdhury, T. A. (2021). Fostering learner autonomy through cooperative and collaborative learning. Shanlax International Journal of Education, 10(1), 89-95.
  • Cobb, P. (2007). Putting philosophy to work: Coping with multiple theoretical perspectives. In F. K. Lester, Jr. (Ed.), Second handbook of research in mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 3-38). Information Age Publishing.
  • Cochran-Smith, M., & Lytle, S. L. (2009). Inquiry as stance: Practitioner research for the next generation. Teachers College Press.
  • Colwell, J., & Enderson, M. C. (2016). “When I hear literacy”: Using pre-service teachers’ perceptions of mathematical literacy to inform program changes in teacher education. Teaching and Teacher Education, 53, 63-74.
  • Darling-Hammond, L., & McLaughlin, M. W. (2011). Policies that support professional development in an era of reform. Phi Delta Kappan, 92(6), 81-92.
  • De Lange, J. (2003). Mathematics for literacy. In B.L. Madison, & L. A. Steen (Eds.), Quantitative literacy: Why numeracy matters for schools and colleges (pp. 75-89). The National Council on Education and the Disciplines.
  • Dweck, C. (2006). Mindset: The new psychology of success. Random House.
  • Edo, S. I., Hartono, Y., & Putri, R. I. I. (2013). Investigating secondary school students’ difficulties in modeling problems PISA-model level 5 and 6. Indonesian Mathematical Society Journal on Mathematics Education, 4(1), 41-58.
  • English, L. D., & Watters, J. J. (2005). Mathematical Modeling in the Early School Years. Mathematics Education Research Journal, 16(3), 58-79.
  • Erbas, A. K., Kertil, M., Cetinkaya, B., Cakiroglu, E., Alacaci, C., & Bas, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory and Practice, 14(4), 1621-1627.
  • European Commission. (2004). Making progress in promoting entrepreneurial attitudes and skills through primary and secondary education. Final report of the Expert Group “Education for Entrepreneurship”. Enterprise Directorate-General.
  • European Commission. (2010). Towards greater cooperation and coherence in entrepreneurship education. European Commission.
  • European Commission. (2011). Entrepreneurship education: Enabling teachers as a critical success factor. European Commission.
  • European Commission. (2013). Entrepreneurship 2020 Action Plan: Reigniting the entrepreneurial spirit in Europe. European Commission.
  • European Council. (2000). Lisbon European Council 23/24 March 2000–Presidency conclusions.
  • Feldman, A. (2003). Validity and quality in self-study. Educational Researcher, 32(3), 26-28.
  • Freudenthal, H. (1973). Mathematics as an educational task. Reidel.
  • Gatabi, A. R., Stacey, K., & Gooya, Z. (2012). Investigating grade nine textbook problems for characteristics related to mathematical literacy. Mathematics Education Research Journal, 24(4), 403-421.
  • Glaser, B. G. (1965). The constant comparative method of qualitative analysis. Social Problems, 12(4), 436-445.
  • Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155-177.
  • Haara, F. O. (2015). Teachers’ choice of using practical activities – A hierarchical classification attempt. European Journal of Science and Mathematics Education, 3(4), 323-336.
  • Haara, F. O. (2018). Pedagogical entrepreneurship in school mathematics: An approach for students’ development of mathematical literacy. International Journal for Mathematics Teaching and Learning, 19(2), 253-268.
  • Haara, F. O., & Jenssen, E. S. (2016). Pedagogical entrepreneurship in teacher education – What and why? Icelandic Journal of Education, 25(2), 183-196.
  • Haara, F. O., & Jenssen, E. S. (2019). The influence of pedagogical entrepreneurship in teacher education. In J. Lampert (Ed.). The Oxford encyclopedia of global perspectives on teacher education. Oxford University Press.
  • Haara, F. O., Bolstad, O. H., & Jenssen, E. S. (2017). Research on mathematical literacy in schools – Aim, approach and attention. European Journal of Science and Mathematics Education, 5(3), 285-313.
  • Haara, F. O., Jenssen, E. S., Fossøy, I., & Røe Ødegård, I. K. (2016). The ambiguity of pedagogical entrepreneurship: The state of the art and its challenges. Education Inquiry, 7(2), 183-210.
  • Hamilton, M. L., Pinnegar, S., Loughran, J., Russell, T., & LaBoskey, V. (1998). Reconceptualizing teaching practice: Self-study in teacher education. Falmer Press.
  • Johnson, D. W. & Johnson, R. T. (2009). An educational psychology success story: Social interdependence theory and cooperative learning. Educational Researcher, 38(5), 365-379.
  • Kaplinsky, R. (2020). Open middle math: Problems that unlock student thinking, grades 6-12. Stenhouse Publishers.
  • Kemmis, S. (2009). Action research as a practice-based practice. Educational Action Research, 17(3), 463-474.
  • Krawec, J., & Montague, M. (2014). The role of teacher training in cognitive strategy instruction to improve math problem solving. Learning Disabilities: Research and Practice, 29(3), 126-134.
  • Kvale, S., & Brinkmann, S. (2015). Det kvalitative forskningsintervju [The qualitative research interview]. Gyldendal Akademisk.
  • LaBoskey, V. K. (2004). The methodology of self-study and its theoretical underpinnings. In J. J. Loughran, M. L. Hamilton, V. K. LaBoskey, & T. Russell (Eds.), International handbook of self-study of teacher education practices (pp. 817-869). Kluwer Academic Publishers.
  • Lackéus, M. (2013). Developing entrepreneurial competencies: An action-based approach and classification in entrepreneurial education. Chalmers University of Technology.
  • Lackéus, M. (2015). Entrepreneurship in education: What, why, when, how. Entrepreneurship 360. Background paper for OECD.
  • Lackéus, M. (2016). Value creation as educational practice–Towards a new educational philosophy grounded in entrepreneurship? [PhD thesis, Chalmers University of Technology].
  • Lehrer, R., & Schauble, L. (2003). Origins and evaluation of model-based reasoning in mathematics and science. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 59-70). Lawrence Erlbaum.
  • Lehrer, R., & Schauble, L. (2007). A developmental approach for supporting the epistemology of modeling. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modeling and applications in mathematics education (pp. 153-160). Springer.
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Lawrence Erlbaum.
  • Loughran, J. J. (2004). Learning through self-study: The influence of purpose, participants and context. In J. J. Loughran, M. L. Hamilton, V. K. LaBoskey, & T. Russell (Eds.), International handbook of self-study of teaching and teacher education practices (pp. 151-192). Kluwer Academic Publishers.
  • Lund, B., Lindfors, E., Dal, M., Sjøvoll, J., Svedberg, G., Borup Jensen, J., Ovesen, S., Rotefoss, B., Pedersen, O., & Thordardottir, T., (2011). Kreativitet, innovasjon og entreprenørskap i utdanningssystemene i Norden: Bakgrunn og begrepsinnhold basert på politisk initiering og strategivalg [Creativity, innovation, and entrepreneurship in the educational systems on the Nordic venue: Background and conceptual content based on political initiation and strategy choices]. Nordisk Ministerråd.
  • OECD. (2009). PISA 2009 assessment framework: Key competencies in reading, mathematics and science. Organisation for Economic Co-operation and Development.
  • OECD. (2013). OECD skills outlook 2013: First results from the survey of adult skills. Organisation for Economic Co-operation and Development.
  • OKM. (2018). Tasa-arvoisen peruskoulun tulevaisuus [The future of equal basic education]. Opetus-ja kulttuuriministeriö [Ministry of Education and Culture].
  • Palmér, H., & Johansson, M. (2018). Combining entrepreneurship and mathematics in primary school–What happens? Education Inquiry, 9(4), 331-346.
  • Røe Ødegård, I. K. (2015). Pedagogisk entreprenørskap–begrep og begrunnelser [Pedagogical entrepreneurship–Concept and justifications]. In F. O. Haara, & I. K. Røe Ødegård (Eds.), Grunnskolelærerutdanning gjennom pedagogisk entreprenørskap [Teacher education through pedagogical entrepreneurship] (pp. 23-44). Cappelen Damm.
  • Sagar, H. (2014). Teacher change in relation to professional development in entrepreneurial learning [PhD thesis, Göteborgs Universitet].
  • Sawyer, R. K. (2012). Explaining creativity–The science of human innovation. Oxford University Press.
  • Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4-13.
  • Sfard, A. (2014). Why mathematics? What mathematics? In M. Pirici (Ed.), The best writing of mathematics 2013 (pp. 130-142). Princeton University Press.
  • Skolverket. (2019). LGR11 [The national curriculum of Sweden]. Skolverket.
  • Smith, M. S., & Stein, M. K. (2018). 5 practices for orchestrating productive mathematics discussions. Corwin.
  • Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. SAGE.
  • Tai, W. C., & Lin, S. W. (2015). Relationship between problem-solving style and mathematical literacy. Educational Research and Reviews, 10(11), 1480-1486.
  • Thomson, P. (2012). Creative school and system change. In J. Sefton-Green, P. Thomson, K. Jones, & L. Bresler (Eds.), The Routledge international handbook of creative learning (pp. 333-336). Routledge.
  • UK Department of Education. (2014). National curriculum for England to be taught in all local authority-maintained schools.
  • Ulvik, M., Riese, H., & Roness, D. (2016). Å forske på egen praksis. Aksjonsforskning og andre tilnærminger til profesjonell utvikling i utdanningsfeltet [To do research on one’s own practice. Action research and other approaches to professional development within the field of education]. Fagbokforlaget.
  • Utdanningsdirektoratet. (2020). Læreplanverket [The national curriculum of Norway]. Utdanningsdirektoratet.
  • Van Dooren, W., Lem, S., De Wortelaer, H., & Verschaffel, L. (2019). Improving realistic word problem solving by using humor. Journal of Mathematical Behavior, 53, 96-104.
  • Vos, P. (2018). “How real people really need mathematics in the real world”–Authenticity in mathematics education. Education Sciences, 8(4), 1-14.
  • WEF. (2016). The 10 skills you need to thrive in the Fourth Industrial Revolution. World Economic Forum.
  • Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Cambridge University Press.
  • Wiggins, G. (2012). Creative learning. In J. Sefton-Green, P. Thomson, K. Jones, & L. Bresler (Eds.), The Routledge international handbook of creative learning (pp. 320-332). Routledge.
  • Yin, R. K. (2014). Case study research–Design and methods. SAGE.
  • Zeichner, K. (2007). Accumulating knowledge across self-studies in teacher education. Journal of Teacher Education, 58(1), 36-46.