# Pedagogical entrepreneurship in school mathematics: an approach for students’ development of mathematical literacy

## Abstract

Emphasis on the development of the inner qualities thought to make up pedagogical entrepreneurship and use of such entrepreneurship as a strategy in mathematics teaching and learning could be expected to strengthen students’ development of mathematical literacy. This is because problem solving, local cultures and resources, authenticity and action competence are key elements in the development of mathematical literacy and in pedagogical entrepreneurship in mathematics. A foundation for research on an alternative mathematics teaching approach for future decades is suggested based on the relationship between pedagogical entrepreneurship in mathematics and mathematical literacy in the literature and on the description of the contexts and teacher experiences of two best practice examples from the mathematics classroom. Emphasis on pedagogical entrepreneurship in school mathematics through problem solving and authenticity in a learning environment that applauds such approaches to learning of mathematics should be recognized as giving priority to the development of disciplinary literacy in mathematics.## References

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Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in school. British Journal of Developmental Psychology, 3, 21–29.

Cochran-Smith, M., & Lytle, S. L. (2009). Inquiry as stance: practitioner research for the next generation. New York: Teachers College Press.

Colwell, J., & Endreson, 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.

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). Princeton, NJ: The National Council on Education and the Disciplines.

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.

Elo, J. (2015). The benefits and challenges of enterprise education: results from an action research project in the third grade in Finnish basic education. Education Action Research. DOI: 10.1080/09650792.2015.1113886

European Commission (2002). Final report of the expert group “Best procedure” project on education and training for entrepreneurship. Brussels: Enterprise Directorate-General.

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”. Brussels: Enterprise Directorate-General.

European Commission (2007). Key competences for lifelong learning, European reference framework. Luxembourg: Office for Official Publications of the European Communities.

European Commission (2010). Towards greater cooperation and coherence in entrepreneurship education. Brussels: European Commission.

European Commission (2011). Entrepreneurship education: Enabling teachers as a critical success factor. Brussels: European Commission.

European Commission (2013). Entrepreneurship 2020 Action plan. Reigniting the entrepreneurial spirit in Europe. Brussels: European Commission.

Feldman, A. (2003). Validity and quality in self-study. Educational Researcher, 32(3), 26–28.

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

Gellert, U. (2004). Didactic material confronted with the concept of mathematical literacy. Educational Studies in Mathematics, 55, 163–179.

Gibb, A. (1987). Enterprise culture: Its meaning and implications for education and training. Bradford: MCB University Press.

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., & 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. (2013). Pedagogisk entreprenørskap i matematikkfaget [Pedagogical entrepreneurship in mathematics; in Norwegian]. Bedre Skole, 1, 42–45.

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.

Hall, L. A. (2005). Teachers and content area reading: attitudes, beliefs, and change. Teaching and Teacher Education, 21, 403–414.

Hamilton, M. L., Pinnegar, S., Loughran, J., Russell, T., & LaBoskey, V. (Eds.) (1998). Reconceptualizing teaching practice: Self-study in teacher education. London: Falmer Press.

Hopfenbeck, T. N. (2011). Fra teoretiske modeller til klasseromspraksis: Hvordan fremme selvregulert læring? [From theoretical models to classroom practice: How to promote self-regulated learning?; in Norwegian], Norsk Pedagogisk Tidsskrift, 95(5), 360–373.

Kemmis, S. (2009). Action research as a practice-based practice. Educational Action Research, 17(3), 463–474.

Kunnskapsdepartementet [Ministry of Education] (2006). Læreplanverket for kunnskapsløftet [The National curriculum for knowledge promotion in primary and secondary school; in Norwegian]. Oslo: Utdanningsdirektoratet.

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). Dordrecht: Kluwer Academic Publishers.

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). Dordrecht: Kluwer Academic Publishers.

Lund, B., et al. (2011). Kreativitet, innovasjon og entreprenørskap i utdanningssystemene I Norden. TemaNord 2011:517 [Creativity, innovation, and entrepreneurship in the educational systems on the Nordic venue. TemaNord 2011:517; in Norwegian]. Copenhagen: Nordisk ministerråd.

McNiff, J. (2002). Action research for professional development. Concise advice for new action researchers (3rd ed.). http://www.jeanmcniff.com/ar-booklet.asp. Accessed 08 November 2016.

Moberg, K. (2014). Two approaches to entrepreneurship education: the different effects of education for and through entrepreneurship at the lower secondary level. The International Journal of Management Education, 12(3), 512–528.

Moje, E. B. (2008). Foregrounding the disciplines in secondary literacy teaching and learning: a call for change. Journal of Adolescent & Adult Literacy, 52(2), 96–107.

Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175–197.

NOU 2014:7 [Official Norwegian Reports 2014:7] (2014). Elevenes læring i fremtidens skole: et kunnskapsgrunnlag. [Pupils’ learning in the school for the future: a knowledgebase; in Norwegian]. Oslo: Kunnskapsdepartementet.

OECD (2003). The PISA 2003 assessment framework – mathematics, reading, science and problem solving knowledge and skills. Paris: OECD Publications.

OECD (2005). The definition and selection of key competencies. Executive Summary. https://www.oecd.org/pisa/35070367.pdf

OECD (2009). PISA 2009 Assessment Framework. Key competencies in reading, mathematics and science. http://www.oecd.org/pisa/pisaproducts/44455820.pdf

OECD (2010). Ministerial report on the OECD innovation strategy. Key findings. Paris: OECD.

OECD (2013). OECD Skills Outlook 2013. First Results from the Survey of Adult Skills. OECD publishing. http://skills.oecd.org/OECD_Skills_Outlook_2013.pdf

Palmér, H. (2016). What happens when entrepreneurship enters mathematics lessons? In C. Csiskos, A. Rausch, & J. Szitànyi (Eds.), Proceedings of the 40th conference of the international group for the psychology of mathematics education, 4, 27–34.

Pólya, G. (1990). How to solve it? (3rd ed.). London: Penguin.

Røe Ødegård, I. K. (2003). Læreprosesser i pedagogisk entreprenørskap. Å lære i dilemma og kaos [Learning processes in pedagogical entrepreneurship. To learn in dilemmas and chaos; in Norwegian]. Kristiansand: Høyskoleforlaget.

Røe Ødegård, I. K. (2015). Pedagogisk entreprenørskap – begrep og begrunnelser [Pedagogical entrepreneurship – concept and justifications; in Norwegian]. In F. O. Haara, & I. K. Røe Ødegård (Eds.), Grunnskolelærerutdanning gjennom pedagogisk entreprenørskap [Teacher education through pedagogical entrepreneurship; in Norwegian] (pp. 23–44). Oslo: Cappelen Damm.

Ruskovaara, E., & Pihkala, T. (2013). Teachers implementing entrepreneurship education: classroom practices. Education & Training, 55(2), 204–216.

Schoenfeld, A. H. (1993). Teaching mathematical thinking and problem solving. In SÅNN JA! – Rapport fra konferanse om matematikkdidaktikk og kvinner i matematiske fag [THAT’S RIGHT! – Report from conference about mathematics education and women in mathematical subjects]. Oslo: Norsk forskningsråd [Norwegian Research Council], 67–89.

Schraw, G. (2001). Promoting general metacognitive awareness In H. J. Hartman (Ed.), Metacognition in learning and instruction. Theory, research and practice (pp. 3–16). Dodrecht, The Netherlands: Kluwer Academic Publishers.

Sfard, A. (2014). Why mathematics? What mathematics? In M. Pirici (Ed.), The best writing of mathematics 2013. (pp. 130–142). Princeton, New Jersey: Princeton University Press.

Sfard, A., & Prusak, A. (2005). Telling identities: in search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14–22.

Shanahan, T., & Shanahan, C. (2012). What is disciplinary literacy and why does it matter? Topics in Language Disorders, 32(1), 7–18.

Siebert, D., & Draper, R. J. (2008). Why content-area literacy messages do not speak to mathematics teachers: a critical content analysis. Literacy Research and Instruction, 47(4), 229–245.

Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, Virginia: NCTM.

Stylianides, A. J. & Stylianides, G. J. (2013). Seeking research-grounded solutions to problems of practice: classroom-based interventions in mathematics education. ZDM – The International Journal of Mathematics Education, 45(3), 333–341.

Tai, W. C., & Lin, S. W. (2015). Relationship between problem-solving style and mathematical literacy. Educational Research and Reviews, 10(11), 1480–1486.

Tidåsen, C., Westerberg, M., Palmér, H., Leonardson, J., Karlsson, L., Lindh, I., Wilde Björling, M., & Kivimäki, K. (2015). Studying entrepreneurial learning in a primary school setting in Sweden. Paper presented at 3E Conference - ECSB Entrepreneurship Education Conference, Luneburg, Germany.

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

Wæge, K. (2007). Elevenes motivasjon for å lære matematikk og undersøkende matematikkundervisning [Students’ motivation for learning mathematics and investigative mathematics teaching; in Norwegian] (PhD thesis). Trondheim: Norwegian University of Science and Technology.

Yin, R. K. (2014). Case study research – design and methods (5th ed.). London: Sage.

Zeichner, K. (2007). Accumulating knowledge across self-studies in teacher education. Journal of Teacher Education, 58(1), 36–46.

Zimmerman, B. J. (2000). Attaining self-regulation. A social cognitive perspective. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds), Handbook of self-regulation (pp. 13–39). San Diego, CA: Academic Press.

Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in school. British Journal of Developmental Psychology, 3, 21–29.

Cochran-Smith, M., & Lytle, S. L. (2009). Inquiry as stance: practitioner research for the next generation. New York: Teachers College Press.

Colwell, J., & Endreson, 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.

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). Princeton, NJ: The National Council on Education and the Disciplines.

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.

Elo, J. (2015). The benefits and challenges of enterprise education: results from an action research project in the third grade in Finnish basic education. Education Action Research. DOI: 10.1080/09650792.2015.1113886

European Commission (2002). Final report of the expert group “Best procedure” project on education and training for entrepreneurship. Brussels: Enterprise Directorate-General.

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”. Brussels: Enterprise Directorate-General.

European Commission (2007). Key competences for lifelong learning, European reference framework. Luxembourg: Office for Official Publications of the European Communities.

European Commission (2010). Towards greater cooperation and coherence in entrepreneurship education. Brussels: European Commission.

European Commission (2011). Entrepreneurship education: Enabling teachers as a critical success factor. Brussels: European Commission.

European Commission (2013). Entrepreneurship 2020 Action plan. Reigniting the entrepreneurial spirit in Europe. Brussels: European Commission.

Feldman, A. (2003). Validity and quality in self-study. Educational Researcher, 32(3), 26–28.

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

Gellert, U. (2004). Didactic material confronted with the concept of mathematical literacy. Educational Studies in Mathematics, 55, 163–179.

Gibb, A. (1987). Enterprise culture: Its meaning and implications for education and training. Bradford: MCB University Press.

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., & 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. (2013). Pedagogisk entreprenørskap i matematikkfaget [Pedagogical entrepreneurship in mathematics; in Norwegian]. Bedre Skole, 1, 42–45.

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.

Hall, L. A. (2005). Teachers and content area reading: attitudes, beliefs, and change. Teaching and Teacher Education, 21, 403–414.

Hamilton, M. L., Pinnegar, S., Loughran, J., Russell, T., & LaBoskey, V. (Eds.) (1998). Reconceptualizing teaching practice: Self-study in teacher education. London: Falmer Press.

Hopfenbeck, T. N. (2011). Fra teoretiske modeller til klasseromspraksis: Hvordan fremme selvregulert læring? [From theoretical models to classroom practice: How to promote self-regulated learning?; in Norwegian], Norsk Pedagogisk Tidsskrift, 95(5), 360–373.

Kemmis, S. (2009). Action research as a practice-based practice. Educational Action Research, 17(3), 463–474.

Kunnskapsdepartementet [Ministry of Education] (2006). Læreplanverket for kunnskapsløftet [The National curriculum for knowledge promotion in primary and secondary school; in Norwegian]. Oslo: Utdanningsdirektoratet.

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). Dordrecht: Kluwer Academic Publishers.

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). Dordrecht: Kluwer Academic Publishers.

Lund, B., et al. (2011). Kreativitet, innovasjon og entreprenørskap i utdanningssystemene I Norden. TemaNord 2011:517 [Creativity, innovation, and entrepreneurship in the educational systems on the Nordic venue. TemaNord 2011:517; in Norwegian]. Copenhagen: Nordisk ministerråd.

McNiff, J. (2002). Action research for professional development. Concise advice for new action researchers (3rd ed.). http://www.jeanmcniff.com/ar-booklet.asp. Accessed 08 November 2016.

Moberg, K. (2014). Two approaches to entrepreneurship education: the different effects of education for and through entrepreneurship at the lower secondary level. The International Journal of Management Education, 12(3), 512–528.

Moje, E. B. (2008). Foregrounding the disciplines in secondary literacy teaching and learning: a call for change. Journal of Adolescent & Adult Literacy, 52(2), 96–107.

Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175–197.

NOU 2014:7 [Official Norwegian Reports 2014:7] (2014). Elevenes læring i fremtidens skole: et kunnskapsgrunnlag. [Pupils’ learning in the school for the future: a knowledgebase; in Norwegian]. Oslo: Kunnskapsdepartementet.

OECD (2003). The PISA 2003 assessment framework – mathematics, reading, science and problem solving knowledge and skills. Paris: OECD Publications.

OECD (2005). The definition and selection of key competencies. Executive Summary. https://www.oecd.org/pisa/35070367.pdf

OECD (2009). PISA 2009 Assessment Framework. Key competencies in reading, mathematics and science. http://www.oecd.org/pisa/pisaproducts/44455820.pdf

OECD (2010). Ministerial report on the OECD innovation strategy. Key findings. Paris: OECD.

OECD (2013). OECD Skills Outlook 2013. First Results from the Survey of Adult Skills. OECD publishing. http://skills.oecd.org/OECD_Skills_Outlook_2013.pdf

Palmér, H. (2016). What happens when entrepreneurship enters mathematics lessons? In C. Csiskos, A. Rausch, & J. Szitànyi (Eds.), Proceedings of the 40th conference of the international group for the psychology of mathematics education, 4, 27–34.

Pólya, G. (1990). How to solve it? (3rd ed.). London: Penguin.

Røe Ødegård, I. K. (2003). Læreprosesser i pedagogisk entreprenørskap. Å lære i dilemma og kaos [Learning processes in pedagogical entrepreneurship. To learn in dilemmas and chaos; in Norwegian]. Kristiansand: Høyskoleforlaget.

Røe Ødegård, I. K. (2015). Pedagogisk entreprenørskap – begrep og begrunnelser [Pedagogical entrepreneurship – concept and justifications; in Norwegian]. In F. O. Haara, & I. K. Røe Ødegård (Eds.), Grunnskolelærerutdanning gjennom pedagogisk entreprenørskap [Teacher education through pedagogical entrepreneurship; in Norwegian] (pp. 23–44). Oslo: Cappelen Damm.

Ruskovaara, E., & Pihkala, T. (2013). Teachers implementing entrepreneurship education: classroom practices. Education & Training, 55(2), 204–216.

Schoenfeld, A. H. (1993). Teaching mathematical thinking and problem solving. In SÅNN JA! – Rapport fra konferanse om matematikkdidaktikk og kvinner i matematiske fag [THAT’S RIGHT! – Report from conference about mathematics education and women in mathematical subjects]. Oslo: Norsk forskningsråd [Norwegian Research Council], 67–89.

Schraw, G. (2001). Promoting general metacognitive awareness In H. J. Hartman (Ed.), Metacognition in learning and instruction. Theory, research and practice (pp. 3–16). Dodrecht, The Netherlands: Kluwer Academic Publishers.

Sfard, A. (2014). Why mathematics? What mathematics? In M. Pirici (Ed.), The best writing of mathematics 2013. (pp. 130–142). Princeton, New Jersey: Princeton University Press.

Sfard, A., & Prusak, A. (2005). Telling identities: in search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14–22.

Shanahan, T., & Shanahan, C. (2012). What is disciplinary literacy and why does it matter? Topics in Language Disorders, 32(1), 7–18.

Siebert, D., & Draper, R. J. (2008). Why content-area literacy messages do not speak to mathematics teachers: a critical content analysis. Literacy Research and Instruction, 47(4), 229–245.

Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, Virginia: NCTM.

Stylianides, A. J. & Stylianides, G. J. (2013). Seeking research-grounded solutions to problems of practice: classroom-based interventions in mathematics education. ZDM – The International Journal of Mathematics Education, 45(3), 333–341.

Tai, W. C., & Lin, S. W. (2015). Relationship between problem-solving style and mathematical literacy. Educational Research and Reviews, 10(11), 1480–1486.

Tidåsen, C., Westerberg, M., Palmér, H., Leonardson, J., Karlsson, L., Lindh, I., Wilde Björling, M., & Kivimäki, K. (2015). Studying entrepreneurial learning in a primary school setting in Sweden. Paper presented at 3E Conference - ECSB Entrepreneurship Education Conference, Luneburg, Germany.

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

Wæge, K. (2007). Elevenes motivasjon for å lære matematikk og undersøkende matematikkundervisning [Students’ motivation for learning mathematics and investigative mathematics teaching; in Norwegian] (PhD thesis). Trondheim: Norwegian University of Science and Technology.

Yin, R. K. (2014). Case study research – design and methods (5th ed.). London: Sage.

Zeichner, K. (2007). Accumulating knowledge across self-studies in teacher education. Journal of Teacher Education, 58(1), 36–46.

Zimmerman, B. J. (2000). Attaining self-regulation. A social cognitive perspective. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds), Handbook of self-regulation (pp. 13–39). San Diego, CA: Academic Press.

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2018-09-04

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Articles