Session Information
10 SES 13 C JS, Advancing Secondary and Upper Secondary Mathematics Education: Innovative Approaches to Teaching and Learning
Joint Session NW10 & NW24
Contribution
For some time, mathematics education research has focused on relating mathematical literacy to students’ everyday lives (e.g., Bolstad, 2020; Freudenthal, 1973). Haara (2018) suggests that one way of combining the development of mathematical literacy and relevance for students is through pedagogical entrepreneurship. Pedagogical entrepreneurship is action-oriented teaching and learning in a social context, where the student is active in the learning process and where personal features, abilities, knowledge, and skills provide the foundation and direction for the learning processes. Such an approach entails the use of teaching methods that give students authority and activate learning awareness. It requires working methods that improve students’ creative abilities and beliefs about their own skills, provide a basis for seeing opportunities around them, and motivate them to become development stakeholders in the community (Haara & Jenssen, 2019). A focus on entrepreneurial learning, thus, requires priorities regarding both processes and products in school subjects, which in turn means that a learning environment that emphasizes authenticity and student activity is considered fundamental.
Haara et al. (2017) noted that researchers have concluded that specific attempts to work directly with mathematical literacy through mathematics alone does not work, and that it seems that teaching for mathematical literacy calls for something else than traditional mathematics teaching. Haara (2018) showed that problem-solving features, problem relevance, and student activity are recognized as valuable for the development of mathematical literacy, and that these could be emphasized through a pedagogical entrepreneurship approach. Smith and Stein (2018) provide further support for the influence of creativity and tolerance for ambiguity in school mathematics, through emphasis on problem solving and teaching based on problem-solving approaches.
However, despite thorough work within the mathematics education research community to put emphasis on mathematical modelling and unravel how this may be done with young students (e.g. Gravemeijer, 1999), this remains an issue in need of attention. According to Erbas et al. (2014), a mathematical model “is used to understand and interpret complex systems in nature” (p. 1622). When applying a modelling process in the teaching of mathematics,the underlying assumption is that students can learn fundamental mathematical concepts meaningfully during the modelling process in which they need the concepts while addressing a real-life problem-solving situation (Lesh & Doerr, 2003). Based on previous research it seems clear that emphasis on both mathematical literacy and mathematical modelling is better with a touch of relevance and real-world problem relation than with traditional word problems or quasi-real problems (Vos, 2018).
The purpose of this study is to respond to the calls regarding mathematical modelling (Blum (2002) and Erbas et al. (2014)) and mathematical literacy (Sfard (2014) and Bolstad (2020)), and to present and discuss how pedagogical entrepreneurship and mathematical modelling may be combined to pave the way for the further development of mathematical literacy in upper primary school. The area of statistics is used in this study as an example to illustrate the possibilities for such a combined effort, and the research question asked is therefore: How can pedagogical entrepreneurship and mathematical modelling combine to pave the way for learning statistics in upper primary school? Addressing this question provides the opportunity to discuss the possibilities for students’ development of mathematical literacy, with emphasis on pedagogical entrepreneurship and mathematical modelling.
Method
The fact that I was the lecturer involved in this study, places it within an action research perspective, influenced by self-study methodology (Cochran-Smith & Lytle, 2009). This method asks me as a lecturer to reflect on my practice for the purpose of improving it and the practice of others. The study involved teacher education students who carried out an assignment meant for upper primary school students, and then reflected on their own practice as teachers with an aim of improving their own and others’ practice. Together, we tried to understand the roles both as a student and as a teacher from the inside and out, rather than from the outside and in. Hence, to answer the research question in a trustworthy manner and offer mathematics teaching arguments for a “reframed thinking and transformed practice of the teacher” (LaBoskey, 2004, p. 844), I made it a priority to be as close as possible to the actual activity, and thereby sacrificed some observational distance on the altar of relevance. This means that I chose the assignment to use in the teaching, tutored student groups, organized the presentations, and was responsible for the analysis of data. The self-study perspective offered data from two sources: teacher education students’ reports from completing the assignment, and the lecturer’s observations. The study provides close contact with actual teaching and learning experiences, as well as research perspectives on these experiences through the discussion of possibilities and necessities regarding a relationship between pedagogical entrepreneurship in mathematics, mathematical modelling, and mathematical literacy. The theme and design of this study required that the lecturer/researcher be part of the collected data and, thereby, in an unconscious manner, choose the experiences and impressions that would be subject to analysis. This may seem to be a rather unpredictable way to work in classroom research, but this is not a study about mathematics teaching and learning seen from the outside. It is an article about mathematics teaching opportunities experienced from the inside. Blum’s (2015) four reasons for emphasis on mathematical modelling and three key factors for a pedagogical entrepreneurship approach (Haara & Jenssen, 2019) produced the analytical framework. However, I regard the phenomenological condensation of impressions produced through the work done by the teacher education students, and my observations related to their work, to be inspired by the constant comparative analysis method (Glaser, 1965).
Expected Outcomes
In this study I focus 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 has called for a review of the relationship between pedagogical entrepreneurship in mathematics, mathematical modelling, and mathematical literacy. It involved identification of elements from pedagogical entrepreneurship and their relation to mathematical modelling, and presentation of a best practice example in which the pedagogical entrepreneurship approach and mathematical modelling were used. The conclusion is 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. Problem solving and scientific rigor are key in both mathematical modelling and pedagogical entrepreneurship, and the idea behind both is to interpret one’s results and apply them in real-world practice. Therefore, 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. The reported study shows that it is possible to plan for learning of scientific approaches, data collection, mathematical modelling, and value for others, while learning statistics, in upper primary school. This planning needs to be based on the acknowledgement of compulsory school students as a resource when they are in school. They do not have to wait until they have finished school but can help move society forward while they learn mathematics and how to work scientifically. Development of mathematical literacy occurs through emphasis on relevance, which is identified as the application of mathematical modelling and real-life viability checks of mathematical work, and through providing value for others, identified as the application of pedagogical entrepreneurship in mathematics for local sustainability and development.
References
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 The Proceedings of the 12th International Congress on Mathematical Education (pp. 73–96). Springer. Bolstad, O. H. (2020). Teaching and Learning for Mathematical Literacy (Ph.D. thesis). University of Agder. Cochran-Smith, M., & Lytle, S. L. (2009). Inquiry as stance: Practitioner research for the next generation. Teachers College Press. Erbas, A. K., Kertil, M., Çetinkaya, B., Çakiroglu, E., Alacaci, C., & Bas, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches, Educational Sciences: Theory and Practice, 14(4), 1621–1627. Freudenthal, H. (1973). Mathematics as an educational task. D. Reidel. 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. (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. (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. 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. 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. Sfard, A. (2014). Why mathematics? What mathematics? In M. Pirici (Ed.), The best writing of mathematics 2013 (pp. 130–142). Princeton. Smith, M. S., & Stein, M. K. (2018). 5 practices for orchestrating productive mathematics discussions (2nd ed.). Corwin. Vos, P. (2018). “How real people really need mathematics in the real world” – Authenticity in mathematics education. Education Sciences, 8(4), 1–14.
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