Argumentation is crucial for developing deep learning in mathematics. As Sawyer (2013) summarised in his introduction to the Handbook of Learning Sciences, “deep learning requires that learners understand the process of dialogue through which knowledge is created, and they examine the logic of an argument critically” (p. 4).  Deep learning, therefore, includes using argumentation to substantiate points and to critical reflect on others’ argumentation. This is in alignment with the skills that preservice teachers must gain in their teacher education. These include:

Mathematical language and thinking are developed through activities that promote reasoning, argumentation and justification. Mathematics teachers must be able to implement and understand mathematical processes and arguments, and analyse proposals from others in terms of validity and potential. (Munthe & Melting, 2016, p. 23, own translation)

Mathematical argumentation is important because it is a core component of school mathematics, due to its strong connection to proof (Enge & Valenta, 2015). It is also through argumentation that students show they have mastered the conventions of school mathematics and belong to the community of successful learners (Cobb & Hodge, 2002). In reviewing earlier research, Kleve (2015) suggested that not all Norwegian school students would have equal access to essential mathematical genres, what she called secondary discourses, because the students came with a range of different everyday conversation styles, or primary discourses, which were more or less in alignment with secondary discourses. Similarly, Kempert, Saalbach, and Hardy (2011) suggested that lack of fluency in the language of instruction could have an impact on bilingual students possibilities for understanding the “definitions, explanations, and argumentations” (p. 548) needed for solving mathematics word problems, which have a particular structure. Thus, there is a need for teachers to understand how some groups of students have their opportunities to learn mathematics reduced because of an unfilled need to systematically develop mathematical argumentation skills (Erath, Prediger, Quasthoff, & Heller, 2018) and that multilingual students bring with them existing language resources that can be utilised in their learning (Planas, 2018).

Argumentation with mathematics is also important as it provides an opportunity for students to explore the world through mathematics. Ernest (2002) stated that learning mathematics should result in students being “able to understand and begin to answer important questions relating to a broad range of social uses and abuses of mathematics” (p. 6). Multilingual students, like other students, need to learn to critique existing societal issues with mathematics and promote their ideas through argumentation. Yet, moving mathematical arguments into societal conversations is not straight forward (Aguilar & Blomhøj, 2016) and for some students the unfamiliarity of the societal contexts may affect their willingness to engage in these types of arguments (see for example, Lubienski, 2007).

References

Aguilar, M. S., & Blomhøj, M. (2016). The role of mathematics in politics as an issue for mathematics teaching. In P. Ernest, B. Sriraman & N. Ernest (Eds.), Critical mathematics education: Theory, praxis and reality (pp. 253-272). Charlotte, NC: Information Age Publishing.

Cobb, P., & Hodge, L. L. (2002). A relational perspective on issues of cultural diversity and equity as they play out in the mathematics classroom. Mathematical Thinking and Learning, 4(2&3), 249–284.

Enge, O., & Valenta, A. (2015). Student teachers’ work on reasoning and proving. In H. Silfverberg, T. Kärki & M. S. Hannula (Eds). Nordic research in mathematics education – Proceedings of NORMA 14, Turku, June 3-6, 2014. (pp. 61-70).

Erath, K., Prediger, S., Quasthoff, U., & Heller, V. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: The case of explaining to learn and learning to explain. Educational Studies in Mathematics, 99(2), 161-179.

Ernest, P. (2002). Empowerment in mathematics education. Philosophy of Mathematics Education, 15. http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome15/empowerment.htm

Kempert, S., Saalbach, H., & Hardy, I. (2011). Cognitive benefits and costs of bilingualism in elementary school students: The case of mathematical word problems. Journal of Educational Psychology, 103(3), 547-561.

Kleve, B. (2015). Mathematics in a literacy perspective: Meta awareness for all pupils. In H. Silfverberg, T. Kärki & M. S. Hannula (Eds). Nordic research in mathematics education – Proceedings of NORMA 14, Turku, June 3-6, 2014. (pp. 297-306).

Lubienski, S. T. (2007). Research, reform, and equity in U. S. mathematics education. In N. i. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 10-23). New York: Teachers College Press.

Munthe, E. & Melting, J. (2016). Nasjonale retningslinjer for grunddskolelærerutdanning, trinn 1-7. … Available from: http://www.uhr.no/documents/Godkjent_1_7_010916.pdf

Planas, N. (2018). Language as resource: A key notion for understanding the complexity of mathematics learning. Educational Studies in Mathematics, 98(3), 215-229.

Sawyer, R. K. (2013). Introduction: The new science of learning. In K. Sawyer (Ed.) Handbook of the learning sciences (pp.1-16). Cambridge: Cambridge University Press.