We contend that engaging in critical mathematics education contexts provides opportunities to show the value of mathematics in democratic societies, and the necessity for appropriate argumentation strategies. This is a very important component of learning mathematics which makes mathematics accessible for all. School children in the earliest years of school have been shown to engage in important societal issues and reason about them (English, 2010). Investigating societally important issues will support both preservice teachers’ and school students’ need to understand mathematical ideas at a deep level. This is particularly necessary for multilingual students, who are learning mathematics and the language of instruction simultaneously (de Araujo, Smith, & Sakow, 2015).  Crespo (2003) found that it was only through working with school students that preservice teachers understood how to provide mathematics problems that challenged students’ thinking.

The purpose for critical mathematics education is multi-dimensional:

A successful critical mathematics education must succeed in empowering the learner, first to overcome internal inhibitions and perceptions of inadequacy, second to question the teacher, the subject, and the constraints of school, and third to question the “facts” and edicts of authority at large in society. (Ernest, 2002, p. 1)

The following example is inspired by Eikset and Meaney (2018). It illustrates how critical mathematics education could be integrated with argumentation at the teacher education level. Preservice teachers are introduced to the idea of using fairy stories to engage students. Using proportional reasoning, they determine the height of a giant, based on a hand-print. To do this task, preservice teachers would use ICT and draw on understandings of mathematical modelling to argue why their result was reasonable. The discussion would then move to the skin colour of good and bad characters in fairy stories and the implications for students to feel included into mathematics learning. This would lead to a mathematical investigation of the skin colours of characters in fairy stories in a local library. The results would be the basis for determining what distribution of colours is reasonable and require the preservice teachers to argue using proportional reasoning for a critical mathematics education purpose. Preservice teachers would then develop these ideas into related tasks, which they would implement on practicum with school students.

However, teaching and learning critical mathematics education is not without tensions. Jablonka and Gellert (2010) suggest that there is a tension between the two aims of critical mathematics education: gaining mathematical understanding; and being able to critique political inequities. This is because “[c]ritical mathematics literacy intends to be simultaneously a pedagogy of access and a pedagogy of dissent” (p. 43). This tension makes it difficult for teachers to combine both aims in their teaching and even if they achieve this, it is challenging for learners to understand how these aims are connected. The level of reflection required by learners is extremely high, as they make adjustments so that they can operate effectively while transitioning between contexts which require mathematical knowledge and critique of political inequities.

References

Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243-270.

de Araujo, Z., I, J. K., Smith, E., & Sakow, M. (2015). Preservice teachers´ strategies for supporting English language learners. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez, (Eds.). (2015). Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 648-655). East Lansing, MI: Michigan State University.

Eikset, A. & Meaney, T. (2018, forthcoming). When does a difference make a difference? Teaching about language diversity in mathematics teacher education. Nordic Studies in Mathematics Education, 23(4), 225-246.

English, L. D. (2010). Young children’s early modelling with data. Mathematics Education Research Journal, 22(2), 24-47.

Ernest, P. (2002). Empowerment in mathematics education. Philosophy of Mathematics Education, 15. Retrieved from: http://people.exeter.ac.uk/PErnest/pome15/empowerment.htm

Jablonka, E. & Gellert, U. (2010). Ideological roots and uncontrolled flowering of alternative curriculum conceptions. In U. Gellert, E. Jablonka & C. Morgan (Eds.) Proceedings of 6th International Mathematics Education and Society Conference, 20-25 March 2010, Berlin (pp. 31-49). Berlin: Freie Universität. Available from: http://www.ewi-psy.fu-berlin.de/en/v/mes6/research_papers/index.html