In his leading book Pedagogy of the Oppressed, Freire mentioned two terms; oppressed and oppressor, to portray a repressive society in which the oppressed are dominated by oppressors in terms of political, economic, and social aspects of society. 

To overcome the structure of a controlled system, Freire proposed critical pedagogy as a way of humanization and liberation (Freire, 1971). According to Freire, education is not neutral; it is either a tool for maintaining an available system or a tool of practice for freedom with which they discover the way towards transformation of the worlds they find themselves in (Taskin& Kucuk, 2017). The main idea of critical pedagogy is that “education must not serve as a passive reproduction of existing social relations and power relations” (Skovsmose, 1985, p.348).

Freire proposed a problem-posing education system based on the educational praxis of reflection and action through conscientization. Students are seen as independent thinkers who can criticize problems with their efforts, justify their opinions, and construct their questions to understand their surroundings through individual autonomy.

Drawing upon Freire’s “pedagogy of the oppressed”, Frankenstein (1983) and Skovsmose (1985) related mathematics education and critical pedagogy firstly as critical mathematics education (CME), in the USA and Europe respectively (Aslan-Tutak, Bondy, Adams, 2011). In general, CME aims for students to be ready for future social and political engagements, to be conscious and participative citizens, along with the lifelong learning of mathematics as a discipline (Skovsmose, 1994).

Mathematics education is not value-neutral. Borba and Skovsmose (1997) criticized the ideology of certainty in mathematics:

We see the ideology of certainty as a general and fundamental frame of interpretation for an increasing number of issues which transform mathematics in a “language of power”. This view of mathematics – as a perfect system, as a pure, as an infallible tool if well used – contributes to political control. (p.17)

Traditional mathematics classes focus on the single correct answers. Through this true-false paradigm, mathematics becomes to be seen as independent from human effect  (Skovsmose, 1994b). This perspective of mathematics confirms people that mathematics is not for everyone, just for “skilled” people from birth. Therefore, without considering the ideology of certainty of mathematics, mathematics education might serve for the oppression (Borba & Skovsmose, 1997). 

Due to the teacher's role in determining how mathematics is handled in the classroom, it’s important to examine mathematics teachers' awareness of CME. In this regard, the study (Inan, 2021) focused on preservice mathematics teachers who have been volunteering to teach mathematics to disadvantaged students as part of a weekend school, and this paper is part of that study. The aim of the paper is to present the findings of a participant’s views of teaching and learning mathematics in the context of CME that may inform teacher education practices. The authors will share case study findings for the following research question:  

How does a mathematics preservice teacher who voluntarily teaches mathematics at a program for students of low-income families interpret and reflect on teaching and learning mathematics, as a component of CME awareness?

The participant was teaching mathematics voluntarily to students of low-income families, and his view was investigated based on reflection and interpretation through interviews. The exploratory case study design was chosen to answer the research question. A case study is a robust research strategy, which is useful when holistic and in-depth exploration and investigation of problems are needed (Zainal, 2007). The major of Winston (pseudonym name) was secondary mathematics education. The participant was in the third year of the university, and he claimed his motivation for teaching at weekend school as just having an experience of teaching in the classroom. During his teaching experience, he said that he had not been aware of the teaching strategies, and he stated that he was learning those through the pedagogical course, Teaching Methods in Science and Mathematics, which he took by the time this interview was conducted. Moreover, he claimed that he experienced teacher-centered mathematics education not only as a student but also as a teacher. Data was collected through (i) the focus group interview and (ii) the individual semi-structured case-based interview. The case for the individual interview was a video of mathematics instruction implementing CME. The video (The Learning Exchange, n.d.-a) was chosen presented on the website of The Learning Exchange (“About the Learning Exchange”, n.d.-b), which provides research-based tools for educators in order to improve student achievements, and it shows the aspects of CME as developed in the scope of research of CME. The video of instruction was divided into 5 parts by the researchers: activation, problem-solving, accountable talk, choosing students’ works, and consolidation. The participant interpreted and reflected upon at the end of each video section answering semi-structured interview questions. The instruction included mathematical and critical aspects of CME, and the semi-structured interview questions were constructed with respect to those aspects. After data transcription of the focus group interview, open coding was applied. The emerged codes were grouped under each question. For the individual interviews, the participants watched the video of instruction implementing CME, and they answered the questionnaire in three parts (introduction, case-based, and conclusion parts), including questions of social justice awareness and mathematics-related beliefs. For the individual interviews, after data transcription, we applied the line-by-line coding following thematic analysis. The data analysis process was inductive.

In the focus group interview, Winston defined learning mathematics, focusing on how questions. The steps of the problem-solving process were important for him, and he described teaching mathematics as a transmission of knowledge. When interpreting and reflecting on the case of the video of mathematics instruction implementing CME, the following codes emerged: meaningful learning, constructing their knowledge, learning in groups and individually, which would have correspondence in the scope of CME (Alrø & Skovsmose, 2004). Nevertheless, this doesn’t mean that the participant had a CME approach because the codes could be interpreted under student-centered or constructivist approaches which critical pedagogy was rooted in. Furthermore, Winston faced dilemmas in his explanations. He highlighted students’ self-monitoring process based on teaching methods to fix students’ misunderstandings and mistakes while mentioning a risk for students not getting correct answers in this process. This interpretation could be explained through the ideology of certainty: “mathematics – as a perfect system, as a pure, as an infallible tool if well used – contributes to political control” (Borba & Skovsmose, 1997, p.17). Besides, Winston was in another dilemma while explaining the teacher’s use of tasks to connect social justice to mathematics. Winston praised the teacher’s initiation in students’ thinking process for a social problem, whereas he questioned the appropriateness of this social problem for that age group. Therefore, his views of teaching and learning mathematics may be neutral and apolitical even though he had mentioned the constructive and student-centered methods. Overall, the participant had a limited CME view due to his experience both as a student and a teacher. Neither teaching voluntarily nor having classroom time with disadvantaged students was enough for CME awareness. Preservice teachers need to appreciate the importance of grasping the mathematics concepts in the context of socio-political and economic realities (Bartolome, 2004).

Alrø, H., & Skovsmose, O. (2004). Dialogic learning in collaborative investigation. Nordisk Matematikkdidaktikk, 9(2), 39-62. Aslan Tutak, F., Bondy, E., & Adams, T. L. (2011). Critical pedagogy for critical mathematics education. International Journal of Mathematical Education in Science and Technology, 42(1), 65-74. Bartolome, L. I. (2004). Critical pedagogy and teacher education: Radicalizing prospective teachers. Teacher education quarterly, 31(1), 97-122. Borba, M. C., & Skovsmose, O. (1997). The ideology of certainty in mathematics education. For the learning of Mathematics, 17(3), 17-23. Frankenstein, M. (1983). Critical mathematics education: An application of Paulo Freire's epistemology. Journal of Education, 315-339. Freire, P. (1971). Pedagogy of the oppressed. (M. B. Ramos, Trans.) New York: Seabury Press. Inan, H. G. (2021). Exploring Critical Mathematics Awareness of Undergraduate Voluntaries Teaching Mathematics. (Unpublished master’s thesis). Bogazici University, Istanbul, Turkey. Skovsmose, O. (1985). Mathematical education versus critical education. Educational Studies in Mathematics, 16(4), 337-354. The Learning Exchange. (n.d.-a). Teaching Mathematics Through a Social Justice Lens. Retrieved March 31, 2020, from https://thelearningexchange.ca/projects/teaching-mathematics-through-a-social-justice-lens/?pcat=999&sess=3 The Learning Exchange. (n.d.-b). About The Learning Exchange. Retrieved March 31, 2020, from https://thelearningexchange.ca/#about Zainal, Z. (2007). Case study as a research method. Jurnal kemanusiaan, 5(1).