Summary
Raygoza, M. C. (2016). Counting the experiences and beliefs of secondary teachers striving to teach mathematics for social justice in urban schools. Urban Education. http://doi.org/10.1177/0042085916672289
This is a timely piece that adds secondary teachers' voices and experiences to the research literature about teaching mathematics for social justice (TMfSJ). While there are a few other studies focusing on practicing teachers' experiences with TMfSJ, we need more and this is a welcome contribution.
Raygoza is "a former teacher who taught mathematics in an urban school and connected mathematics to social (in)justice issues" (p. 11). She interviewed 15 secondary teachers who "self-identified as striving to teach mathematics about, with, and for social justice (Wager, 2008)" (p. 7).
She had three research questions:
What are the commitments of teachers striving to teach mathematics for social justice in urban schools?
What do they experience as the greatest challenges in their work?
What do they envision (and fight for) for the future of urban mathematics education?
She identifies five commitments the teachers had: (a) empowering urban youth as math students and social change agents, (b) teaching mathematics conceptually with relevance to students' lives, (c) building mathematically rigorous social justice lessons over time through critical praxis, (d) developing an interdisciplinary approach to teaching, and (e) learning from and building with others in solidarity.
Raygoza also identifies three barriers to TMfSJ: (a) high-stakes reform: increasing testing, decreasing teaching and curricular autonomy; (b) a lack of curricular examples, resources, and time; and (c) beyond mathematics, beyond education: poverty, racism, and intersectional systemic inequity affecting urban youth.
Standardized Tests, Math for Understanding, and Social Justice Math
No teacher argued that addressing social justice issues in mathematics is incompatible with preparing students to learn about mathematics tested on high-stakes exams, but they brought up how the exams often do not capture students' mathematical thinking. (pp. 18-19)
This quote raises an issue that I think is in need of greater research and attention and goes beyond TMfSJ to include mathematical modeling and the use of real-world contexts more generally. To think about this, first consider the type of learning goals we may have (and potentially try to assess--although I think formal, standardized assessment needs to play a much smaller role in education):
Rote math: We may want students to memorize certain facts (e.g., times table) and carry out particular algorithms correctly (e.g., adding two numbers using the "carry the ten" algorithm).
Math with Understanding (MwU): We may want students to be able to adapt flexibly to unfamiliar problems and to select or invent strategies to problems as needed.
Practices & Processes (PPs): Somewhat related to MwU, we may want students to be able to engage in problem solving, to justify or prove their answer, and to be able to communicate their thinking (these ideas are embodied rather anemically by the Common Core's eight Standards for Mathematical Practice (SMPs), and much more richly by the five practice standards in NCTM's 2010 Principles and Standards)
Mathematical Modeling (MM): Mathematical modeling usually falls under the PPs (it's SMP4 and it is addressed under the connections standard in the Principles and Standards). However, I think there is potentially a qualitative difference between engaging in mathematical modeling and many of the other PPs, so I pull it out here. I see the other PPs as attending primarily to mathematical objects and the relationships between them (do we know why an algorithm works mathematically?). While work with the MwU and the PPs may begin with real-world contexts, it is generally in service of constructing and understanding mathematical objects (see below). In contrast, MM involves an active, consistent, and intentional focus on the real world and the complexities and details of that world.
Critical Analysis (CA): We may want students to question and critique their world using mathematics.
Next let's consider some ways we might teach:
Traditional/teacher-centered: Teacher or text demonstrates a method with sample problems, students practice. Generally, the implicit goal is to transmit information from the teacher/text to the student with as few errors as possible.
Teaching Math for Understanding/student-centered (TMfU): I would classify much of the reform efforts (and accompanying research) stemming out of NCTM's 1989 and 2010 standards as falling into this category. This generally involves using what I call stepping-stone problems, in which simple, imaginable contexts are used without telling children a specific method for how to solve the problem (e.g., "4 people fairly share 6 equal-sized blocks of clay. How much clay does each person get?" as a means of introducing fractions). While there is a "real-world" context involved it is not the primary focus. The context (and students' informal understanding of it) serves simply as a stepping-stone for constructing mathematical objects and unpacking the relationships between them. These problems (or at least types of problems) are generally carefully selected based on research about how (a) how children are likely to make sense of the context, and (b) children's conceptions of important mathematical concepts (such as fractions, rates, place-value, etc.) develop.
Simplified Applications (SA): After students learn math (either traditionally or with understanding) they apply them to relatively routine "real-world" contexts in predictable and formulaic ways.
Teaching with Mathematical Modeling (TwMM): Spending some instructional time engaging students in mathematical modeling, which involves messy real-world contexts where a significant aspect of the work involves (a) making decisions about how to interpret and make sense of the context, and (b) deciding how it can be analyzed/solved mathematically.
Teaching Math for Social Justice (TMfSJ): In some cases this is just a unique case of TwMM where the context involves a social or political issue, controversy, or injustice. In other cases it might be a unique case of using simplified applications where students apply previously-learned math to a context as fed to them by a teacher (I don't expect many would advocate for this form of TMfSJ, but I do think it ends up occurring in practice in some cases). In other cases, there might be an attempt to blend TMfU with a substantive real-world context. I think this often leads to conflicting foci. In TMfU there is often an intentional goal of moving away from the real-world context to construct "abstract" mathematical objects, whereas in TwMM and social justice more generally, there is an intentional focus on the context as an object of study and investigation in its own right (see Felton-Koestler, 2015; Gutstein, 2006).
What are the various relationships between these kinds of teaching (these different genres of mathematics) and the possible learning goals above? I have no problem telling my prospective teachers that:
We know that TMfU will lead to stronger outcomes on PPs and MwU and about equal outcomes on rote math.
We have good evidence that kids will be bad at (and in fact likely get worse at) MM if we don't teach it (TwMM).
I'm pretty confident that (although I don't know a study on this) kids won't learn CA if we don't engage them in it (TMfSJ).
Beyond that, though, I don't know what to tell them:
How does TwMM affect MwU or just rote math for that matter (since that is emphasized on some assessments)?
How do the various forms of TMfSJ affect rote math, MwU, and PPs?
I don't have clear answers to these questions and I think they need attention. It seems possible to me that there may very well be trade-offs among theses different forms of teaching that don't exist with traditional vs. TMfU because their foci can be so different. I personally think that if there are trade-offs they are likely worth it, but it would be good to have a sense of what they are.
Lack of Curricular Examples
Obviously, this is one thing I hope to help address with this website (although my focus is more on K-8). As time goes I hope we can develop a growing body of resources teachers can draw on. The teachers in the article emphasized they are not necessarily looking for ready-made lessons, but ideas they can build from. They also discussed the intense work involved in researching and creating one's own lessons.
This is another understudied area in my opinion: what knowledge and resources do teachers need if they are going to engage in TMfSJ? What is the mathematical knowledge involved in piecing together these lessons, either when starting with something or when building from scratch? What is the real-world knowledge about the topic? How do the two interact? In what way does a general critical perspective inform the design of these tasks?
Talking about Sex and Gender
One last thought. Following Wood (2016), I would like to push Raygoza (and all of us) on the language she uses related to "sex" and "gender." She conflates them in a couple of places and uses terms like "male" and "female" for gender. Wood suggests reserving these terms (along with "intersex") for sex and terms like "man", "woman", "genderqueer", etc. for gender. Of course, research participants may not always use those terms when self-identifying, so another option would be to include a footnote indicating that the author does see a difference between sex and gender, but that these were the terms the participants used when asked to identify their gender.
References
Felton-Koestler, M. D. (2015). Mathematics education as sociopolitical: prospective teachers’ views of the What, Who, and How. Journal of Mathematics Teacher Education. http://doi.org/10.1007/s10857-015-9315-x
Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. New York: Routledge.
Wood, M. B. (2016). Gender ≠sex ≠sexual orientation: A commentary on Gomez and Siy’s case. In Cases for mathematics teacher educators: Facilitating conversations about inequities in mathematics classrooms (pp. 107–111).