This post is part 2 of 3 in a series responding to three questions from some students who read my post on privilege and oppression in math ed. This post addresses the second question:
2. As educators, how might they integrate such alternative perspectives if they are often left out of major decisions like curricula?
I'll be honest, this is hard. This is also a huge question. There are a lot of different levels we (classroom teachers, administrators, policy makers, scholars and teacher educators, parents, and the general public) need to be working at. I'm going to focus the most on the classroom level because it's something teachers can do now, but I'll also touch on a couple of other levels of change that need to happen.
In the Classroom
One level we can work at, pretty immediately, is at the level of the classroom. How do we change both the mathematical content/curriculum itself and how students experience that curriculum? There are a number of approaches we can take. Dr. Rubel's article (see series opener for context) provides one excellent way of thinking about some of the different approaches. I use a similar, but slightly different organization here.
All of the approaches I discuss below are good for all students, but they are especially important for minoritized students who are less likely to find themselves valued by our educational system.
Making Math Understandable: Student-Centered Math Teaching
My blog series What Do You Think? focuses on child-centered approaches to mathematics. In short this involves posing real problems to students (things you have not already told them how to do), asking them to develop their own strategies (with guidance and support as needed), having discussions about these strategies, and making connections across different strategies. There is a large body of research supporting this approach to teaching mathematics and it is endorsed by all major math ed professional organizations. It also informs the Common Core standards (although perhaps not as strongly as some might like).
This approach to teaching math makes it more accessible to more students because it allows for more diverse ways of thinking about mathematics.
This approach does not really change the focus of the curriculum. You still want kids to understand fractions and know how to add and subtract with them, you just teach this content to them in a way that fosters deeper and more flexible understanding.
Expanding Access: Complex Instruction
Child-centered teaching makes math more accessible and understandable. Moreover, standards from major organizations like the National Council of Teachers of Mathematics (NCTM) include explicit attention to ensuring that all students have access to the curriculum. However, just engaging in student-centered math teaching does not generally include an explicit, conscientious focus on providing access for all students (for example, if you read many articles in the vein of student-centered teaching, there will be little explicit discussion of concrete strategies for increasing access to all students).
Complex Instruction (see here for a brief overview) fills this gap (Smarter Together!, Strength in Numbers, Designing Groupwork). It looks at a variety of instructional techniques that build on student-centered teaching, but also include an explicit, ongoing, conscientious focus on making sure that all students are challenged, engaged, and valued in the (math) classroom.
Like student-centered teaching, Complex Instruction does not really change the focus of the curriculum. You still want kids to understand fractions, you just teach it in a way that (a) fosters deeper and more flexible understanding, and (b) increases the likelihood that all students develop this understanding.
Bringing in Students' Lives: Funds of Knowledge
Dr. Rubel talks about Culturally Relevant Pedagogy in her article, and that could fit here as well, but in my own work I tend to focus more on a body of work called Funds of Knowledge. This is all about getting to know and your students, their families, and the community. You do this in order to identify the strengths and assets (or funds of knowledge) that your students bring to the classroom. The original work involved teachers essentially taking on the roles of anthropologists to learn about their students, which may go beyond what is realistic for everyday teachers not working with a university team. However, the general principles can be adapted to any classroom. I often have my future teachers interview their students; others have their future teachers complete a community walk. Many schools use home visits to reach out to and learn about their students and their lives.
This approach does involve changing the curriculum. A genuine funds of knowledge approach would often involve curricular units and investigations into topics that come from students' lives. Students might connect with local businesses and solve a problem they have or a parent with expertise in gardening might visit as part of a broader gardening unit that connects to mathematical concepts like area and perimeter.
Doing this work is hard. It takes time getting to know families and students (although if we can support educators so they feel valued and don't burn out, then they can stay in schools and develop relationships with communities over longer periods of time). It also involves being able to think flexibly about mathematics. What does it mean to design a math unit around gardening or local businesses? What does it look like to investigate the mathematics of games and sports that children play? If students enjoy nature, what does a mathematically rigorous investigation of deer populations look like?
These are non-trivial questions, and to be frank we don't know a lot about the knowledge it takes to plan these kinds of lessons. One productive area of expertise is supporting teachers in learning to teach mathematical modeling (although this is also an area in need of more research). As we develop stronger collections of examples of these types of lessons teachers can (in some cases) modify them for their own use.
Greater Diversity of Contributions: Multicultural Math
While Funds of Knowledge is about connecting math to students' lives, we can also highlight the contributions of all peoples to mathematics around the world and throughout history. While I'm sure there are curricula out there that do this better than others, it's not a topic I'm as fluent in. The Crest of the Peacock offers a non-European perspective on the history of mathematics and work on ethnomathematics does as well (for example). There are also more teacher-oriented books, like Africa Counts and other books by Claudia Zaslavsky, and Math is a Verb. There are also examples of schools that take an Afrocentric approach to their curriculum.
In my opinion this approach sort of changes the content. It depends some on how far you take it. If you still teach the Pythagorean Theorem but provide more information about the history of it, then that doesn't really change the content. If you explore aspects of mathematics, like the symmetries involved in Islamic Geometric Patterns, which are not traditionally in the high school curriculum, then it might involve a more fundamental change.
Teaching Math for Social Justice
Finally, we might use mathematics to explore, analyze, and try to address social and political issues and injustices. This is one of the main areas I focus on. Mathematics is one valuable lens for exploring things like income inequality, racial disparities in arrests and prison sentences, rates of pollution, the racialized and class-based differences in who bears the brunt of environmental damage, segregation in schools, etc.
There are some resources available for integrating real-world topics into the math curriculum. These have the benefit of engaging students with topics that may matter more to them, but they may not apply to the lives of your students: Rethinking Mathematics, Math that Matters, and Reflecting the World are three examples.
This approach does change the content. While you would still include plenty of student-centered math and you'd still want your kids to learn about fractions and algebra and all the other typical school-math content, you'd also be using math to explicitly investigate social and political issues. The real world would be particularly real in these classrooms because you'd have to take the context seriously (at least when doing lessons investigating social issues). Here math is one tool for questioning our world, wondering why it is the way it is (especially in cases of unfairness), and imagining how we could change things for the better.
As with the funds of knowledge approach, this is challenging work and ripe with tensions between focusing on "the math" and "the context." Also similarly, there are more and more examples being generated that teachers may be able to adapt to their classroom and mathematical modeling is one productive avenue for approaching these topics.
Beyond the Classroom
Everything I said above is great and these are all things I advocate for classroom teachers to do, but they're also notoriously difficult. The field of mathematics education, including the largest professional organization, has been pushing for student-centered teaching (the first thing on my list) for decades and by many measures has not made a lot of progress (teaching is a huge field and for a variety of reasons, including the way education policy is set and shifts in the U.S. it has been quite difficult to consistently change practice on a wide scale).
Add to that the complexity of integrating complex instruction, diverse perspectives, students' funds of knowledge, and social issues and it's a significant challenge for teachers when math curricula and standards and state tests (which are perhaps more important in terms of the pressures on teachers) are generally not organized around these ideas.
So there also needs to be work to push for inclusion (real, genuine inclusion) of these ideas in both standards and state tests (also the role of testing in our educational system needs to be dramatically reimagined and reduced). While I don't think this is very likely, one potential area to push is on mathematical modeling. It is already included as a standard in the Common Core and it is widely used in a number of math-related disciplines, including the natural and social sciences. However, its treatment on both tests and in most classrooms is often anemic at best.
We also need to be communicating with parents and the general public about how math could be so much more than the mindless computations many of them experienced as children.
Finally, I would also advocate for working to diversify the teaching force. What are we doing to make teaching an attractive and accessible career for all peoples? The more diverse the profession the more likely you are to have new ideas and innovations because different experiences might provide different ways of looking at educational issues. It is also important for young people to see a variety of teachers who are similar to and different from them in a variety of ways.
Previous in series: Missing Content
Next in series: Reverse Racism
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