The same is true with other social, ecological, and cultural issues: You need mathematics to have a deep grasp of the influence of advertising on children; the level of pollutants in the water, air, and soil; and the dangers of the chemicals in the food we eat. Math helps students understand these issues, to see them in ways that are impossible without math; for example, by visually displaying data in graphs that otherwise might be incomprehensible or seemingly meaningless.
As an example, consider racial profiling. That is, it is difficult to declare that racial profiling occurs unless there is a sufficiently large data set and a way to examine that data. If, for example, 30 percent of drivers in a given area are African Americans, and the police stop six African American drivers and four white drivers, there is weak evidence that racial profiling exists.
But if police stop African American drivers and whites, then there is a much stronger case. The explanation lies in mathematics: In an area where only 30 percent of the drivers are black, it is virtually impossible for almost 60 percent of more than 1, people stopped randomly by the police to be black. The underlying mathematical ideas — dis proportionality, probability, randomness, sample size, and the law of large numbers that over a sufficiently large data set, the results of a probability simulation or of real-world experiences should approximate the theoretical probabilities — all become part of the context that students must understand to really see, and in turn demonstrate, that something is amiss.
Thus with a large data set, one can assert that a real problem exists and further investigate racial profiling. When teachers use data on sweatshop wages to teach accounting to high school students or multi-digit multiplication to upper-elementary students, students can learn math, but they can also learn something about the lives of people in various parts of the world and the relationship between the things we consume and their living conditions.
Moreover, to understand some issues, students need to combine math with other subjects. The unemployment rate changes depending on these decisions. Thus math needs social studies, and social studies needs math. Rethinking math also means using culturally relevant practices that build on the knowledge and experiences of students and their communities. Many of these approaches have been developed by teachers and then described and theorized by researchers of color, such as Gloria Ladson-Billings and William Tate.
Moses summarized the importance of these connections in his book on the project:. We get them to reflect on these, drawing on their common culture, then to form abstract conceptualizations out of their reflection, and then to apply the abstraction back on their experience.
You can think of it as a circle or clock: At 12 noon students have an experience; at a quarter past they are thinking about it; at half past they are doing some conceptual work around their reflections; and at a quarter to they are doing applications based on their conceptual work.
In the Algebra Project this movement from experience to abstraction takes the form of a five-step process that introduces students to the idea that many important concepts of elementary algebra may be accessed through ordinary experiences.
Each step is designed to help students bridge the transition from real life to mathematical language and operations. Because of this connection with real life, the transition curriculum is not only experiential; it is also culturally based.
The experiences must be meaningful in terms of the daily life and culture of the students. One key pedagogical problem addressed by the curriculum is that of providing an environment where students can explore these ideas and effectively move toward their standard expression in school mathematics. As students develop deeper understandings of social and ecological problems that we face, they also often recognize the importance of acting on their beliefs.
Rethinking Mathematics spotlights several examples of student activism. Once they are engaged in a project, like finding the concentration of liquor stores in their neighborhood and comparing it to the concentration of liquor stores in a different community, they recognize the necessity and value of understanding concepts of area, density, and ratio.
These topics are often approached abstractly or, at best, in relation to trivial subjects. Social justice math implicitly tells students: These skills help you understand your own lives — and the broader world — more clearly. Teachers and preservice teachers sometimes ask: How do I get started integrating social justice concepts in my math class? Our best advice is to take a little at a time. Another way is to get to know your students and their communities well and listen closely to the issues they bring up.
Many of our own social justice projects started from conversations with students about their lives or from knowing about issues in their communities. Certainly working in a school that has a conceptually strong foundational mathematics curriculum is helpful. Teachers cannot easily do social justice mathematics teaching when using a rote, procedure-oriented mathematics curriculum. Likewise a text-driven, teacher-centered approach does not foster the kind of questioning and reflection that should take place in all classrooms, including those where math is studied.
By saying this, we do not wish to imply that if teachers use a conceptually based curriculum that embraces the standards put forth by the National Council of Teachers of Mathematics NCTM — such as Investigations in the elementary grades, Mathematics in Context or Connected Mathematics Project for the middle grades, and Interactive Mathematics Program in high school — such a curriculum will automatically guide students towards a social justice orientation.
In fact, these programs have an unfortunate scarcity of social justice connections. But a strong, conceptually based foundational curriculum can be a great asset to social justice math teaching, because it can encourage students to critique answers, question assumptions, and justify reasoning. These are all important dispositions toward knowledge that teachers can integrate into their social justice pedagogy. Occasionally, a teacher needs to defend this kind of curriculum to supervisors, colleagues, or parents.
A social justice approach to math is the appropriate type of math for these unjust times. Other, traditional forms of math are often too abstract, promote student failure and self-doubt, and, frankly, are immoral in a world as unjust as ours. Traditional math is bad for students and bad for society. The two of us have been teaching math for a combined total of more than 50 years — one of us in a bilingual 5th-grade classroom in a public elementary school and the other in inner-city public middle and high schools, in alternative high schools, and at the college level.
Our perspectives on teaching math for social justice have been shaped by our own involvement in movements for social justice during the past four decades — the Civil Rights Movement, anti-war movements, educational justice movements, and other campaigns. For information on other such projects, see Resources, page Those who wrote for this book, and those who write for the magazine Rethinking Schools, are always encouraged not only to explain what they teach and why they try certain things, but to reflect on how they would do things differently next time.
In that spirit we recognize that, as white male educators, our experiences have their own limitations and, if we were to do this book over, we would work harder to increase the representation of authors of color. We encourage all educators who teach math, particularly educators of color, to write about their experiences teaching math for social justice and to consider submitting articles for possible publication in Rethinking Schools.
Simply put, teaching math in a neutral manner is not possible. They each present a problem to their students. The first teacher presents this one:. A group of youth aged 14, 15, and 16 go to the store. They buy a total of 12 candy bars. How much do they spend, not including tax? Each worker earns 43 cents an hour and works a hour shift each day. How much does each worker make in one day, excluding any fees deducted by employers?
While both problems are valid examples of applying multi-digit multiplication, each has more to say as well. The first example has a subtext of consumerism and unhealthy eating habits; the second has an explicit text of global awareness and empathy. Both are political, in that each highlights important social relations. These choices teach students three things:. These all contribute to disempowering students and are objectively political acts, though not necessarily conscious ones.
To paraphrase Freida, the 9th grader quoted above, we need to encourage students to defend their rights and to recognize the injustices around them. By counting, analyzing, and acting, we will help students and ourselves better read the world and remake it into a more just place. Updated spending estimates, budget numbers and other resources mentioned in the article.
Page Is Environmental Racism Real? By Larry Miller Additional resources and details of how a class took action based on the lesson. Yes, We Can! For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study.
In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry. Book Reg. Product Description Product Details Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry.
Reprint of the Addison-Wesley Publishing Co. Differential Geometry. Differential Topology: An Introduction. Geometry and Light: The Science of Invisibility.
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