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Practice: Graphic organizers that incorporate languaging

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Practice: Graphic organizers that incorporate languaging

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I was able to find an example of a graphic organizer that helps students break down word problems. It gives students the space to translate the information in the language of choice and to include different representations.

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Multilingual word walls also provide students with visual representations of math vocabulary and normalize having multiple languages in a class. Along with sentence frames, having a word wall can invite students to begin math discussions in the languages they prefer and create meaning.

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TPE 2: Creating and Maintaining Effective Environments for Student Learning

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TPE 2: Creating and Maintaining Effective Environments for Student Learning

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TPE 2: Creating and Maintaining Effective Environments for Student Learning also states that teachers should create positive and inclusive learning environments that promote student learning, socio-emotional growth, reflect diversity and multiple perspectives, and are culturally responsive. Incorporating translanguaging and meaningful math problems and cultural connections can build and contribute to a learning environment where all students feel comfortable sharing comprehensively and holistically.

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TPE 1: Engaging and Supporting All Students in Learning 

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TPE 1: Engaging and Supporting All Students in Learning 

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TPE 1: Engaging and Supporting All Students in Learning focuses on connecting content to student identities and experiences to create engagement and emphasizes familial and community connections as a way to support students. A core belief of translanguaging centers around how students’ language practices and cultural understandings come from what they acquire at home, in their communities, and in school and established families and communities as sources of knowledge and support (Garcia 56).

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Using sentence frames and starters can help emergent bilinguals begin to construct and translate their reasoning into English. It can be used as an invitation to all students to encage in a mathematical discussion.

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Practice: Thinking Routine-Claim, Support, Question 

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Practice: Thinking Routine-Claim, Support, Question 

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Project Zero's Thinking Routine Toolbox has thinking routines that can guide discussions in any discipline! They also have pdf of their routines in Spanish to offer some support to emergent bilinguals.

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In this excerpt from Rethinking Mathematics, a teacher uses the community issue of displacement as an anchor for mathematical discussion and exploration. This is a great example of utilizing issues that are important to your students to ground the math content.

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Article: A Discourse Primer for Science Teachers

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Article: A Discourse Primer for Science Teachers

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This article emphasizes the need for talk in a learning environment and how talk takes different forms in a science classroom.

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Article: Translanguaging as a vehicle for appropriation of Mathematical meanings

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Article: Translanguaging as a vehicle for appropriation of Mathematical meanings

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This article shows a math teacher in a dual immersion school utilize translanguaging to help students make meaning of the content they were studying.

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Article: Using what matters to students in bilingual mathematics problems (Higinio Dominguez)

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Article: Using what matters to students in bilingual mathematics problems (Higinio Dominguez)

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In this study, Dominguez argues that bilingual students are more engaged in the problem solving process if the problems reflect their values and issues they face in their everyday lives. They are also more inclined to use their different languaging practices when presented with those problems.

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Final Paper: Translanguaging in a Math Classroom

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Final Paper: Translanguaging in a Math Classroom

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Providing Opportunities for Multilingualism

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To normalize encourage emergent bilinguals to participate and make connections in their languages, you can create a cognate chart or a word wall with vocabulary in their languages.

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I have yet to read this book in its entirety but I have read excerpts. This book has some great examples of how math teachers made the content in their classroom responsive to their students. By bringing in meaningful problems, you give emergent bilinguals an opportunity to share their wealth of knowledge and language practices.

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"Who would have thought that math could be taught through such compelling social issues as racial profiling, the war in Iraq, and environmental racism? This superb book is an extraordinary collection of ideas for any teacher who wants to bring passion, engagement, and social justice to the mathematics classroom."

, Felton G. Clark Distinguished Professor of Education, Southern University, Baton Rouge and author of Multiplication Is for White People

"An invaluable resource! Rethinking Mathematics has the potential to change the basic ways we think about and teach one of the most important subjects in schools today. With clarity and insight, it shows how teachers who are dedicated to social justice can act on their commitments in a subject that has for too long been seen as simply a technical area."

- Michael W. Apple, John Bascom Professor of Curriculum and Instruction and Educational Policy Studies, University of Wisconsin-Madison

"From the songs of Sweet Honey in the Rock we know that 'We who believe in freedom cannot rest.' Now from the pages of Rethinking Mathematics we know that 'We who believe in freedom cannot rest' until we ensure that the learning and teaching of mathematics sings of social justice. We should all learn its new songs."

- Bob Moses, President and Founder of the Algebra Project

"The premise of this book is that mathematics is not just a set of rules and procedures to be memorized and regurgitated, but a relevant set of tools to make sense of the social injustice and power imbalances in our society. Mathematics teachers at any level interested in motivating their students should read this book."

- Thomas A. Romberg, Bascom Professor of Education, Professor Emeritus, University of Wisconsin-Madison

"For experienced math teachers, we always want to find ways to bring 'real-life' situations into the math class. Gutstein and Peterson make a great attempt at pulling math back from the abstract to the concrete. After reading just a few of these articles, I was already finding ways to talk about social issues without looking too contrived or off-track from my curriculum."

JosŽ Vilson, Middle school math teacher and writer

Rethinking Mathematics: Introduction to the Second Edition
Teaching Social Justice by the Numbers
By Eric (Rico) Gutstein and Bob Peterson
I thought math was just a subject they implanted on us just because they felt like it, but now I realize that you could use math to defend your rights and realize the injustices around you. [N]ow I think math is truly necessary and, I have to admit it, kinda cool. It's sort of like a pass you could use to try to make the world a better place.
- Freida, 9th grade, Chicago Public Schools
Some students would prefer to have a dentist drill their teeth than to sit through a math class. Others view math class as a necessary but evil part of getting through school. Still others enjoy playing and working with numbers and problems.

We agree with Freida. Math is often taught in ways divorced from the real world. The alternative we propose in this book is to teach math in a way that helps students more clearly understand their lives in relation to their surroundings, and to see math as a tool to help make the world more equal and just.

In a "rethought" math class, teachers make mathematics more lively, accessible, and personally meaningful for students, who in turn learn in more depth.

The articles in this book provide examples of how to weave social justice issues throughout the mathematics curriculum and how to integrate mathematics into other curricular areas. This approach seeks to deepen students' understanding of society and to prepare them to be critical, active participants in a democracy.

The elementary school, middle school, high school, and college teachers who have contributed to this book also note the many potential benefits of such a social justice approach to mathematics. Among them:

Students can recognize the power of mathematics as an essential analytical tool to understand and potentially change the world, rather than merely regarding math as a collection of disconnected rules to be rotely memorized and regurgitated.

Students can deepen their understanding of important social issues, such as racism and sexism, as well as ecology and social class.

Students can connect math with their own cultural and community histories and can appreciate the contributions that various cultures and peoples have made to mathematics.

Students can understand their own power as active citizens in building a democratic society and become equipped to play a more active role in that society.

Students can become more motivated to learn important mathematics.

These benefits come both when teachers reshape the mathematics curriculum with a social justice vision and when they integrate social justice mathematics across the curriculum into other subjects, such as social studies, science, health, reading, and writing.
An Essential Tool for Understanding and Changing the World
To have more than a surface understanding of important social and political issues, mathematics is essential. Without mathematics, it is impossible to fully understand a government budget, the impact of a war, the meaning of a national debt, or the long-term effects of a proposal such as the privatization of Social Security. 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. This issue only becomes meaningful when viewed through a mathematical lens, whether or not the "viewer" appreciates that she or he is using mathematics. 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 612 African American drivers and 423 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 1,000 people stopped randomly by the police to be black.

When teachers weave social justice into the math curriculum and promote social justice math "across the curriculum," students' understanding of important social matters deepens. 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. (See "Sweatshop Accounting," page 78, and "Sweatshop Math," page 256.)
Connecting Math with Students' Cultural and Community Histories
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. A guiding principle behind much of this work is that teachers should view students' home cultures and languages as strengths upon which to build, rather than as deficits for which to compensate. In "Race, Retrenchment, and the Reform of School Mathematics" (page 42), Tate offers the simple example of a teacher's failure to reach her students because she uses story problems that are not grounded in the students' culture; while Luis Ortiz-Franco ("Chicanos Have Math in Their Blood," page 95) encourages teachers to teach about the base 20 Mayan number system as a way to emphasize, to both Chicano students and others, that math has deep roots in indigenous cultures in the Americas. David Levine's article about the Algebra Project started by Bob Moses (see "Radical Equations," page 147) provides another example of teachers connecting with students' cultural and community histories to promote deeper student learning. Moses summarized the importance of these connections in his book on the project:

[I]n the Algebra Project we are using a version of experiential learning; it starts with where the children are, experiences that they share. 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.

Understanding Their Power as Active Citizens
Rethinking Mathematics spotlights several examples of student activism. These include 5th grade Milwaukee students writing letters to social studies textbook publishers based on their mathematical analysis of slaveholding presidents and textbooks' failure to address this issue (see "Write the Truth," page 226); New York City students who measured their school space, calculated inequities, and then spoke out against these inequities in public forums (see "'With Math, It's Like You Have More Defense,'" page 129); and students who used math to convince their school administration to stop making so many obtrusive PA announcements (see the activity "Tracking PA Announcements," page 208).
Motivated to Learn Important Math Getting Started
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. One way is to identify a concept/skill that you are teaching as part of your regular curriculum and relate it to a lesson idea in this book (or on the website for this book, www.rethinkingschools.org/math). Teach the lesson or unit and then gauge how successful it was in terms of student motivation, student understanding of the math concepts, and the deepening of the students' knowledge about the particular social issue.

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. For example, see the activity "Environmental Hazards," page 52, in which high school students investigate contamination in their own neighborhoods.

The media are also potential sources of projects, because current issues both affect students' lives and have mathematical components that teachers can develop into social justice projects. For example, see "Home Buying While Brown or Black," page 61.

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.

Occasionally, a teacher needs to defend this kind of curriculum to supervisors, colleagues, or parents. One approach is to survey your state's math standards (or the national standards) and to find references to "critical thinking" or "problem-solving" and use those to explain your curriculum. Also, the NCTM clearly states that "mathematical connections" between curriculum and students' lives are important.

But it's important for teachers to recognize that social justice math is not something to sneak into the cracks of the curriculum. It's not something about which we should feel defensive. What we're talking about here is something that helps students learn rich mathematics, motivates them, and is really what math is all about. 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.
Views on Math and Social Justice
In addition to the benefits outlined at the beginning of this introduction, an important aspect of a social justice approach to teaching math is that it must include opening up the "gates" that have historically kept students of color, women, working-class and low-income students, and students with perceived disabilities out of advanced mathematics tracks and course offerings. The Algebra Project mentioned above, for example, seeks to ensure that "gatekeeper" classes like algebra don't prevent large numbers of historically disenfranchised students from succeeding in higher education. (For information on other such projects, see Resources, page 259.)

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.
Isn't Math Teaching Neutral?
While reading these articles, some people might question whether it's appropriate to interject social or political issues into mathematics. Shouldn't math teachers and curriculum, they might say, remain "neutral?"

For example: Let's say two teachers use word problems to teach double-digit multiplication and problem-solving skills. 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. Candy bars are on sale for 43¢ each. They buy a total of 12 candy bars. How much do they spend, not including tax?

The second teacher, meanwhile, offers a very different problem:

Factory workers aged 14, 15, and 16 in Honduras make McKids children's clothing for Walmart. Each worker earns 43 cents an hour and works a 14-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.

When teachers fail to include math problems that help students confront important global issues, or when they don't bring out the underlying implications of problems like the first example here, these are political choices, whether the teachers recognize them as such or not. These choices teach students three things:

1. They suggest that politics are not relevant to everyday situations.

2. They cast mathematics as having no role in understanding social injustice and power imbalances.

3. They provide students with no experience using math to make sense of, and try to change, unjust situations.

These all contribute to disempowering students and are objectively political acts, though not necessarily conscious ones.

As high school teacher Larry Steele details in his article "Sweatshop Accounting" (page 78), the seemingly neutral high school accounting curriculum in fact approaches the world in terms of markets and profit-making opportunities. Not everything that counts gets counted, Steele says, and thus the "neutral" curriculum actually reinforces the status quo.

We believe it's time to start counting that which counts. 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.

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In this expanded and updated edition of Rethinking Mathematics, more than 50 articles show how to weave social justice issues throughout the mathematics curriculum, as well as how to integrate [...]