I recently read a proposal for an innovative school and it set me thinking about math. It wasn’t the proposal’s numbers that got my mind going, but rather the approach to structuring math into the curriculum. I disagreed with it.
The plan called for the curriculum to be divided into three areas — math/science, the arts (including fine arts and language arts), and history/philosophy. Blocks of time were set aside for a unified approach in each area. As I mulled over the proposal and thought of my experience in a self-contained fifth-grade classroom, I realized I was uneasy with the proposed curricular divisions, specifically the assumption that science and math belong together as an unified block. It reminded me of how some elementary teachers integrate the curriculum by lumping language arts and social studies together in one strand, and math and science in another.
It also raised several questions for me. Why place math and science together, and not math and social studies? What are the political and pedagogical assumptions behind such an approach? Why shouldn’t reformers advocate math in all subject areas? Why not have “math across the curriculum,” comparable to “writing across the curriculum?”
One reason reformers have advocated changes in how math is structured is because of the historic problems with math instruction itself: rote calculations, drill and practice ad nauseum, endless reams of worksheets, and a fetish for “the right answer.” These have contributed to “number numbness” among students, and ultimately among the general population when students become adults.
But the problem is deeper than a sterile teacher-centered and text-driven approach. “Number numbness” also has its roots in how math is segregated in schools and kept separate from the issues that confront students in their daily lives. Most students don’t want to do abstract exercises with numbers or plod through text-based story problems that have them forever making change in some make-believe store. The curriculum rarely encourages students to link math and history, math and politics, math and literature — math and people.
There are unfortunate consequences when math is isolated. First, the not-sosubtle message is that math is basically irrelevant except for success in future math classes, or if you want to be a scientist or mathematician. Second, students learn that math is not connected to social reality in any substantive way. Thus students approach math in the abstract and never are encouraged to seriously consider the social and ethical consequences of how math is sometimes used in this society. Third, if students are not taught how math can be applied in their lives, they are robbed of an important tool to help them fully participate in society. An understanding of math and how numbers and statistics can be interpreted is essential to effectively enter most debates on public issues such as welfare, unemployment, and the federal budget. For example, even though the minimum wage is higher than it has ever been, in constant dollars it is the lowest in 40 years. But you need math to understand that.
When I first began teaching 15 years ago, I was dissatisfied with “number numbness,” but wasn’t sure what to do about it. My growth as a teacher first came in the area of language arts and reading. I increasingly stressed that students should write for meaningful purposes, and read books and stories that were connected to their lives. Thus I had children read and discuss whole books, conducted writing workshops, and had students read and write in science and social studies. My math, however, remained noticeably segregated from the rest of the curriculum, even though I increasingly emphasized problem solving and the use of manipulatives.
More recently, with the help of my teacher colleague Celín Arce and publications from the National Council of Teachers of Mathematics, I have begun to view math as akin to language. I believe that math, like language, is both a discipline unto itself and a tool to understand and interact with the world and other academic disciplines. Just as written and oral language helps children understand their community, so can written and oral mathematics. Just as teachers stress the need for “writing across the curriculum,” I believe it is important to advocate “math across the curriculum.” Just as students are expected to write for meaningful purposes, they should do math for meaningful purposes.
Plans to integrate math into science are a step in the right direction. And assuming that the science curriculum is “meaningful,” the teaching of mathematics will improve. But I believe linking math with science is only a beginning, and should be followed with integration of math across the curriculum. I have found that my fifth graders, for instance, are particularly interested in social issues. Thus integrating math with social studies is an effective way to bring math alive for the students. (Before I go any further, I want to make two important clarifications. First, I don’t mean to imply that distinct math “mini-lessons” aren’t important. They are, just as such lessons are necessary in reading and writing. I also want to make clear that integrating math with social studies does not necessarily make the teaching more student-centered or the content more concerned with issues of social justice. Those important components depend on the teacher’s philosophical and pedagogical beliefs.)
In the past few years I have tried in a variety of ways to integrate mathematics — from the simplest understanding of number concepts to more complex problem solving — with social studies. In the interests of clarity (my classroom life is never so neatly ordered), I outline these approaches as: Connecting Math to Students’ Lives; Linking Math and Issues of Equality; Using Math to Uncover Stereotypes; Using Math to Understand History.
CONNECTING TO STUDENTS
The starting point of many teachers is to build on what students bring into the classroom, and to connect curriculum to the students’ lives. Math is a great way to do this. I usually start the year with kids exploring, in small groups, how math is used in their homes and communities. They scour newspapers for numbers, cut them out, put them on poster paper and try to give sense to their meanings, which at times is difficult. They interview family members about how they use math and write up their discoveries. As part of a beginning-of-the-year autobiography, they write an essay “numeric me” tying in all the numbers that connect to their lives, from height and weight, to number of brothers and sisters, to addresses, phone numbers, and so forth. I also ask them to write a history of their experiences in math classes, what they think about math, and why.
This process starts a year-long conversation on what we mean by mathematics and why it is important in our lives. As the class increasingly becomes sensitive to the use of numbers and math in news articles, literature, and in everyday events, our discussions help them realize that math is more than computation and definitions, but includes a range of concepts and topics — from geometry and measurements to ratios, percentages, and probability.
As part of the autobiography project we also do a timeline. We start by putting the students’ birthdates and that of their parents and grandparents on a class timeline that circles the outer perimeter of my classroom (and which is used throughout the year to integrate dates that we come across in all subject areas). The students also make their own time lines — first of a typical day and then of their life. In these activities, students use reasoning skills to figure out relations between numbers, distance, time, fractions and decimals.
I also use another beginning-of-the-year activity that not only builds math skills but fosters community and friendship. The whole class discusses what a survey or poll is and brainstorms questions that they would like to ask each other. After I model one survey, each student surveys their classmates about a different topic. Kids, for example, have surveyed classmates on their national origin, their favorite fast food restaurant, music group, or football team, or what they think of our school’s peer mediation program. Each student tabulates his or her survey data, makes a bar graph displaying the results, and reflects on what they have learned in writing. Later in the year they convert the data into fractions and percentages and make circle graphs. I encourage the students to draw conclusions from their data, and hypothesize why the results are the way they are. They then present these conclusions orally and in writing.
This activity is particularly popular with my students, and often they will want to do more extensive surveys with broader groups of people. The activity lays the basis for more in-depth study of polling and statistics around issues such as sampling, randomness, bias, and error. For extensive curricular ideas on the use of polls and statistics in social studies, see The Power of Numbers curriculum published by the Educators for Social Responsibility.
MATH AND INEQUALITY
To help my students understand that mathematics is a powerful and useful tool, I flood my classroom with examples of how math is used in major controversies in their community and in society at large. I also integrate math with social studies lessons to show how math can help one better understand our society’s inequalities. Kids are inherently interested in what is “fair,” and using math to explore what is and isn’t “fair” is a great way to get kids interested in all types of math concepts, from computation, to fractions, percentage, ratios, averages, and graphing.
For example, during October and November, there is often lots of discussion of poverty and hunger in my classroom, related either to the UNICEF activities around Halloween or issues raised by the Thanksgiving holiday. This is a good time to use classroom simulation exercises to help the children understand the disparity of wealth in the United States and around the world. In one lesson (explained in detail in “World Poverty and World Resources” in Rethinking Our Classrooms) I provide information on the distribution of population and wealth in the six continents, and then have the children represent that information using different sets of color chips. After working with the students so they understand the data, we do a class simulation using a map of the world that is painted onto our playground. Instead of chips to represent data we use the children themselves, and I tell them to divide themselves around the playground map in order to represent the world’s population distribution. I then use chocolate chip cookies, instead of chips, to represent the distribution of wealth, and hand out chocolate chip cookies accordingly. As you can imagine, some kids get far more chocolate chip cookies than others, and lively discussions ensue. Afterwards, we discuss the simulation and write about the activity.
Not only does such a lesson connect math to human beings and social reality, it does so in a way that goes beyond paper and pencil exercises; it truly brings math alive. I could just tell my students about the world’s unequal distribution of wealth. But that wouldn’t have the same emotional impact as when they see classmates in the North American and European sections of the map get so many more cookies even though they have so many fewer people.
I also use resources such as news articles on various social issues to help the students analyze inequality. The students, again in small groups, study data such as unemployment or job trends, convert the data into percentages, make comparisons, draw conclusions, and make graphs. This is a great way to help students understand the power of percentages. Because they also use a computerized graph-making program, they realize how the computer can be a powerful tool.
One group, for example, looked at news stories summarizing a university report on the 10,000 new jobs created in downtown Milwaukee due to commercial development. According to the report, African Americans held fewer than 8% of the new jobs, even though they live in close proximity to downtown and account for 30% of the city’s population. In terms of the higher-paying managerial jobs, Latinos and African Americans combined held only 1%, while white residents who are overwhelmingly from the suburbs took almost 80% of the new managerial jobs. Using this data, my students made bar graphs and pie graphs of the racial breakdown of people in different jobs and in the city population. They compared the graphs and drew conclusions. They then did a role play with some students pretending to be representatives of community organizations trying to convince the mayor and major corporations to change their hiring practices. What began as a math lesson quickly turned into a heated discussion of social policy. At one point, for example, a student argued that the new jobs should be split 1/3 Black, 1/3 Latino and 1/3 white, because those are the three principal nationality groups in Milwaukee. Others disagreed. Needless to say, this led to an extensive discussion of what is “fair,” of reasons why minorities had so few of the jobs created downtown, and what it would take for things to be different.
MATH, STEREOTYPES, AND VOICE
It is important for students to be aware of whose voice they are hearing as they read history books or the newspaper, or watch a movie. Who gets to narrate history matters greatly, because it fundamentally shapes the readers’ or viewers’ perspective. We can analyze these things with kids and help them become more critical readers of the books and other media. In this process math plays an important role.
I usually start with something fairly easy. I have my students analyze children’s books on Columbus, tabulating whose views are represented. For instance, how many times do Columbus and his men present their perspective, versus the number of times the views of the Taíno Indians are presented. The students, using fractions and percentages, make large graphs to demonstrate their findings and draw potential conclusions. Large visual displays — bar graphs made with sticky tape, for instance — are good points of reference to discuss and analyze. Math concepts of percentages, proportions, and comparisons can be used to help kids discuss the statistics they’ve uncovered and the graphs they’ve made.
A similar tabulation and use of percentages can be used to analyze popular TV shows for the number of“put downs” versus “put ups,” who is quoted or pictured in newspapers, stereotypes of females in popular cartoons, who is included in textbooks, and who is represented in the biography section of the school library. (See “Math and Media” in Rethinking Our Classrooms: Teaching for Equity and Justice, 1994.)
NUMBERS AND HISTORY
As we study history in my classroom, we pay particular attention to dates and data. I try to highlight those numbers that relate to social movements for equity and justice. For example, as we look at women’s struggle for equality we try to imagine what it was like for Susan B. Anthony to go to work as a teacher and get paid $2.50 a week, exactly half the salary of the previous male teacher. Lots can be done with such a statistic — from figuring out and graphing the difference on an annual or lifetime basis, to looking for wage differentials in other occupations and time periods, including the present. I have found children particularly interested in looking at the wages paid to child workers — whether it be in coal mines or textile mills. We compare such wages to the price of commodities at the time, to the wages of adult workers, and to the wealth that was accumulated by the owners of industry. Such historical connections can be easily linked to present-day concerns over U.S. child labor and minimum wage laws or to international concerns over multinational corporations exploiting child labor in Asia to make consumer goods for their worldwide markets.
One math/history connection that can range in sophistication depending on the level of the students is to look at who is represented in different occupations and areas of power in our society, and how that has changed over time. For example, students can figure out what percentage of the signers of the Constitution were slave holders, common working people, women, wealthy businessmen who held bonds, and so forth. A similar exercise would be to analyze U.S. Presidents, or the people our country has chosen to honor by putting their faces on currency and coins. Such historical number-crunching can take a contemporary turn if you have students analyze the gender and racial breakdown of the U.S. House and Senate, the editors of major newspapers, or the CEOs of the Fortune 500.
It’s important for students to understand that such numbers are not permanent fixtures of our social structure, but have changed as result of social movements such as the Civil Rights or women’s movements. To demonstrate this, a teacher might have students tally the current percentage of African Americans or women in selected professional occupations and compare it to the 1960s, before the rise of affirmative action.
Another area is to teach the history of math, pointing out the contributions of various non-European cultures and civilizations to mathematical thought. Greek mathematicians, for instance, were heavily influenced by their predecessors and counterparts in Africa and Asia. Arab mathematicians inspired European Renaissance scholars. The Mayans were one of the first peoples to develop the concept of zero and make sophisticated mathematical calculations. I have used a unit on the Mayan counting system of a base 20 with my 5th graders to demonstrate such sophistication and to help students expand their understanding of place value.
The level of sophistication and complexity of the math we use in our classrooms naturally depends on the developmental level of our students. Teachers, however, too often underestimate what students are capable of doing. To the degree that I am able to provide quality instruction, clear modeling, and activities that are purposeful, I am usually pleased with the enthusiasm with which my kids take on such math-based projects and the success they have in doing them.
I have found that as a result of trying to implement “math across the curriculum” — and in particular, integrating math and social studies — my students’ interest and skill in math have increased, in terms both of their understanding of basic concepts and of their ability to solve problems. Furthermore, they can better clarify social issues, understand the structures of society, and offer options for better social policies.
Kids need every tool they can get to make this world — their world — a better place. Mathematics is one such important tool.
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