Most real-world interactions with mathematics involve reading. Tax preparation instructions, college financial aid, health insurance policies, car loans, and mortgage documents are just a few of the complex texts containing technical vocabulary and content that students could encounter after high school. (Some students may even be helping family members with these types of texts, now.) Our students therefore need to learn how to decode mathematical language. To enable this learning, students should be exposed to a wide variety of reading materials in math classrooms.
Three Types of Math Texts
Two obvious choices for math-laden reading are textbooks and popular books about mathematics. Learning math from a textbook is a daunting task, yet it's a skill that students will need both in college and in the workplace. One way to build this capability is by having students read explanations of a particular concept from several different textbooks and then discuss the merits of each explanation. On the "reading for pleasure" front, encourage students to read books such as Alex's Adventures in Numberland by Alex Bellos or Damned Lies and Statistics by Joel Best, or steer them toward articles on websites like sport.maths.org that discuss the connections between math and athletics.
A third category of reading material includes articles and technical documents supported by mathematical concepts. This type of reading allows students to evaluate both mathematical and rhetorical arguments. Here are a few examples:
- Students read credit card offers or payday loan details, analyze the text and the math, and decide if the advertising is deceptive.
- Students read articles or book chapters (including, possibly, excerpts from local building codes) about designing roofs. They use the garnered information to design a roof and possibly build a scale model.
- Students find blog entries about American football's quarterback rating formula (or any other rating formula), debate the formula's merits, and create their own formula for a metric of interest.
- Students begin a problem-based learning (PBL) unit by reading a project brief created by the teacher or the students themselves. For example, perhaps a fictional neighborhood is asking the local airport to change flight paths to reduce noise. The brief includes opinion statements from stakeholders and technical details about noise analysis and airplane descent paths.
Forms of Writing in Math
Writing in math class also offers many benefits: students are pushed towards metacognition and can engage their passions and opinions; while teachers can uncover mathematical misconceptions and get to know their students better. Here are some types of math writing that students can do.
Describing their work on a particular problem
It's surprisingly difficult to put mathematical thought processes into words. It requires metacognitive thinking as students consider, "Why did I choose to do this step?" "What was my overall strategy?" From the teacher's point of view, words can reveal more of a student's internal mathematical world than symbols alone. Students may be able to flawlessly execute a procedure but have minor (or serious) misconceptions about what they're doing, or they may have interesting, alternative ways of thinking about a concept that can benefit the whole class.
Explaining a mathematical concept
The process of explaining a concept to a real or fictional "other" allows for information synthesis and solidification and uncovers gaps in understanding. Possible prompts to achieve this type of writing in math class include "Explain to your younger sibling who hasn't taken Geometry how to …" or "Create a study guide for next year's students on …" or "Explain what is most important to know about …" Students can discuss how different audiences require different writing styles. Mathematical vocabulary, sentence structure, and level of detail will all vary based on the age and background of the audience.
Writing definitions of mathematical terms
Creating a mathematical definition is a strenuous exercise in precise writing. Even simple words like circle and rectangle can be challenging to define precisely. Interestingly, definitions of basic math terms can differ by author. For example, some textbook definitions of "trapezoid" include parallelograms; in other definitions, parallelograms are excluded. Writing definitions presents a great opportunity for kids to debate which is correct and to dissect the implications of each one. This exercise also helps students consider how word meanings change depending on context. For example, the word "rational" in daily life means "based on reason or logic," but in math, it refers to a number formed by taking the ratio of two other numbers.
Contributing to online discussions
Students who do not enjoy speaking in class may enjoy contributing to online discussions. Possible prompts include:
- Which method do you prefer for solving quadratic equations, and why? Give examples to support your argument.
- Is sine, cosine, or tangent your favorite trigonometric function? Why? (This sounds silly, but it prompts interesting insights into students' understanding of the functions.)
- Write and post a word problem related to the current unit. Solve at least two of your classmates' problems.
Writing position papers backed by mathematical evidence
A key shift in the implementation of the Common Core State Standards for English language arts and literacy is an emphasis on evidence-based writing. Math provides excellent opportunities to build this skill. Position paper tasks allow students to express their opinions and can engage adolescents' natural passions for justice, environmentalism, or sports. You can use these tasks to develop students' concepts of argument and evidence. They're also an avenue for teachers to get to know students better.
For example, I asked a class of 11th graders to act as college admissions officers deciding which test to accept from applicants: the SAT (which more or less grades on a bell curve) or the ACT (which more or less does not grade on a bell curve). As part of the assignment, students had to explain the math that undergirds bell curves. These students were actively engaged in the initial stages of their college searches, and their personal experiences shaped their thoughtful, passionately written arguments. I learned about their struggles and successes with this stressful process, and my students had an emotional reason to learn the math.
For another project, students read articles about cities that misuse yellow traffic light timing to bring in revenues from photo enforcement tickets. (Short duration yellow lights can lead to more red light violations.) Students calculated safe stopping distances at various intersections under different assumptions, and investigated our own neighborhood's yellow light timing. At the end of the project, students took a position on our local traffic light efficacy and wrote a letter-to-a-fictional-editor. The positions they took were backed by their mathematical computations and informed by their opinions. (For example, should yellow light timing be based on drivers obeying or exceeding the speed limit?)
Don't Wait for a Word Problem
Math increasingly requires strong literacy skills, and a closer look at the curriculum reveals ample opportunities for students to develop those skills. Deliberate inclusion of literacy in a math classroom is no longer an add-on or at the whim of the teacher; it's a critical part of the curriculum. Everybody wins when literacy is consciously addressed in math class: students grow their literacy skills and improve their mathematical understanding, while teachers gain insights into students' personalities and mathematical thinking.