Math In Plain English

Literacy Strategies for the Mathematics Classroom

Amy Benjamin

• Publisher: Routledge
• Year: 2013
• Print ISBN: 9781138129832
• eBook ISBN: 9781317926740
• Edition: 1
• Topic: Bildung
• Subtopic: Bildung Allgemein

Do word problems and math vocabulary confuse students in your mathematics classes? Do simple keywords like "value" and "portion" seem to mislead them?

Many words that students already know can have a different meaning in mathematics. To grasp that difference, students need to connect English literacy skills to math. Successful students speak, read, write, and listen to each other so they can understand, retain, and apply mathematics concepts.

This book explains how to use 10 classroom-ready literacy strategies in concert with your mathematics instruction. You'll learn how to develop students who are able to explain to themselves - and communicate to others - what problems mean and how to attack them.

Embedding these strategies in your instruction will help your students gain the literacy skills required to achieve the eight Common Core State Standards for Mathematics. You'll discover the best answer to their question, "When am I ever going to use this?"

The 10 Strategies:

1. Teaching mathematical words explicitly
2. Teaching academic words implicitly
3. Reinforcing reading comprehension skills that apply to mathematics
4. Teaching mathematics with metaphor and gesture
5. Unlocking the meaning of word problems
6. Teaching note-taking skills for mathematics
7. Using language-based formative assessment in mathematics
8. Connecting memorization to meaning in mathematics
9. Incorporating writing-to-learn activities in mathematics
10. Preparing students for algebraic thinking

STRATEGY 1

Teaching Mathematical Words Explicitly

Excellent teachers of mathematics use plain English to teach the words of mathematics explicitly. They understand that etymology illuminates meaning. They help students make connections between strange-sounding mathematical words (polygon, trinomial, denominator) and familiar words (tricycle), as well as words that students learn (or will learn) in other disciplines (polytheism). Learning about how words are related through etymology is a fascinating life-long pursuit that excellent teachers of mathematics include in their explanations about terminology.

When I ask mathematics teachers what the biggest stumbling block is in “reading the math,” they invariably reply that it is vocabulary. The words of mathematics tend to be long, unfamiliar sounding, and unfamiliar to look at—that is, having letters that are rare in conversational vocabulary: a lot of x, y, z, and strange consonant combinations: rh, ph, gn. The sheer unfamiliarity of the appearance of the “math words,” combined with the daunting length of the words creates a stumbling block between the reader and the text.

In what we will call ordinary text (as opposed to technical mathematical language), unfamiliar words are often nestled in enough context that the reader can figure out the meaning, if not on the first exposure, then perhaps through subsequent exposures. With mathematical terminology, the words cannot be figured out through contextual clues. Chances are, the new words are introduced with explicit definitions at the outset of a chapter. After that, you’re on your own. “We told you once what congruent angles are, now here’s a bunch of congruent angles that go about having all kinds of adventures and getting into all kinds of scrapes and problems that you have to figure out.”

Many mathematical terms have more than one personality. Words like value, property, associate, solve, and even find are used broadly in conversation, but very narrowly in the world of mathematics. It’s as if they have a “home” personality, which the student knows, but then they adopt a whole new personality when they go to work for math. For math, they suit up and put on a math “game face.” This math game face does bear a resemblance to the familiar, conversational meaning, but not all students can deepen their understanding of a mathematical term by connecting it to its vernacular meaning. We must teach students to make these connections if we want them to understand mathematical terms on a deeper level.

Unfortunately, many teachers, in their desire to get students to use mathematical terms precisely, deny that the conversational meaning altogether! “Forget what you think you know about the word ray (or value, property, area, square, etc.). It doesn’t mean what you think it means. In mathematics, it means something different.” The problem with this approach is that it strips the student of the most valuable resource for learning that she has: background knowledge. The better strategy is to acknowledge and draw from background knowledge about words, open the door to connectedness, and then narrow the word from its familiar meaning to its mathematical meaning in a way that integrates the mathematical meaning into the student’s schema. (Appendix 1, page 101, gives detailed etymology that will help you illuminate these connections.)

Then, there are those mathematical phrases that need to be treated as single words. The student needs to process phrases like base ten system, side of an angle, and greatest common factor as units—immediately recognizable codes in the language of mathematics.

The words of mathematics, then, fall roughly into three categories:

• Mathematics only: Words that we are likely to encounter only in the world of mathematics: milligram, frustum, radian, rhombus, quotient, etc.
• Multiple meaning: Words that have a specific meaning when used in the world of mathematics, but that have another meaning when used in other academic fields or in conversation: function, line, point, evaluate, improper, etc.
• Phrases of mathematics: Words that, when put together, mean more than the sum of their parts; phrases are to be understood as a whole, as if they were single words: common denominator, sum of the squares, lowest common multiple, linear equation, etc.

Teaching the Words of Mathematics and the Academic Words Surrounding Them

How do words—any words—get learned and stay learned? And, what is specific about the words of mathematics—math words, we’ll call them—that might deserve special consideration?

To shed light on how words get learned and stay learned, I will refer to the theories of Stephen Krashen (2004), whose work in the field of second language acquisition can be applied to learning technical terminology in one’s native language. In other words, let’s think about what works well in expanding language capacity in general, and then apply those principles to expanding our students’ language capacity to include the language of the world of mathematics.

Krashen sets forth five hypotheses about second language acquisition. Let’s look at each and consider its applicability to learning the words of mathematics.

Acquisition-Learning Hypothesis

This theory posits that we learn a second language in two ways. The first is naturally, by being exposed to the target language in a meaningful context. In the process of attempting to communicate in the target language, a person picks up both the words and the grammar of that language. The learner is concentrating on purpose-driven communication, not language acquisition, but language acquisition results naturally and unconsciously.

The second means of learning a language is through direct, orderly instruction in the target language.

As this applies to mathematics class, we already know what the direct, orderly instruction looks like. And we already rely heavily on this means: Picture the teacher—supplemented by her mathematics textbook—defining and giving examples and illustrations of the mathematical terms. This type of instruction could be made better by incorporating the etymologies of the mathematical terms so that they may be linked to other words already in the students’ vocabulary. (See Appendix 1, page 101, for an annotated list of common word components used in mathematical language.) The more connections and associations that are made to any new terminology, the more memorable and meaningful the learning of the terms will be.

For teachers to improve their direct instruction in the vocabulary of mathematics, they need to learn more about how words of mathematics are connected to familiar words and expand their explanations accordingly. In so doing, they are building the habit in their students of making similar kinds of connections.

Now let’s expand the model to incorporate natural language acquisition. When students are given opportunities to communicate in authentic problem-solving situations about mathematics, when they are listening to their teachers not as strictly information givers but as cosolvers of the problem, when students strive to express themselves mathematically, cued by a person fluent in the language of mathematics, we have what Krashen refers to as acquisition.

To illustrate, picture yourself in a cooking class. The master chef explains the key terms to be used in a recipe that you are about to prepare. These terms include terms about process (verbs): stir, mix, separate, blend, blanche. The terms refer to the ingredients and tools (nouns): cilantro, shallots, Chinese eggplant, wok. If you were not fluent in the language of cooking, you would learn the verbs by watching and doing the processes, and you would learn the nouns by seeing them. And, in the context of authentic communication, you would hear key words repeatedly. But you would hear not only these key words: you would hear a set of supportive words that are often used in the cooking field: words of sequence, words about temperature, words about the condition and texture of food. You would absorb more words than you realized. Some of these words would come into your full control; others, you would learn to a lesser degree, and you may come into full control of them as you continue your experiences and communication about cooking. By communication, we mean more than just listening to the master chef. To learn a language, we need to use the language as novices. A language learner needs to repeat directions, ask questions, create analogies, ask for clarification, rephrase information.

As it is with any specialized vocabulary, so it is with mathematical words! The more your students are given opportunities to engage in authentic communication in mathematics, the more their mathematical vocabulary will grow in depth and scope.

Monitor Hypothesis

Krashen’s second theory is called the monitor hypothesis: This facet of language learning may be described as the development of intuition about what sounds right/what sounds wrong in the language and how to correct it. To develop the internal monitor that allows us to edit and correct our own language, we need to be steeped in the language. As students hear and read the language of mathematics, they develop their internal monitors only if they are given ...

Table of contents

• Cover
• Title Page
• Copyright Page
• Acknowledgements
• Meet the Author
• Free Downloads
• Table of Contents
• User’s Guide
• Introduction
• Strategy 1 Teaching Mathematical Words Explicitly
• Strategy 2 Teaching Academic Words Implicitly
• Strategy 3 Reinforcing Reading Comprehension Skills that Apply to Mathematics
• Strategy 4 Teaching Mathematics with Metaphor and Gesture
• Strategy 5 Unlocking the Meaning of Word Problems
• Strategy 6 Teaching Note-Taking Skills for Mathematics
• Strategy 7 Using Language-Based Formative Assessment in Mathematics
• Strategy 8 Connecting Memorization to Meaning in Mathematics
• Strategy 9 Incorporating Writing-to-Learn Activities in Mathematics
• Strategy 10 Preparing Students for Algebraic Thinking
• Appendix 1 Word Components Commonly Seen in Math Language: Or…Words Have Cousins?
• Appendix 2 Making Connections in Vocabulary
• Works Cited