Building math vocabulary skills

Building Math Vocabulary Skills Patty Norman Logan Toone Davis School District

Mathematics as a Second Language The degree to which a student knows a word may vary, and that level of word knowledge has implications for vocabulary instruction. Dale and O‘Rourke (1986) identified four levels of word knowledge: 1. I never saw it before 2. I’ve heard of it, but I don’t know what it means 3. I recognize it in context - it has something to do with… 4. I know it

Mathematics as a Second Language A particular solution to a differential equation is a function y=f(x) that satisfies the differential equation. A general solution is an expression with arbitrary constants that represents the family of all particular solutions. What vocabulary has to be known in order to translate the definition? Defining or translating does not in itself create an understanding of the language .

ELL Strategies Students do not learn mathematical vocabulary by memorizing definitions. Rather, they construct meaning for mathematical vocabulary by actually doing authentic and meaningful mathematics. The teacher must be purposeful in constructing learning experiences that direct the student’s attention to specific vocabulary.

Definitions alone are not sufficient to know a word and it is not necessary to be able to define a word in order to know it. Definitions provide information about the word; however, students also need to know how the word functions in different contexts. For students to learn the word, they benefit from a meaningful explanation of the word, rather than simply a definition. Stahl & Fairbanks (1986) found that providing students with both definitional and contextual information significantly improves comprehension.

ELL Strategies Language Objectives Focus on developing students’ vocabulary Brainstorm Outline Draft Revise Edit Justify opinions Negotiate meaning Provide detailed explanations Stating conclusions Summarizing information Making comparisons

Strategies: Semantic Maps New Concept Characteristics Characteristics Characteristics Characteristics Category Example Example Example What it’s Not

Strategies: Semantic Maps Polynomial Function A function consisting of a monomial or a sum of monomials Terms have coefficients and a variable raised to a power (degree) In standard form if terms are written in descending order of exponents (L-R) Functions f ( x ) = 3 x 2 + 2 x + 1 Variables don’t have negative exponents. Variables are not in the exponent position. Variables can’t have rational exponents (roots, etc.) f ( x ) = a n x n + a n -1 x n -1 + … + a 1 x + a 0

Try One … Vertical Angle Pairs Characteristics Characteristics Characteristics Characteristics Category Example Example Example What it’s Not

Angle Aerobics Line Ray Line segment Midpoint Acute Obtuse Right Slide/Translation Flip Reflection Turn/Rotation Congruent Similar

Writing Students use targeted vocabulary to reflect on and organize their thoughts around related mathematical ideas—e.g. journals, justification of solution strategies, etc.

Quick Pic Book Vocabulary Self-Selection Strategy: Personal Dictionaries “ When students are shown how to identify key content vocabulary, they become adept at selecting and learning words they need to know, and given opportunities to practice, comprehension improves.” (Shearer, Ruddell, & Vogt, 2001)

Students learn mathematics best by using it, and understanding the language of math gives students the skills they need to think about, talk about, and assimilate new math concepts as they are introduced.

Much instruction focuses students on “doing” mathematics, yet this deprives them of the words they need to communicate what they are learning in relevant ways. Mathematical language is used and understood around the world, and conventional mathematics vocabulary gives learners the means of communicating those concepts universally.

Using Correct Vocabulary An example ….

Definitions of “variable” --Nichols & Schwartz, Mathematics Dictionary and Handbook

Definitions of “variable” --Kaplan, McMullin, Algebra to Go: A Mathematics Handbook

Definitions of “variable” --Holt, Pre-Algebra , 2008

Are we using the proper terms?

When we use “letters” All letters are not variables! A letter can represent a quantity that varies (variable), but it can also represent an unknown constant.

What is x ? A “variable” or an “unknown constant”?

So … Should we really be saying “ solve for the variable” “ isolate the variable” “ get the variable all by itself”

Textbooks Even do it Sometimes -- Houghton Mifflin, 6 th Grade Math , 2007

Textbooks Even do it Sometimes -- McDougall Littell, Algebra 2 , 2007

Who Cares? Discuss why it might be important to distinguish between constants and variables with your students.

Building math vocabulary skills

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