Building Math Vocabulary Skills

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Building Math Vocabulary Skills

• Patty Norman
• Logan Toone
• Davis School District

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Why Build Vocab. Skills?
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Why Build Vocab. Skills?
expression
equation
function
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Why Build Vocab. Skills?
Evaluate
Simplify
Solve
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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
  ORourke (1986) identified four levels of word
  knowledge
• 1. I never saw it before
• 2. Ive heard of it, but I dont know what it
  means
• 3. I recognize it in context - it has something
  to do with
• 4. I know it

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Mathematics as a Second Language

• A particular solution to a differential equation
  is a function yf(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.

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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 students
  attention to specific vocabulary.

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• 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.

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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

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Strategies Semantic Maps
Category
Characteristics
What its Not
Characteristics
New Concept
Characteristics
Characteristics
Example
Example
Example
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Strategies Semantic Maps
A function consisting of a monomial or a sum of
monomials
Functions
Terms have coefficients and a variable raised to
a power (degree)

• Variables dont have negative exponents.
• Variables are not in the exponent position.
• Variables cant have rational exponents (roots,
  etc.)

Polynomial Function
In standard form if terms are written in
descending order of exponents (L-R)
f (x) an x n an-1 x n-1 a1x a0
f (x) 3 x 2 2 x 1
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Try One
Category
Characteristics
What its Not
Characteristics
Vertical Angle Pairs
Characteristics
Characteristics
Example
Example
Example
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Angle Aerobics

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

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Writing

• Students use targeted vocabulary to reflect on
  and organize their thoughts around related
  mathematical idease.g. journals, justification
  of solution strategies, etc.

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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)

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Journal
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• 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.

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• 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.

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Using Correct Vocabulary

• An example .

Variable
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Definitions of variable

• --Nichols Schwartz, Mathematics Dictionary
  and Handbook

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Definitions of variable

• --Kaplan, McMullin, Algebra to Go A
  Mathematics Handbook

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Definitions of variable

• --Holt, Pre-Algebra, 2008

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Are we using the proper terms?
Variable
constant
unknown
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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.

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What is x ?

• A variable or an unknown constant?

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What is x ?

• A variable or an unknown constant?

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What is x ?

• A variable or an unknown constant?

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What is x ?

• A variable or an unknown constant?

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What is x ?

• A variable or an unknown constant?

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What is x ?

• A variable or an unknown constant?

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So

• Should we really be saying
• solve for the variable
• isolate the variable
• get the variable all by itself

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Textbooks Even do it Sometimes

• -- Houghton Mifflin, 6th Grade Math, 2007

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Textbooks Even do it Sometimes

• -- McDougall Littell, Algebra 2, 2007

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Textbooks Even do it Sometimes

• -- McDougall Littell, Algebra 2, 2007

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Who Cares?

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