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Decoding Vocabulary in Mathematics:

Don’t Become a Victim!

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Does math vocabulary take you hostage?

Math

Vocabulary

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Are your students robbed of knowledge and understanding because of math vocabulary?

VocabularyMath

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Don’t Become a

VICTIM

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• What is the definition of a whole number?

• What is the definition of an even number?

• What is the definition of an odd number?

A Quick Review…

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One student answered that 6 and 10 were odd numbers.

Why?

A Hostage Situation…

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When the student was asked to explain odd numbers he replied, “Those whole numbers are not multiples of two.”

What he meant by “whole numbers”:

6, 8, 9, 10 and maybe 3

6, 9, and 10 were odd because the number of “holes” was not a multiple of two

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A Math Vocabulary

VICTIM

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A Hostage Situation…

Power

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A Hostage Situation…Power

What does it mean in everyday language?

What does it mean in mathematical language?

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A Hostage Situation…

Mean

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A Hostage Situation…Mean

What does it mean in everyday language?

What does it mean in mathematical language?

MEAN

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How Could These Words Hold You Hostage?

• Odd

• Difference

• Similar

• Product

• Base

• Fact

• Range

• Plane

• Regular

• Variable

• Pi

• Radical

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The Most Victimizing of All…

a

of

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Show that a number divisible by 6 is even.

We are not asking for a specific example, but rather any number divisible by 6 is even.

Three and a fourth

We really mean three and one fourth

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Take the area of a triangle.

We mean the inside of the triangle

The square of the hypotenuse

We mean the area of the square that can be constructed on the hypotenuse

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A Four Case Scenario…

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Case 1The Case Of Very Similar Meaning

• Some words mean nearly the same thing in “English” vocabulary and “math” vocabulary

• Ex: Area, Origin

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Case 2The Case Of Almost Similar Meaning

• Some words from “English” vocabulary gives hints or roots to understand their meaning as “math” vocabulary

• Ex: Combination, Quadrant

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Case 3The Case Of the Wildly Different Meaning

• Some words from “English” vocabulary give no meaning to the same word in “math” vocabulary

• In fact, these words often lead to great confusion

• Ex: Volume, Radical, Similar, Plane

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Case 4The Case Of the Multiple Mathematical

Meanings

• Some words in math have two distinct mathematical meanings

• Ex: square, range, cube

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So, What Can We Do To Help Our Students Understand Math

Vocabulary?

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Would Having Students Put Vocabulary Into Organizers

Lessen Confusion?

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What Should We Be Careful NOT To Do?

• Numerator and Denominator become “Top” and “Bottom”

• Fractions become “over”• Division becomes “cancel”• Algebra terms are “moved”• Simplify becomes “reduce”

In an effort to assist students with vocabulary teachers try to make the math easier…

Contents of this slide adapted with permission from Phil Sanderson

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Why NOT to use “Cancel”

2x + 1

2x + 2= ?

1

2

2x + 1

2x + 2=

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Why NOT to use “Move”

An Algebraic Proof

4(x + 1) = 8

4x + 4 = 8

4x = 4

x = 1

Given

Distributive Property

Subtraction Property of Equality

Division Property of Equality

?? The “Move” Property ??

?? The “Move” Property ??

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What Other Words Have You Heard Teachers Use To Make

the Math “Friendlier?”

How Does That Affect the Math Content?

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The Result…

• Students learn tricks rather than understanding the math

• This is fostered by incorrect vocabulary

VICTIM

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Make vocabulary a conscious of your planning and instruction.

Don’t become a

VICTIM

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Decoding Vocabulary in Mathematics:

Don’t Become a Victim!

Presented by:

The College of William and Mary

Tidewater Team

tidewaterteam@wm.edu