1 Decoding Vocabulary in Mathematics: Don’t Become a Victim!

42510011 0010 1010 1101 0001 0100 1011

1

Decoding Vocabulary in Mathematics:

Don’t Become a Victim!

42510011 0010 1010 1101 0001 0100 1011

2

Does math vocabulary take you hostage?

Math

Vocabulary

42510011 0010 1010 1101 0001 0100 1011

3

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

VocabularyMath

42510011 0010 1010 1101 0001 0100 1011

4

Don’t Become a

VICTIM

4251

0011 0010 1010 1101 0001 0100 1011

5

• 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…

4251

0011 0010 1010 1101 0001 0100 1011

6

One student answered that 6 and 10 were odd numbers.

Why?

A Hostage Situation…

4251

0011 0010 1010 1101 0001 0100 1011

7

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

4251

0011 0010 1010 1101 0001 0100 1011

8

A Math Vocabulary

VICTIM

4251

0011 0010 1010 1101 0001 0100 1011

9

A Hostage Situation…

Power

4251

0011 0010 1010 1101 0001 0100 1011

10

A Hostage Situation…Power

What does it mean in everyday language?

What does it mean in mathematical language?

4251

0011 0010 1010 1101 0001 0100 1011

11

A Hostage Situation…

Mean

4251

0011 0010 1010 1101 0001 0100 1011

12

A Hostage Situation…Mean

What does it mean in everyday language?

What does it mean in mathematical language?

MEAN

4251

0011 0010 1010 1101 0001 0100 1011

13

How Could These Words Hold You Hostage?

• Odd

• Difference

• Similar

• Product

• Base

• Fact

• Range

• Plane

• Regular

• Variable

• Pi

• Radical

4251

0011 0010 1010 1101 0001 0100 1011

14

The Most Victimizing of All…

a

of

4251

0011 0010 1010 1101 0001 0100 1011

15

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

4251

0011 0010 1010 1101 0001 0100 1011

16

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

4251

0011 0010 1010 1101 0001 0100 1011

17

A Four Case Scenario…

4251

0011 0010 1010 1101 0001 0100 1011

18

Case 1The Case Of Very Similar Meaning

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

• Ex: Area, Origin

4251

0011 0010 1010 1101 0001 0100 1011

19

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

4251

0011 0010 1010 1101 0001 0100 1011

20

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

4251

0011 0010 1010 1101 0001 0100 1011

21

Case 4The Case Of the Multiple Mathematical

Meanings

• Some words in math have two distinct mathematical meanings

• Ex: square, range, cube

4251

0011 0010 1010 1101 0001 0100 1011

22

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

Vocabulary?

4251

0011 0010 1010 1101 0001 0100 1011

23

Would Having Students Put Vocabulary Into Organizers

Lessen Confusion?

4251

0011 0010 1010 1101 0001 0100 1011

24

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

4251

0011 0010 1010 1101 0001 0100 1011

25

Why NOT to use “Cancel”

2x + 1

2x + 2= ?

1

2

2x + 1

2x + 2=

4251

0011 0010 1010 1101 0001 0100 1011

26

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 ??

4251

0011 0010 1010 1101 0001 0100 1011

27

What Other Words Have You Heard Teachers Use To Make

the Math “Friendlier?”

How Does That Affect the Math Content?

4251

0011 0010 1010 1101 0001 0100 1011

28

The Result…

• Students learn tricks rather than understanding the math

• This is fostered by incorrect vocabulary

VICTIM

4251

0011 0010 1010 1101 0001 0100 1011

29

Make vocabulary a conscious of your planning and instruction.

Don’t become a

VICTIM

42510011 0010 1010 1101 0001 0100 1011

30

Decoding Vocabulary in Mathematics:

Don’t Become a Victim!

Presented by:

The College of William and Mary

Tidewater Team

tidewaterteam@wm.edu