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

2. 2 Does math vocabulary take you hostage? Math Vocabulary

3. 3 Are your students robbed of knowledge and understanding because of math vocabulary? Vocabulary Math

4. 4 Don’t Become a VICTIM

5. 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…

6. 6 One student answered that 6 and 10 were odd numbers. Why? A Hostage Situation…

7. 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

8. 8 A Math Vocabulary VICTIM

9. 9 A Hostage Situation… Power

10. 10 A Hostage Situation…Power What does it mean in everyday language? What does it mean in mathematical language?

11. 11 A Hostage Situation… Mean

12. 12 A Hostage Situation…Mean What does it mean in everyday language? What does it mean in mathematical language? MEAN

13. 13 How Could These Words Hold You Hostage? Odd Difference Similar Product Base Fact Range Plane Regular Variable Pi Radical

14. 14 The Most Victimizing of All… a of

15. 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

16. 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

17. 17 A Four Case Scenario…

18. 18 Case 1 The Case Of Very Similar Meaning Some words mean nearly the same thing in “English” vocabulary and “math” vocabulary Ex: Area, Origin

19. 19 Case 2 The Case Of Almost Similar Meaning Some words from “English” vocabulary gives hints or roots to understand their meaning as “math” vocabulary Ex: Combination, Quadrant

20. 20 Case 3 The 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

21. 21 Case 4 The Case Of the Multiple Mathematical Meanings Some words in math have two distinct mathematical meanings Ex: square, range, cube

22. 22 So, What Can We Do To Help Our Students Understand Math Vocabulary?

23. 23 Would Having Students Put Vocabulary Into Organizers Lessen Confusion?

24. 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

25. 25 Why NOT to use “Cancel” 2x + 1 2x + 2 = ? 1 2 2x + 1 2x + 2 =

26. 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 ??

27. 27 What Other Words Have You Heard Teachers Use To Make the Math “Friendlier?” How Does That Affect the Math Content?

28. 28 The Result… Students learn tricks rather than understanding the math This is fostered by incorrect vocabulary VICTIM

29. 29 Make vocabulary a conscious of your planning and instruction. Don’t become a VICTIM

30. 30 Decoding Vocabulary in Mathematics: Don’t Become a Victim! Presented by: The College of William and Mary Tidewater Team tidewaterteam@wm.edu