Transcript Slide 1
Decoding Vocabulary in Mathematics: Don’t Become a Victim! 0011 0010 1010 1101 0001 0100 1011 1 2 4 1 Does math vocabulary take you hostage? Math 0011 0010 1010 1101 0001 0100 1011 Vocabulary 1 2 4 2 Are your students robbed of knowledge and understanding because of math vocabulary? 0011 0010 1010 1101 0001 0100 1011 Math Vocabulary 1 2 4 3 Don’t Become a 0011 0010 1010 1101 0001 0100 1011 1 2 4 4 A Quick Review… • What is the definition of a whole number? 0011 0010 1010 1101 0001 0100 1011 • What is the definition of an even number? 1 2 4 • What is the definition of an odd number? 5 A Hostage Situation… 0011 0010 1010 1101 0001 0100 1011 One student answered that 6 and 10 were odd numbers. Why? 1 2 4 6 When the student was asked to explain odd numbers he0100 replied, “Those whole 0011 0010 1010 1101 0001 1011 numbers are not multiples of two.” What he meant by “whole numbers”: 6, 8, 9, 10 and maybe 3 1 2 4 6, 9, and 10 were odd because the number of “holes” was not a multiple of two 7 0011 0010 1010 1101 0001 0100 1011 A Math Vocabulary 1 2 4 8 A Hostage Situation… 0011 0010 1010 1101 0001 0100 1011 Power 1 2 4 9 A Hostage Situation…Power 0011 0010 1010 1101 0001 0100 1011 What does it mean in everyday language? What does it mean in mathematical language? 1 2 4 10 A Hostage Situation… 0011 0010 1010 1101 0001 0100 1011 Mean 1 2 4 11 A Hostage Situation…Mean 0011 0010 1010 1101 0001 0100 1011 What does it mean in everyday language? What does it mean in mathematical language? 1 2 4 MEAN 12 How Could These Words Hold You Hostage? 0011 0010 1010 1101 0001 0100 1011 • • • • • • Odd Difference Similar Product Base Fact • • • • • • Range Plane Regular Variable Pi Radical 1 2 4 13 The Most Victimizing of All… 0011 0010 1010 1101 0001 0100 1011 a of 1 2 4 14 Show that a number divisible by 6 is even. 0011 0010 1010 1101 0001 0100 1011 We are not asking for a specific example, but rather any number divisible by 6 is even. Three and a fourth 1 2 4 We really mean three and one fourth 15 Take the area of a triangle. 0011 0010 1010 1101 0001 0100 1011 We mean the inside of the triangle The square of the hypotenuse 1 2 4 We mean the area of the square that can be constructed on the hypotenuse 16 A Four Case Scenario… 0011 0010 1010 1101 0001 0100 1011 1 2 4 17 0011 0010 1010 1101 0001 0100 1011 The Case Of Very Similar Meaning 1 2 • Some words mean nearly the same thing in “English” vocabulary and “math” vocabulary • Ex: Area, Origin 4 18 0011 0010 1010 1101 0001 0100 1011 The Case Of Almost Similar Meaning 1 • Some words from “English” vocabulary gives hints or roots to understand their meaning as “math” vocabulary • Ex: Combination, Quadrant 2 4 19 0011 0010 1010 1101 0001 0100 1011 The Case Of the Wildly Different Meaning 1 • 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 2 4 20 0011 0010 1010 1101 0001 0100 1011 The Case Of the Multiple Mathematical Meanings 1 • Some words in math have two distinct mathematical meanings • Ex: square, range, cube 2 4 21 0011 0010 1010 1101 0001 0100 1011 So, What Can We Do To Help Our Students Understand Math Vocabulary? 1 2 4 22 0011 0010 1010 1101 0001 0100 1011 Would Having Students Put Vocabulary Into Organizers Lessen Confusion? 1 2 4 23 What Should We Be Careful NOT To Do? 0011 0010 1010 1101 0001 0100 1011 In an effort to assist students with vocabulary teachers try to make the math easier… 1 2 • Numerator and Denominator become “Top” and “Bottom” • Fractions become “over” • Division becomes “cancel” • Algebra terms are “moved” Contents of this slide • Simplify becomes “reduce” adapted with permission 4 from Phil Sanderson 24 Why NOT to use “Cancel” 0011 0010 1010 1101 0001 0100 1011 2x + 1 2x + 2 2x + 1 =? 1 = 2 4 2x + 2 1 2 25 Why NOT to use “Move” 0011 0010 1010 1101 0001 0100 1011 An Algebraic Proof 4(x + 1) = 8 Given 4x + 4 = 8 4x = 4 x=1 1 Distributive Property 2 4 Subtraction ?? The “Move” Property Property of Equality ?? Division ?? The “Move” Property Property of Equality ?? 26 What Other Words Have You Heard Teachers Use To Make the Math “Friendlier?” 0011 0010 1010 1101 0001 0100 1011 1 2 How Does That Affect the Math Content? 4 27 The Result… 0011 0010 1010 1101 0001 0100 1011 • Students learn tricks rather than understanding the math • This is fostered by incorrect vocabulary 1 2 4 28 Make vocabulary a conscious of your planning and instruction. 0011 0010 1010 1101 0001 0100 1011 Don’t become a 1 2 4 29 Decoding Vocabulary in Mathematics: Don’t Become a Victim! Presented by: The College of William and Mary Tidewater Team 0011 0010 1010 1101 0001 0100 1011 1 2 4 [email protected] 30