ALGEBRAIC VOCABULARYAn Underestimated Factor in Learning Algebra

Presented by Dr. Terrence R. Sundeen and Dr. Nancy J. McCormick

NADE 2003 Austin, Texas

READABILITY

The readability of a textbook involves the determination of an approximate grade level at which

materials are written.

READABILITY FORMULAS• Fry Readability Graph - Based on length of sentences and number of syllables in a selection

http://school.discovery.com/schrockguide/fry/fry.html

• McLaughlin’s SMOG Readability Formula - Based on the number of polysyllabic words

http://web.ucdmc.ucdavis.edu/edu/HealthEd/Guide/Read.htm

• Gunning’s FOG Index - Based on sentence length and words with three or more syllables

http://www.fpd.finop.umn.edu/groups/ppd/documents/information /writing_tips.cfm

• Raygor’s Readability Estimate - Based on sentence length and long words (those with six or more letters)

http://engfac.byu.edu/Novelinks/reading strategies/Anthem/raygor general.htm

FRY READABILITY GRAPH

Data from Fry Readability Graph (Graphic scanned from Cheek and Cheek, 1983, p.254.)

READABILITY

All of these readability formulas consider only two

elements in determining the level of a material –

vocabulary and sentence length. There are many

other elements to consider some of which are

prior student experiences, teacher’s introduction

of information, format of materials, student

involvement in learning, awareness of purpose for

reading, organization of information, and interest

in content.

EXAMPLES OF WELL AND POORLY DEFINED VOCABULARY TERMS

• Constants – numbers that do not contain variables.

• Discriminant – If the discriminant is positive or zero, the quadratic equation will have real number solutions.

• Constant – a number whose value does not vary.

• Discriminant – When b²-4ac simplifies to 0, … .

Thus there is only one rational solution,

-b/2a. Whenever the discriminant is positive, there will be two real number solutions.

A SUGGESTED CORE PRE-ALGEBRA VOCABULARY LIST

• NUMBERS Number Systems: Natural (or Counting) Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Properties: Commutative (Addition and Multiplication) Associative (Addition and Multiplication) Distributive Sets: Subset Empty Set Union Intersection Opposite: (Additive Inverse or Negative of) Prime Number Composite Number

A SUGGESTED CORE PRE-ALGEBRA VOCABULARY LIST• VARIABLES

Variable (English and Greek Letters)• TERMS

Term

Degree

Like and Unlike terms

Exponential: Exponent (or power)

Base

Radicals: Index

Radical sign

Radicand

Root

Rational• ALGEBRAIC EXPRESSIONS

Rational Expression

Polynomial (monomial, binomial, and trinomial)

A SUGGESTED CORE PRE-ALGEBRA VOCABULARY LIST• EQUATIONS

Equation: Linear

Quadratic

Open Sentence

Function: Domain

Range

Inverse

Absolute Value Equations• INEQUALITIES

Inequality Symbols (<, >, <, or >)

Absolute Value Inequalities• SOLUTIONS

Solution Set

Graph: Number Line• PROBLEM SOLVING METHODS

Factoring

Graphing: Rectangular (or Cartesian) Coordinate System

A SUGGESTED CORE PRE-ALGEBRA VOCABULARY LIST

X- and Y-Axes

Quadrants

Ordered Pair

Origin

Line

Slope

Y-intercept

X-intercept

TECHNIQUES FOR PRESENTATION

Techniques to accommodate different learning styles:

• Visual

• Auditory

• Tactile

VOCABULARY GAMES

• www.quia.com 30-day free trial period to create

your activities which can include: Flashcards Concentration Game Matching Word Search

Create a list of words and their definitions. Quia automatically makes the activities and gives URL for students to access.

Example: www.quia.com/jg/326260.html

1-yr subscription is $49.

Vocabulary For Activities

JEOPARDY TEMPLATES

Search engine (www.google.com) to find “jeopardy in the classroom”

• www.teachnet.com PowerPoint template to make your own game of jeopardy

• www.netxv.net/esc/technology/InstructionalTechnology/templates/powerpoint.htm

Example of a jeopardy.ppt file• Many Others

ORAL QUIZZES

• Like the spelling tests in elementary school, students are read the definitions and they write the correct vocabulary word that corresponds with each definition.

• For students to access outside of the classroom, you can make PowerPoint slides, to put on your Web site, that incorporate the “sound” of spoken definitions.

AUDIO FLASHCARD 1

• Definition • Vocabulary Word

AUDIO FLASHCARD 2

• Definition • Vocabulary Word

VOCABULARY ACTIVITY TO FORM GROUPS

• Give each student a card as they come into the classroom that has either a vocabulary word or a definition.

• Have the students find the student with the word or the definition that corresponds with their card.

• After the students are in pairs, you can form groups of two or three pairs for a group activity.

PYTHAGOREAN THEOREM• The sum of the squares

of the legs of a right triangle is equal to the square of the hypotenuse.

• Let students see this definition “illustrated” with a hands on activity using graph paper.

• Internet activities using manipulations online

http://www.ies.co.jp/math/java/geo/pytha2/pytha2.html

TOOLS OF ASSESSMENT

• Vocabulary Quizzes (written and oral).

• Vocabulary on Tests (matching, true/false, multiple choice items).

• In-Class Worksheets for Daily Grades

• Games for Review Work