An Underestimated Factor in Learning Algebra
Presented by
Dr. Terrence R. Sundeen and
Dr. Nancy J. McCormick
NADE 2003
Austin, Texas

The readability of a textbook involves the determination of an approximate grade level at which materials are written .

• 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.)

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 to accommodate different learning styles:
• Visual
• Auditory
• Tactile

• 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.

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/InstructionalT echnology/templates/powerpoint.htm
Example of a jeopardy.ppt file
• Many Others

• 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.

• Definition • Vocabulary Word

• Definition • Vocabulary Word

• 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.

• 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/mat h/java/geo/pytha2/pytha
2.html

• Vocabulary Quizzes (written and oral).
• Vocabulary on Tests (matching, true/false, multiple choice items).
• In-Class Worksheets for Daily Grades
• Games for Review Work