Fostering Conceptual Understanding in a Developmental Algebra Classroom

AMATYC 2009

Las Vegas, NV

Nov 13th 2009

Gowribalan A. Vamadeva

gowribalan.vamadeva@uc.edu

University of Cincinnati

BACKGROUND

o ASU – 1995 - 1999• Developmental Algebra & Intermediate Algebra – • Traditional Curriculum – Text Used Pat – Mckeague

o BCC – 1999 - 2005• Pre Algebra, Two Part Pre Algebra, Introductory

Algebra, Algebraic Skills, Elementary Algebra• Mixture of reform curriculum & traditional curriculum

– Text Used Aufman, Martin Gay, & Alice Kaseburg • More Reformists than Traditionalists

o UC – 2005 - Present• Elementary Algebra I, Elementary Algebra II, &

Elementary Algebra III• Traditional Curriculum – Text Used Martin Gay & Lial

Hornsby

ELEMENTARY ALGEBRA I –MATH 091

 Topics include Fractions, Decimals, Integers,Rational Numbers, Variable Expressions,

Ratios,Rates, Proportions, Percents, Geometry,Probability & Statistics

ELEMENTARY ALGEBRA II –MATH 092

Topics include First degree equations &inequalities, Functions & linear functions,

Linear inequalities, Systems of linear equations &inequalities, Rules of Exponents, and

Polynomials.  

ELEMENTARY ALGEBRA III –MATH 101

Topics include Factoring & solving polynomial equations, Rational expressions & equations, Rational exponents & Radical expressions & equations, Quadratic equations, & quadratic functions

 

GRAPHING EQUATIONS & INEQUALITIES

The Rectangular Coordinate System Graphing Linear Equations Intercepts Slope Equations of Lines Introduction to Functions Graphing Linear Inequalities in two variables

TRADITIONAL DEFINITIONS OF THE SLOPE OF A LINE &

FUNCTIONS

Slopeo The slope of a line is a measure of the slant or steepness of a lineo The slope is the ratio of the vertical change in y to the horizontal

change in xo The slope of a line is a ratio that compares the vertical change with the

corresponding horizontal change as we move along the line from one point to another

Functionso A function is a relation in which no two ordered pairs have the same

first coordinates and different second coordinateso A function is a relation in which, for each value of the first component

of the ordered pairs, there is exactly one value of the second component

CONCEPTUAL & REFORM IDEAS IN MATH 092

Distinguish between Ratios and Rates Average Rate of Change

• rate of change & slope• slope • slope & equations of lines

Function basics • lesson plan• functions I.pdf• functions II.pdf• absolute value function.pdf

Outside Class Project• end of year project 092.pdf

CONCEPTUAL & REFORM IDEAS IN

MATH 101

• course outline• rational function introduction• radical functions• Innovative Approach

introduction to rational equations – DLA, ILD, Student Practice, & Summary – handout

• quadratic translations leading to vertex form• basic functions & properties• end of year project

SOME IDEAS FROM MATH 091

o Number Sense• If a million seconds went by, how many days

have gone by?• If a billion seconds went by, how many days

have gone by?• If a trillion seconds went by, how many days

have gone by?o Linear Equations in one variable -

applications• fulcrum idea• college football bowl game

LEARNING OUTCOMES Identify and distinguish among different families

of functions: linear, quadratic, rational, and radical by interpreting graphical, symbolic, numerical, and verbal representations.

Demonstrate the mathematical skills appropriate for each course

Use the appropriate function model to analyze and solve application problems

Use a graphing calculator when appropriate to explore and solve problems

Explain how a function model relates to an applied situation and interpret problem solutions in the context of the situation.

ACTIVE LEARNING METHODS

Examples drawn from real life and skills learned in context

Group learning activities, instructor led discussions

Active participation and team work are essential Problems are approached using a variety of

perspectives Summary

 

Examples:1) slope and linear functions(DLA).pdf

2) Rational Equations.pdf

3) Dick Aufman – Materials

CONCLUSION DON’T LET GO YOUR PHILOSOPHIES THERE IS ALWAYS SOME TIME FOR

REFORM METHODS PROJECTS ARE NOT JUST IN CALCULUS

AND BEYOND PEER LED LEARNING APPRECIATED

OVER TIME HOW MANY FACTORING, SIMPLIFYING,

AND SOLVING PROBLEMS? ONE STRUCTURE DOES NOT FIT ALL

THANK YOU

MATHEMATICS DEPARTMENTS AT BROOKDALE CC ANDTHE UNIVERSITY OF CINCINNATI