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Fostering Conceptual Understanding in a Developmental Algebra Classroom AMATYC 2009 Las Vegas, NV

Fostering Conceptual Understanding in a Developmental Algebra Classroom AMATYC 2009 Las Vegas, NV Nov 13 th 2009 Gowribalan A. Vamadeva gowribalan.vamadeva@uc.edu University of Cincinnati. BACKGROUND. ASU – 1995 - 1999 Developmental Algebra & Intermediate Algebra –

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Fostering Conceptual Understanding in a Developmental Algebra Classroom AMATYC 2009 Las Vegas, NV

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  1. 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

  2. BACKGROUND • ASU – 1995 - 1999 • Developmental Algebra & Intermediate Algebra – • Traditional Curriculum – Text Used Pat – Mckeague • 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 • UC – 2005 - Present • Elementary Algebra I, Elementary Algebra II, & Elementary Algebra III • Traditional Curriculum – Text Used Martin Gay & Lial Hornsby

  3. ELEMENTARY ALGEBRA I –MATH 091 Topics include Fractions, Decimals, Integers, Rational Numbers, Variable Expressions, Ratios, Rates, Proportions, Percents, Geometry, Probability & Statistics

  4. 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.

  5. Elementary Algebra III –MATH 101 Topics include Factoring & solving polynomial equations, Rational expressions & equations, Rational exponents & Radical expressions & equations, Quadratic equations, & quadratic functions

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

  7. Traditional Definitions of the Slope of a line & Functions Slope • The slope of a line is a measure of the slant or steepness of a line • The slope is the ratio of the vertical change in y to the horizontal change in x • 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 Functions • A function is a relation in which no two ordered pairs have the same first coordinates and different second coordinates • 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

  8. 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

  9. 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

  10. Some Ideas from MATH 091 • 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? • Linear Equations in one variable - applications • fulcrum idea • college football bowl game

  11. 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.

  12. 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

  13. 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

  14. THANK YOU MATHEMATICS DEPARTMENTS AT BROOKDALE CC ANDTHE UNIVERSITY OF CINCINNATI

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