Visual College Algebra for Teachers
Abstract:
In this talk we will discuss using concrete algebra piece models to build
conceptual understanding of algebraic processes and operations for pre-service
K-8 teachers. We will exhibit examples of using visual techniques in a variety
of curriculum contexts, from integer operations to solving quadratic
equations.
One-page description:
College Algebra for Teachers is a mathematics content course for pre-service
K-8 teachers at Western Oregon University. This course is centered on the
rich Visual Math / Math in the Mind’s Eye curriculum (
http://www.mlc.pdx.edu/).
Students explore the basics of algebraic structures, expressions and equations
with an emphasis on problem solving and hands-on activities. The focus of this
course is on visualization of algebraic relationships and operations.
Students start by modeling integers and integer operations with black
(positive) and red (negative) tiles. These processes set the stage for
understanding equation manipulations later in the course. Then students move
to modeling algebraic expressions and equations with a whole number domain
using black and red algebra pieces. The visual model allows student to make
the jump from the concrete visual model to abstract thinking with ease. By
the end of the course, students are modeling algebraic equations with a real
number domain using white (neutral) algebra pieces. These models allow
students to conceptualize and find meaning in algebraic manipulations.
Throughout the course, models are connected to paper and pencil algorithms and
graphical techniques. This is a particularly powerful course which often
entirely changes student perspectives and attitudes as they gain genuine
understanding of algebra and algebraic techniques.
In this talk we will share the main models we use through a series of selected
activities. We will focus on the ramifications of using the visual techniques
for student conceptual understanding and for the mathematical confidence of
the students.