Strategies and Practices to
Promote Algebraic Thinking
Associate Professor of Mathematics
• Many students struggle with developing generalizations for
• Bridge the gap between their concrete experiences in prior
mathematics courses and the abstract symbolic work in later
• Students need help to make sense of this increasing abstraction
• By developing students’ facility in using multiple representations
you give them a powerful tool for success in advanced
M&M activity on decay
1. Count how many total M&M’s there are in your
packet. This is the initial value.
2. Shake up M&M’s and drop the candies on a piece of
3. Count how many have “m” on top
4. Record on paper.
5. Remove these candies and repeat Steps 2-4 until no
candies with “m” on top appear
6. Record results in Excel spreadsheet and model the
Tiling the Border of a Pool
Consider the problem of
designing the most costefficient cylindrical juice can
that holds 20 cubic inches of
This problem requires
students to bring together
understanding of surface
area and volume, and ability
to use variables to represent
Technology and Algebraic Thinking
A spreadsheet can be a powerful ally
in facilitating algebraic thinking
Summary of Spreadsheets
• A spreadsheet can be used to unify algebraic, tabular and graphical
representations of an abstract concept.
• Gives valuable insight which may not be gained by just pencil and paper
• Shows students the power of technology to explore and make conjectures
which would otherwise be very difficult or impossible.
• Helping students build such insight is invaluable as they move on to other
courses and their professions.
Algebraic Concepts and Connections
What comes to your mind
at the mention of algebra?
GeoGebra vs Graphing Calculator
The ability to interact dynamically with a graph
sets GeoGebra apart from many other
graphing software and calculators
What is GeoGebra?
• Free and open source software created Markus Hohenwarter of
• A multi-platform dynamic mathematics software that joins
geometry, algebra, tables, graphing, statistics and calculus in one
What is GeoGebra?
Graphics, algebra and tables are connected
and fully dynamic
Can easily create interactive learning
materials as web pages
Solution of Equations
• Relate algebraic representation to graphical representation
• Recast an equation as an intersection of the graphs of two functions
• Explore nature of solutions
• Multistep applications hold student interest and
get them to connect with the mathematics they
• New algebraic skills that are introduced are now
in some context.
• Gives some rationale for why we define
mathematical objects the way we do.