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Misconceptions in Algebra Steve Rhine, Ed. D. Willamette University Graphing
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Misconceptions in Algebra
Steve Rhine, Ed. D.Willamette University
Graphing
What does it mean to understand graphing?
Write down everything you can think of regarding
what it takes to understand how to make
and interpret graphs.
Students’ Understanding of Graphing
Results from NAEPGraph the equation y = 5x - 8 [25%]
Graph an equation given (-3,0) & (0,5) [5%]
Other ResearchStudents can easily graph ordered pairs
Students struggle with the meaning of axes
Students lack a sense of infinity
How many points lie between (2,5) & (3,7)?none: 18%, one: 42%, #: 22%
Plot Points problem/Video: Boy 10/Girl 13
What does it mean to understand graphing?
1.There are an infinite number of points between two points.
What does it mean to understand graphing?
Which axis is x, y, and z? How do you know?
What does it mean to understand graphing?
What does it mean to understand graphing?
• There are an infinite number of points between
two points.
• Must have consistent intervals on each axis
• Numerical order
• Scaling must be the same along each axis but can
be different between axes
•The origin is zero
Discrete v. continuous
1 2 3 4 5 6 7 8 9 10 11 12
0.37
0.42
Postal Rates
What does it mean to understand graphing?
• There are an infinite number of points between
two points.
• Must have consistent intervals on each axis
• Numerical order
• Scaling must be the same along each axis but can
be different between axes
• The origin is zero
• Graphs can be continuous or discrete
Understanding Axes
Students & Graphing
Journeys
Boy 11/Girl 11
students & graphing
Ramirez Family Vacation
Boy 9/Girl 12/Girl 13
What does it mean to understand graphing?
• There are an infinite number of points between
two points.
• Must have consistent intervals on each axis
• Numerical order
• Scaling must be the same along each axis but can
be different between axes
• The origin is zero
• Graphs can be continuous or discrete
• Rate of change: the dynamic between axes
The Economy is doing fine!
The Economy is in ruins!
Two stories-same data
Strategies
How to Lie with StatisticsAd Campaign
Have students take an issue and campaign for and against an idea using the same data for both ads.
Act as a company and the competition’s advertising agency. For example, whether it is Burger King making better burgers or that you should buy a Macintosh over a PC. Use the same data for both ads.
WHAT DOES IT MEAN TO UNDERSTAND GRAPHING?
• There are an infinite number of points between
two points.
• Must have consistent intervals on each axis
• Numerical order
• Scaling must be the same along each axis but can
be different between axes
• The origin is zero
• Graphs can be continuous or discrete
• Rate of change: the dynamic between axes
• Changes in axes numbering can communicate
different ideas
Iconic translation
Draw a graph describing a ball thrown from one
person to another. Use time and distance as your
axes.
Iconic Translation
Action Grapher
Strategies:Numberless graphs
A boy raises a book over his head and lets it fall
DATA REPRESENTATION
DATA ANALYSIS
STRATEGIES: EXPERIMENTATION
www.vernier.com
nlvm.usu.eduilluminations.nctm.orgApple Grapher
