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Misconceptions in Algebra. Steve Rhine, Ed. D. Willamette University. Graphing. Students’ Understanding of Graphing. Results from NAEP Graph the equation y = 5x - 8 [25%] Graph an equation given (-3,0) & (0,5) [5%] Other Research Students can easily graph ordered pairs - PowerPoint PPT Presentation
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Misconceptions in Algebra
Steve Rhine, Ed. D.Willamette University
Graphing
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%
What does it mean to understand graphing?
What does it mean to understand graphing?
5 10 15-15 -10 -5
604020
-20-40-60
5 10 15-12 -8 -4
15105
-4-8-12
3 6 9-12 -5 -1
15105
-15-20-25
What does it mean to understand graphing?
Consistent intervals
Numerical order
Scaling must be the same along each axis but can be different between axes
The origin is zero
Graphs can be discrete or continuous
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?
Infinity between points
Rate of change
Changes in axes’ numbering can communicate different ideas
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.
Iconic translation
Draw a graph describing a ball thrown from one
person to another. Use time and distance as your
axes.
Iconic Translation
Distance
Time
Bike Graph
Strategies:Numberless graphs
A boy raises a book over his head and lets it fall
DATA REPRESENTATION
DATA ANALYSIS
STRATEGIES: EXPERIMENTATION
Green Globs www.sunburst.com
Project Interactivatewww.shodor/com/interactivate
www.vernier.com
nlvm.usu.eduilluminations.nctm.orgApple Grapher
Steve Rhine, Ed. [email protected]
web.me.com/rhine5/ATP