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. D.srhine@willamette.edu

web.me.com/rhine5/ATP