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Mathematical Thinking CATs || Fault Finding and Fixing || Plausible Estimation
Creating Measures || Convincing and Proving || Reasoning from Evidence

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Classroom Assessment Techniques
'Fault Finding and Fixing' Tasks

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Description
A collection of situations, graphs, diagrams and charts is presented that have already been interpreted by someone (in some cases in a newspaper). These interpretations are usually flawed. The students' task is to critique the interpretation or representation and say how it may be improved. The
task collection begins with elementary (though common) mistakes involving percentages, then presents problems involving combinations and chance. Some tasks require graphical interpretation, and others require the interpretation of statistical data. Many of the tasks are taken from everyday experiences, and mistakes in published materials such as newspapers and books.

The mistakes are ones that are made commonly, and it is likely that students in some classes will endorse the misconceptions exposed in the tasks.

Example of "Fault Finding and Fixing" Task

Presidential Popularity
The following headline and chart appeared in the June 14, 1994 issue of USA Today newspaper.
Clinton approval rating up
A graph of time versus President Clinton's approval.  The approval rating peaks around 60% and goes down to 37%.  The date range is from January 26, 1993 thru June 12, 1994.  The line goes up and down several times bottoming in May, 1993 and peaking in January, February, and September 1993 and in January, 1994.

Source: USA TODAY/CNN/Gallup Poll of 756 adults by telephone on June 11-12. Margin of error: 4 percentage points.

The accompanying story, entitled "With Clinton home, voters lighten up," read in part:

    With D-Day observances over and President Clinton back home, voters' attitudes toward the president are settling down a bit. Now that attention is back on the economy, health care and crises in Bosnia and Haiti, a USA Today/CNN/Gallup Poll taken over the weekend [of June 12] shows Clinton's job performance rating inching upward to 49% ... It's an improvement from a poll taken [on June 6] as Clinton was in Europe marking the 50th anniversary of the Allied invasion of Normandy, which showed approval dropping to 46% ...

Write a letter to the editor of USA Today explaining why the assertion "Clinton approval rating up" might be regarded as questionable or misleading. Be concise (editors prefer letters that are brief and to the point) but convincing (give mathematical evidence to support your claims).



Assessment Purposes


Limitations
Little mathematical knowledge is assumed apart from fundamental ideas around percentages, graphical interpretation and data display, and chance and proportion. However, students are required to understand the concepts, not simply to demonstrate competence in using routine procedures, and must use their knowledge to make sense of situations.

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Mathematical Thinking CATs || Fault Finding and Fixing || Plausible Estimation
Creating Measures || Convincing and Proving || Reasoning from Evidence


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