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


Classroom Assessment Techniques
'Reasoning from Evidence' Tasks

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Cartoon image of a kitty cat.  Cat is animated on mouse over with the word C-A-T appearing. Malcolm Swan
Mathematics Education, University of Nottingham

Jim Ridgway
School of Education, University of Durham

Newspapers, television and the web present citizens with assertions, and arguments often based on plausible 'mathematical' reasoning. Much of this is intended to persuade, impress, and affect behavior. It is therefore an important life skill to be able to analyze data and interpretations of data, argue critically and make informed decisions based on sound reasoning.

For students who choose a career in mathematics, science, and/or science, and/or engineering, the development of this skill in analyzing data is central to the discipline.

Usually data are analyzed via computer. Some teachers use these tasks (deodorant example) to assess students' abilities to use computer packages such as Excel to support their mathematical thinking.

The tasks require students to analyze unsorted data. This will assess students' abilities to organize information, represent it in a meaningful way, and draw sensible conclusions.


Instructor Preparation Time: Minimal if use existing tasks.
Preparing Your Students: Students will need some coaching on their first task.
Class Time: 45 minutes.
Disciplines: Appropriate for all, requires proportional reasoning and graphical skills. Superior solutions can often be created using a spreadsheet.
Class Size: Any.
Special Classroom/Technical Requirements: None, unless the data analysis is done via computer.
Individual or Group Involvement: Either.
Analyzing Results: Intensive for formal scoring for large classes. Best used as an informal way to get your students thinking mathematically.
Other Things to Consider: Fairly demanding task for students who are unfamiliar with open-ended problems.

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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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