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

### Classroom Assessment Techniques 'Fault Finding and Fixing' Tasks

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Malcolm Swan
Mathematics Education, University of Nottingham
Malcolm.Swan@nottingham.ac.uk

Jim Ridgway
School of Education, University of Durham
Jim.Ridgway@durham.ac.uk

WHY USE FAULT FINDING AND FIXING TASKS?
Newspapers, television and other media offer assertions and argument often based on plausible 'mathematical' reasoning. It is therefore an important life skill to be able to analyze a statement or argument critically, and to correct fallacious reasoning.

One of the most important skills of any mathematician is the ability to spot then remediate plausible errors in his or her own work and in the work of others. These tasks provide practice at this key skill.

There are a number of well-known misconceptions held by students of mathematics, many of which persist undetected into the college years. These misconceptions need to be identified and remedied, to avoid major conceptual problems, later. Many of the 'Fault finding and fixing' tasks make use of common misconceptions, and so the task set can play a diagnostic role.

WHAT ARE FAULT FINDING AND FIXING TASKS?
The tasks in this package (an example) offer students a number of mathematical mistakes which they are asked to diagnose and rectify. These require students to analyze mathematical statements and deduce from the context the part that is most likely to contain the error (there may be more than one possibility), explain the cause of the error and rectify it. Such tasks can be quite demanding. It is often more difficult to explain the cause of another's seductive error than to avoid making it oneself. Contexts include: percentages; graphical interpretation; and reasoning from statistical data.

WHAT IS INVOLVED?

 Instructor Preparation Time: Minimal if use existing tasks. Preparing Your Students: Students will need some coaching on their first task. Class Time: Some tasks take 5 minutes; others as much as 45 minutes. Tasks can be assembled in a number of combinations. Disciplines: Appropriate for all, requires proportional reasoning and graphical skills. Class Size: Any. Special Classroom/Technical Requirements: None. 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. Useful for identifying common student misconceptions. Other Things to Consider: Fairly demanding task for students who are unfamiliar with open-ended problems.