Go to Collaborative Learning Go to FLAG Home Go to Search
Go to Learning Through Technology Go to Site Map
Go to Who We Are
Go to College Level One Home
Go to Introduction Go to Assessment Primer Go to Matching CATs to Goals Go to Classroom Assessment Techniques Go To Tools Go to Resources

Go to CATs overview
Go to Attitude survey
Go to ConcepTests
Go to Concept mapping
Go to Conceptual diagnostic tests
Go to Interviews
Go to Mathematical thinking
Go to Fault finding and fixing CAT
Go to Plausible estimation CAT
Go to Creating measures CAT
Go to Convincing and proving CAT
Go to Reasoning from evidence CAT
Go to Performance assessment
Go to Portfolios
Go to Scoring rubrics
Go to Student assessment of learning gains (SALG)
Go to Weekly reports

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

(Screen 1 of 4)
Go to next page

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 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.

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.


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.

  Go to next page

Tell me more about this technique:

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

Got to the top of the page.

Introduction || Assessment Primer || Matching Goals to CATs || CATs || Tools || Resources

Search || Who We Are || Site Map || Meet the CL-1 Team || WebMaster || Copyright || Download
College Level One (CL-1) Home || Collaborative Learning || FLAG || Learning Through Technology || NISE