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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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Teaching Goals

Suggestions for Use
Introducing 'Fault finding and fixing' tasks for the first time.
You might choose to introduce 'Fault finding and fixing' as a core element of mathematical thinking. Identifying and fixing mistakes early makes problem solving in mathematics far easier! The relevance of 'Fault finding and fixing' skills to everyday life is immediately obvious, and provides a clear justification for the use of these materials.

Providing guidance as students work on 'Fault finding and fixing' tasks.
Research evidence shows that correcting student misconceptions is enhanced by 'cognitive conflict'. This means that situations are established where the student is made aware of the existence of the gap between what they believe to be true, and the actual situation. Group work can provide a good source of this conflict, if students disagree about the truth or otherwise of the statements being made. As a teacher, you might choose to provoke the cognitive conflict as much as possible, and avoid giving correct answers. Students who struggle to disentangle their misconceptions are likely to learn more than students who are simply told the correct answer to the particular problem they face. Asking for student explanations as part of class review can be powerful; it is worth identifying students who are likely to offer conflicting views.

Reporting out of individual or group work
If you decide to organize a whole group discussion on what students came up with, it is useful to decide the degree to which you will participate in these discussions. You can facilitate the students' discussion, having them defend their ideas and write their ideas on the board, while adding almost none of your own. During discussions, you are likely to pose further questions that provoke debate. At some point, you are likely to want to review the answers to individual tasks, and to emphasize the need for fault finding and fixing as a key component of mathematical thinking.

Formal and informal use of 'Fault finding and fixing' tasks
There is a considerable variety of tasks in this task set, and the time required on each task ranges from just a few minutes to a whole class period. Tasks can be used formally - by assembling tests from the task collection - or informally, by dropping a 'Fault finding and fixing' task into your regular instruction, for example. In formal assessment (where you grade the assignment as an examination), do not intervene except where specified. Even modest interventions - reinterpreting instructions, suggesting ways to begin, offering prompts when students appear to be stuck - have the potential to alter the task for the student significantly.

In informal assessment (an exercise, graded or non-graded), you may want to be less rigid in giving the students help. Under these circumstances, you may reasonably decide to do some coaching, talk with students as they work on the task, or pose questions when they seem to get stuck. In these instances you may be using the tasks for informal assessments-observing what strategies students favor, what kinds of questions they ask, what they seem to understand and what they are struggling with, and what kinds of prompts get them unstuck. This can be extremely useful information in helping you make ongoing instructional and assessment decisions.

Group work versus individual work
These tasks are appropriate for group work. Students can discuss the claims made, and disagreements are likely to lead to enhanced learning. The
CL-1 Collaborative Learning web site can provide instructions on how to use group work effectively within the classroom. Conversely, an analysis of individual work may give you more clues as to misconceptions held by individual students.

Presumed background knowledge
Little mathematical knowledge is assumed apart from fundamental ideas around percentages, graphical interpretation and data display, and chance and proportion.

Step-by-Step Instructions

  1. Prepare by reading through the 'Fault finding and fixing' tasks on your own and coming up with your own solutions.
  2. Hand out copies of the task to students, either working individually or in groups.
  3. State the your goals for the 'Fault finding and fixing' task, emphasizing that they should be able to defend both their choice of method and the reasoning which leads to their answer.
  4. Walk around and listen to students as they discuss and work through the problems, providing guidance as necessary.
  5. Have students present their solutions, either in written or verbal form.

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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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