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

### Classroom Assessment Techniques 'Convincing and Proving' 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 CONVINCING AND PROVING TASKS?
Proof lies at the heart of mathematics and mathematical thinking, yet many students will have had little exposure to proofs in high school. This CAT introduces the notions of convincing and proving and illustrates several kinds of proof commonly encountered in mathematics. These tasks are intended to assess how well students are able to argue logically, use examples and counterexamples to support their reasoning and identify breakdowns in rational argument. In addition, some tasks reveal common student misconceptions students make in their reasoning.

WHAT ARE CONVINCING AND PROVING TASKS?
These tasks are of two types.

• The first type asks students to evaluate a set of statements as "always, sometimes or never true". Students are expected to offer examples, counterexamples, and reasons for their decisions.
• The second type requires the student to evaluate "proofs" and distinguish the correct from the flawed.

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: 45 minutes. Disciplines: Appropriate for students who are expected to be able to argue logically. Requires some basic algebraic 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. Other Things to Consider: Some of the later tasks are intellectually demanding.