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
'Convincing and Proving' 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

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.

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.


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.

  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