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

Classroom Assessment Techniques
Mathematical Thinking
(Screen 1 of 5)


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
"Most assessment practices seem to emphasise the reproduction of imitative, standardised techniques. I want something different for my students. I want them to become mathematicians  not rehearse and reproduce bits of mathematics....Assessment doesn't have to be an isolated, threatening business; it's not just answers, but approaches..." Malcolm Swan
"Thinking mathematically is about developing habits of mind that are always there when you need them  not in a book you can look up later. For me, a big part of education is about helping students develop uncommon common sense. I want students to develop ways of thinking that cross boundaries  between courses, and between mathematics and daily life...People should be able to tackle new problems with some confidence..." Jim Ridgway
WHY USE THE MATH CATs?
The Mathematical Thinking Classroom Assessment Techniques (Math CATs) are designed to promote and assess thinking skills in mathematics.
WHAT ARE THE MATH CATs?
The Mathematical Thinking Classroom Assessment Techniques (Math CATs) are designed to promote and assess thinking skills in mathematics. Few faculty have difficulty finding or developing tools which assess the specific mathematical techniques which they teach; a challenge which faculty do face is to find ways to promote and assess the development of mathematical thinking  notably to help students know what to do when faced with problems which are not identical to the technical exercises commonly encountered in mathematics classes.
Here we define mathematical thinking as
...the development of a mathematical point of view  valuing the process of mathematization and abstraction and having the predilection to apply them; and the development of competence with the tools of the trade, and using those tools in the service of the goal of understanding structure. (Schoenfeld, 1992)
The Math CATs are designed to address this challenge by offering ways to assess and instill a broad range of the mathematical thinking skills important for students in the science, mathematics, engineering, and technology disciplines. These skills include:
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.

Disciplines: 
Varies with specific CAT.

Class Size: 
Any.

Special Classroom/Technical Requirements: 
None except for Reasoning from Evidence CAT.

Individual or Group Involvement: 
Either.

Analyzing Results: 
Varies with specific CAT.

Other Things to Consider: 
Fairly demanding task for students who are unfamiliar with openended problems.

Tell me more about this technique:
Mathematical Thinking CATs  Fault Finding and Fixing  Plausible Estimation
Creating Measures  Convincing and Proving 
Reasoning from Evidence
