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

### Classroom Assessment Techniques 'Creating Measures' 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

We constantly "mathematize," or construct measures for, physical and social phenomena and use these models to make decisions about our everyday lives. These can vary from measures of simple quantities (such as "speed" or "steepness") to complex and subjective social ones (such as "quality of life" or "best universities"). Since these measures are mathematical models of some phenomenon, they are open to criticism and improvement, especially when considering their usefulness.

These tasks (an example) provide a fun and interesting way to assess your students' abilities to "mathematize" concepts and show students that there can be many different formal, quantitative measures of such concepts. More importantly, they emphasize that measures differ in their utility; some are more useful than others in representing concepts.

A 'Creating Measures' task consists of a series of questions that prompt students to evaluate an existing measure of an intuitive concept, and then, to create and evaluate their measure of this concept (for example, to determine the steep-ness of a staircase). These tasks take about 45 minutes of class time, but can also be done outside of class.

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 all, requires little mathematical technique. 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: Fairly demanding task for students who are unfamiliar with open-ended problems.