Classroom Assessment Techniques 'Creating Measures' Tasks (Screen 4 of 4)

Variations
The tasks included in this site can be downloaded and used without modification. If you choose to develop your own 'Creating Measures' task, you can follow the pattern used in these tools:

• Give students a warm-up discussion to make sure they understand the concept that they are trying to mathematize;
• Provide a measure, ask them to apply this measure to various examples, and to evaluate the usefulness of that measure;
• Ask them to come up with their own measure and apply it to various examples; and,
• Ask them to evaluate the usefulness of that measure.

For example, you could ask students to devise a measure for the "readability" of a piece of text. You might propose "average sentence length" as a starting measure then offer a number of texts for them to rank order using your suggested measure. They could then evaluate the usefulness of that measure using their own "gut feeling." You could use the following question to motivate this inquiry:

• Does text A feel more difficult than text B?
• What does the measure ignore?

They may then try to improve the measure by considering other factors such as average word length, average number of words or syllables per sentence, percentage of polysyllabic words, use of passive or active voice and so on. After arriving at their own individual measures, students may like to compare their own rank ordering of texts with each other in order to evaluate them.

For more formal assessment, you might choose a task from the materials available at the end of this CAT, then strip out a number of the steps which provide support in coming to a solution. In this way, you can assess the extent to which students have internalized these analytic skills.

Analysis
Student work can be measured against three criteria:

• whether students can use a given measure and identify its limitations;
• whether they can define their own quantitative measure; and,
• the degree to which they can explore the utility of this measure.

This generic scoring rubric may be modified and adapted for specific tasks.

Category of performance	Typical response
The student needs significant instruction	Student can use a given measure of a concept, but cannot identify its limitations. Student cannot devise a different measure of the concept.
The student needs some instruction	Student can use a given measure of a concept and identify some of its limitations. Student may suggest a different measure of the concept, but it may not be numerical.
The student's work needs to be revised	Student can use a given measure of a concept and identify its limitations. The student can also formulate a precise numeric measure, but does not evaluate the measure or discuss where it is appropriate.
The student's work meets the essential demands of the task	Student can use a given measure of a concept and identify its limitations. The student can also formulate a precise numeric measure and can evaluate the utility of that measure.

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Introduction
Description, Purpose, and Limits
Goals, Use, and Instructions
Variations and Analysis
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Tools

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