PBS Teachers™

Bottles and Divers
(Rates of Change)
High School Math Project

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Procedure	Tips from Ellen
Assessment	Resources
Extensions & Adaptations	Ideas for Discussion
Mathematically Speaking	More Lessons: Grades 9-12

Tips from Ellen

Cues for Asking Good Questions

A key ingredient in reform mathematics is enhancing discourse in the classroom, and effective questioning can be a key to effective discussion. Dimensions of Learning is an approach that has taken the best of what we know about the relationships between how we think and how we learn and created a framework to help teachers plan and deliver instruction. Dimension 3 relates to thinking which extends and refines knowledge, and offers a list of different types of questions which promote different kinds of thinking and learning.

The following chart is presented as a resource. Many teachers create a cue card or chart for themselves as a handy reference in planning or teaching. You might create a goal for yourself of ensuring that you use at least four types of questioning in each lesson.

Comparison	Identifying and articulating similarities and differences between things. Example: How are these things alike? different?
Classification	Grouping things into definable categories on the basis of their attributes. Example: Into what groups could you organize these things? What are the rules for membership?
Induction	Inferring unknown generalizations or principles from observation or analysis. Example: Based on the observations we have listed, what conclusions might you draw?
Deduction	Inferring unstated consequences and conditions from given principles and generalizations. Example: If we accept these generalizations as true, what conclusions necessarily follow?
Error Analysis	Identifying and articulating errors in your own thinking or in that of others. Example: How is the reasoning in this argument misleading?
Constructing Support	Building a system of support or proof for an assertion. Example: What facts would support this claim?
Abstracting	Identifying and articulating the underlying theme or general pattern of information. Example: What pattern do you see?
Analyzing Perspective	Identifying and articulating your personal perspectives on issues as well as others' perspectives. Example: How might someone else see this, and what reasoning might they use to support their position?