Chapter 2

All but one of these methods can be used to demonstrate mathematical understanding of a concept.

• Draw a diagram
• Explain the meaning using words
• Create a graph
• mimic the work of another

An non-example of a physical manipulative in math is...

• connecting cubes
• spinner
• website
• all of the above

Identify the worst example of mathematical proficiency.

• strategic competence
• procedural fluency
• conceptual understanding
• rote memorization

Which is the best way to pose a task to students so that they experience "doing mathematics"?

• Have the student take the problem home and solve, then bring it back to school to discuss.
• Teach the skill that is needed to solve the problem first, then give this problem as an extension.
• Share the problem, ask students to explore, stop them to see how they are doing, and let them keep going.
• Give an example of how to do a problem that is similar to the one you have selected, but slightly easier, so that students know what to do.

Doing mathematics is...

• finding and exploring regularity and order and then making sense of it.
• duplicating or mimicking processes teachers have modeled and provided time for independent practice on.
• imitating what the teacher shows the class.
• rote memorization and isolated practice with no cohesion. 

In the real world of problem solving and doing mathematics...

• answers require justification.
• duplicating or mimicking processes teachers have modeled and provided time for independent practice on.
• imitating what the teacher shows the class.
• rote memorization a 

The best non-example of procedural fluency in mathematics is...

• being accurate and quick at using standard algorithms for each operation.
• student's ability to be flexible and employ creative thought.
• student's ability to choose an appropriate strategy
• a productive disposition when it comes to solving a problem

A math task can only be labeled as "doing mathematics" if...

• it involves an open-ended problem.
• requires looking for patterns and order.
• engages the learner in reasoning mathematically.
• it is fun.

Effective learning practices in mathematics do not include ...

• building on prior knowledge.
• creating opportunities for reflective thought.
• encouraging multiple approaches to solving a problem.
• providing an algorithm prior to allowing students to discover patterns and order in a problem.

Teachers should interpret math errors as...

• An insight into misconceptions students might have.
• a misapplication of their prior knowledge in the new situation.
• None of the above.
• Both insight into misconceptions and misapplication are possibilities.