Guiding Questions to
Help Select Mathematical Investigations, Tasks, or Problems

Criteria 1 - It is approachable.

What is needed to do the problem or investigation?

Actually do the problem or investigation or imagine doing it and ask:

1. How can the problem or investigation be done?
2. What needs to be known to successfully complete it?
3. Is the information needed to successfully complete the problem or investigation either known by the student or available for the student within the problem or investigation.
4. What ways could you visualize students doing the problem or investigation? (pre operationally or concretely.)
5. What materials are needed?
6. Would using different materials make it better?
7. What are the steps in different solutions?
8. What could be written down or recorded?

Criteria 2 - The purpose for doing it is worthwhile.

What is the Purpose of the problem or investigation?

1. What ideas will the problem or investigation develop?
2. How would the ideas be classified concepts, generalizations, big ideas, benchmarks, landmarks, heuristics, thinking skills, problem solving skills, habits of the mind, dispositions, attitudes)?
3. Is there connections to other mathematical ideas?
4. Could there be connections to other processes, dispositions/attitudes, or perspectives of mathematics.
5. It will create a desire for students to want to communicate mathematically.
6. Will students be able to extend these ideas?
7. Doing the problem or investigation will increase the opportunities for students to interact as a community with mathematical interests.

Criteria 3 - It is reasonable to expect doing it will accomplish the purpose for doing it.

How Does the problem or investigation Accomplish the Purpose?

1. Can the problem or investigation promote the required reflective thought for students to construct understanding?
2. Is it possible to do the problem or investigation without much reflective thought? IF so, can the problem or investigation be modified so that students will be required to think?
3. What must students reflect on to do the problem or investigation?
4. What ideas must students use to complete the problem or investigation?

Criteria 4 - It is teacher friendly.

What Does the Teacher Have to Do?

1. What materials and information might it be necessary to focus student's attention for them to successfully complete the problem or investigation?
2. What directions need to be given?
3. How directive do you want to be? Will directions be oral? Written? Demonstrated?
4. How should students be grouped?