Guiding Questions to
Prepare Mathematical Investigations, Tasks, or Powerful Problems
Iimagine doing the investigation and answer these questions:
Questions to think about how to make it more approachable:
 How can the problem or investigation be done?
 What needs to be known to successfully complete it?
 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.
 What ways could students visualize the problem or investigation?
(pre operationally or concretely.)
 What materials are needed?
 Would using different materials make it better?
 What are the steps for different solutions?
 What can be written down or recorded?

Questions to think about to make it more purposeful:
 What ideas will the problem or investigation develop?
 What different concepts, generalizations,
big ideas, benchmarks, and landmarks will used or constructed?
 Is there connections to other mathematical ideas: problem solving heuristic, representations, problem
solving strategies, proof and reasoning, communication, connections, habits of the mind, dispositions, attitudes)?
 How will it create a desire for students to want to communicate mathematically?
 how will students be able to extend these ideas?
 how will doing the problem or investigation increase the opportunities for students to interact as a community with mathematical interests.

Questions to think about so it will accomplish the purpose for doing it.
 Can the problem or investigation promote the required reflective thought
for students to construct understanding?
 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?
 What must students reflect on to do the problem or investigation?
 What ideas must students use to complete the problem or investigation?

Questions to think about to make it more teacher friendly.
 What materials and information might it be necessary
to focus student's attention for them to successfully complete the
problem or investigation?
 What directions need to be given?
 How directive do you want to be? Will directions be
oral? Written? Demonstrated?
 How should students be grouped?

Dr. Robert Sweetland's Notes ©