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 ©