Suggestion 1: Encourage students to take accountability for their own learning of mathematics.
- let the students lead with their ideas
- value their ideas (even crazy guesses)
- build on their ideas and use them, don't ignore or dismiss them
Suggestion 2: As you circulate in the room and notice that different groups have different approaches to the same problem, make time to have each group present their solution to the group. Encourage the listeners to value (notice) one thing in the presentation and ask one question (wonder) of the presenting group.
Suggestion 3: Give each group of students a different PoW. Have them present their problem and solution to the group.
Suggestion 4: Consider returning to work on a problem again at a later date. Start that session by having students read each other's explanations. Encourage reflection. Allow revision. The goal is not to be over and done. The goal is to think, communicate, reflect, revise, and improve.
Suggestion 5: Make use of the Solution and Commentary link to create either a handout or a Word file to project in the workshop. We talked about the idea that timing/sensitivity is key but these examples of thorough explanations can be used as examples and expectations.
Suggestion 6: Are there students who stand out as facilitators? Look for students in a group who ask good questions. Encourage noticing and wondering as opposed to showing and telling.
Suggestion 7: As the workshops get under way (the first few weeks or possibly longer) make it a habit to mix up the groups! Look for students who facilitate and spread them around. Look for show-and-tellers and spread them around. Reinforce the behavior you are looking for -- praise the facilitators and, perhaps, have a private (positive) word with the show-and-tellers explaining what the goal is -- noticing and wondering!
Suggestion 8: Have a conversation with the students about the Problem Solving Process. Encourage them to think about the steps of the Writing Process. Remind them that in STEM courses they'll also encounter the Engineering Process and, of course, the Scientific Process or Method.
Suggestion 9: The Standards for Mathematical Practice describe varieties of expertise that mathematics students should strive to improve. These practices rest on important processes and proficiencies in problem solving, reasoning and proof, communication, representation, making connections, adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition. The specific Mathematical Practices are:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Read specifics about each practice on the site of the Common Core State Standards.