I try to use reflection in math class, especially with problems that are challenging or complex. Here are some questions to ask:
Cognitive Skills type (questions or stems)
What is priority #1 in this problem?
Which symbol do you want to ask about?
My first step will be to ...
How many steps will there be for completion of this problem?
This problem LOOKS difficult because...
Write a question about this problem for the teacher, or a partner, or the author...
Affective type
Which problem did you enjoy more?
If you were offered a "life-line" for one problem, which would you choose and why?
Which did you like better: the problem with fractions or the problem with square roots? Why?
If your partner was stuck, what could you do or say to help them?
Were you and your partner successful on the problems? What did you do together that enabled you to be successful?
What did you feel was the most difficult part of this problem? Does your partner agree/disagree? Why?
Do you like to work as part of a group in problems like this? Was your partner helpful?
Additional
Draw a diagram to represent the solving of this problem...
What is your answer was 3.215693......? Does it make sense for this equation?
Complete: This problem reminds me of (or is like)...
How would a mathematician have written the solution? How would a chef have written the solution? Would it be different? Why?
Can you create your own problem and have your partner (or me) solve it?
Is there another problem that has this same answer? Can you create one?
These questions are sometimes placed at the end of practice problems, or at the end of a test/quiz. The question and response is a conversation between the student and myself. I can make an additional comment and return the conversation to the student.
Students use vocabulary, goal setting skills, prioritizing, creativity, and they realize that I respect and value their perceptions of the challenging material.
Cognitive Skills type (questions or stems)
What is priority #1 in this problem?
Which symbol do you want to ask about?
My first step will be to ...
How many steps will there be for completion of this problem?
This problem LOOKS difficult because...
Write a question about this problem for the teacher, or a partner, or the author...
Affective type
Which problem did you enjoy more?
If you were offered a "life-line" for one problem, which would you choose and why?
Which did you like better: the problem with fractions or the problem with square roots? Why?
If your partner was stuck, what could you do or say to help them?
Were you and your partner successful on the problems? What did you do together that enabled you to be successful?
What did you feel was the most difficult part of this problem? Does your partner agree/disagree? Why?
Do you like to work as part of a group in problems like this? Was your partner helpful?
Additional
Draw a diagram to represent the solving of this problem...
What is your answer was 3.215693......? Does it make sense for this equation?
Complete: This problem reminds me of (or is like)...
How would a mathematician have written the solution? How would a chef have written the solution? Would it be different? Why?
Can you create your own problem and have your partner (or me) solve it?
Is there another problem that has this same answer? Can you create one?
These questions are sometimes placed at the end of practice problems, or at the end of a test/quiz. The question and response is a conversation between the student and myself. I can make an additional comment and return the conversation to the student.
Students use vocabulary, goal setting skills, prioritizing, creativity, and they realize that I respect and value their perceptions of the challenging material.
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