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Reading closely, constructing viable arguments, critiquing others’ reasoning and using academic language are also practices of proficient math students.
To help students develop these skills, a math teacher might:
- ask students to explain and discuss their thinking processes aloud
- use a hand signal to agree or disagree with a strategy
- give multiple approaches to a problem and ask students describe which ones are rational and why
Errors can be opportunities for learning!
Successful math students can struggle productively and are comfortable changing their approach and trying new strategies if they don’t get the answer right the first time.
Here are some strategies students use to make sense of and persevere in solving a math problem:
1. Understand the problem. Ask yourself:
What are you asked to find or show?
Can you restate the problem in your own words?
Can you think of a picture or a diagram that might help you understand the problem?
Is there enough information to enable you to find a solution?
Do you understand all the words used in stating the problem?
Do you need to ask a question to get the answer?
2. Make a plan. Possible strategies might include:
Guess and check
Make an orderly list
Consider special cases
Use direct reasoning
Solve an equation
Look for a pattern
Draw a picture
Solve a simpler problem
Use a model
Use a formula
Use your head
3. Carry out the plan. Choose one. Persevere. If it continues not to work, discard it and choose another one.
4. Review/extend. Take the time to reflect and look back at what you’ve done, what worked and what didn’t.
Here are some questions that can help your child become a productive math student:
“Why do you think that?”
“Why is that true?”
“How did you reach that conclusion?”
“Does that make sense?”
“Can you make a model to show that?”
“Does that always work? Explain.”
“Is that true for all cases? Explain.”
“Can you think of a counterexample?”
“How could you prove that?”
“What assumptions are you making?”
“What would happen if…? What if not?”
“Do you see a pattern? Can you explain the pattern?”
“What are some possibilities here?”
“Can you predict the next one? What about the last one?”
“How did you think about the problem?”
“What decision do you think he/she should make?”
“What is alike and what is different about your method of solution and his/hers?”