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Cognitive and metacognitive strategies |
| Planning |
- What is the task that I am being asked to perform?
- What concepts and processes do I need to use?
- What information is relevant, implicit or explicit?
- Is some information missing?
- Do I need to break the task down?
- How much time will I need to perform this task?
- What resources will I need?
- What do I need to establish a work plan?
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Comprehension
and
discrimination
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- Am I able to extract the information contained in the registers (type) of representation involved?
- Which terms seem to have a mathematical meaning different from their meaning in everyday language?
- What is the purpose of the task? Am I able to explain it in my own words?
- Do I need to find a counterexample to prove that what I am stating is false?
- Is all the information pertaining to the situation relevant? Is some information missing?
- Is there any way I can illustrate the steps involved in the task?
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| Organization |
- Should I group, list, classify, reorganize or compare data? Should I use diagrams to show the relationships between objects or data?
- Can I use objects or technological tools to simulate the situation?
- Can I use a table or chart? Should I draw up a list?
- Are the main ideas in my approach well represented?
- What concepts and mathematical processes should I use?
- What registers (types) of representation (words, symbols, figures, graphs, tables, etc.) could I use to translate this situation?
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| Development |
- Can I represent the situation mentally or in written form?
- Have I solved a similar problem before?
- What additional information could I find using the information I already have?
- What mathematical concepts could apply? What related properties or processes could I use?
- Have I used the information that is relevant to the task? Have I considered the unit of measure, if applicable?
- Can I see a pattern?
- Which of the following strategies could I adopt?
- Use trial and error
- Work backwards
- Give examples
- Make suppositions
- Break the task down
- Change my point of view or strategy
- Eliminate possibilities
- Simplify the task (e.g. reduce the number of data, replace values by values that can be manipulated more readily, rethink the situation with regard to a particular element or case)
- Translate (mathematize) a situation using a numeric or algebraic expression
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Regulation
and
control
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- Is my approach effective and can I explain it?
- Can I check my solution using reasoning based on an example or a counterexample?
- What have I learned? How did I learn it?
- Did I choose an effective reading strategy and take the time I needed to fully understand the task?
- What are my strengths and weaknesses?
- Did I adapt my approach to the task?
- What was the expected result?
- How can I explain the difference between the expected result and the actual result?
- What strategies used by my classmates or suggested by the teacher can I add to my repertoire of strategies?
- Can I use this approach in other situations?
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| Generalization |
- In what ways are the examples similar or different?
- Which models can I use again?
- Can the observations made in a particular case be applied to other situations?
- Are the assertions I made or conclusions I drew always true?
- Did I identify examples or counterexamples?
- Did I see a pattern?
- Am I able to formulate a rule?
- Am I able to interpolate or extrapolate?
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| Retention |
- Is what I learned connected in any way to what I already know?
- Which concepts are the most important for identifying other concepts?
- Under what conditions does a certain process work? On what properties is it based?
- Am I able to illustrate or modify the concepts and processes I know?
- What characteristics would a situation need in order for me to reuse the same strategy?
- Would I be able to repeat the task again on my own?
- What methods did I use (e.g. repeated something several times to myself or out loud; highlighted, underlined, circled, recopied important concepts; made a list of terms or symbols)?
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| Development of automatic processes |
- Did I find a solution model and list the steps involved?
- Did I practise enough in order to be able to repeat the process automatically?
- Am I able to effectively use the concepts learned?
- Did I compare my approach to that of others?
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| Communication |
- Did I show enough of my work so that my approach was understandable?
- What registers (types) of representation (e.g. words, symbols, figures, diagrams/graphs, tables) did I use to interpret a message or convey my message?
- Did I experiment with different ways of conveying my mathematical message?
- What method could I use to convey my message?
- What methods would have been as effective, more effective or less effective?
- Did I follow the rules and conventions of mathematical language?
- Did I adapt my message to the audience and the communication intent? How can I adapt it?
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| Other strategies |
| Affective strategies |
- How do I feel?
- What do I like about this situation?
- Am I satisfied with what I am doing?
- What did I do particularly well in this situation?
- What methods did I use to overcome difficulties and which ones helped me the most to reduce my anxiety? stay on task? control my emotions? stay motivated?
- Am I willing to take risks?
- What did I succeed at?
- Do I enjoy exploring mathematical situations?
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| Resource management strategies |
- Whom can I turn to for help and when should I do so?
- Did I accept the help offered?
- What documentation (e.g. glossary, ICT) should I use? Will it be helpful?
- What manipulatives can help me in my task?
- Did I estimate correctly the time needed for the activity?
- Did I plan my work well (e.g. planned short, frequent work sessions; set goals to attain for each session)?
- What methods should I use to stay on task (e.g. appropriate environment, available materials)?
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