| Cognitive and metacognitive strategies |
| Strategies |
Reflection |
| Planning |
- What is the task that I am being asked to do?
- What prior learning do I need to use?
- What information is relevant?
- Do I need to break the problem down?
- How much time will I need to do this task?
- What resources will I need?
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| Comprehension |
- Which terms seem to have a mathematical meaning different from their meaning in everyday language?
- What is the purpose of the question? Am I able to explain it in my own words?
- Do I need to find a counter-example to prove that what I am stating is false?
- Is all the information in the situation relevant? Is some information missing?
- What kind of diagram could demonstrate the steps involved in the task?
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| Organization |
- Should I group, list, classify, reorganize or compare the data, or use diagrams (representations that show the relationships between objects or data)?
- Can I use concrete objects or simulate or mime 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 type of representation (words, symbols, figures, diagrams, 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?
- Have I used the information that is relevant to the task? Have I considered the unit of measure, if applicable?
- What mathematical expression translates the situation?
- Can I see a pattern?
- Which of the following strategies could I adopt?
- Make systematic trials
- Work backwards
- Give examples
- Break the problem down
- Change my point of view
- Eliminate possibilities
- Simplify the problem (e.g. reduce the number of data values, replace values by values that can be manipulated more easily, rethink the situation with regard to a particular element)
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| Regulation |
- Is my approach effective and can I explain it?
- Can I check my solution using reasoning based on an example or a counter-example?
- What I have I learned? How did I learn it?
- Did I choose an effective strategy and take the time I needed to fully understand the problem?
- What are my strengths and weaknesses?
- Did I adapt my approach to the task?
- What was the result expected?
- 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?
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| Retention |
- 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)?
- Would I be able to solve the problem again on my own?
- What characteristics would a situation need in order for me to reuse the same strategy?
- Is what I learned connected in any way to what I already knew?
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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 work so that my approach was understandable?
- What forms of representation (words, symbols, figures, diagrams, tables, etc.) did I use to interpret a message or convey my message?
- Did I experiment with different ways of conveying my mathematical message?
- Did I use an effective method to convey my message?
- What methods would have been as effective, more effective or less effective?
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| Other strategies |
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Reflection |
| 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 are my successes?
- 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) did I use? Was it helpful?
- What manipulatives helped me in my task?
- Did I estimate the time needed for the activity correctly?
- Did I plan my work well (e.g. planned short, frequent work sessions; set goals to attain for each session)?
- What methods did I use to stay on task (appropriate environment, available materials)?
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