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Mathematics

Examples of Strategies

The strategies that are helpful for the development and use of the three mathematics competencies are integrated into the learning process. It is possible to emphasize some of these strategies, depending on the situation and educational intent. Since students must build their own personal repertoire of strategies, it is important to encourage them to become independent in this regard and help them learn how to use these strategies in different contexts.

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?
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?
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?
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)
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?
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?
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?
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?
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?
Other strategies
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?
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)?