Mathematics

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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. Students can be encouraged to explore strategies associated with other subject areas, such as reading strategies, as these can be very useful to fully understand all aspects of a question or situation. Please note that the strategies listed below can be used in any order or sequence.

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?
Comprehension
and
discrimination
  • 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?
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?
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
Regulation
and
control
  • 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?
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?
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)?
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 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?
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?
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)?
1.  These examples are based on strategies developed by the students in elementary school. They are considered to be necessary, if not indispensable, regardless of the level.

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