Mathematical Thinking

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Mathematical thinking is central to mathematics learning; it is the glue that both develops and holds mathematics learning together. It involves:

  • Looking for patterns and relationships
  • Logical reasoning
  • Making connections

The role of the teacher is to present the mathematics in ways that are accessible:

  • Using whole class ‘ping pong’ style – a recurring cycle of problem, discussion, feedback during a lesson, rather the traditional input-activity-plenary approach.
  • Avoid cognitive overload – ensure small secure steps in learning, don’t try and do too much in one lesson, let the point be the point.
  • Repetition and stem sentences – this technique enables the teacher to provide a sentence stem for children to communicate their ideas with mathematical precision and clarity. These sentence structures often express key conceptual ideas or generalities and provide a framework to embed conceptual knowledge and build understanding.
  • Learning facts to automaticity – find out more about this in our fluency section.
  • Variation and intelligent practice – find out more about this in our variation section.
  • Dong Nao Jin – a Shanghai colloquialism meaning ‘use your head’, usually presented at the end of a lesson which is challenging or trick question for students, which may let the students puzzle again and think about the knowledge in another way.



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