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Making connections : Post 16 Level 2 : Mathematics-specific Pedagogy

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Post 16 Level 2
Making connections
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1. How confident are you that you can support learners in making connections between mathematical representations and topics?

a. Activity One


These cards (below) from Improving learning in mathematics focus learners’ attention on a specific aspect of algebraic notation. Learners are expected to interpret each representation and match them together if they have an equivalent meaning.

Problem 1

Your task is to create a different set of cards that will encourage learners to interpret some other representations in mathematics.

  • These might include words, algebraic symbols, pictures, graphs, tables, geometric shapes, etc.
  • Try to create cards that require learners to distinguish between representations that they often confuse such as (3n)2 and 3n2 in the example.


Mathematical concepts have many representations; words, diagrams, algebraic symbols, tables, graphs and so on. Activities such as the one above are intended to allow these representations to be shared, interpreted, compared and grouped in ways that allow learners to construct meanings and links between the underlying concepts.

In most mathematics teaching and learning, a great deal of time is already spent on the technical skills needed to construct and manipulate representations. These include, for example, adding numbers, drawing graphs and manipulating formulae. While technical skills are necessary and important, this diet of practice must be balanced with activities that offer learners opportunities to reflect on their meaning. These activities provide this balance.

Learners focus on interpreting rather than producing representations. Perhaps the most basic and familiar activities in this category are those that require learners to match pairs of mathematical objects if they have an equivalent meaning. This may be done using domino-like activities. More complex activities may involve matching three or more representations of the same object.

Typical examples might involve matching:

  • times and measures expressed in various forms (e.g. 24-hour clock times and 12-hour clock times)
  • number operations (e.g. notations for division)
  • numbers and diagrams (e.g. decimals, fractions, number lines, areas)
  • algebraic expressions (e.g. words, symbols, area diagrams)
  • statistical diagrams (e.g. frequency tables, cumulative frequency curves).

The discussion of misconceptions is also encouraged if carefully designed distracters are also included.

From: Improving learning in mathematics: challenges and strategies Malcolm Swan

“The good thing about this was, instead of like working out of your textbook, you had to use your brain before you could go anywhere else with it. You had to actually sit down and think about it. And when you did think about it you had someone else to help you along if you couldn’t figure it out for yourself, so if they understood it and you didn’t they would help you out with it. If you were doing it out of a textbook you wouldn’t get that help.” A GCSE learner at High Pavement College quoted in Improving learning in mathematics.

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