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Maths concept maps

This is a series of framework statements that have been developed in significant areas of mathematics. They: 

  • provide information about the key mathematical ideas involved

  • link to relevant ARB resources, and 

  • suggest some ideas on the teaching and assessing of that area of mathematics.

These concept maps are added to as further research and trialling in the respective areas are conducted.

Probability (2010)
Probability is all around us. It underpins both statistical investigations and statistical literacy. While the main thrust is on quantitative probability, qualitative probability is also addressed. Key probability ideas and common misconceptions are also covered.

Basic facts (2009)
This looks at the usual addition, subtraction, multiplication, and division basic facts. It also extends these to larger numbers, and to fractions, decimals and percentages as well. Students who have a good vocabulary of basic facts are able to concentrate on other aspects of mathematical problems.

Algebraic patterns (2009)
The study of patterns is a key part of algebraic thinking. It is important that students are able to recognise and analyse patterns and make generalisations about them.
Patterns can be created from shapes, sounds, colours or numbers. They can be visual or spatial, repeating or growing. Students can continue a given pattern, find missing elements, identify general rules, or make up their own pattern.

Fractional thinking

This provides a concept map of teaching and learning issues for fractions.  It looks at partitioning, part-whole understanding of fractions, equivalence, and fractions as operators.  Links to relevant ARB resources are also provided.

Algebraic thinking
This concept map highlights key areas of Algebraic thinking that influence students' ability to solve algebraic equations in later years.  The concepts covered are equality, additive identity, commutativity, and associativity.  Links to relevant ARB resources are also provided.

Computational estimation
This gives a general introduction to computational information, including some important mathematical skills and attitudes that the research indicates are needed to be an effective estimator. It includes a directory of different types of estimation, and includes a description of a range of estimation techniques.


Journalling in Mathematics
This is about the benefits of journalling in Mathematics.  It includes a range of practical ideas for journalling in the maths classroom, and links to some relevant ARB resources.


Other big maths ideas and concept maps based upon an ongoing research programme at NZCER will be added as they are completed.  Currently concept maps about Algebraic patterns and Basic facts are being developed.


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