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How can practical resources support the development of mathematical understanding?

Created on 20 April 2010 by ncetm_administrator
Updated on 08 April 2013 by ncetm_administrator


What is a good learning environment to promote mathematical learning?

This strand is about the environment where children are learning mathematics; the resources they use and how they use them, the space where they learn and the walls they look at, and how this all supports the mathematical learning.
In this strand you will:

  • consider resources that are available in your school to support the development of children’s mathematical understanding
  • explore how the classroom environment can be used to stimulate and reinforce learning
  • reflect on the best use of the classroom space to support 
  • develop your ideas about the role of ICT in mathematical learning.

When you have completed this strand you will:

  • have a clear picture of what resources are available in your school for teaching mathematics
  • have a better understanding of the importance of the classroom environment as a tool for supporting learning in mathematics
  • understand how the classroom and resources that are used to support learning in mathematics, may need to be different for different children
  • have built your opinion about how ICT can, and cannot help children’s learning in mathematics.

There has long been a belief that practical resources and activities significantly enhance children’s understanding of, and ability to use mathematical ideas with confidence.

What resources are available for children to use in mathematics in your school. 
Make a list of the five most used items in mathematics lessons your own class.
Next to each one, make a note of how they are used.
Try to be specific, rather than saying, for example’ ‘for addition’.

Ask two colleagues to make a list of the five most used items in mathematics lessons in their classes and what they are used for?
What is the same about your lists? What is different?

This is the summary from research into the use of Numicon as a mathematical model:
Our findings show striking evidence of children (from all ability groups) responding positively to visual structured images and the related programme of activities. Colleagues in other schools who have adopted the approach since dissemination of the findings report similar responses, as do ITT students using the approach. We feel this justifies much larger scale development work to further test the findings, especially since the approach enables achievement of the National Numeracy Strategy’s objectives in the Framework. Other research into arithmetic teaching suggests that current approaches in many schools, and in many published mathematics materials, continue both to underplay confident, relational mental arithmetic and to allow children to build their arithmetic laboriously upon limiting counting procedures. Unfortunately the models and images for number recently published by the National Numeracy Strategy do not include any references to structural apparatus. We find this disappointing in the light of the many children’s successes with Catherine Stern’s images and approaches that we have seen, but perhaps classroom teachers will continue to choose for themselves approaches and equipment that they know work.
Learning about numbers with patterns using structured visual imagery (Numicon) to teach arithmetic
Romey Tacon and Ruth Atkinson with Dr Tony Wing
Summary of a research project carried out at an infant school in England

Do you think the findings from this research are applicable to other mathematical resources?

Consider one other mathematical resource from your list, and one from a colleague’s list.
Record your thoughts in your Personal Learning Space. How does this resource help the children build mental images in mathematics?

You can read more about Learning Theories in this PDF document.

Supporting children to build their own mental images
The most helpful role of practical equipment in mathematical learning, is to support the children in building their own mental images. The chart Models and images for multiplication and division is just one of six charts available from the National Strategies, aimed at supporting teachers with the use of appropriate models and images in six key areas of learning.
The chart gives an indication of the wide range of images children need to be able to interpret before they really understand multiplication and division. This helps adults understand why a true understanding of these operations takes time to build.

The Models and Images charts can be used to share with children, or as a resource for teachers to illustrate the complexity of the ideas illustrated, to enable teachers to identify appropriate activities and resources to support their children. There is also a DVD of support material available

The Mathemapedia entry Selecting and using resources for learning at KS2 may also be helpful when thinking about the resources used in your school.

Record your thoughts in your Personal Learning Space.

Consider how resources are used in your class and other classes in your school.
Drag and drop these statements into the appropriate place on the line. There are two copies of every statement so you can complete one diagram for your own class, and one for summarising practice in the rest of the school, or in another classroom. 

How do you think mathematical resources can support mathematical learning?
List a few ideas in your Personal Learning Space.

Have a look at the Key Elements (Primary) area of the Excellence in Mathematics Leadership (EiML) materials: Learning Environment and Resources. After viewing this, you may wish to add to your list.

Here are some examples from the links above that you may wish to try:
  • have an area of the room where resources are kept temporarily- ie. a ‘These things might help you this week’ table
  • develop a culture where the children are expected to use resources to model what they are doing, and to explain how they are using them
  • identify a key resource and spend time building children’s understanding of how it works. Keep it on their work tables permanently for a while
  • teach the adults who work with the children how the resource can help the children
  • ask the children how they visualise numbers- identify resources that support their visualisations. 

Something to share from Issue 4 of the NCETM Primary Magazine gives a framework for a staff meeting about resources and how they are used.

Summarise your thoughts on the use of resources to help children’s mathematical learning in your Maths Subject Leader folder. Keep a list of the maths resources that you have in school and a prioritised wish list for those you would like to have when budget permits.





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