The aim of these sessions is to highlight how important the development of number sense, in particular the development of arrays, supports learners algebraic thinking. The session also highlights how a particular set of manipulatives, called Algebra tiles, currently being introduced in upper primary and secondary schools can be used to support algebraic thinking and learning.
Developing key concepts in number remains a focus within the East Ayrshire Numeracy and Mathematics Strategy.
Developing learners number sense is key to ensuring all learners can thrive within a rich numeracy and mathematics curriculum where learners have the opportunity to develop their conceptual understanding, procedural fluency and mathematical thinking.
As we plan learning, teaching and assessment across key concepts in numeracy there are a number of strategies and approaches that can incorporated into teaching and learning which supports conceptual understanding, procedural fluency and develop mathematical thinking. An approach which has been shown to support learners in developing conceptual understanding is the Concrete, Pictorial, Abstract (CPA) approach. CPA is an approach to teaching that develops a deep and sustainable understanding of maths. Developed by American psychologist, Jerome Bruner, whose premise was that children’s conceptual understanding develops from being actively engaged in three stages of learning: enactive, iconic and symbolic. The enactive, iconic and symbolic stages of learning are now more commonly referred to as Concrete, Pictorial and Abstract (CPA) stages of learning.
Numicon Resources
This section has been developed as a follow up to the Introduction to Numicon Training provided by the East Ayrshire SAC Team.
Numicon resources include more than just the numicon tiles. Numicon resources provide a range of resources to support the development of number sense by providing concrete materials to support numeracy and maths teaching and learning. This video provides an overview of the resources available in our East Ayrshire schools and some ideas of how effective planning, learning, teaching and assessment can maximise the use of these manipulatives.
Numicon CfE Planning Support Documents These documents provide guidance on how to plan for the use numicon resources across all Experiences and Outcomes from Early to Third Level
The tasks in this feature use Cuisenaire rods to help learners visualise and explore the links to be made between proportionality, equivalence, comparison, difference and pattern. If you do not have physical rods, then their Cuisenaire Environment or Mathsbot Cuisenaire will be a useful supplement.
Although some teachers associate their use more with primary classrooms, Cuisenaire rods can be a powerful visualisation tool to help students of all ages solve problems about fractions, ratio and proportions. In this feature, we introduce our new Cuisenaire interactive environment with tasks designed to promote visualising and strategic thinking.
This session is provided to follow up on the Number Talks training provided by the East Ayrshire SAC Team.
Number Talks provide regular opportunities for learners to engage in mathematical discourse and build on strategies across addition, subtraction, multiplication and division. A Number Talk is a brief, ongoing, daily routine that helps students develop computational fluency through the opportunity to share their thinking processes to solve a mathematical problem aloud. The link below will take you to professional development materials and links to Number Talks resources:
The East Ayrshire Fractional Reasoning twilight training inputs contain references to using number talks in relation to assessing learners understanding as they develop their understanding of fractions, decimals and percentages. The blog posts Teaching Fractions Part 1 and Teaching Fractions Part 2 provides videos of these inputs and links to resources to support the planning, learning, teaching and assessment in relation to rational numbers with specific references to Number Talk resources.
The Power of Arrays and Using Algebra Tiles
A particular set of manipulatives, called Algebra tiles, are currently being introduced in upper primary and secondary schools to support algebraic thinking and learning. The CLPL sessions in the link below highlight how important the development of number sense, in particular the development of arrays, supports learners algebraic thinking leading to the effective use of algebra tiles.
Teaching fractions, decimal fractions and percentages is perceived to be difficult to do well and for learners fractions, decimal fractions and percentages are commonly found to be difficult for them to learn. This series of videos looks at how the development of fraction sense can be incorporated into maths lessons and how this conceptual understanding of fractions can be developed to improve learners understanding of fractional relationships.
In the second part of this series we will look at the decimal fraction and percentage representations of rational numbers and how the links between fractions, decimals and percentages can be developed with learners.
Teaching fractions, decimal fractions and percentages is perceived to be difficult to do well and for learners fractions, decimal fractions and percentages are commonly found to be difficult for them to learn. This series of videos looks at how the development of fraction sense can be incorporated into maths lessons and how this conceptual understanding of fractions can be developed to improve learners understanding of fractional relationships.
The first part of the series looks at the 6 Big Ideas that underpin understanding of fractional relationships and how particular materials and visuals can support understanding. The second part looks at how links and connections can be made to connect fractions, decimal fractions and percentages. A glow login will be required to access the materials.
