LEARNING OUTCOMES
By the end of this chapter, you will:
• understand the central importance of patterns in early childhood and primary school mathematics
• understand the importance of mathematical structure and its relevance to children's learning of mathematics
• use sequences effectively to find and justify rules, and to explain
• represent and resolve number sentences, equivalence and equations
• be able to describe relationships between variables
• be able to use technology effectively to explore algebraic situations.
KEY TERMS
• Algebraic thinking: Thinking that considers the general relationships between numbers, rather than the manipulation of numbers
• Equation: A number sentence that states two quantities are equal
• Equivalence: A state of being equal or equivalent; balanced
• Generalisation: The formalisation of general concepts; general statements that can be used to form conclusions
• Pattern: A set of objects or numbers in which each is related to the others according to a particular regularity or rule
• Variable: A value that can change within a problem or set of operations
Until fairly recently, algebra was regarded as the domain of the secondary school years in most countries. In addition, it was often regarded in quite narrow ways by non-mathematics teachers, parents and students themselves as being concerned with the manipulation of symbols according to tightly prescribed rules. Recent attention to algebra in the primary school has not regarded it as appropriate that such a narrow view of algebra be taken, leading to the use of terms such as ‘pre-algebra’ or ‘early algebra’ to describe the mathematics involved.
In this chapter, it is recognised that students’ understanding of algebra in the secondary school rests on foundations that are laid in the primary school, as reflected in the Australian Curriculum: Mathematics and in the New Zealand Mathematics Curriculum. These foundations are concerned with key algebraic ideas about patterns and generalisations, rather than with symbolic representations of these using xs and ys. This chapter explores developmental models associated with patterns and algebraic concepts, with a focus on how ICT and other resources can be used to develop algebraic thinking.
Linking with curriculum
In the Australian Curriculum: Mathematics, Patterns and Algebra is included as a sub-strand within Number and Algebra.
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