Learning outcomes
After studying this chapter, you should be able to:
• discuss the importance of mathematics in modern society, including fundamental aspects of mathematical literacy and numeracy
• describe the Proficiency Strands of the Australian Curriculum: Mathematics
• summarise the key features of some important theories about student learning
• identify some ways in which teachers can promote student engagement in mathematics lessons.
Introduction
The purpose of this chapter is to consider the nature of mathematics, its importance in the lives of twenty-first century students, and to discuss some key theories about how learning takes place. The chapter begins with a description of some of the key knowledge, skills and understandings that today's students need in order to participate fully in modern society. Next, we discuss some of the significant developments in theories about how students learn mathematics and some implications of these theoretical approaches for your work as a teacher. The chapter concludes with a look at how we might engage students more productively in mathematics lessons in order to cultivate positive attitudes to the subject among students and to improve their learning outcomes. At various points in the chapter we shall discuss some relevant scholarship and research that may provide guidance for your work of teaching mathematics in secondary classrooms. We will also explore some of the HOTmaths resources (www.hotmaths.com.au) that you could use in your lessons and you will have an opportunity to reflect on their significance.
Key terms
• Behaviourism: a theory of learning that is mainly concerned with observable behaviour and assumes that learners respond passively to external stimuli.
• Constructivism: a cognitivist theory of learning that views the learner as an active constructor of knowledge.
• Engagement: the level of attentiveness, interest and curiosity that students exhibit when they are learning.
• Financial literacy: the ability to manage money and financial risks effectively and responsibly in order to achieve one's financial goals.
• Gestaltism: a theory that suggests that the mind processes wholes first, before attending to constituent parts.
• Numeracy: the ability to understand and work flexibly and efficiently with numbers and other mathematical concepts to solve a variety of problems across a range of contexts.
• Socioculturalism: a view of learning that emphasises how learning does not take place solely within the mind of the individual, but also through one's interactions with others.
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