This chapter begins with an overview of the key components of lesson planning and what this looks like in the context of a mathematics lesson. We consider approaches to planning that focus on developing a sound conceptual understanding of important mathematical concepts. We then look at how the use of technology can be planned for and capitalised on to support students’ learning, including in an online environment, and within the context of a 21st century classroom. The latter part of the chapter uses classroom snapshots and case studies to show how mathematical skills, knowledge and understanding can be developed through the use of inquiry over a series of lessons.

Educationally, we are in an exciting time in terms of geometrical investigations in the classroom. While the manipulation of concrete materials to enable student construction of two-dimensional figures and three-dimensional objects has been readily available for many years, there are a growing number of mathematics classrooms that have access to dynamic geometry software and interactive sites that enable real-time creation and exploration of geometric figures and their properties. In fact, in some pockets of society, students’ access to a mobile device is in a similar manner to how classrooms of the 1980s used pen and paper as a resource. While, in jest, mobile devices may be referred to ‘an extension of the brain’, in its regular use as an instant source of information and exploration there is an element of this use that can be exploited for positive gain in the mathematics classroom. This chapter explores the development of geometrical concepts and the manner in which we can facilitate exploratory experiences to assist students in their development.

This chapter delves into the challenges and rewards of working in remote areas of countries such as Australia and small Pacific nations. Teaching strategies are presented to assist in maintaining a positive learning environment in remote and small Pacific-nation classrooms. The importance of the relationships among and between parents, students, teachers and other community members is explored, along with practical suggestions for making the most of the available resources. This chapter explores strategies for making the most of available resources and the invaluable professional experience of working in these areas.

Until 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 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 v. 9.0. These foundations are concerned with key algebraic ideas about patterns and generalisations, rather than with symbolic representations of these, such as x and y. This chapter explores developmental models associated with patterns and algebraic concepts, with a focus on developing algebraic thinking.

Schools are technology rich. Teachers routinely now use digital tools for reporting, communications within school and with parents, for maintaining class records, for preparing materials and so on. Some schools use online teaching programs or electronic textbooks. With NAPLAN moving to become fully online (see Chapter 19) there is a need for both teachers and students across the primary years to be confident and creative users of digital technology. Each chapter in this book has included examples and strategies for integrating digital tools into the teaching of mathematics across a range of mathematical content areas.

This chapter considers the range of possible education support roles in the mathematics classroom that a teacher may work with. This chapter presents effective ways of working collaboratively with education support workers and explores positive planning of learning experiences which considers the affordances of various education support workers’ roles.

This chapter examines suitable statistics questions for investigation by children of different ages, using a cycle of problem, plan, data, analysis and conclusion (PPDAC) (Wild & Pfannkuch 1999). The importance of variation in data and different types of variables and the difference between a population and a sample are investigated. Readers will explore different ways of displaying data to ‘tell a story’. The importance of drawing inferences from data and the uncertainty associated with these inferences are discussed. Readers will engage in activities that use technology to support the development of statistical understanding.

Measurement is an aspect of the mathematics curriculum that has wide usage in everyday life. A basic level of knowledge, skills and confidence in measurement is very much part of being numerate. An analysis of the measuring process suggests that children learn to measure first by becoming aware of the physical attributes of objects and how they compare with other objects. Estimation is a significant aspect of measurement and should be seen as an integral part of the measurement process. The ability to estimate is enhanced when students have strong spatial awareness and are able to visualise and represent measurement situations in their heads. Students therefore need to be given plenty of opportunities to engage in measurement activities that focus on developing a sound understanding of the attribute being measured, along with the act of measuring.

Uncertainty is a part of everyday life. We live with a range of situations that inherently have an element of uncertainty in them – for example, crossing the road, going on holiday, or making a major purchase – but we often ignore the embedded chance in these activities. Risk is acknowledged in many activities, and much effort is expended in identifying these risks and minimising any potential negative outcomes. In schools, for example, a risk assessment is required prior to any excursion with children. Probability is the strand of mathematics that addresses uncertainty. This chapter explores ideas relating to probability in the mathematics classroom.

This chapter addresses the challenges associated with moving from being a pre-service teacher into being a member of the teaching profession. It explores ideas associated with testing and the pressures this can place on students and teachers; collecting evidence of teaching effectiveness for both accreditation and personal development; keeping a professional portfolio; and becoming a full member of a professional learning community. At all times mathematics, and its teaching and learning, is at the centre of the discussion.

Developing computational skills and the concepts that underpin proportional reasoning is a large component of the primary mathematics curriculum. Moving children’s thinking towards proportional reasoning will be covered in more detail in Chapter 6. The research base about the development of number concepts in individual students goes back many years and is too large to address in detail (e.g. Björklund et al., 2020; Whitacre et al., 2020). In this chapter, the focus is on effective teaching to enhance learning: developing computational skills, the relationships between different operations and moving from additive to multiplicative thinking.

The Australian Curriculum: Mathematics v. 9.0 (ACARA 2022) is structured around six content strands: Number, Algebra, Measurement, Space, Statistics and Probability. An expectation of mathematical proficiency has been embedded into curriculum content across all strands. It is expected that students will develop and apply mathematical understanding, fluency, reasoning and problem-solving as they learn mathematical content. It is these areas that typically receive the most attention in mathematics classrooms, particularly as there are requirements to assess and report on students’ progress in these strands. The Australian Curriculum v. 9.0 also identifies seven general capabilities, which encompass knowledge, skills, behaviours, and dispositions, and three cross-curriculum priorities: Aboriginal and Torres Strait Islander histories and cultures, Asia and Australia’s engagement with Asia, and Sustainability. However, Atweh, Miller and Thornton (2012) contend that these areas receive minimal reference in the content descriptions and elaborations, leading to the impression that they are only given lip service. This chapter will provide an overview of the general capabilities and cross-curriculum priorities, and will also identify ways in which these aspects of the curriculum can be enacted into authentic mathematical experiences for students.

We use proportional reasoning every day, often without being aware that we are reasoning in terms of two quantities that vary in relation to each other – that is, as one quantity increases or decreases, so does the other. I may decide to buy two tins of tomatoes. The price of each tin is the same, so if I purchase double the number of tins, the amount I pay also doubles. Despite using this thinking informally quite regularly, it is surprising how many people have trouble with this concept. Doubling or trebling a quantity is one thing, but what about wanting one-and-a-half times, or only needing one-fifth of something? These calculations can become very tricky. Often we make some kind of estimate and end up with either too little or too much of something.

Proportional reasoning is used widely to solve a range of everyday problems from ‘best buys’ to understanding data presented in tables. It underpins scaling problems such as scale drawings of house plans and currency conversions, and appears in many other situations, including the Australian electoral system.

This book is grounded in empirically evidenced developmental models and linked closely to practical classroom practice. While many classrooms have been resourced with equipment such as base-10 materials, counters, shape kits, mobile devices, dice kits, drawing tools and interactive whiteboard (IWB) technology, and even a laptop trolley in some cases, extensive professional development is required to enable the range of classroom resources to be transformed into teaching tools. The difficulty faced by the teaching profession is in integrating a wide range of teaching approaches and resources to weave a pedagogically sound learning sequence. This book provides mathematics teachers and pre-service teachers with detailed teaching activities that are designed and informed by research-based practices. The aim is to provide you with a sensible and achievable integration of available educational tools, with research-based approaches to mathematical development that provide for the mathematical needs of all learners. It is intended for primary pre-service teachers, and teachers looking for ways to enhance their teaching of primary mathematics, to assist them to design student tasks that are meaningful and to use educationally sound ways to improve their mathematics teaching.

This chapter looks at appropriate early childhood pedagogy, particularly as it applies to the early learning of mathematics. The importance of play and recognition of children’s prior learning is emphasised throughout. Although many of the experiences and learning documented focus on number, we acknowledge that children’s early mathematical learning extends beyond number into areas such as geometry, measurement and spatial awareness.

Australian classrooms are becoming increasingly diverse. In addition to a wide range of mathematical abilities, primary teachers of mathematics must meet the needs of children from varied cultural backgrounds, many of whom have had different mathematical experiences. Children who have physical, intellectual, social or emotional difficulties may be included in the mainstream classroom. There may also be children who are classified as gifted and talented in one or more domains. All have the capacity to learn mathematics, and the right to experience mathematics suitable to their learning needs. Although this chapter addresses issues relating to inclusion in primary mathematics classrooms, it does not pretend to provide a special education focus. The needs of children with specific disabilities can be highly technical, and it is well beyond the scope of this chapter to try to deal with all the detailed requirements and concerns that may be encountered. Rather, this chapter aims to help the primary teacher deal with the reality of mathematics teaching in modern classrooms, where there may be children with very diverse learning and mathematical needs. Many students are not categorised as having a disability but have information processing delays. These students will benefit from the same approaches as those with recognised disabilities.