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Page 1 of 2

Early Mathematical Explorations
  • Nicola Yelland, Carmel Diezmann, Deborah Butler
  • Published online:
    06 August 2018
    Print publication:
    20 January 2014
  • Early Mathematical Explorations shows readers how to provide young children with rich mathematical learning environments and experiences. This book presents teachers with a sound theoretical framework to encourage children to become numerate in the twenty-first century. It shows that mathematical learning can occur in a variety of ways, including when children explore ideas through play, problem solving and problem posing; engage in a rich variety of multimodal learning experiences; pursue self-directed activities and cooperate with others; and make connections between ideas and experiences in their everyday worlds. Chapters 2 and 3 explore the ways in which mathematical understandings can be supported from birth to five years. Chapters 4–9 provide an overview of mathematics in the early primary years. The final chapters illustrate the contexts and connections that can be made in early mathematical learning. Early Mathematical Explorations is an essential resource for pre- and in-service teachers alike.

  • Chapter 8 - Space

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 192-212

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the importance of knowledge of space in the early years – it enables children to explore the world around them and develop the vocabulary to label and talk about it

  • the role of shape in children’s understanding of space, and the related concepts of location and transformation

  • the seven spatial perception skills.

    • In addition to the ability to work with numbers and reason logically, children need opportunities to develop their spatial skills and understanding of shape, location and transformation, and to engage in geometric or spatial reasoning. This form of knowledge is referred to broadly as spatial sense – an important objective of mathematics education in the 21st century. Some aspects of spatial sense are evident in the drawings from seven-year-old Laura’s journal (see below). Compared to her age peers, Laura has a well-developed spatial sense. However, her drawings suggest that she needs to develop an understanding of the relative size of adults and children. Hence, encouraging children to express themselves through drawing provides an insight into their spatial sense. Comparing a child’s drawings over time is one method of monitoring the progression of his spatial sense.

  • Chapter 5 - Number

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 94-138

  • Summary

    Overview

    In this chapter you will become familiar with:

  • ways to represent quantity using physical items, words and numerals

  • activities to encourage children to count, compare and order numbers

  • ways to foster conceptual understanding of place value in the base 10 number system

  • how mathematical operations on a quantity increase or decrease its value.

    • Number knowledge is fundamental to understanding mathematical situations in the everyday world. To develop this understanding, young children need a range of experiences, such as counting, recognising and writing numerals, composing and decomposing numbers, and simple operations. Children’s understandings can be supported by the use of physical materials and tools that aid thinking. For example, the calculator is a useful tool when children are learning to count by twos and fives because children can check what they are saying with what the visual display of the calculator is showing. It is also useful for checking answers when children have completed an operation. Throughout their school years, children are expected to acquire increasingly complex understandings of number. Hence, it is important for children to master simple concepts and gradually build their proficiency with number.

  • Chapter 6 - Patterns and algebra

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 139-158

  • Summary

    Overview

    In this chapter you will become familiar with:

  • describing, copying, extending and creating repeating patterns

  • identifying the ‘rule’ in growing patterns, and continuing and creating these patterns

  • the notion that the rule to extend a growth pattern in number is the same as a function to change the value of a set of numbers

  • finding key mathematical relationships among numbers or sets of numbers.

    • Recognising and working with patterns is fundamental to mathematics. Some patterns have units that repeat. Continuing a repeating pattern involves simply copying the repeating unit and adding it onto the existing pattern. There are also growth patterns. In a growth pattern, each new term includes the one before and grows according to an inbuilt ‘rule’. The rule in the growth pattern below is to copy the letters and include the next letter of the alphabet.

  • Chapter 9 - Chance and data

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 213-229

  • Summary

    Overview

    In this chapter you will become familiar with:

  • activities designed to raise children’s awareness of the role of chance in everyday life

  • activities focusing on developing children’s knowledge and skills in collecting, organising, representing and interpreting data.

    • Chance and data is a relatively new concept area in mathematics for young children. Chance includes ideas of randomness and probability that are relevant to everyday life – for example, in games involving spinners. Data includes collecting, organising, representing and interpreting information. For example, data can be collected in a survey, organised in a table and represented on a graph. Someone looking at the graph needs to be able to interpret the information that was collected in the survey. Understanding data is particularly important in the information-rich age of the 21st century. Children’s experiences of chance and data in the mathematics program should enrich their understanding of the world around them, so it is important that these experiences have personal relevance. Playing games with dice or reading a television guide and a bus timetable are examples of children interpreting data in meaningful contexts.

  • Chapter 1 - Mathematics for the 21st century

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 1-10

  • Summary

    On a visit to a classroom, Nicola (N), an early childhood educator, had the following conversation with Tessa (T), a Year 3 child:

  • N: What are you doing, Tessa?

  • T: Another maths sheet.

  • N: Oh great! I love doing maths. What is this one about?

  • T: Adding sums [said glumly].

  • N: Do you like doing maths, Tessa?

  • T: No. It’s boring and anyway why should I when my teacher hates it too?

  • N: Does she really hate it? How do you know that?

  • T: She never smiles when we do maths.

    • This anecdote indicates the strength of young children’s perceptions of the learning environment. It also highlights the fact that some adults lack confidence in and enthusiasm for mathematics. This book is designed to support teachers, parents and caregivers in providing a rich mathematical environment for children in their early years (birth to eight years of age). Young children who have worthwhile and interesting mathematical experiences have the opportunity to acquire mathematical understandings and positive attitudes towards mathematics. This enables them to become numerate and use mathematics effectively in their daily lives.

  • Chapter 3 - Mathematical learning in the first five years of life

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 28-74

  • Summary

    Overview

    In this chapter you will become familiar with:

  • activities suitable to encourage the use of the beginning processes for young children in the first five years of life

  • the importance of using language, children’s literature and playful explorations as sources for mathematical experiences in the early years. This includes traditional materials such as books and manipulatives as well as new technologies.

    • From the time a baby is born, she uses her five senses (taste, touch, smell, sight and hearing) to investigate the world. In the years from birth to five, there is a dramatic change in her physical growth, capabilities and skills. It is exciting when a baby says her first word or takes her first steps. It is equally wondrous when she successfully makes a tower of blocks or completes a puzzle independently. Building with blocks and puzzle making are two examples of early experiences that facilitate the development of mathematical thinking. Increasingly, from the age of two, young children are also experiencing using new technologies in a range of activities. Tablet technologies can support early multimodal learning which, when supported by parents, caregivers and teachers, not only enables children to link the two-dimensional experience of using these technologies with ‘real-world’ activities and contexts, but also enriches language acquisition. Encouragement from adults and conversations about activities will help children to connect the mathematical understandings that are relevant to their everyday lives. During these early years, parents, caregivers and teachers play an important role in creating contexts for using mathematical language and supporting the use of the beginning processes and concepts of mathematics that children will encounter in a wide variety of situations. These early experiences are fundamental to enabling the young child to feel confident and competent about doing mathematics in school and being numerate in the 21st century.

  • Chapter 4 - The young child at school

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 75-93

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the key concept areas in mathematics for young learners – number, measurement, space, chance and data, and patterns and algebra – and the way they relate to the ‘Big Ideas’ in mathematics

  • the mathematical processes that form the basis of the mathematics curriculum in schools

  • the importance of fostering positive attitudes towards mathematics, particularly through the careful selection and design of tasks

  • the substantial variation in children’s understanding and performance in mathematics and the need for responsive teaching.

    • In the years before starting school, the young child has had many experiences that provide the foundation for mathematical understandings. A child stacking pots and pans begins to learn about ordering. When Dad counts with Sam, or Mum reads The Three Little Pigs to Simon, they are helping their children to develop an understanding of numbers. Children also develop an understanding of mathematics through everyday activities. At the shops, seeing people buying groceries provides some understanding of the value of coins and how we exchange coins for goods. Children enjoy acting out everyday mathematical situations that they have seen, such as ‘playing shops’. When children play together they have an opportunity to learn from each other and to use mathematical language, such as ‘price’, ‘money’, ‘how much’ or ‘change’. When the young child goes to school, he will continue to build on these foundations of mathematical learning.

  • Chapter 11 - Designing mathematical experiences for numeracy in the 21st century

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 252-269

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the ways in which mathematical understandings support numeracy in the 21st century

  • the elements in the design cycle that can be used to create effective teaching and learning contexts for numeracy

  • using child-centred assessment to maximise individual learning potential.

    • The chapters in this book have considered the foundational concepts and processes of mathematics that are fundamental in establishing confidence and competence in the early years. The book has considered some of the ways in which these concepts and processes can be incorporated into learning activities designed by teachers and caregivers, and encountered and experienced in the early years of a child’s life. It has explored the concepts of number, measurement, space, chance and data, and patterns and algebra, since these form the basis of the mathematics curriculum in many countries, and shown how they might be incorporated into early childhood learning experiences. A critical link has been made between the acquisition of confidence and competence in mathematics and becoming numerate in the 21st century. That is, we need to be able to understand and use mathematical concepts and processes in order to function effectively in the 21st century. Throughout a child’s life, she will encounter problems, challenges and technologies that require the application and successful use of mathematical concepts and processes.

  • Chapter 7 - Measurement

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 159-191

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the ways in which measurement can be an important part of children’s everyday lives and how measuring experiences can be personally relevant to them

  • the understanding that measuring is about the quantity of a particular unit of measurement

  • using different measures in order to teach children which measures are appropriate for a particular measuring context.

    • Measurement is part of a young child’s everyday life. Initially, children are exposed to measuring through interactions with adults. We measure children’s height and mass. We give children money to buy a drink. We tell children when it is time to go to play. But as children get older, they need first-hand experiences to develop their ability to measure many different attributes − length, area, volume, capacity, mass, time and money. Measuring is finding out ‘how much’ there is of a particular attribute. It involves an understanding of the attribute to be measured, and knowledge of an appropriate unit of measure and how to measure with this unit. It also requires good number understanding.

  • Chapter 10 - Contexts and connections

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 230-251

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the ways in which mathematical understandings can be used in everyday life and in projects designed by teachers or instigated by young children

  • the importance of using mathematics in our everyday lives

  • the need to challenge, extend and build children’s capacities for posing and solving problems in realistic contexts.

    • Working with topics or on projects that derive from young children’s spontaneous interests is an excellent way to create contexts for learning that are meaningful and enable learners to connect mathematics to their personal, cultural and everyday lives. In this chapter three topics are illustrated. The first topic, Ourselves, focuses on the child. The second topic, Celebrations, considers traditional events in an integrated approach to the curriculum. It is a very useful topic for those living in multicultural communities, as it enables different cultures to understand some of the main ideas inherent in a particular culture or community group. The final topic, Out and About, explores mathematical ideas in everyday community life. The activities related to these topics are intended as starting points for investigations.

  • Chapter 2 - Early mathematical understandings

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 11-27

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the beginning processes for early mathematical understandings – describing attributes, matching, comparing, ordering, sorting and patterning

  • the mathematical concepts of number, measurement, space, and chance and data, and the ways in which these relate to the everyday experiences of young children

  • the importance of language in exploring mathematics in the early years, as well as the use of children’s literature to support mathematical thinking

  • playful explorations as a pedagogical process to stimulate early mathematical learning.

    • Young children are curious from the moment they are born. They look around them, explore objects that they encounter and communicate with utterances in interactions with others. From birth to five years of age, which is generally when compulsory schooling begins, there are many different ways in which the foundations for mathematical understandings are established. The activities and experiences are usually informal and play-based, but there are also opportunities for teachable moments in which a teacher might consolidate particular language or highlight relationships that are fundamental to mathematical thinking and understandings. For example, when telling a child the story of The Very Hungry Caterpillar by Eric Carle, there are many opportunities for the adult to create contexts for understanding mathematical concepts and processes. These are shown in Table 2.1. As well as spanning the concepts of number, measurement, space, and chance and data, these opportunities provide a context for using language to communicate ideas and understandings about the various relationships that occur in the story.

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