Foundations of Primary Mathematics Education: An introduction to curriculum, pedagogy and content - Brossura

West, John

Brossura

ISBN 10: 1760529699 ISBN 13: 9781760529697

Casa editrice: Routledge, 2019

Riassunto

Many pre-service teachers admit to feeling unsure about the mathematics they will have to teach in primary school. Others find it difficult to know how to apply the theories of teaching and learning they study in other courses to the teaching of mathematics.

This book begins by outlining some of the key considerations of effective mathematics teaching and learning. These include understanding student motivation, classroom management, overcoming maths anxiety and developing a positive learning environment. The authors also introduce the curriculum and assessment processes, and explore the use of ICT in the maths classroom. Part B outlines in a straightforward and accessible style the mathematical content knowledge required of a primary teacher. The content extends beyond the primary level to Year 9 of the Australian Curriculum as, while primary teachers may not have to teach this content, knowing it is a key part of being a strong teacher and will assist pre-service teachers to meet the requirements of the LANTITE (the Literacy and Numeracy Test for Initial Teacher Education students).

Featuring graphics and worked examples and using clear and friendly language throughout, this is the essential introduction for students wishing to begin teaching primary mathematics with confidence and enthusiasm.

'The writing style is clean and uncomplicated; exactly what my maths education students need. The blend of theories, curriculum, planning, assessment and mathematical content knowledge strikes the balance that is missing in many texts.' -- Dr Geoff Hilton, University of Queensland

Su questo libro

Informazioni sull?autore

Dr John West is a Lecturer in Mathematics Education at Edith Cowan University. He has taught mathematics at primary, secondary and tertiary levels. Dr Fiona Budgen is a Senior Lecturer in the School of Education at Edith Cowan University. She and John have a strong research interest in primary mathematics education and identifying and supporting numeracy needs of first year students.

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Foundations of Primary Mathematics Education

An Introduction to Curriculum, Pedagogy and Content

By John West

Allen & Unwin

Copyright © 2019 John West and Fiona Budgen
All rights reserved.

ISBN: 978-1-76052-969-7

Contents

1 Introduction, 
Part A: Mathematics Teaching, 
2 Understanding the Profession, 
3 Motivation, 
4 Planning, 
5 The Learning Environment and Building Relationships, 
6 The Learning Process, 
7 Unpacking the Curriculum, 
8 Assessment and Reporting, 
9 Using Technology, 
Part B: Mathematical Knowledge, 
10 Whole Numbers, 
11 Fractions, 
12 Decimals and Percentages, 
13 Measurement, 
14 Geometry, 
15 Patterns and Algebra, 
16 Statistics, 
17 Probability, 
Acknowledgements, 
Glossary, 
Answers to Exercises, 
References, 
Image Acknowledgements, 
Index, 

CHAPTER 1

Introduction

Welcome to the second edition of Foundations of Primary Mathematics Education. This book has evolved from a need to provide pre-service teachers with subject knowledge in mathematics alongside current knowledge and beliefs about teaching and learning. This is reflected in the choice of title, Foundations of Primary Mathematics Education, rather than simply Foundations of Primary Mathematics. Many pre-service teachers admit to feeling unsure about the mathematics they will have to teach in primary school. Others comment on the difficulties they have in recognising how the theories of teaching and learning they meet in other parts of their course can be applied when teaching mathematics. Part A of this book briefly outlines many of the current beliefs about effective teaching and learning. You will investigate these in more detail in other parts of your teacher education course, so the purpose here is to show how they relate to the teaching and learning of mathematics.

Part B provides the mathematical content knowledge that you will require as a primary teacher. The content of this section extends beyond the primary level to about Year 9 of the Australian Curriculum. While you may not have to teach this content, knowing it is a key part of being a strong teacher of primary mathematics. An understanding of where the primary content is leading will help you to teach with more accuracy and purpose. In order to avoid confusion, content that goes beyond the primary domain has been identified throughout Part B with this icon:

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In order to graduate, all pre-service teachers must pass a literacy and numeracy test known as LANTITE (Australian Council for Educational Research [ACER], 2017). As this is a test for all teachers, it is not exclusively focused on primary-level mathematics. The extended range of mathematical content in this book will assist pre-service teachers with aspects of their subject knowledge that may require attention.

The current context of mathematics education

According to the Australian Curriculum, Assessment and Reporting Authority (ACARA), 'learning mathematics creates opportunities for and enriches the lives of all Australians' (ACARA, 2017). In contrast, many students' experiences of school mathematics are profoundly negative. All too often the outcome of school mathematics is for students to develop an aversion to the subject that precludes them from achieving their full potential.

In 2013, the WA Department of Commerce commissioned a study of Science, Technology, Engineering and Mathematics (i.e., STEM) education in WA schools. The study involved a review of existing research and interviews with representatives of the three education sectors as well as a broad range of organisations that provide support for STEM education in Western Australia. The study revealed that the achievement of Australian primary and secondary students in STEM subjects has declined significantly in the last two decades.

The Trends in International Mathematics and Science Study (TIMSS) is a comparison of student achievement in mathematics and science in different countries and is conducted every four years. The data obtained from international benchmarking studies such as TIMSS allow educational trends to be examined over time. For example, the mathematical achievement of Australian students has fallen from being significantly above that of the United States and England in 1995 to significantly below these countries in 2007 (Brown, 2009).

In 2007, Australian students were ranked 14th behind Hong Kong, Singapore, Chinese Taipei and Japan, followed by a group of eight European countries and the United States. Students in all of these countries achieved significantly higher average scores than those in Australia. Nevertheless, the mathematical achievement of Year 4 students in Australia remained above the international average and was significantly higher than that of 20 countries, including Sweden and New Zealand (Thomson, Wernert, Underwood & Nicholas, 2008).

By 2011, the Year 4 TIMSS achievement data revealed that Australia's ranking had fallen again, this time to 18th place, with Australian students being significantly outperformed by students from 17 other countries. Significant concerns were also raised about the very low proportion of Australian students reaching the advanced achievement benchmarks. According to TIMSS 2011, only 10% of Australian students reached the advanced benchmark compared to 43% of students from Singapore (Mullis, Martin, Foy & Arora, 2012).

Widespread concern about Australia's declining performance in STEM subjects has prompted calls from the Australian Chief Scientist for urgent action at national level (Office of the Chief Scientist, 2012). Despite this, Australia's achievement has continued to decline against our international competitors. Data from the 2015 TIMSS benchmarking study revealed that Australian students were ranked 28th in the world for mathematical achievement, having been significantly outperformed by 21 countries including Kazakhstan (International Association for the Evaluation of Educational Achievement [IEA], 2016).

In addition to the decline in achievement, TIMSS data has revealed that there is a significant decline in Australian students' attitudes towards mathematics between Year 4 and Year 8. There are also major disparities in student achievement levels, attitudes and rates of participation in STEM subjects according to socio-economic status, location, race and gender. Of particular concern in states such as Western Australia is the widening achievement gap between metropolitan and non-metropolitan students and between Indigenous and non-Indigenous students (Hackling, Murcia, West & Anderson, 2014).

Participation rates in advanced or specialised mathematics subjects declined in all Australian states and territories between 1991 and 2007. For example, in Western Australia the participation rate in Calculus was 13.9% in 1992, which dropped to 7.7% by 2007 (Ainley, Kos & Nicholas, 2008). It has been suggested that part of the reason for this decline was that advanced mathematics was no longer a prerequisite subject for a range of university courses.

The Programme for International Student Assessment (PISA) provides data on the comparative performance of 15-year-old students in the OECD countries. PISA studies are conducted every three years. The 2012 PISA data revealed that the achievement gap between the highest 25% and lowest 25% of Australian students, based on their socioeconomic status, is equivalent to 2.5 years of schooling. A similar achievement gap exists between Indigenous and non-Indigenous students, while a lesser gap exists between metropolitan and regional students (Thomson, De Bortoli & Buckley, 2013).

There are also concerns that the proportion of Australian university graduates in STEM fields is lower than in leading Asian economies. Over the ten-year period from 2001 to 2010, the proportion of Australian undergraduate students enrolled in STEM courses fell from 23.7% to 18.8%. In comparison, 64% of students in Japan, 52% in China, 40.6% in South Korea and 33% in Russia are enrolled in STEM courses (Office of the Chief Scientist, 2012).

In a survey of Australian secondary schools, Harris and Jensz (2006) found that three out of four schools reported difficulty in recruiting suitably qualified mathematics teachers. McConney and Price (2009) found that there is a much higher incidence of out-of-field teaching in poor communities, rural and remote schools and 'hard to staff' metropolitan schools, and that this is a major contributor to the relative underachievement of students in these schools.

Structure of this book

Many of the topics introduced in this book will be revisited and developed over the course of your primary education degree.

This chapter has reviewed the current context of STEM education in Australia. The next chapter explores the nature of teachers' work, notions of effective teaching and the professional standards that all teachers are required to meet. Chapter 3 addresses the complex topic of motivation, including the challenges faced by educators in overcoming mathematics anxiety and fixed mindsets. Behavioural, cognitive and social learning explanations of human behaviour are discussed.

A great deal of teacher time is spent on planning, a topic which is addressed in detail in Chapter 4. Chapter 5 'The Learning Environment and Building Relationships' and Chapter 6 'The Learning Process' deal with classroom management and student learning. Chapter 7 explores the structure of the Australian Curriculum: Mathematics, including the rationale and the content and proficiency strands. Strategies for 'Assessment and Reporting' are discussed in Chapter 8, including strategies used by teachers to gather diagnostic, formative and summative assessment data and for communicating this to parents. Chapter 9 explores the ways in which teachers make use of technology both in and outside of the classroom.

Part B of the book deals with specific aspects of mathematical content. Chapter 10 explores whole numbers, place value and operations. Chapter 11 discusses important fraction concepts and calculations and Chapter 12 reviews decimals and percentages. Chapter 13 addresses measurement, while Chapter 14 reviews geometry. Chapter 15 provides an introduction to number patterns and sequences, which form the basis for developing algebra skills. Chapters 16 and 17 discuss statistics and probability, respectively.

Language plays a crucial role in the teaching and learning of mathematics. This book contains a glossary of the mathematical terms used in the primary years. The way in which terms are used in mathematical contexts often differs from their conventional usage. It is vital that teachers model correct usage of mathematical terminology and this begins with a strong foundation of content knowledge.

CHAPTER 2

Understanding the Profession

Teachers play a significant role in shaping the society of the future. There is no doubt that teachers are highly influential role models for students. For this reason, teachers are expected to meet the highest professional and ethical standards.

Teachers' work

The best teachers have a well-developed personal understanding of the structure and principles of the mathematics that they are teaching (Haylock & Manning, 2014). They display confidence in their mathematical content knowledge and their ability to teach mathematics to children.

A primary school teacher's work requires the planning, teaching and assessment of mathematics. This involves setting appropriate learning goals, selecting activities and resources that will support learning, answering children's questions, and identifying and addressing their errors or misconceptions. In order to do this, teachers must have a sound understanding of the mathematics that the children are learning.

The most effective teachers will relate their subject knowledge to their pedagogical knowledge; that is their understanding of how children learn at different ages and how to support that learning. This synthesis of content knowledge and pedagogy is known as pedagogical content knowledge (PCK). For a teacher of primary mathematics this means knowing what conceptions and preconceptions children are likely to bring with them, knowing which concepts are likely to be easy or difficult for students to learn and knowing how to build a concept using resources, explanations and demonstrations so that it is comprehensible to children of different ages and backgrounds. The key message here is that effective pedagogical content knowledge is dependent upon a deep understanding of primary-level mathematics concepts and skills.

Overcoming mathematics anxiety

It is extremely common for students to develop a dysfunctional relationship with mathematics as a result of their schooling. For many people, the study of mathematics leads to anxiety, a sense of powerlessness, and erosion of their sense of self-efficacy. According to Westwood (2000), 'many intelligent people after an average of 1500 hours of instruction ... still regard mathematics as a meaningless activity for which they have no aptitude ... to think that all our effort has led to a situation of fear and loathing is depressing' (p. 31).

Ideally, students should come to view mathematics as a tool that they can use with confidence and understanding as a result of their schooling. The way in which teachers relate to mathematics is extremely important since students learn from observation and imitation. According to Bandura (1989), students are more likely to learn behaviours that are perceived as beneficial.

Teachers who themselves have had negative experiences of mathematics can unconsciously model anxiety, fear or avoidance behaviour to their students. The effect can be to perpetuate a cycle that can profoundly limit students' future learning opportunities and, ultimately, their career choices. The teacher has a crucial role to play in modelling a positive approach to mathematics.

There are a number of ways in which teachers can model a positive approach to mathematics. For example, teaching mathematics in authentic contexts can highlight the relevance and usefulness of the skills that are being taught. In addition, problem-solving activities allow students to draw together ideas from across the curriculum to create richer, more interesting problems to explore. In this way, students can begin to develop an appreciation of mathematics as a valuable problem-solving tool.

In recent years there has been increasing awareness that mathematics anxiety is an all too common outcome of school mathematics. Mathematics anxiety has been recorded in students as young as five years of age and it can develop into a debilitating, lifelong condition (Boaler, 2016). When students feel stressed, working memory becomes blocked and students cannot access the mathematical facts they know. Thus the onset of timed testing accounts for the beginning of maths anxiety in approximately one-third of students (Boaler, 2014).

Neurological research has revealed that mathematics anxiety activates both fear and pain responses in the brain. When students' brains are busy regulating their emotions, their performance and efficiency, even on simple tasks, can be impaired. Indeed, highly mathematics-anxious individuals perceive a 'subjective feeling of visceral threat' when confronted with a mathematical task (Artemenko, Daroczy & Nuerk, 2015, p. 2). Increased activation in the pain perception network is observed when a student is presented with a mathematical task but not during the task itself, explaining why mathematics-anxious individuals try to avoid mathematics. While doing mathematical tasks, highly mathematics-anxious individuals experience increased activation in the amygdala, which is the part of the brain known for fear perception. Its activation during a mathematical task confirms that these students are afraid of mathematics (Artemenko et al., 2015).

As noted in Chapter 1, there are concerns about Australian children's declining levels of achievement in mathematics. Some of this decline has been attributed to teaching standards. It is true that many primary teachers feel insecure in their knowledge of the mathematics they have to teach. This has resulted in some schools attempting to assist teachers by purchasing commercial resources that can be implemented across all year levels. Rather than supporting teachers to become better teachers of mathematics, the result is often that teachers rely on these schemes to make their decisions about teaching for them and fail to provide 'careful, systematic and appropriate explanation of mathematical concepts, procedures and principles' (Haylock, 2006, p. 1).

Effective teaching

There is a great deal of evidence to suggest that one of the most important factors affecting student learning is the effectiveness of the classroom teacher (Hattie, 2012). Effective teachers have a rich knowledge of the content that they need to teach and appropriate strategies with which to teach it. They can create and maintain a safe and supportive learning environment. An effective teacher can improve the learning outcomes of all students in their class; this is particularly the case in mathematics (Hattie, 2016).

Effective teachers constantly strive to enhance their practice by using research to inform their instructional choices (Sullivan, 2011). In recent years there have been many developments in the educational and neurological research that have implications for the teaching and learning of mathematicsin the classroom. By seeking out appropriate professional learning opportunities, teachers can ensure that their students benefit from the latest research on how students learn mathematics.

Some teachers also choose to participate in research studies as a way of improving their effectiveness. Partnerships between schools and universities have several benefits. Working with universities ensures that schools benefit from the latest research. University researchers who work in association with schools can focus on important issues that affect teachers and students. Collaboration between schools and universities allows pre-service teachers to benefit from examples of best practice that occur in schools.

(Continues...)

Excerpted from Foundations of Primary Mathematics Education by John West. Copyright © 2019 John West and Fiona Budgen. Excerpted by permission of Allen & Unwin.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Dettagli dell?edizione

• Editore: Routledge
• Data di pubblicazione: 2019
• Lingua: Inglese
• ISBN 10: 1760529699
• ISBN 13: 9781760529697
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 264
• Contatto del produttore: non disponibile