Supporting Early Mathematical Development

Practical Approaches to Play-Based Learning

Caroline McGrath

• Publisher: Routledge
• Year: 2010
• ISBN:
  9781136998447
• Edition: 1
• Topic: Education
• Subtopic: Education General

Supporting Early Mathematical Development is an essential text for current Early Years practitioners and students, offering an excellent blend of theory and practice that will enable you to provide successful mathematical education for children from birth to eight years old. Charting the delivery of mathematical development in Playgroups, Children's Centres, Nurseries and Primary Schools, it forges links between current practice and fundamental Early Years principles and makes suggestions for creating effective pedagogies in maths teaching.

Promoting mathematical development through play-based learning, this book presents:

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• a wealth of practical multi-sensory teaching strategies

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• instructional methodologies

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• activity ideas incorporating play, books, songs, cookery and the outdoors

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• examples of children's work

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• advice on translating theory into practice

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• questions for reflective practice.

Throughout the book, Caroline McGrath breaks down the complexity of teaching and learning mathematics into simple steps and guides readers through possible gaps in their knowledge, bringing fresh enthusiasm to teaching mathematics. This is an invaluable resource for practitioners and trainee teachers wishing to strengthen their mathematical teaching and professional practice, or for students on a wide range of Early Years courses.

Section 1

1
Fear, anxiety and other emotions

‘No passion so effectually robs the mind of all its powers of acting and reasoning as fear’

Edmund Burke (1729–1797)

The aims of this chapter are to understand:

• Fear, anxiety and other emotions of trainee practitioners

• Children’s changing mathematical disposition

• Mathematical influence of parents or carers

Introduction

As early years educators, if we can continue a balance between that spark of our own childhood and the smoulder of our adult hopes and fears, we can keep the fire alive. We can experience what educator really means behind qualifications and planning and like steps going back up the track of our dreams, we get higher and nearer seeing further and wider inside ourselves and the children we teach.

Mathematics is a hard subject. It relies on the links of a chain joining up; a weak or missing link changes the strength of the chain before and beyond it. Mathematics is both magical and delicate. Mathematical delicacy can be difficult to see inside as we peel back layers to find the birthplace of ideas.

Boaler comments that ‘far too many students hate mathematics and that for many it is a source of anxiety and fear’ (2009: 5). A colourful spectrum of emotions is associated with mathematics, ranging from sage green satisfaction, to mid-red fear, to dark black dread. The early years experience determines where we find ourselves on this spectrum later in life; so it is important we ensure children experience early success.

Trainee practitioners have a difficult task supporting early mathematical development, as not only must they tune into the thinking of qualified practitioners, but they also depend on the knowledge of those they model, attaching this to their own subject knowledge, which may be stronger or weaker than either the children’s or adults’ they are with.

Children are born mathematical (Pound 2008) and we will explore why some children lose their initial positive disposition towards mathematics and how we can enable them to retain a positive belief in themselves.

Parents’ or carers’ attitudes towards mathematics will also influence the children we work with and they too need to be guided to support their children’s mathematical development in order to nurture their self-esteem and motivation.

Questions to reflect on:

Why is it important to realize my own attitude towards mathematics?

How will I ensure children keep a positive disposition towards mathematics?

What emphasis can be placed on parents supporting their children’s mathematical development?

Mathematics

The magic of mathematics can surprise or mystify us. There is satisfaction in solving a mathematically based question. Mathematics of the real world is different and surprisingly engaging (Boaler 2009). A Foundation Degree student excitedly explained how mathematics helped with the task of measuring up for curtains, realizing the need to visualize more material than for just the width of a window; when mathematics filters into everyday life, ‘its appeal for us lies in the intellectual or aesthetic satisfaction that we derive from it’ (Liebeck 1984: 13).

Mathematics is a subject in which a majority of the population lacks confidence (Pound 2008), perhaps owing to having an ‘inherently judgmental nature’ (Chinn 2009). It is perceived by many as difficult and not rooted in reality. Pound acknowledges that ‘the abstract nature of mathematics and concern for accuracy make mathematics a hard subject’ (2008: 12). There is a hierarchy of abstractions to build and abstract language to learn which constitute a unique challenge. The exposure of correct or incorrect answers distinguishes it from other subjects.

Unfortunately it has become socially acceptable to admit to being ‘no good at maths’. This attitude needs to be weeded out, as it is not conducive to creating a future generation of competent mathematicians. The balance needs to tip to realizing that ‘not being comfortable with numbers is as disempowering in our society as not being able to read’ (Pound 2008: 5).

Government statistics show that every year around 6 per cent of 11 year olds in England leave primary school with very poor numeracy skills (below National Curriculum level 3 in mathematics). The Every Child a Chance Trust (2009) indicates that this failure to address numeracy difficulties incurs a £2.4 billion cost to the country, hindering employability and contributing to poor self-esteem, which affects mental health. Boaler boldly states that ‘maths classrooms need to catch up not only to help future employers and employees, or even to give students a taste of authentic maths, but to prepare young people for their lives’, (2009: 9). On qualifying, trainee practitioners will be in a position to influence this ‘catch–up’ if they are equipped with subject knowledge, have understanding of how children learn and become enveloped in an enthusiasm for mathematics.

Foundation Degree students

Before Foundation Degree programmes were Higher National Diplomas (HNDs), with an optional module dedicated to Curriculum Mathematics. I was nervous of teaching the Curriculum Mathematics module; I had taught mathematics in nurseries and primary schools, but I had not taught older students how to do this. Initially the students lacked confidence and competence, but on completion of the module, students’ comments were encouraging:

‘I have enjoyed carrying out this assignment, although my initial thoughts were that I would not like this assignment because I do not like Maths. I found it interesting and beneficial to my learning of maths …’

(Student written comment HND 2006)

Another learner wrote,

‘I really enjoyed this module, where in the beginning I had negative views on doing maths. Now I have gained in confidence in teaching mathematics to children …’

(Student written comment HND 2006)

The final comment shows the value of learning how to teach early years mathematics,

‘This module has given me a completely new outlook on maths. I feel more confident with maths in placement. Moreover, this module has brought to light the importance of giving children opportunities to develop their mathematics in a meaningful way …’

(Student written comment HND 2006)

The delivery of the HND Curriculum Mathematics module identified that students had variable levels of confidence and benefited from learning how to teach mathematics in a ‘meaningful way’, something Hughes (1986) highlights the need for.

When they started the module the students were asked to keep a journal for a week, recording their mathematical experiences. A fabulous collection of car journeys, rounds of drinks, cookery, sleep, and haircuts were documented. The students realized they ‘already know and can do, a great deal of mathematics’ (Cooke 2000: 1). This broke down initial resistance to what was a threat for some and, over time, they embraced and even enjoyed this module.

The Foundation Degree programme, which replaced the HND, does not include mathematics even though learners are studying at a comparable level. Teaching the HND students elicited the emotions and subsequent satisfactions of tackling what was an area of anxiety; the Foundation Degree programme does not necessarily meet this need.

A placement visit brought this shortfall to light. Sarah was supporting a numeracy session; her role was to reinforce the class teacher’s message to a small group of children. As the lesson progressed I sensed Sarah’s almost tangible lack of confidence as she struggled to demonstrate the task or answer children’s questions. Group work was difficult for her, as the children had not grasped what was to be done and Sarah herself could not express the ideas or guide the children.

This is an uncomfortable position to be in; students naturally want to help children and knowing that you can’t when the expectation is that you will, creates a negative state. Afterwards Sarah was honest, expressing her anxiety and this led me to research the views and experiences of other students. Initially, I expected students would resist admitting a potential weakness, but they were in fact relieved to discuss the issue. As par...

Table of contents

• Contents
• List of tables
• List of figures
• Acknowledgements
• Introduction
• Section 1
• Section 2
• Section 3
• Appendix
• References
• Index