Ros Sutherland
Open University Press | 2006 | 166 páginas | pdf | 1,7 Mb
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- Why do students find learning mathematics difficult? Can anything be done about this?
- What can we learn from mathematics lessons in which students are motivated to struggle with difficult mathematical ideas?
- How can teachers make sense of the research which is available, and use it to improve practice in real classrooms?
This book explores the factors that influence young people’s learning of mathematics. It uses a holistic, socio-culturally informed approach to show how all young people can be encouraged to engage with and learn mathematics.
Rich examples from classroom practice are used to connect theory and practice. The role of mathematical tools, including information and communications technologies, is discussed. A key focus of the book is the link between teaching and learning, including different ways in which teachers can design and orchestrate mathematical learning environments.
This important, accessible and relevant book is essential reading for student teachers of mathematics as well as all qualified mathematics teachers in secondary schools.
Contents
Acknowledgements viii
1 Teaching, Learning and Mathematics 1
Opening remarks 1
Research-informed practice 1
Theory as a way of seeing 2
A socio-cultural perspective 4
Mathematical tools 5
Teaching and learning mathematics 7
Designing for learning 8
Disjunctions between research, policy and practice 9
Concluding remarks 10
2 Cultures of Mathematics Education 12
Opening remarks 12
Mathematics curricula 13
Textbooks and mathematics education culture 15
Approaches to teaching mathematics 23
Concluding remarks 24
3 Ways of Knowing Mathematics 26
Diversity and learning 26
Out-of-school mathematical practices 27
Mathematics and out-of-school uses of ICT 29
Scientific and spontaneous concepts 32
Concluding remarks 36
4 Ways into the World of Mathematics 38
Opening remarks 38
Teacher-proofing the classroom? 39
Students as creative and constructive problem solvers 41
Teacher and tools 42
An illustrative vignette – learning statistics in the primary school 43
Concluding remarks 49
5 Teaching and Learning as Reciprocal Activity 51
What is teaching? 51
Communities of inquiry 52
Shared mathematical working spaces – learning algebra 53
Shared mathematical working spaces – learning functions and graphs 59
Concluding remarks 62
6 Digital Tools for Learning Mathematics 64
Mathematics and computer programming 64
ICT and learning mathematics 66
Algebra and spreadsheets in the secondary school 67
Algebra and spreadsheets in the primary school 71
Concluding remarks 73
7 Designing for Learning 75
Opening remarks 75
Teachers as designers 77
Design initiatives for mathematics 79
Partnership between teachers and researchers 80
Research-informed practice 82
Out of the classroom – design as a thought experiment 83
Into the classroom – teaching in the moment 87
Reflection, evaluation and redesign 88
Concluding remarks 89
8 Learning Geometry 90
Introductory remarks 90
Partnership between teachers and researchers 90
Structuring resources – the schools 92
Structuring resources – the curriculum 94
Structuring resources – the students 94
Learning geometry – research-informed practice 97
Out of the classroom – design as a thought experiment 98
Into the classroom – learning about quadrilaterals 101
Into the classroom – learning geometry and proof 110
Reflections on Marnie’s design initiative 115
Concluding remarks 116
9 Theory as a Way of Seeing 119
Introductory remarks 119
Culture and mathematics learning 120
Mathematical tools 121
Appropriating and appropriate mathematics 124
Teaching, tools and transformation 127
Language, community and mathematical learners 128
Why theory? 130
10 Integrating Research, Policy and Practice 133
Introductory remarks 133
Unintended effects of educational reforms 134
Teachers as enabled professionals 135
A question of scale 137
References 140
