Julian Williams – författare

The mistakes children make in mathematics are usually not just ‘mistakes’ - they are often intelligent generalizations from previous learning. Following several decades of academic study of such mistakes, the phrase ‘errors and misconceptions’ has recently entered the vocabulary of mathematics teacher education and has become prominent in the curriculum for initial teacher education.

The popular view of children’s errors and misconceptions is that they should be corrected as soon as possible. The authors contest this, perceiving them as potential windows into children’s mathematics. Errors may diagnose significant ways of thinking and stages in learning that highlight important opportunities for new learning.

This book uses extensive, original data from the authors’ own research on children’s performance, errors and misconceptions across the mathematics curriculum. It progressively develops concepts for teachers to use in organizing their understanding and knowledge of children’s mathematics, offers practical guidance for classroom teaching and concludes with theoretical accounts of learning and teaching.

Children’s Mathematics 4-15 is a groundbreaking book, which transforms research on diagnostic errors into knowledge for teaching, teacher education and research on teaching. It is essential reading for teachers, students on undergraduate teacher training courses and graduate and PGCE mathematics teacher trainees, as well as teacher educators and researchers.

The mistakes children make in mathematics are usually not just ‘mistakes’ - they are often intelligent generalizations from previous learning. Following several decades of academic study of such mistakes, the phrase ‘errors and misconceptions’ has recently entered the vocabulary of mathematics teacher education and has become prominent in the curriculum for initial teacher education.

The popular view of children’s errors and misconceptions is that they should be corrected as soon as possible. The authors contest this, perceiving them as potential windows into children’s mathematics. Errors may diagnose significant ways of thinking and stages in learning that highlight important opportunities for new learning.

This book uses extensive, original data from the authors’ own research on children’s performance, errors and misconceptions across the mathematics curriculum. It progressively develops concepts for teachers to use in organizing their understanding and knowledge of children’s mathematics, offers practical guidance for classroom teaching and concludes with theoretical accounts of learning and teaching.

Children’s Mathematics 4-15 is a groundbreaking book, which transforms research on diagnostic errors into knowledge for teaching, teacher education and research on teaching. It is essential reading for teachers, students on undergraduate teacher training courses and graduate and PGCE mathematics teacher trainees, as well as teacher educators and researchers.

Improving Learning by Widening Participation in Higher Education presents a strong and coherent rationale for improving learning for diverse students from a range of socio-economic, ethnic/racial and gender backgrounds within higher education, and for adults across the life course. Edited by Miriam David, the Associate Director of the ESRC’s highly successful Teaching and Learning Research Programme, with contributions from the seven projects on Widening Participation in Higher Education (viz Gill Crozier and Diane Reay; Chris Hockings; Alison Fuller and Sue Heath; Anna Vignoles; Geoff Hayward and Hubert Ertl; Julian Williams and Pauline Davis; Gareth Parry and Ann-Marie Bathmaker), this book provides clear and comprehensive research evidence on the policies, processes, pedagogies and practices of widening or increasing participation in higher education. This evidence is situated within the contexts of changing individual and institutional circumstances across the life course, and wider international transformations of higher education in relation to the global knowledge economy. Improving Learning by Widening Participation in Higher Education also considers: the changing UK policy contexts of post-compulsory education; how socio-economically disadvantaged students – raced and gendered – fare through schools and into post-compulsory education; the kinds of academic and vocational courses, including Maths, undertaken; the changing forms of institutional and pedagogic practices within higher education; how adults view the role of higher education in their lives. This book, based upon both qualitative studies and quantitative datasets, offers a rare insight into the overall implications for current and future policy and will provide a springboard for further research and debate. It will appeal both to policy-makers and practitioners, as well as students within higher education.

Improving Learning by Widening Participation in Higher Education presents a strong and coherent rationale for improving learning for diverse students from a range of socio-economic, ethnic/racial and gender backgrounds within higher education, and for adults across the life course. Edited by Miriam David, the Associate Director of the ESRC’s highly successful Teaching and Learning Research Programme, with contributions from the seven projects on Widening Participation in Higher Education (viz Gill Crozier and Diane Reay; Chris Hockings; Alison Fuller and Sue Heath; Anna Vignoles; Geoff Hayward and Hubert Ertl; Julian Williams and Pauline Davis; Gareth Parry and Ann-Marie Bathmaker), this book provides clear and comprehensive research evidence on the policies, processes, pedagogies and practices of widening or increasing participation in higher education. This evidence is situated within the contexts of changing individual and institutional circumstances across the life course, and wider international transformations of higher education in relation to the global knowledge economy. Improving Learning by Widening Participation in Higher Education also considers: the changing UK policy contexts of post-compulsory education; how socio-economically disadvantaged students – raced and gendered – fare through schools and into post-compulsory education; the kinds of academic and vocational courses, including Maths, undertaken; the changing forms of institutional and pedagogic practices within higher education; how adults view the role of higher education in their lives. This book, based upon both qualitative studies and quantitative datasets, offers a rare insight into the overall implications for current and future policy and will provide a springboard for further research and debate. It will appeal both to policy-makers and practitioners, as well as students within higher education.

Improving Learning by Widening Participation in Higher Education presents a strong and coherent rationale for improving learning for diverse students from a range of socio-economic, ethnic/racial and gender backgrounds within higher education, and for adults across the life course.

Edited by Miriam David, the Associate Director of the ESRC’s highly successful Teaching and Learning Research Programme, with contributions from the seven projects on Widening Participation in Higher Education (viz Gill Crozier and Diane Reay; Chris Hockings; Alison Fuller and Sue Heath; Anna Vignoles; Geoff Hayward and Hubert Ertl; Julian Williams and Pauline Davis; Gareth Parry and Ann-Marie Bathmaker), this book provides clear and comprehensive research evidence on the policies, processes, pedagogies and practices of widening or increasing participation in higher education. This evidence is situated within the contexts of changing individual and institutional circumstances across the life course, and wider international transformations of higher education in relation to the global knowledge economy.

Improving Learning by Widening Participation in Higher Education also considers:

the changing UK policy contexts of post-compulsory education;

how socio-economically disadvantaged students – raced and gendered – fare through schools and into post-compulsory education;

the kinds of academic and vocational courses, including Maths, undertaken;

the changing forms of institutional and pedagogic practices within higher education;

how adults view the role of higher education in their lives.

This book, based upon both qualitative studies and quantitative datasets, offers a rare insight into the overall implications for current and future policy and will provide a springboard for further research and debate. It will appeal both to policy-makers and practitioners, as well as students within higher education.

Improving Learning by Widening Participation in Higher Education presents a strong and coherent rationale for improving learning for diverse students from a range of socio-economic, ethnic/racial and gender backgrounds within higher education, and for adults across the life course.

Edited by Miriam David, the Associate Director of the ESRC’s highly successful Teaching and Learning Research Programme, with contributions from the seven projects on Widening Participation in Higher Education (viz Gill Crozier and Diane Reay; Chris Hockings; Alison Fuller and Sue Heath; Anna Vignoles; Geoff Hayward and Hubert Ertl; Julian Williams and Pauline Davis; Gareth Parry and Ann-Marie Bathmaker), this book provides clear and comprehensive research evidence on the policies, processes, pedagogies and practices of widening or increasing participation in higher education. This evidence is situated within the contexts of changing individual and institutional circumstances across the life course, and wider international transformations of higher education in relation to the global knowledge economy.

Improving Learning by Widening Participation in Higher Education also considers:

the changing UK policy contexts of post-compulsory education;

how socio-economically disadvantaged students – raced and gendered – fare through schools and into post-compulsory education;

the kinds of academic and vocational courses, including Maths, undertaken;

the changing forms of institutional and pedagogic practices within higher education;

how adults view the role of higher education in their lives.

This book, based upon both qualitative studies and quantitative datasets, offers a rare insight into the overall implications for current and future policy and will provide a springboard for further research and debate. It will appeal both to policy-makers and practitioners, as well as students within higher education.

This open access book is the first major publication on the topic of “Interdisciplinary Mathematics Education” and arose from the work of the first International Topic Study Group of the same name at the ICME-13 conference in Hamburg in 2016. It offers extensive theoretical insights, empirical research, and practitioner accounts of interdisciplinary mathematics work in STEM and beyond (e.g. in music and the arts). Scholars and practitioners from four continents contributed to this comprehensive book, and present studies on: the conceptualizations of interdisciplinarity; implementation cases at schools and tertiary institutions; teacher education; and implications for policy and practice. Each chapter, and the book itself, closes with an assessment of the most significant aspects that those involved in policy and practice, as well as future researchers, should take into account.

This book provides an essential introduction to the state-of the-art in interdisciplinary Mathematics Education. First, it begins with an outline of the field’s relevant historical, conceptual and theoretical backgrounds, what “discipline” means and how inter-, trans-, and meta-disciplinary activities can be understood. Relevant theoretical perspectives from Marx, Foucault and Vygotsky are explained, along with key ideas in theory, e.g. boundaries, discourses, identity, and the division of labour in practice. Second, the book reviews research findings of mainly empirical studies on interdisciplinary work involving mathematics in education, in all stages of education that have become disciplined. For example, it reports that a common theme in studies in middle and high schools is assessing the motivational benefits for the learner of subsuming disciplinary motives and even practices to extra-academic problem-solving activities; this is counter-balanced by the effort needed to overcome the disciplinary boundaries in academic institutions, and in professional identities. These disciplinary boundaries are less obviously limitations in middle and primary schools, and in some vocational courses. Third and finally, it explores selected case studies that illustrate these concepts and findings, both in terms of the motivational benefits for learners and the institutional and other boundaries involved.