Jim Ridgway

Education for mathematics in the workplace

Introduction G. Vergnaud. Section 1: Mathematical Knowledge in School and at Work. Preface J. Evans. 1. The Transfer of Mathematics Learning from School to Work not Straightforward but not Impossible Either! J. Evans. 2. Working Knowledge: Mathematics in Use R. Noss, et al. 3. Forms of Mathematical Knowledge Relating to Measurement in Vocational Training for the Building Industry M. Eberhard. 4. The Integration of Mathematics into Vocational Courses J. Gillespie. 5. Mathematical Means and Models From Vocational Contexts - A German Perspective R. Straesser. Section 2: Bringing School and Workplace Together. Preface S.L. Forman, L.A. Steen. 6. Working Mathematics for Learners with Lower Abilities P. van der Zwaart. 7. Classroom Teachers Doing Research in the Workplace J. Hogan, W. Morony. 8. Making Authentic Mathematics Work for All Students S.L. Forman, L.A. Steen. 9. Mathematics Knowledge as a Vocational Qualification T. Wedge. Section 3: Educating Future Workers. Preface J. Williams. 10. Geometry at Work - Examples from the Building Industry A. Bessot. 11. Teaching Mathematics to Shop-Assistant Apprentices Exploring Content and Didactical Situations C. Hahn. 12. Developing a New Mathematics Curriculum for Post-Compulsory Education G. Wake, J. Williams. Section 4: Research Methods for Mathematics at Work. Preface R. Zevenbergen. 13. The Mathematical Needs of Engineering Apprentices J. Ridgway. 14. Identification of Some Mathematical Needs Linked to the Use of Mathematics at Work A. Mercier. 15. Ethnography and the Situatedness of Workplace Numeracy R. Zevenbergen. 16. Visibility of Mathematical Objects Present in Professional Practice A. Bessot. Conclusion R. Straesser. Index of Subjects. Index of Authors. Author Affiliations.

Challenging minds? Students’ perceptions of computer-based World Class Tests of problem solving

World Class Arena is a British government initiative to assess and develop the skills of gifted and talented children. Part of the strategy is to use computer-based tests. Students attempt tasks that require them to engage in higher-order problem solving, often in interactive, realistic, contexts. This study reports observations and interviews in schools. Students found tasks engaging and motivating, despite the unfamiliarity of the problem types and the challenging nature of the items. Students had no problems working with computers. They were sometimes distracted by attractive graphics, and sometimes used poor heuristics when attempting tasks. The study provides evidence that a computer environment can provide new ways to assess the problem solving skills of highly able students.

Vygotsky, informatics capability, and professional development

Vygotsky asserted that intellectual tools such as writing and science change human cognition, and human cultures. Informatics is a new tool which promises new sorts of cognitive development, and has already produced a good deal of cultural change. How can we enculturate educational reform associated with informatics? In particular, how can we change classroom practice? This paper describes some approaches to professional development, and highlights their strengths and weaknesses. It argues that people need to be offered ways to change which are consistent with their current theories of personal and professional development; tools are needed which directly suit their current needs; and there is a need to engender a belief in lifelong development throughout the educational system. A set of criteria for evaluating attempts to support professional development is offered, and suggestions are made about how informatics itself, and IFIP, can support the process.

Problematising Evidence-based Policy and Practice

Evidence-based policy and practice (EBPP) is widely advocated, and for good reason. Here, some challenges to EBPP are identified, illustrated by a large-scale evaluation of a major curriculum development project. Problems include: changes in educational goals, which necessitate the development of new measures of attainment; different time lines over which different patterns of result emerge; the challenge of defining a complex treatment, such as a new curriculum; and the variability of effect size in different classrooms. Several approaches are offered as responses to these challenges. The paper argues that much of the work on EBPP has focused on practice rather than on policy. Evidence-based policy will require detailed work on descriptions of systems and on systems change; more significantly, it will require the development of a new field of endeavour, associated with macro-systemic change, that is to say, the study of systems undergoing radical change.

What GATE Did: an exploration of the effects of the CATE criteria on students’ use of information technology during teaching practice

Information technology (IT) has assumed an increasingly important role in the English primary school curriculum. The CATE criteria (DES, 1989b) require that student teachers develop competencies in...

Assessing Mathematical Thinking Via FLAG

Teachers of undergraduate mathematics face a range of problems which include an increasing number of less well qualified students, and increasing academic diversity in the student population. Students face courses which are radically different from mathematics courses encountered in school; they often face assessment systems which are ill-aligned to course goals, and which use assessment methods likely to encourage a surface rather than a deep approach to learning. The paper describes materials developed by the MARS group for the US National Institute for Science Education for use on their FLAG Web site. Collections of assessment materials can be downloaded free of charge which assess a range of valuable process skills in mathematics — proof, reasoning from evidence, estimation, creating measures, and fault finding and remediation. They are designed to offer a wide repertoire of assessment styles, as part of a process of encouraging a broadening of teaching and learning styles.

Using evidence about teacher development to plan systemic revolution

In England and Wales Information Technology (IT) is to be used to support the teaching of all subjects; in addition, all students have an entitlement to IT capability. Data from several surveys are reported, which do not match this vision of IT. Rather, IT is seen by teachers to be concerned with the acquisition of technical skills, or as a support for administration: a small number are terrified of IT, rather more are unconvinced of the benefits of IT, and only a minority of teachers use IT to support their teaching. Teacher concerns regarding IT are reported. Finally, the paper offers a model of school development which highlights the changing demands on teachers as IT is integrated progressively into the curriculum.

Developing Statistical Literacy in Students and Teachers

While statistical literacy is gaining much more recognition as something that all citizens need in order to function fully in modern society, there is much less agreement as to exactly what is meant by the term. This chapter discusses what statistical literacy is, why it is important for children at school and for teachers, and the need for our understanding to evolve to keep pace with developments worldwide. It explores the potential of new curricula introduced in South Africa and New Zealand, and the work being done in many different countries by statistical agencies to support teachers’ statistical literacy. A case study where naive students and teachers develop skills by engaging with complex evidence on a topic of real social import is also described.

When Basic Mathematics Skills Predict Nothing: implications for education and training

Abstract A study was conducted into the mathematical needs of engineering apprentices, triggered by a decline in the basic number skills of applicants. The mathematical challenges of engineering differ from the mathematics taught in school. In particular, great precision is required and different techniques; a good deal of practical problem solving is necessary, too. Conventional measures of educational attainment had high predictive validity; a test created to sample the mathematical skills directly involved in engineering had low predictive validity. We conclude that perfect mathematical technique is essential in engineering; the competencies learned from a broad‐based education generalise to practical work; acquisition of mathematical technique does not; technical perfection is not a ‘foundation’, but rather is a component of mathematical education; mathematics education should encourage the development of a broad range of skills and some successful application of technique; and the deployment of skill...

The Mathematical Needs of Engineering Apprentices

A study was conducted into the mathematical needs of engineering apprentices, triggered by a decline in the basic number skills of applicants reported by employers. This study explored and confirmed the reported decline. The mathematical needs of apprentices were investigated in a number of ways, including an ethnographic study, interviews, and the exploration of the psychometrics of predicting apprentice performance. The ethnographic study revealed that mathematical challenges of engineering differ from the mathematics taught in school. In particular, great precision is required, applied to a variety of mathematical techniques; a good deal of practical problem solving is necessary, too. The psychometric study revealed that conventional measures of educational attainment had high predictive validity; a test created to sample the mathematical skills directly involved in engineering had low predictive validity. Therefore, high-level skills required for a successful educational career generalise to practical work, whilst the acquisition of mathematical technique does not. One can conclude that ‘basic skills’ are not a foundation but rather are a component of mathematical education. It follows that mathematics education should encourage the development of a broad range of skills; practising the deployment of skills in a range of contexts should be encouraged.