Measurement: everywhere and nowhere in secondary mathematics

School mathematics is commonly structured into number, algebra, geometry and statistics. This raises the issue of where to place ideas within the topic of measurement since some aspects of measurement (such as measuring length or area) have a geometrical component, while other aspects of measurement (such as time or money) are about number. Furthermore, when actual measures are unknown, relationships between measures can be expressed – and this is one of the roots of algebra. Additionally, probability can be thought of as a form of measure (of uncertainty) and the various measures of data variation, such as standard deviation, can also be viewed as a form of measurement. All these considerations mean that the placing of measurement in the mathematics curriculum can be problematic for curriculum designers and policy makers; and equally tricky for teachers to teach in the most effective way. Informed by a review of the research basis for teaching key ideas in secondary school mathematics, this paper argues that measurement is both everywhere and nowhere in secondary mathematics; that is, measurement occurs across the topics that comprise secondary school mathematics, but the ideas of measurement are so scattered that the teaching of measurement in secondary school mathematics may lack some focus that might store up problems for learners as they progress with mathematics

Research bibliography: dynamic geometry software

This bibliography lists research that has investigated the use of dynamic geometry software (DGS) in the teaching and learning of mathematics. The bibliography is not intended to be exhaustive; rather it includes the major studies across the range of research that has been published

Book review: Teaching Mathematics with ICT, written by Adrian Oldknow and Ron Taylor, Continuum Press, 2000, ISBN 0-8264-4806-2 (pbk)

This book aims to provide practical advice on ways of using ICT to improve pupils' learning in mathematics. It covers the use of spreadsheets, TI Interactive, Derive, Logo, dynamic geometry software, and graphing calculators. The book is primarily aimed at teachers of mathematics in the secondary age-range, although teachers working outside this age-range should find plenty of food for thought. It is a book that should certainly appeal to mathematics teachers. It is not an easy book with instant answers but a book that will reward working with over time

Graphing calculators in the teaching and learning of mathematics: a research bibliography

This review suggests that using graphing calculators in mathematics education can enable students to approach situations graphically, numerically and symbolically, and can support students’ visualisation, allowing them to explore situations which they may not otherwise be able to tackle (and thus perhaps enable them to take their mathematics to a more advanced level). In this way, using graphing calculators can lead to higher achievement among students, perhaps through increased student use of graphical solution strategies, improved understanding of functions, and increased teacher time spent on presentation and explanation of graphs, tables and problem solving activities (compared with students not using such calculators). The impact of the availability of this form of calculator on teaching methods and curricula appears to have been more limited, with teachers reportedly tending to use graphing calculators as an extension of the way they have always taught, rather than provoking any radical change in style of teaching or design of the curriculum

The value of learning geometry with ICT: lessons from innovative educational research

This chapter reviews research on using ICT to support the teaching of geometry. The research selected focuses on learners’ use of interactive geometry software, the design of suitable teaching and learning activities, and the nature of relevant teacher professional development. The central theme of the chapter is that while ICT has considerable potential in enlivening the teaching and learning of school mathematics (and geometry in particular), there is much to take account of in terms of enabling this potential to be fully realise

Critical review of geometry in current textbooks in lower secondary schools in Japan and the UK

This paper reports on an initial analysis of current best-selling textbooks for lower secondary schools in Japan and the UK (specifically Scotland) using an analytic framework derived from the study of the textbooks in the “Trends in International Mathematics and Science Study” (TIMSS). Our analysis indicates that, following the specification of the mathematics curriculum in these countries, Japanese textbooks set out to develop students’ deductive reasoning skills through the explicit teaching of proof in geometry, whereas comparative UK textbooks tend, at this level, to concentrate on finding angles, measurement, drawing, and so on, coupled with a modicum of opportunities for conjecturing and inductive reasoning

Online mathematics enrichment: an evaluation of the NRICH project

This Executive Summary forms part of the final report of the findings of the independent external evaluation of the NRICH online mathematics project. The evaluation was commissioned by the University of Cambridge, UK as represented by the Millennium Mathematics Project. The evaluation was carried out by the evaluation team from the University of Southampton, UK, during 1998-99. Data collection took place between April and September 1999. An interim report, based on one element of the evaluation, was presented at the NRICH conference held in July 1999.1. The NRICH online mathematics enrichment project began in 1996 with the aim of establishing a permanent national UK centre for curriculum enrichment in mathematics. The project aims to provide mathematical learning support for very able children of all ages through the publication of a regular web-based ‘magazines’ featuring mathematical problems, puzzles, articles and games. University mathematics students act as peer teachers providing an electronic answering service. The centre also offers support, advice and inservice training to teachers, and resources for mathematics clubs. The NRICH website can be found at http://nrich.maths.org.uk/2. Internal evaluations of the project, carried out in 1997 and 1998, suggested that an increasing number of people were accessing the NRICH project website. The evaluations also indicated that teachers using the NRICH materials were generally satisfied with the type of problems presented, and that pupils who worked on the problems developed a richer view of mathematics. 3. The objectives of the external evaluation were to assess how the use of the NRICH website facilities enhances the mathematical development of children who have the potential to go on to study mathematical subjects at university, how the features of the website are used by teachers to help meet the special educational needs of exceptionally able children in mathematics, and the particular contribution of Information Communications Technology to the above. These objectives were derived from the aims of the NRICH project.4. The evaluation design incorporated a range of methods to provide data on the evaluation objectives. The various elements of the evaluation were an analysis of the responses to questionnaires completed by pupils, teachers, and other interested parties (such as parents) who access the NRICH website, a critical review of the NRICH website, together with selected case studies of school, classroom and pupil use of the NRICH project facilities. 5. Analysis of questionnaires completed by 199 pupils, 450 teachers, and 67 ‘friends of NRICH’ (such as parents) revealed that most NRICH users lived in England. This was particularly true of teachers. Over two-thirds of the pupils using NRICH were boys. Approximately the same proportion was white. A large proportion of users accessed NRICH at home. The majority of teachers worked in the state sector (both primary and secondary); ten percent were from private schools. The majority of users of all types were relatively new to NRICH, having been accessing the website for six months or less. The most frequent reason for accessing the NRICH website was to use it as a source of interesting mathematical problems. Most users were not registered with NRICH (a no-fee option open to all). The NRICH site was complimented by all categories of user as providing interesting problems, being attractively presented and generally easy to navigate. 6. The NRICH website was judged by the evaluation team to score highly on each of the website evaluation criteria. The new design of the site, launched in July 1999, was judged to be attractive, functional, easy to navigate, and contain high-quality materials. NRICH compared very favourably with other sites that provide mathematical puzzles, games and problems, and/or an answering service. The NRICH server statistics showed an increase in accesses to the site which was likely to be the result of more people accessing the NRICH site more often.7. In each of the three case study schools, at least one teacher made regular and often frequent use of the NRICH website, though none made use of the wider NRICH facilities available to registered teachers. NRICH was mainly used a source of interesting mathematical problems. Pupil usage of NRICH in the schools was much more varied. Only a very few pupils were aware of NRICH and had accessed the site themselves. While there was some evidence of impact on more able pupils, none of the teachers were able to quantify this impact but all praised NRICH as a very valuable resource.8. The three selected case profiles of pupil usage of NRICH revealed that these particular pupils accessed NRICH no more than once a month. All found the ‘one-to-one’ facility, where they could pose questions to University students, helpful and informative. Such exchanges often left the pupils wanting to know more, a situation the pupils viewed as positive. While few of the exchanges were related to the mathematical problems provided on the NRICH site, all these pupils valued the opportunity of being able to ask questions and receive replies.9. The main impact of NRICH on the more able pupils was in terms of helping them to gain a wider appreciation of mathematics and raising the profile of mathematics as a subject that could be interesting enough to pursue either within or outside school or for further study. Quantifying this impact was beyond the scope of this evaluation. Teachers mostly accessed NRICH to find problems to use in their teaching. The teachers used a variety of approaches to meet the needs of their more able pupils. Some used the NRICH problems with groups of more able children withdrawn from their regular classrooms. Some teachers used NRICH problems as extension material once regular classwork was complete. For some, NRICH was one resource amongst many. Only a few organised an extra-curricular mathematics club based solely around NRICH. The contribution of information communications technology (ICT) to both the enhancement of pupils’ mathematical development and to how teachers made use of the NRICH facilities was associated with the functionality and accessibility of the NRICH site. The interaction that was possible through using ICT was seen as a particular advantage of the NRICH project

An asset management strategy to accommodate a changing climate

Climate change is a significant factor that will affect how people live and work in future. In light of this and of international initiatives on limitations of emissions, the changing climatic conditions will affect the existing building fabric, and inflict a different kind of user demand on corporate property portfolios. A comprehensive literature review has shown that there is an absence of tools and metrics for facilities managers to evaluate the impact of climate change on their organization and develop mitigation and adaptation strategies for their existing and new built corporate property portfolios. There is a little augmentation for accommodating the existing and future climate changes into management of corporate property portfolio. This paper will argue the need to construct a comprehensive strategy for management of corporate property portfolio of large organizations, which will take into consideration climate change mitigation and adaptation

Proof in dynamic geometry contexts

Proof lies at the heart of mathematics yet we know from research in mathematics education that proof is an elusive concept for many mathematics students. The question that this paper raises is whether the introduction of dynamic geometry software will improve the situation – or whether it make the transition from informal to formal proof in mathematics even harder. Through discussion of research into innovative teaching approaches with computers the paper examines whether such approaches can assist pupils in developing a conceptual framework for proof, and in appropriating proof as a means to illuminate geometrical ideas