Bringing the outside world into the mathematics classroom - New approaches to the use of video in the classroom

Many countries are exploring different approaches to create a more relevant mathematics curriculum through the use of real world examples in the classroom. In this paper we will share some of the classroom video resources that have been developed since the last ICTMT: the series World of Maths (Teachers TV 2008) and i-Maths (British Broadcasting Corporation 2008). This also complements the UK’s “STEM” (Science, Technology, Engineering and Mathematics) agenda (Her Majesty's Treasury 2004) which aims to promote STEM subjects to the populus and increase student uptake in STEM related careers and courses

Alluvial terrace development and changing landscape connectivity in the Great Karoo, South Africa. Insights from the Wilgerbosch Riyer catchment, Sneeuberg

Dendritic channel networks in the Wilgerbosch River catchment draining the south side of the Sneeuberg, South Africa, are deeply incised exposing terrace fills of varying thickness and extent. Channel long sections exhibit ‘stepped’ profiles where resistant rock strata cross valley floors but are now partially or completely breached. Using a combination of aerial image analysis, geomorphological mapping, sedimentological investigations (field logging, grain size, and magnetic susceptibility analyses), and geochronology (OSL, 14C), this study demonstrates the patterns and controls on erosion and sedimentation and, to a lesser extent, the age structure of fills in two low-order tributaries (Africanders Kloof and Wilgerbosch Kloof) and several reaches of the higher-order Wilgerbosch River. A conceptual model of terrace development in relation to changing conditions of connectivity is presented. Valley headwaters are dominated by discontinuous palaeochannel and floodout sediments; whilst in second- to fourth-order tributaries, four sedimentologically and stratigraphically distinct terrace fills that exceed the scale and complexity of deposits on the northward side of the Sneeuberg were identified and analysed. The early part of this regional terrace succession highlights the importance of interactions between periglacial and fluvial activity on cut, fill, and pedogenesis around the time of the deglacial period. Terrace development is shown to have been a complex response to reconnection of the channel network with upland colluvial stores resulting in the valleys becoming choked with sediment. This caused a rise in groundwater and formation of extensive calcretised rootmats on valley floors and slopes acting to ‘blanket’ terraces 1 and 2. The thickness and longevity of this blanket is shown to restrict depth of incision in subsequent phases (T3, T4). The deposits in these headwater valleys have, until now, been overlooked as a source of palaeoenvironmental information. This study is the first to demonstrate the role and importance of changing connectivity in 'cut and fill' phases that predate the late eighteenth century European incursion in the Sneeuberg

A predictive model of energy savings from top of rail friction control

In this paper the authors present a predictive model of train energy requirements due to the application of a top of rail friction modifier (TOR-FM) versus dry wheel / rail conditions. Using the VAMPIRE® Pro simulation package, train energy requirements are modeled for two sets of TOR-FM frictional conditions, one using full Kalker coefficients and the other by using a Kalker factor of 18%. Both scenarios use a top of rail saturated coefficient of friction of 0.35. Under both TOR-FM frictional conditions, train energy savings are shown for complete laps of the Transportation Technology Center Inc.’s (TTCI) Transit Test Track (TTT) loop, and also when isolating only the tangent section of the loop. However, the magnitude of energy savings varies greatly depending on the Kalker coefficient factor used, highlighting the need to model this relationship as accurately as possible. These simulation results are compared with data obtained from a field study, in which train energy savings of 5.3% (lap) and 7.8% (tangent) are shown due to the application of TOR-FM

Metallo-Supramolecular Assemblies With Photoresponsive Functionality

This thesis concerns the design of metallosupramolecular architectures incorporating a specific function, namely light-responsive properties, for potential applications in molecular recognition, molecular electronics and as stimuli-responsive materials. This is achieved by employing established geometrically directing metallotectons in combination with novel light-responsive tripodal hosts based on the cyclotriveratrylene scaffold. A novel library of light-responsive molecular hosts have been prepared via novel asymmetrical azobenzene precursors. These light-responsive ligands undergo self-assembly with a variety of Ir(III) metallotectons to give a family of M3L2 metallocryptophanes, thus implanting the light-responsive functionality into these systems. Solution-state analysis indicates these metallocages contain a significant internal space for potential applications in molecular recognition. The photoresponsive properties of both the novel ligands and metallocryptophanes has been explored utilising light of UV and visible wavelengths to toggle between the trans/cis conformations of the embedded azobenzene units, resulting in dramatic structural perturbations in solution, pointing the way to sophisticated applications in molecular recognition. Photophysical analysis of these metallocryptophanes reveals deep blue emission properties, characteristically uncommon for Ir(III) complexes. A series of non-discrete coordination polymers have also been prepared and crystallographically elucidated from the combination of a light-responsive ligand with various Cu(II) and Ag(I) salts. Although light-responsive behaviour is yet to be demonstrated in these systems, a solvent-induced structural rearrangement is observed in one example, potentially promising further sophisticated host-guest properties

Innovative Approaches Using ICT to Support Teaching and Learning Advanced Mathematics

The UK has seen a worrying decline in the number of students taking up Higher Education courses in both Mathematics and ICT. The opportunity exists within an A-level mathematics course for teachers and students to use technology in an imaginative way to enhance the learning experience and to encourage students to consider further study in either discipline.Students taking A-level are taught in a variety of institutions. An A-level mathematics class in an 11-18 school could be a small cohesive group with similar background, prior learning experiences and familiarity with the use of ICT in mathematics. A class in a Further Education college is likely to be much larger and to include students from a wide range of previous institutions whose experiences both with regards to teaching and learning styles and to their use of ICT could vary widely.Catering for the individual teacher and student in these diverse circumstances can be a big deterrent to the use of technology, so in the ICTAM (Interactive Companion to Advanced Mathematics) project [3] the authors have put together a unique collection of software which has been designed to offer something to every A-level mathematics teacher and student, whatever their background institution or technological expertise.The paper considers a range of activities from ICTAM which includes:- • Activities based on files for a wide range of powerful mathematics software. • Its own graphing software Java applet, TIM, which teachers ·can adapt. • Dynamic activities based on real world problems and images • Ideas for different teaching approaches. • Supporting instructions and video demonstrations for student/teacher self-help. • Extension challenges for able students

Innovative multimedia approaches to mathematics education

There are currently three innovative multimedia projects in the United Kingdom which integrate the use of digital video resources to enhance and support mathematics education. These are: o Teachers’ TV (Teachers’ TV 2005); o The Mathematical Toolkit (The UK Mathematical Association/Intel plc, 2005); o The BBC Digital Curriculum BBCjam. (BBC 2005). This paper describes the context for each of these developments and reports on the early impact of each project, as appropriate