Teachers in transition: Moving towards CAS-supported classrooms

In the near future many teachers may be required to incorporate CAS into their teaching practices. Based on classroom observations and interviews over two years, this paper reports how two teachers made the transition from using graphics calculators to CAS calculators while teaching differential calculus to upper secondary school students. Both teachers taught with CAS in ways that were consistent with their beliefs about learning and teaching. Over two years, the teachers' teaching approaches and purpose for use of technology were stable and seemed to be underpinned by their beliefs about learning. In contrast, both teachers made changes to the content they taught (and thus what they used technology for) in response to new institutional knowledge. Content choice seemed to be underpinned by the teachers' purpose for teaching. Other influences impacted on what the teachers taught and how they taught it: the teachers' content knowledge, their pedagogical content knowledge, and the lack of legitimacy of CAS as a tool for learning and during examinations in the trial school and wider educational community. The extent of differences noted between the responses of just two teachers indicates that there will be many responses to using CAS in classrooms, as teachers aim to achieve different learning goals and interpret their responsibilities to students in different ways.     

A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

A method for investigating the orientational behaviour of fibrous particles in gaseous flow

A method is described by which the angular orientation distribution of fibrous particles carried in a gaseous stream may be investigated. The method is based upon the interpretation of the spatial intensity distribution or scattering profile of laser light scattered by individual fibres. The scattering instrument used to capture the profiles is described, and the mathematical computation required to ascertain the orientation of each particle at the measurement point is detailed. Illustrative results are given for a study of airborne micromachined silicon particles of 12 μm length and 1.0 μm by 1.5 μm cross-section. The method is currently being employed by the authors to investigate ways of improving the orientation control over nonspherical particles in systems such as aerodynamic particle sizers and particle shape classifiers, since lack of particle orientation control is known to adversely affect the measurement accuracy of both these types of instrument.     

The utilization of chemical shift and spin-lattice (T1) relaxation time data for the discrimination of isomeric indenoisoxazoles

Treatment of 2-pivaloyl-1,3-indandione with hydroxylamine leads to the formation of a pair of isomeric indenoisoxazoles, the product formed dependent upon the cyclization conditions. Under acidic conditions, 8-t-butylindeno[1,2-c]isoxazol-7-one ( 5 ) is formed while under neutral or basic conditions, an oxime, 2 , is generated which may then be cyclized under acidic conditions to give 3-t-butylindeno[1,2-c]isoxazol-4-one ( 4 ). Although these isomeric indenoisoxazoles may be discriminated by chemical means, we were interested in developing an unequivocal method for distinguishing these and potentially other isomeric pairs by spectroscopic means. A ¹³C-nmr based method for the discrimination of these isomers which is based on the utilization of chemical shift arguments and spin-lattice relaxation data is thus presented.     

Quantum mechanical coupled-channel collision-induced dissociation calculations with hyperspherical coordinates

A time-independent coupled-channel method, using hyperspherical coordinates, has been developed for calculating quantum mechanical collision-induced dissociation probabilities for collinear atom-diatom systems in which the exchange reaction can also occur. The results for a model potential energy surface are compared with quasi-classical trajectory calculations and discussed.     

Benzodiazepine analogues. Part 21. 13C NMR analysis of benzoxathiepine derivatives

The influence of substituents and structure on the 13C NMR spectra of four series of benzoxathiepine derivatives has been investigated. Signal assignments in the 13C NMR spectra have been facilitated by the use of several predictive methods, permitting comparison of their relative efficacy.