CiteULike: rmagf's library [88 articles]

Computer Assisted Assessment: How many questions are enough?

Rosie Cornish — 2006-03-03T23:59:02-00:00

(February 2006)

Currently many universities make use of computer assisted assessment (CAA) as part of student assessment. Often these assessments take the form of a test where each question is randomly selected from a bank of alternatives. In this situation, the number of possible tests can be very large. For example, a test may have five questions and for each question there may be a bank of ten alternatives. The number of possible tests would be 105. This paper addresses the issue of how many tests, on average, need to be generated before all available questions have appeared at least once. By means of probability theory and the use of a computer algebra package, results are generated for a number of typical situations. Some surprising results are reported. For the example quoted above, it is found that, on average, only forty-three tests need to be generated before all available questions will have appeared at least once. The implications of these results, with reference to plagiarism, are discussed. Recommendations on how to reduce the possibility of plagiarism are provided.

IT was twenty years ago today …

Cliff Beevers — 2006-02-19T02:04:39-00:00

Maths CAA Series: Jan 2006 (January 2006)

Since 1985 a team at Heriot-Watt University have delivered CAL/CAA software to undergraduates [1, 2]. Currently, the CAA package developed over two decades is offering formative testing to 25,000 school pupils on 60,000 courses through the SCHOLAR Programme [3] and summative assessment in an extension of PASS-IT [4,5] in two dozen Scottish secondary schools in a one-year trial. Formative online assessment within the university continues on a number of courses too. This article attempts to chronicle the successful ingredients of the Heriot-Watt CAA software, highlight the important milestones over the years and look forward to future work.

Technology mediated post-compulsory mathematics: An activity theory approach

Gail Fitzsimons — 2005-12-22T06:04:49-00:00

International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 7. (October 2005), pp. 769-777.

This article draws on a sociocultural activity theory approach to identify considerations in the development of technology mediated mathematics education for learners at the post-compulsory level. It suggests that the use of technology should be aligned with the intended goals and objectives of the learning. In particular, it is necessary to take into account contexts both inside and outside of the institution where mathematical knowledges and skills may be transformed as tools or artefacts in the process of pursuing extra-mathematical objectives. To this end, the article incorporates findings from theoretical and case study research into adult numeracy in the workplace.

Investigation of interactive online visual tools for the learning of mathematics

KL Jacobs — 2005-12-22T06:03:18-00:00

International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 7. (October 2005), pp. 761-768.

For many years, educators have been discussing benefits of educational practices such as the use of real-world examples, visualisation, interactivity, constructivism, self-paced learning and self-paced testing. Macromedia Flash MX has been used to develop online modules for the course Differential Equations offered at the University of South Australia that utilize these practices. This paper demonstrates the following innovative features of the modules that provide an effective online learning environment: Online multiple-choice quizzes with randomized numeric values is a unique form of assessment that will be discussed. The integration of a wide range of effective learning principles into online modules will be the focus of this paper.

An innovative learning model for computation in first year mathematics

EJ Tonkes — 2005-12-22T06:01:43-00:00

International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 7. (October 2005), pp. 751-759.

MATLAB is a sophisticated software tool for numerical analysis and visualization. The University of Queensland has adopted Matlab as its official teaching package across large first year mathematics courses. In the past, the package has met severe resistance from students who have not appreciated their computational experience. Several main factors contribute: first, the software is numerical rather than symbolic, providing a departure from the thinking patterns presented in lectures and tutorials. Second, many students cannot see a direct connection between the laboratory exercises and core course material from lectures. Third, the students find hurdles to entry as commands often return incomprehensible error messages and don’t execute, and programs are difficult to write and debug. Overall, the details of the mathematics are lost in trying to negotiate the software. After considerable effort in tuning, it appears that a sequence of innovations has captured student support and added considerable value to both the computational and traditional learning process.

Towards student instrumentation of computer-based algebra systems in university courses

Sepideh Stewart — 2005-12-22T05:59:55-00:00

International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 7. (October 2005), pp. 741-749.

There are many perceived benefits of using technology, such as computer algebra systems, in undergraduate mathematics courses. However, attaining these benefits sometimes proves elusive. Some of the key variables are the teaching approach and the student instrumentation of the technology. This paper considers the instrumentation of computer-based algebra systems (CAS) by first- and second-year university students. The responses to a survey of the classes showed that instrumentation was more advanced for the second year students. The progress of each group is described and a number of student categories are outlined, in terms of their attitude to the computer and their instrumentation level.

Effective tutorial programmes in tertiary mathematics

Greg Oates — 2005-12-22T05:57:45-00:00

International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 7. (October 2005)

Papers presented at earlier Delta conferences reported on the use of collaborative tutorials and peer-tutors in undergraduate mathematics courses at The University of Auckland. This paper reports on significant developments within the Department's programmes, including the extension of the collaborative small-class tutorials to cover all first-year undergraduate courses in the department. It provides evidence of the effectiveness of the tutorial programme, as gauged from a survey of students’ perceptions. Many of the students enrolled in the Tutoring in Mathematics course that initially trains and provides the peer-group tutors continue on as tutors in other mathematics courses within the Department. Some subsequently enrol in the University's Graduate Diploma in Teaching (Secondary). The effects of the tutoring course on tutors continuing to tutor at higher levels, and their performances as novice teachers in the Diploma course are examined.

EAL undergraduates learning mathematics

B Barton — 2005-12-22T05:55:36-00:00

International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 7. (October 2005)

This paper reports on a third study in a series aimed at investigating the issues surrounding the learning of mathematics at The University of Auckland by students who have English as an Additional Language (EAL students). As well as summarizing the earlier studies, it presents some new data showing that the problems experienced by EAL students are not experienced by first language English students (L1 students). The consequences of these studies for undergraduate mathematics at The University of Auckland are explored using English language proficiency data for the whole of the 2005 undergraduate mathematics cohort. This data shows that the consequences of having large numbers of EAL students in an undergraduate mathematics cohort are likely to be much more important than expected, and that recent initiatives to raise literacy entrance levels are having some effect.

Analysis of student beliefs in a tertiary preparatory mathematics course

C Carmichael — 2005-12-22T05:52:29-00:00

International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 7. (October 2005), pp. 713-719.

Every year approximately 800 students enrol in the tertiary preparatory course TPP7181 at the University of Southern Queensland. Successful completion of this course will allow students to enrol in either further preparatory level mathematics courses or undergraduate study. For many of the students enrolled in this course, the study of mathematics was undertaken quite some time ago and usually in a school setting. Drop out rates for this course are quite high and it is hypothesized that motivation may be a key factor in determining student success or otherwise. In this study scales assessing self-efficacy were utilized in an attempt to gauge aspects of the motivation of students enrolled in the course. Initial results suggest that only specific measures of student confidence predict their performance and that both gender and age mediate the strength of this prediction.

Undergraduate students’ performance and confidence in procedural and conceptual mathematics

Johann Engelbrecht — 2005-01-20T00:29:54-00:00

International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 7. (October 2005), pp. 701-712.

The general perception is that high school teaching of mathematics in South Africa tends to be fairly procedural and that students that enter university are better equipped to deal with procedural problems rather than conceptual. This study compares the conceptual and procedural skills of first-year calculus students in life sciences. Also investigated is students’ confidence in handling conceptual and procedural problems. The study seems to indicate that these students do not perform better in procedural problems than in conceptual problems. They are more confident of their ability to handle conceptual problems than to handle procedural problems. Furthermore the study seems to indicate that students do not have more misconceptions about conceptual mathematics than about procedural issues.

Computer Assisted Assessment in Elementary Algebra (Experiences and points of view from the APLUSIX project)

Denis Bouhineau — 2005-11-25T01:25:46-00:00

(November 2005)

Since 2000, we have been working on a project for a global computer system dedicated to the teaching and learning of formal elementary algebra at secondary level schools. During a first phase, from 2000 to 2003, most of our work has been employed with the conception and realisation of a microworld for doing actively elementary algebra. This period has lead to the APLUSIX environment [Nicaud 2004], a tool dedicated to the first activities concerning algebra (resolution of equations, factorisation and expansion of polynomials). It was principally a piece of software devoted to students, based on the concept of a microworld, which means that a set of objects and relations were defined internally to represent algebraic expressions and represented externally in the most natural way, allowing activities in elementary algebra with direct-manipulation and intuitive advanced editing. The main principles used to develop this environment were, first, to let students freely and easily build and transform algebraic expressions, as they can do on paper, and second, to give permanent but not intrusive epistemic feedback on the syntactic and semantic correctness of the reasoning followed by the students. Experiments conducted in classes from K7 to K11 have shown that learning occurs with the use of the APLUSIX microworld [Nicaud 2005].

Enhanced scattering from a thin film with one-dimensional disorder

Y Tamura — 2005-11-21T02:47:31-00:00

Waves in Random and Complex Media, Vol. 15, No. 2. (May 2005)

This paper deals with a TE plane wave scattering from a thin film with one-dimensional disorder by means of the stochastic functional approach. The thin film is one-dimensionally inhomogeneous in the horizontal direction with infinite extent, and is homogeneous in the vertical direction with finite thickness. Based on an approximate wavefield representation in terms of a Wiener–Hermite expansion in a preceding paper (Tamura et al., 2004, Waves in Random Media, 14, 435–465), the first- and second-order incoherent scattering cross-sections are presented in explicit forms and scattering properties are discussed. The scattering properties vary entirely with the film thickness. In a case where the thickness is smaller than a few wavelengths in the thin film, enhanced scattering and associated enhanced scattering may appear as sharp peaks or dips on the second-order incoherent scattering distribution if the thin film has guided wave modes. When the thickness becomes sufficiently larger than the wavelength inside the film, a new enhanced scattering phenomenon appears as gentle peaks on the second-order incoherent scattering distribution in four special directions. Such four directions are the directions of forward scattering, specular reflection, backscattering, and the symmetrical direction of forward scattering with respect to the normal of the film surface. The first-order incoherent scattering occurs distinctly in four such directions. Such enhanced scattering is independent of the existence of the guided wave modes inside the thin film, and deeply relates to the structure of the thin film with one-dimensional disorder that has infinite correlation in the vertical direction. For SiC and glass thin films having one-dimensional disorder with a Gaussian correlation and three types of exponential correlation, the first- and second-order incoherent scattering cross-sections are illustrated in figures. The narrow enhanced scattering peaks appear for the glass film in a thin case. The gentle enhanced peaks turn up for both the SiC and glass films in a thick case. Furthermore, the optical theorem is calculated for several cases. It is then found that the error of the optical theorem decreases and the performance of the wavefield is improved by taking into account the second-order incoherent scattering.

Observation of sunlight enhanced backscattering from the sea bottom near the beach

Yu Bliokh — 2005-11-21T02:37:40-00:00

Waves in Random Media, Vol. 14, No. 3. (July 2004)

The paper describes a natural manifestation of the enhanced backscattering effect in conditions when sunlight is scattered by the sea bottom covered by shallow rippled water. In this system the water surface plays the role of a phase screen that focuses the light on the bottom, while the sandy bottom acts as a set of random single scatterers.

A critical survey of approximate scattering wave theories from random rough surfaces

Tanos Elfouhaily — 2005-11-21T02:16:33-00:00

Waves in Random Media, Vol. 14, No. 4. (October 2004), pp. R1-R40.

This review is intended to provide a critical and up-to-date survey of the analytical approximate methods that are encountered in scattering from random rough surfaces. The underlying principles of the different methods are evidenced and the functional form of the corresponding scattering amplitude or cross-section is given. The reader is referred to the original papers in order to obtain the explicit expressions of the coefficients and kernels. We have tried to identify the main strengths and weaknesses of the various theories. We provide synthetic tables of their respective performances, according to a dozen important requirements a valuable method should meet. Both scalar acoustic and vector electromagnetic theories are equally addressed.

The Uses of Learning Outcomes

Trevor Hussey — 2005-11-20T05:18:39-00:00

Teaching in Higher Education, Vol. 8, No. 3. (July 2003), pp. 357-368.

This paper argues that learning outcomes need to be reclaimed from their current use as devices for monitoring and audit, and returned to their proper use in aiding good teaching and learning. We require a broader, flexible and more realistic understanding of learning outcomes, better suited to the realities of the classroom and of practical use to those teachers who wish to respond to the enthusiasm of their students. To this end, a new model is produced that starts from the idea of an articulated curriculum, and embraces both intended and emergent learning outcomes. The model employs the distinction between predicted and unpredicted learning outcomes, together with the distinction between those that are desirable and those that are undesirable. The resulting account is intended to aid understanding of the nature and proper use of learning outcomes in teaching and learning.

Know what I mean? Enhancing student understanding of assessment standards and criteria

Berry O'Donovan — 2005-11-20T05:07:15-00:00

Teaching in Higher Education, Vol. 9, No. 3. (July 2004), pp. 325-335.

In recent years there has been an increasing emphasis in higher education on the explicit articulation of assessment standards and requirements, whether this emanates from calls for public accountability or is based on ideas of good educational practice (Ecclestone, 2001). We argue in this article that a single-minded focus on explicit articulation, whilst currently the dominant logic of higher education, will inevitably fall short of providing students and staff with meaningful knowledge of standards and criteria. Inherent difficulties in the explicit verbal description of standards and criteria make a compelling argument for the consideration of the role of structured processes that support the effective transfer of both explicit and tacit assessment knowledge. With reference to both empirical evidence and the literature, we propose a conceptual framework for the transfer of knowledge of assessment criteria and standards that encompasses a spectrum of tacit and explicit processes, which has proven to be effective in practice in improving student performance.

Traditional face-to-face and web-based tutorials: a study of university students' perspectives on the roles of tutorial participants

Jill Sweeney — 2005-11-20T05:04:01-00:00

Teaching in Higher Education, Vol. 9, No. 3. (July 2004), pp. 311-323.

Despite considerable research on the outcomes of teaching approaches at the tertiary level, there have been very few investigations of students' perspectives on the different approaches. This study, based on a series of in-depth interviews with students who completed a unit using traditional face-to-face tutorials and web-based bulletin-board tutorials, addresses the deficit. The findings highlight the differences in students' perspectives on the two types of tutorials, including the perceived role played by the tutor, themselves and their peers. The study suggests that a balance is needed between the two types of approaches.

Students evaluating teachers: exploring the importance of faculty reaction to feedback on teaching

Sarah Moore — 2005-11-20T04:58:36-00:00

Teaching in Higher Education, Vol. 10, No. 1. (January 2005), pp. 57-73.

This study investigates university teachers' perceptions of and reaction to students' structured feedback on various aspects of their teaching. It begins by reviewing the literature on student evaluations of teaching and on the important issues associated with performance feedback in general. Using semi-structured qualitative data gathered from a group of lecturers who voluntarily participated in a formative student evaluation process at the University of Limerick, the researchers analyse the types of reactions and perceptions that this data reveals. Questions relating to the perceived accuracy, predictability and rationale for change are explored. Finally, the implications for the development or enhancement of student feedback systems are outlined and discussed.

Lecturer and first year student (mis)understandings of assessment task verbs:'Mind the gap'

Kevin Williams — 2005-11-20T04:52:10-00:00

Teaching in Higher Education, Vol. 10, No. 2. (April 2005), pp. 157-173.

This paper examines the way in which a cohort of first year Chemistry students interpreted commonly used assessment task verbs and compared these responses with their lecturers' usage of these terms. The results of the research suggest that the gap between the understandings held by students new to university, and those held by lecturers, is of sufficient a nature to indicate that changes in practice are needed to contribute to fair assessment practices. The paper argues that understanding assessment as a Discourse, which exists alongside (but also independent of) general and discipline-specific academic Discourse, will help explain the substantial gap between student understandings and lecturer usage of assessment terms. Students must become members of this Discourse community in order to gain mastery within it. This requires deliberate exposure to the language, values and practices of academic assessment through examples used in every-day teaching practice and through scaffolded formative assessment.

Increasing success for Underserved Students. Redesigning Introductory Courses

Carol Twigg — 2005-11-14T06:52:28-00:00

(2005)

A report examining the impact of the redesign techniques developed by the program in course redesign on the success of adult students, students of color and low-income students.

Course Content Dictionary for sharing on-line educational materials

Jouni Karhima — 2005-08-29T00:18:59-00:00

(August 2005)

A Course Content Dictionary (CCD) describes the topics covered in a mathematics course in a tree like form. With the CCD an author can classify the produced materials and share them with other instructors who can browse through the classification to search for suitable content for their courses. It also enables a collaboration to produce a basic mathematics course, as each author can concentrate on specific topics. We believe that such a classification works very well for mathematics because basic courses are quite similar across different universities and high schools but it is of course applicable for other disciplines as well. The WebALT project develops a CCD technology, a repository of mathematical on-line exercises indexed by the CCD, and tools to author CCDs and link materials to the CCD. An xml schema has been defined for describing the CCD and an editor according to this schema.

Cognitive Styles and Distance Education

Yuliang Liu — 2005-08-09T07:54:14-00:00

Online Journal of Distance Learning Administration, Vol. 8, No. 2. (2005)

Distance education is a new and vital force in higher education. The design and application of distance learning is of central concern to many educators. Research has been conducted from a variety of perspectives in this area. However, there is not much research about how to adapt the design of distance education to students’ cognitive styles. This review is designed to address this issue. This article involves four sections: (a) an overview of the construct of cognitive styles, (b) major dimensions of cognitive styles, (c) major characteristics of distance education, and (d) applications of cognitive styles to the design of distance education.

Use and Reuse of Simulations in Mathematical Online Assessment

Ruth Thomas — 2005-08-02T05:57:01-00:00

(June 2005)

The focus of this paper is the use of simulations in assessment. The paper describes the work undertaken by Heriot-Watt University and the JeLSIM partnership. It looks at the drivers behind the pilot project integrating simulations and online assessment, explains the technology and then explores and demonstrates the potential of the system within a mathematical domain.

Further experiences with the personal response system in statistics teaching

Ernst Wit — 2005-06-07T08:29:45-00:00

(June 2005)

This article sets out a preliminary balance of the pros and cons following three full years of experience of using a wireless multiple-choice system in a service course of statistics teaching. As pointed out by several commentators, the system can easily be applied to statistics as well as any other subject, and the multi-choice system does not restrict the types of questions that can be asked. The output files from the personal response system have been used for some preliminary post-processing of the students answers. This provides some idea of how the correct and incorrect answers are distributed over the class. Student feedback on the use of the system is almost exclusively positive. In the opinion of the present author, the only negative aspect of the system, is the set-up and break-up time as well as the amount of time it takes to record an answer from the full class. If these time-constraints can be overcome, then the aim is to expand the use of the personal response system to all of the lectures here in Glasgow.

A Diagnostic Test with an Automatically Linked Revision Plan

Paul Robinson — 2005-06-01T08:54:20-00:00

(May 2005)

An in-depth study of Diagnostic Testing, carried out in Autumn 2002 [1], noted that 85% of the institutes which took part in the survey would use a diagnostic environment which automatically linked to self-study and support material if one were available. This paper describes one such computer-based system which has been in use since December 2002. The tests are easy to set, which means that they can be implemented very quickly if necessary. The experiences within three institutions, Tallaght Institute of Higher Education, the University of Portsmouth and Glasgow Caledonian University are described and indicate that the tests have been used in a variety of ways, in addition to the one recommended by the Engineering Council for students embarking on a mathematics-based degree course[2]. The results can be exported for use in Excel, or using additional software created in Portsmouth, analysed using Correspondence Analysis. On completion of the test, each student is provided with a personal Revision Plan which can be printed out or used interactively. No special security measures have to be in place when the students sit the test, since all the questions have random parameters. It is possible to monitor the completion of the recommended repair material electronically, although this is only done in one of the instances of its use described here.

Reflection and transmission of waves across a gap between two semi-infinite elastic plates on water

Hyuck Chung — 2005-05-28T04:05:08-00:00

The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 58, No. 1. (2005), pp. 13-15.

We describe a new approach to investigating the waves that propagate across a gap of finite width between two semi-infinite elastic plates floating on water of finite depth. The velocity potential for the fluid motion satisfies Laplace's equation, with the linearized free-surface boundary condition in the gap and thin plate equations modelling the elastic plates. The method of solution is based on the residue calculus technique (RCT) which was previously used by the authors to solve the semi-infinite ice-sheet problem. We highlight the advantages and limitations of the RCT when applied to the finite-gap and related problems.

A Study Into The Effects Of eLearning On Higher Education

Gurmak Singh — 2005-05-14T03:58:06-00:00

Journal of University Teaching & Learning Practice, Vol. 2, No. 1. (2005), pp. 13-24.

The Internet is a technological development that has the potential to change not only the way society retains and accesses knowledge but also to transform and restructure traditional models of higher education, particularly the delivery and interaction in and with course materials and associated resources. Utilising the Internet to deliver eLearning initiatives has created expectations both in the business market and in higher education institutions. Indeed, eLearning has enabled universities to expand on their current geographical reach, to capitalise on new prospective students and to establish themselves as global educational providers. This paper examines the issues surrounding the implementation of eLearning into higher education, including the structure and delivery of higher education, the implications to both students and lecturers and the global impact on

Scattered and free waves over periodic beds

R Porter — 2005-05-08T07:06:25-00:00

Journal of Fluid Mechanics, Vol. 483 (2003), pp. 129-163.

The behaviour of water waves over periodic beds is considered in a two-dimensional context and using linear theory. Three cases are investigated: the scattering of waves by a finite section of periodic topography; the Bloch problem for infinite periodic topography; and sloshing motions over periodic topography confined between vertical boundaries. Connections are established between these problems. A transfer matrix method incorporating evanescent modes is developed for the scattering problem, which reduces the computation to that required for a single period, without compromising full linear theory. The problem of the existence of Bloch waves can also be posed on a single period, leading to a close relationship between it and the scattering problem. Sloshing motions over periodic beds, which may be regarded as special cases of the Bloch problem, are also found to have a significant connection with wave scattering. Integral equations methods allied to the Galerkin approximation are used to resolve the three problems numerically. In particular, the full linear solution for Bragg resonance is presented, allowing the accuracy of existing approximations to this phenomenon to be assessed. The selection of results given illustrates the main features of the work.

Analytical solutions for forced long waves on a sloping beach

Phili Liu — 2005-05-08T06:46:55-00:00

Journal of Fluid Mechanics, Vol. 478 (2003), pp. 101-109.

We derive analytic solutions for the forced linear shallow water equation of the following form: for x>0, in which Y(x,t) denotes an unknown variable, f(x,t) a prescribed forcing function and b a positive constant. This equation has been used to describe landslide-generated tsunamis and also long waves induced by moving atmospheric pressure distributions. We discuss particular and general solutions. We then compare our results with numerical solutions of the same equation and with the corresponding solutions of the nonlinear depth-integrated equations and discuss them in terms of landslide-generated tsunamis.

Weakly nonlinear surface waves over a random seabed

Chian Mei — 2005-05-08T06:37:27-00:00

Journal of Fluid Mechanics, Vol. 475 (2003), pp. 247-268.

We study the effects of multiple scattering of slowly modulated water waves by a weakly random bathymetry. The combined effects of weak nonlinearity, dispersion and random irregularities are treated together to yield a nonlinear Schrdinger equation with a complex damping term. Implications for localization and side-band instability are discussed. Transmission and nonlinear evolution of a wave packet past a finite strip of disorder is examined.

Tsunami run-up and draw-down on a plane beach

Georg Carrier — 2005-05-08T06:29:18-00:00

Journal of Fluid Mechanics, Vol. 475 (2003), pp. 79-99.

Tsunami run-up and draw-down motions on a uniformly sloping beach are evaluated based on fully nonlinear shallow-water wave theory. The nonlinear equations of mass conservation and linear momentum are first transformed to a single linear hyperbolic equation. To solve the problem with arbitrary initial conditions, we apply the Fourier–Bessel transform, and inversion of the transform leads to the Green function representation. The solutions in the physical time and space domains are then obtained by numerical integration. With this semi-analytic solution technique, several examples of tsunami run-up and draw-down motions are presented. In particular, detailed shoreline motion, velocity field, and inundation depth on the shore are closely examined. It was found that the maximum flow velocity occurs at the moving shoreline and the maximum momentum flux occurs in the vicinity of the extreme draw-down location. The direction of both the maximum flow velocity and the maximum momentum flux depend on the initial waveform: it is in the inshore direction when the initial waveform is predominantly depression and in the offshore direction when the initial waves have a dominant elevation characteristic.

Trapping of waves by a submerged elliptical torus

M Mciver — 2005-05-08T06:03:28-00:00

Journal of Fluid Mechanics, Vol. 456 (2002), pp. 277-293.

An investigation is made into the trapping of surface gravity waves by totally submerged three-dimensional obstacles and strong numerical evidence of the existence of trapped modes is presented. The specific geometry considered is a submerged elliptical torus. The depth of submergence of the torus and the aspect ratio of its cross-section are held fixed and a search for a trapped mode is made in the parameter space formed by varying the radius of the torus and the frequency. A plane wave approximation to the location of the mode in this space is derived and an integral equation and a side condition for the exact trapped mode are obtained. Each of these conditions is satisfied on a different line in the plane and the point at which the lines cross corresponds to a trapped mode. Although it is not possible to locate this point exactly, because of numerical error, existence of the mode may be inferred with confidence as small changes in the numerical results do not alter the fact that the lines cross.If the torus makes small vertical oscillations, it is customary to try to express the fluid velocity as the gradient of the so-called heave potential, which is assumed to have the same time dependence as the body oscillations. A necessary condition for the existence of this potential at the trapped mode frequency is derived and numerical evidence is cited which shows that this condition is not satisfied for an elliptical torus. Calculations of the heave potential for such a torus are made over a range of frequencies, and it is shown that the force coefficients behave in a singular fashion in the vicinity of the trapped mode frequency. An analysis of the time domain problem for a torus which is forced to make small vertical oscillations at the trapped mode frequency shows that the potential contains a term which represents a growing oscillation.

Bragg scattering of random surface gravity waves by irregular seabed topography

Fabric Ardhuin — 2005-05-08T05:48:34-00:00

Journal of Fluid Mechanics, Vol. 451 (2002), pp. 1-33.

The Bragg scattering of random, non-stationary surface gravity waves by random topography on a gently sloping bottom is investigated. A correction is given of previously published expressions for the triad wave–wave–bottom interaction source term in the spectral energy balance equation, and the result is reconciled with deterministic theories for the reflection of waves from sinusoidal seabed undulations. For both normal and oblique incidence, the stochastic and deterministic theories are equivalent in the limit of long propagation distances. Even for relatively short distances (for example two bottom undulations), the reflected energy predicted by the stochastic source term formulation is generally within 15% of values predicted by deterministic theories. The detuning of Bragg resonance by refraction and shoaling is discussed, suggesting practical validity conditions for the stochastic theory. The effect of bottom scattering on swell propagation is illustrated with numerical model computations for the North Carolina continental shelf using high-resolution bathymetry and an efficient semi-implicit scheme to evaluate the bottom scattering source term and integrate the energy balance equation. Model results demonstrate the importance of forward scattering of waves that propagate at large oblique angles over bottom features with typical scales of one to several surface wavelengths. This process contributes significantly to the directional spread of swell on the continental shelf by diffusing energy, in the spectrum, around the mean wave direction. Back-scattering, caused by bottom features with crests parallel to those of the surface waves and wavelengths close to half the surface wavelength, is weak, owing to the sharp roll-off of the bottom elevation spectrum at high wavenumbers. Model predictions are consistent with field measurements.

Accurate refraction–diffraction equations for water waves on a variable-depth rough bottom

Yehud Agnon — 2005-05-08T05:39:22-00:00

Journal of Fluid Mechanics, Vol. 449 (2001), pp. 301-311.

The extended mild-slope equation and the modified mild-slope equation have been used successfully to study refraction–diffraction of linear water waves by steep bottom roughness. Their consistency has been questioned. A systematic derivation of these model equations exposes and illuminates their rationale. Their good performance stems from an accurate representation of (Class I) Bragg resonance. As a benchmark test case, we consider scattering by a sloping bottom with random roughness. The rates of scattering found for the mean field in both of the approximate models agree exactly with the full theory for scattering by small roughness. This greatly improves the limited agreement which was found for the mild-slope equation, and establishes the validity of the above model equations. The study involves operator calculus, a powerful method for simplifying problems with variable coefficients. The augmented mild-slope equation serves to consistently derive accurate model equations.

Slow flow of a Bingham fluid in a shallow channel of finite width

Chian Mei — 2005-05-08T05:11:51-00:00

Journal of Fluid Mechanics, Vol. 431 (2001), pp. 135-159.

We present a theory for the three-dimensional flow of a Bingham-plastic fluid in a shallow and wide channel. Focusing attention on slow flows appropriate for gentle slopes, low discharge rates or the final stage of deposition, we ignore inertia and apply the long-wave approximation. For steady flows, the velocity distribution, total discharge, and section-averaged flux are obtained analytically in terms of the fluid property and the geometry of the channel cross-section. Nonlinear stationary waves, which connect a uniform depth upstream to another uniform depth downstream, are then investigated, for both wet and dry beds. A numerical scheme is applied to calculate the transient flow evolution. The final development of the stationary wave due to steady discharge upstream is obtained numerically and the relation between the tongue-like shape of the wave front and the fluid property is discussed. The phase speed of the stationary wave is also derived analytically. Finally, the transient spreading of a finite fluid mass released from a reservoir after a dam break is simulated numerically. The transient development of the front and the final extent of deposition are examined.

Interaction of water waves with three-dimensional periodic topography

R Porter — 2005-05-08T05:00:05-00:00

Journal of Fluid Mechanics, Vol. 434 (2001), pp. 301-335.

The scattering and trapping of water waves by three-dimensional submerged topography, infinite and periodic in one horizontal coordinate and of finite extent in the other, is considered under the assumptions of linearized theory. The mild-slope approximation is used to reduce the governing boundary value problem to one involving a form of the Helmholtz equation in which the coefficient depends on the topography and is therefore spatially varying. Two problems are considered: the scattering by the topography of parallel-crested obliquely incident waves and the propagation of trapping modes along the periodic topography. Both problems are formulated in terms of ‘domain’ integral equations which are solved numerically. Trapped waves are found to exist over any periodic topography which is ‘sufficiently’ elevated above the unperturbed bed level. In particular, every periodic topography wholly elevated above that level supports trapped waves. Fundamental differences are shown to exist between these trapped waves and the analogous Rayleigh–Bloch waves which exist on periodic gratings in acoustic theory. Results computed for the scattering problem show that, remarkably, there exist zeros of transmission at discrete wavenumbers for any periodic bed elevation and for all incident wave angles. One implication of this property is that total reflection of an incident wave of a particular frequency will occur in a channel with a single symmetric elevation on the bed. The zeros of transmission in the scattering problem are shown to be related to the presence of a ‘nearly trapped’ mode in the corresponding homogeneous problem. The scattering of waves by multiple rows of periodic topography is also considered and it is shown how Bragg resonance – well-established in scattering of waves by two-dimensional ripple beds – occurs in modes other than the input mode.

On uniqueness and trapped modes in the water-wave problem for vertical barriers

N Kuznetsov — 2005-05-08T04:37:21-00:00

Wave Motion, Vol. 33, No. 3. (March 2001), pp. 283-307.

Uniqueness in the linearised water-wave problem is considered for a fluid layer of constant depth containing two, three or four vertical barriers. The barriers are parallel, of infinite length in a horizontal direction, and may be surface-piercing and/or bottom mounted and may have gaps. The case of oblique wave incidence is included in the theory.A solution for a particular geometry is unique if there are no trapped modes, that is no free oscillations of finite energy. Thus, uniqueness is established by showing that an appropriate homogeneous problem has only the trivial solution. Under the assumption that at least one barrier does not occupy the entire fluid depth, the following results have been proven: for any configuration of two barriers the homogeneous problem has only the trivial solution for any frequency within the continuous spectrum; for an arbitrary configuration of three barriers the homogeneous problem has only the trivial solution for certain ranges of frequency within the continuous spectrum; for three-barrier configurations symmetric about a vertical line, it is shown that there are no correspondingly symmetric trapped modes for any frequency within the continuous spectrum; for four-barrier configurations symmetric about a vertical line, the homogeneous problem has only the trivial solution for certain ranges of frequency within the continuous spectrum.The symmetric four-barrier problem is investigated numerically and strong evidence is presented for the existence of trapped modes in both finite and infinite depth. The trapped mode frequencies are found for particular geometries that are in agreement with the uniqueness results listed above.

Decomposition methods for wave scattering by topography with application to ripple beds

P Chamberlain — 2005-05-08T04:29:06-00:00

Wave Motion, Vol. 22, No. 2. (September 1995), pp. 201-214.

A method is described for determining those approximations to wave scattering by bed topography which are based on second-order ordinary differential equations. The development of a decomposition method allows the scattering matrix for an extended section of varying topography to be assembled in a piecemeal fashion. In particular, the scattering matrix for a ripple bed, consisting of an arbitrary number of periodic undulations, is expressed in terms of the scattering properties of a single ripple. The structure obtained reveals the main features of ripple bed scattering, including resonant reflection at certain frequencies. The analysis is allied to numerical calculations to compare five different models of ripple bed scattering.

Wave scattering by periodic arrays of breakwaters

R Porter — 2005-05-08T04:21:08-00:00

Wave Motion, Vol. 23, No. 2. (March 1996), pp. 95-120.

Oblique incidence of plane waves upon an infinite array of in-line periodic screens or breakwaters in finite water depth is considered using linear water-wave theory. The number of reflected or transmitted waves is a function of the angle of incidence and the ratio of wavelength to array periodicity. A simple matrix formulation is provided for all the reflection and transmission coefficients arising from a particular set of parameters, using a formulation based either on the unknown velocity through a gap or on the unknown pressure difference across a breakwater screen. Integral properties of functions related to these unknowns form the basis of the matrix structure, the functions themselves satisfying a set of integral equations which are solved using a Galerkin approximation that gives highly accurate approximations with very few terms in the expansion. The problem is extended to consider two identical parallel arrays and it is shown that there exists zeros of both reflection and transmission. Finally, a wide-spacing approximation is derived for two arrays based on the accurate results found from the single array problem, where the two arrays do not have to be identical, but must have the same periodicity.

Scholarship of Teaching: a model

K Trigwell — 2005-05-08T02:31:08-00:00

Higher Education Research & Development, Vol. 19, No. 2. (July 2000), pp. 155-168.

In this paper we present a model which describes the scholarship of teaching. We first explore what scholarship of teaching means, both in terms of the way it is represented in the literature and also the way it is understood by academic staff themselves. From this information, we derive a multi-dimensional model of scholarship of teaching which captures the variation found in the literature and empirical studies. In the final section, we illustrate how the model is used in informing the design of programs for development of the scholarship of teaching in universities.

Developing the Scholarship of Teaching in Higher Education: a discipline-based approach

M Healey — 2005-05-08T02:19:23-00:00

Higher Education Research & Development, Vol. 19, No. 2. (July 2000), pp. 169-189.

There is an international debate about the development of the scholarship of teaching. It is argued here that the scholarship of teaching needs to be developed within the context of the culture of the disciplines in which it is applied. The scholarship of teaching involves engagement with research into teaching and learning, critical reflection of practice, and communication and dissemination about the practice of one"s subject. This provides a challenging agenda for the development of subject-based teaching. Implementing this agenda includes applying the principles of good practice in the disciplines; developing the status of teaching; developing the complementary nature of teaching and research; and undertaking discipline-based pedagogic research. The paper is illustrated with particular reference to the discipline of geography.

WALLIS: a Web-based ILE for Science and Engineering Students Studying Mathematics

Manolis Mavrikis — 2005-05-07T07:55:39-00:00

AIED2003 :: Conference on Artificial Intelligence in Education 2003, Sydney Australia (July 2003)

This paper, after briefly describing our context and the problems faced by science and engineering students studying mathematics, presents WALLIS, a webbased system that is being developed to address some of these problems. Keeping in mind pedagogy and the development of a learner-centred application, we first describe the iterative methodology which we employed, and theories (such as constructivism and contingent instruction) that influence the system’s design and the feedback it provides. Finally we briefly present some results that the system’s integration provides despite its early stages, and could be particular useful for similar projects.

Students evaluating teachers: exploring the importance of faculty reaction to feedback on teaching

Sarah Moore — 2004-12-28T15:40:49-00:00

Teaching in Higher Education, Vol. 10, No. 1. (January 2005), 57.

This study investigates university teachers' perceptions of and reaction to students' structured feedback on various aspects of their teaching. It begins by reviewing the literature on student evaluations of teaching and on the important issues associated with performance feedback in general. Using semi-structured qualitative data gathered from a group of lecturers who voluntarily participated in a formative student evaluation process at the University of Limerick, the researchers analyse the types of reactions and perceptions that this data reveals. Questions relating to the perceived accuracy, predictability and rationale for change are explored. Finally, the implications for the development or enhancement of student feedback systems are outlined and discussed.

Self-regulated learning about university teaching: an exploratory study

Carolin Kreber — 2005-05-07T07:24:12-00:00

Teaching in Higher Education, Vol. 10, No. 1. (January 2005), pp. 75-97.

While research on self-regulated learning has been proliferating over the past decade, also within higher education settings, only very few studies apply the notion of self-regulated learning to teaching. We offer this exploratory study as a contribution to our understanding of the role of self-regulated learning in university instructors' growth as teachers. Thirty-one academic science staff participated in semi-structured interviews designed to explore whether they engage in self-regulatory processes when learning about teaching. Interview questions were based on two theories: Zimmerman's self-regulated learning cycle and Kreber and Cranton's scholarship of teaching model. Cluster analyses revealed different patterns of responses for various subgroups of staff. For the two main groups, Chi-square analyses identified the specific variables on which differences between groups were observed. Participation in certain educational development activities as well as discipline affiliation was shown to be associated with self-regulated learning processes. We make concrete suggestions for how future research on self-regulated learning about teaching can build on these findings and conclude the article with some recommendations for the practice of educational development.

Towards improving students' attendance and quality of undergraduate tutorials: a case study on law

Mashood Baderin — 2005-05-07T07:01:26-00:00

Teaching in Higher Education, Vol. 10, No. 1. (January 2005), pp. 99-116.

As part of continual efforts towards improving learning and teaching in the faculty, lecturers in the law faculty of the University of the West of England (UWE), Bristol debated the question of students' attendance and quality of tutorials in a recent email discussion amongst themselves. At the end of the debate the need for further research on the subject was highlighted, which initially spurred the research subsequently developed into this journal article. The article explores, through a discursive and comparative analysis of questionnaire responses, how to improve students' attendance and quality of undergraduate law tutorials. The analysis is equally relevant for other courses in which tutorials are employed as a mode of learning and teaching.

Serving Mathematics in a distributed e-learning environment

CJ Sangwin — 2005-04-23T02:03:02-00:00

(April 2005)

This article describes the work of the recent serving mathematics in a distributed e-learning environment project. The project, which ran from September 2004 to the end of March 2005, was funded by the JISC and enabled an unusual level of collaboration between colleagues to develop the mathematical e-learning tools described in this article.

Keeping Control using Computer Aided Assessment

WH Foster — 2005-04-14T07:28:46-00:00

(December 2004)

Many lecturers of Mathematics and Statistics courses in Higher Education have long cherished the principle that the courses they teach belong to them and they have full control of delivery and assessment subject to the formal syllabus requirements. On top of this, it is recognised that important courses at First Year level which lay the foundation for mathematical and statistical skills can be further improved and controlled by monitoring the performance of students; supplying timely remedial work; and providing further exercises and assignments when needed. This article discusses the impact of computer based techniques on these different aspects of maintaining control of courses. The advent of VLEs and developing techniques in CAA and CAL has created both opportunities and problems in the wake of the perceived increased teaching needs at the early stages of degree courses. Amongst the opportunities the modern environments give the chance to: Organise the course using a VLE as a coordinating and resource forum; Provide more scope for practice of basic mathematical and statistical skills through CAA; and employ CAA to provide a method of monitoring student performance. This article discusses the problem of perceived and actual loss of control arising from these opportunities. It is worth noting that institutional VLEs were developed in the USA and Canada where there is less of an ownership culture, especially for lower level courses.

MathQTI and the “Serving Mathematics” project

M Mavrikis — 2005-04-14T07:21:34-00:00

(January 2005)

The JISC-funded "Serving Mathematics in a distributed e-learning environment" project aims to develop open-source software and tools to address the special requirements of Mathematics in the context of e-learning and e-assessment. Part of the project looks into extending the IMS Question & Test Interoperability (QTI) specification [1] in as compatible and convenient way as possible in an attempt to enable the exchange of questions with mathematical context between question engines and authoring tools. The motive behind the need to extend QTI and the limitations of QTI have been described in the past in several meetings, workshops [2,3,4] and mailing lists[5,6]. The main issues are summarised here: • It is not possible to have mathematics in all of the parts of the question (e.g title, statement, feedback) in an interoperable, platform-independent and system-understandable way. • Mathematical questions, their processing and the feedback they provide are easier to write and maintain when variables and random constants are used. • Answers to mathematical questions, more often than not, involve mathematical entities which need to be understood by the system, processed and evaluated appropriately. • Science and Engineering questions often test precision and accuracy of real values. Feedback and scoring needs to be adapted to students' answers. • QTI is weighted towards "teacher provided" response questions in which a student is required to make a certain kind of selection from responses provided by a teacher (for example MCQs). Actually, a teacher more usually would prefer to establish that the student's own answer satisfies certain (mathematical)properties. • Mathematical questions often require the learner to provide an answer for which the form (e.g matrix, fraction, parts of a formula) is already provided (in order, for example, to test specific aspects or even to make it easier for the student to answer). • There are many examples of question structures which research has shown to be useful and effective. These include such things as conditional hints, multiple parts and partial marking. Such features are now reasonably well established in mathematical CAA and their absence provides less flexibility during the question processing and leads to less effective feedback.

Effective reporting for online assessment --- shedding light on student behaviour

David Schofield — 2005-04-14T07:12:27-00:00

(February 2005)

Online assessments can offer students individual and independent learning experiences, which can greatly enhance the teaching and learning process. Feedback, as an important factor in the learning process, is a feature, in one way or another, of many learning theories; through conversation (Laurillard [1]) or through reflection (Kolb [2]). “Action without feedback is completely unproductive for a learner” Diana Laurillard [1]. In online assessment immediate, or synchronous, feedback to a submitted answer can take a number of forms – for a good classification see Mason & Bruning [3]. As valuable as synchronous feedback is, there is also a place for asynchronous feedback that supports student reflection and bolsters learning. In a traditional classroom setting most feedback is of an asynchronous nature and one way of supporting the provision of asynchronous feedback in an online context is through the use of post-assessment reporting. Whilst many assessment systems have reporting facilities, they often do not provide the level of detail required to support the learning process in depth. This article seeks to describe some of the work from a project known as PASS-IT [4] and how effective reporting can enhance formative online assessment. Since 1984 the CALM group at Heriot-Watt University has been developing computer-based assessments [5-9] for delivery to engineering and science students at Heriot-Watt University [10], and to secondary schools through the SCHOLAR Programme [11]. For the last two years development work has been under the remit of a Scottish collaborative project called PASS-IT [4], which has been investigating the delivery of on-line assessments to secondary school children across Scotland.

PASS-IT ON

HS Ashton — 2005-04-14T07:05:02-00:00

(March 2005)

PASS-IT [http://www.pass-it.org.uk/] is a project that has brought together the major Scottish educational agencies with a common goal to investigate how best to exploit e-assessment to enhance flexibility, improve attainment and support teaching and learning in school and college education. PASS-IT has experimented with novel approaches to question design and structure, the role of feedback to support learning and the ability of Computer Aided Assessment (CAA) to measure appropriate learning outcomes in a variety of subjects and levels. Central features of PASS-IT have been to investigate the significance of the medium in test delivery following the work of Greenwood et al [1] and Fiddes et al [2] and the evaluations of the use of steps for partial credit Beevers et al [3] and McGuire et al [4]. The major research findings from phase 1 of the project have been communicated by Ashton et al in two recent papers [5,6]. This present article explains some of the findings of phase 2 of the project with an emphasis on the work in Mathematics.