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Using Problem-based and Peer-assisted Learning in Teaching Mathematics to University Students: Focus on Competence Development
University West, Department of Engineering Science.
University West, Department of Engineering Science.
2009 (English)In: British Educational Research Association conference: BERA 2009, Manchester University, Manchester, UK, 2-5 September 2009, 2009Conference paper, Published paper (Other academic)
Abstract [en]

The harmonisation and internationalisation of higher education systems in Europe driven by the principles encapsulated in the Bologna Declaration [1] are offering new agendas for educators. The shift towards a student centred educational paradigm with the focus on learning outcomes and acquired competences highlights various ways in which this process can be mediated. An appropriate choice of teaching methods is instrumental to a successful educational process. The use of different teaching and learning styles such as discussions, group work, case studies, problem-based learning (PBL), peer-assisted learning (PAL) and critical thinking enables deeper engagement of learners within the learning process and at the same time facilitates the acquisition of professional skills and competences [2, 3].

The paper assesses the impact of PAL and PBL methods applied in teaching Mathematics to students on the 'Land Surveyors' programme, on student experience across generic and subject specific competence development.

The carried out research had the following objectives:

To plan and select tasks for tutorials where students can practise PBL;To design and implement several PAL sessions to facilitate the development of problem solving skills;To design questionnaires to evaluate the quality of student experience;To analyse the challenges university teachers face in implementing innovative approaches to teaching and the competence development.

There is a substantial body of literature on the PAL [e.g. 4] and PBL methodology [e.g. 5, 6]. PAL is an example of a student-to student support scheme grounded in collaborative learning. PAL  is aimed to improve student performance and  develop a range of study skills through creating an informal environment for learning. At the same time PBL encourages deeper learning via meaning construction and connecting ideas. It stimulates collaborative knowledge building process among participants and develops self-directed learning. The introduction of both methods into the educational process at the same has a broad potential.

Our study was carried out in the University Väst, Sweden during 9 weeks in 2008. The 'Core  Mathematics' module (7.5 credits) is one of the cornerstone modules of the 'Land Surveyors' programme curriculum. The competences acquired by students while on this module are fundamental for the future study. 42 first year students on the 'Land Surveyors' undergraduate programme participated in this study. Two pedagogical methods – PAL and PBL have been incorporated into the programme delivery. PBL method has been already introduced before in University Vast in Computer Science programmes [7] and this method was highly appreciated by students. In order to introduce PBL and PAL methods into the course design and to stimulate student involvement in the educational process, it was decided to keep a traditional layout of lectures but to change the way seminars were conducted. PBL method was used throughout the tutorials but three PAL sessions were introduced at the end of the course.

The students were solving applied mathematical problems working in small groups of five. The selection of problems was based on the relevance of the competences acquired through this activity to their future career. The introduction of PAL and PBL methods was focused in particular on the developing problem-solving and analytical skills as well as developing ability to formulate the problem mathematically. A peer tutor from the same student cohort was assigned to each group and training sessions for them were organised. To evaluate the outcomes of this study, the questionnaire was designed where the students could evaluate their learning experience. In addition, the peer tutors were interviewed. The results of the survey were statistically analysed. The results showed that the students evaluated PAL and PBL methods as useful and valuable. The students positively evaluated the peer tutors' performance. They thought that the group leaders were well-prepared, competent and could clearly explain the problems to peers.

The analysed data indicated that over 60 percent of the students estimated that have developed problem solving skills, while 35 percent indicated that they advanced their analytical skills and ability to apply mathematical tools. The students highly rated working in groups and commented on the positive effects of collaboration with peers. In their comments they pointed out that it was easier for them to ask questions, get support and explanation The students perceived the use of PAL and PBL approaches as a useful contribution to their learning experience.

The introduction of non-traditional methods into educational process creates new challenges for tutors. The selection of the problems, the number of students enrolled on the course, the choice of peer tutors, the way how training sessions are organised, the number and timing of the sessions are crucial for the successful implementation of the PAL and PBL.

In conclusion, this study demonstrates that the use PAL and PBL was rewarding and overall well received by the students at University Vast. The results of the final exams showed an improvement in student grades compared to previous years. The opportunity of implementing a more individual and flexible approach to the educational process led to improved generic and subject specific competences.

References

 

1. The Bologna Declaration of 19 June 1999 http://www.ond.vlaanderen.be/hogeronderwijs/bologna/documents/MDC/BOLOGNA_DECLARATION1.pdf

2. Moon, J. (2002) The module and programme development handbook. London: Kogan Page.

3. Ramsden, P. (2003) Learning to teach in higher education (2nd ed). New York: Routledge Falmer.

4. Peer Assisted Learning, Topping, K. and Ehly, S. (Eds.),  Lawrence Erlbaum, 1998

5. Dahlgren, M. (2003) PBL through the looking glass: Comparing applications in computer engineering, psychology, physiotherapy. International Journal of Engineering Education, 19 (5), 672-681.

6. Dahlgren. L. O. (1998) "Problembaserat lärande - Idé, Praktik Och Effeter", Linköpings Universitet.

Nilsson G. and Luchinskaya E. "Developing Competences Using Problem-based Learning: a Case Study of Teaching Mathematics to Computer Science Students", Journal of Research in Teacher Education, 2007, No 3. p 13-21. 

Place, publisher, year, edition, pages
2009.
National Category
Computational Mathematics
Research subject
ENGINEERING, Manufacturing and materials engineering
Identifiers
URN: urn:nbn:se:hv:diva-2378OAI: oai:DiVA.org:hv-2378DiVA, id: diva2:312041
Note
För fulltext kontakt med BERA eller författarenAvailable from: 2010-04-23 Created: 2010-04-23 Last updated: 2011-01-26Bibliographically approved
In thesis
1. Camera Modelling and Calibration with Machine Vision Applications
Open this publication in new window or tab >>Camera Modelling and Calibration with Machine Vision Applications
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Camera modelling and calibration are important parts of machine vision. They can be used for calculating geometric information from images. A camera model is a mathematical projection between a 3D object space and a 2D image. The camera calibration is a mathematical procedure calculating parameters of the camera model, usually based on several images of reference points. These fundamental parts of machine vision are improved in this thesis. One large part is the development of a generic camera model, GCM, that is accurate, computationally efficient and can be used for both conventional, fisheye and even catadioptric cameras. Different models were used in the past for conventional and  omnidirectional cameras and this is a well-known problem, the solution of which is described in this thesis. The accuracy of camera models is improved by introducing new ways of compensating for different distortions, such as radial istortion, varying entrance pupil point and decentring distortion. Calibration is mproved by introducing newmeans of calculating start estimates of camera parameters, from analysing shapes, sizes and positions of the reference points in the images. These start estimates are needed in order to make the calibration converge. Methods for calculating better reference centre points than the centres of gravity are developed in order to increase the accuracy further. Non-trivial null spaces that occur during calibration are identified. Awareness of these improve the calibration. Calibrations with different camera models are implemented and tested for real cameras in order to compare their accuracy. Certain models are better for certain situations, but the overall performance and properties are favourable for the GCM. A stereo vision welding robot system is developed, using the new model. It determines the geometry of a 3D weld joint, so that a robot can follow it. The same system is implemented in a virtual environment using a simulation software. Such simulation is important since it makes it possible to develop robot vision systems off-line.

Place, publisher, year, edition, pages
Chalmers University of Technology: Chalmers reproservice, 2010. p. 159
Series
Doktorsavhandlingar vid Chalmers Tekniska Högskola, ISSN 0346-718X ; 3046
Keywords
Camera model, Camera calibration, Fisheye camera, Catadioptric camera, Stereo vision
National Category
Other Engineering and Technologies not elsewhere specified
Research subject
ENGINEERING, Manufacturing and materials engineering
Identifiers
urn:nbn:se:hv:diva-2343 (URN)978-91-7385-365-1 (ISBN)
Public defence
2010-03-03, C118, Högskolan Väst, Trollhättan, 10:15 (English)
Opponent
Supervisors
Available from: 2010-04-23 Created: 2010-04-20 Last updated: 2010-04-23Bibliographically approved

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