Teaching Mathematics and its Applications - current issue

Does students' confidence in their ability in mathematics matter?

Parsons, S., Croft, T., Harrison, M. — 2009-05-25

Research was conducted into first year engineering students’ learning of mathematics in a university college during 2005–2007. The aims were to understand better students’ confidences and explore which factors affected performance and how these were inter-related. Questionnaires were administered which posed questions regarding previous mathematics qualifications, student confidences, attitude, liking of the subject and motivation. The responses were analysed and compared with marks achieved by the students in their first year engineering mathematics examinations. The majority of students were fairly confident, reported improved confidence acquired during their first year of university study and had positive attitudes. Better mathematically qualified students were generally more confident and successful in mathematics. A regression model was produced which predicted a 12% increase in mathematics marks per increase in GCSE mathematics grade, and 5% increase in marks for each increase in confidence level. Thus, better qualifications (and the skills represented) were shown to be associated with better university marks and student confidence also produced a notable association with the marks achieved. The findings suggest that having attended to the mathematics syllabi, lecturers could seek to boost student confidence in their ability in mathematics as a further means to improve student performance at university.

GeoGebra -- freedom to explore and learn

Fahlberg-Stojanovska, L., Stojanovski, V. — 2009-05-25

We start by visiting the maths section of the web site answers.yahoo.com. Here, anybody can ask a question from anywhere in the world at every possible level. Answers are given by anyone who wants to contribute and then askers/readers rate the responses. A brief look here and it is starkly clear that our young people are struggling and their ability to think logically—that is understand a problem, organize data into knowns and unknowns, explore possibilities and assess solutions is definitely on the decline. In our opinion, this is more insidious than the actual decline in their overall mathematics skills. Further, one is struck by the fact that technology seems to be contributing to this decline when in fact it should be the opposite. We then examine two question/answer cycles in detail and show how the freeware GeoGebra (www.geogebra.org GeoGebraWiki: www.geogebra.org/wiki GeoGebraForum: www.geogebra.org/forum)—which gives the freedom to explore and learn to everyone, everywhere and at any time—can be of tremendous value to pupils and students in their understanding of mathematics from the smallest ages on up.

Factors influencing the transition to university service mathematics: part 1 a quantitative study

Liston, M., O'Donoghue, J. — 2009-05-25

This article reports on a quantitative study carried out into the influence of affective variables, the role of conceptions of mathematics and approaches to learning on students in the transition to Service mathematics at the University of Limerick (UL). Questionnaires were distributed to three groups of first year students on Service mathematics programmes (degree courses where mathematics plays a part in the students’ studies but is not the main focus) at UL, at the beginning of the university academic year 2006/2007. Their attitudes, beliefs, self-concept, conceptions of mathematics and approaches to learning are examined and relationships between specific variables are reported on. The impact these concepts, as well as final secondary school mathematics exam results, have on performance are also discussed.

Change in senior medical students' attitudes towards the use of mathematical modelling as a means to improve research skills

Perry, Z. H., Todder, D. — 2009-05-25

A PUBMED search for ‘mathematical models in medicine’ shows more than 15,000 articles covering almost every field of medicine. We designed a course with the goal of developing the students’ skills in computerized data analysis and mathematical modelling, as well as enhancing their ability to read and interpret mathematical data analysis. The study evaluated the acquisition of research skills and how to understand such data, as well evaluating the students’ feeling of competence. The course was structured as a 1-week (30-h) workshop for final year medical students. The study population consisted of 23 medical students who took the course in the 2005 academic year. Course evaluation used questionnaires that assessed the students’ satisfaction and mathematical knowledge. We found a significant change in the attitudes of our subjects, comparing their before and after attitudes towards their competence in the use of mathematical modelling, academically (i.e. their ability to read and understand articles using math models) as well as medically (i.e. their ability to implement theory that arises from math models to medical applications). We believe that the use of math modelling training in medical education significantly improved the students’ confidence in reading and applying math models in medicine; there is a tendency (albeit insignificant) towards superior results in attitudes of students towards math usage in medicine at large.

Solving second-order ordinary differential equations without using complex numbers

Kougias, I. E. — 2009-05-25

Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex variable analysis, a topic to which the students in question may not have been previously introduced. The purpose of this article is to present an alternative approach in establishing the general solution for such types of equations without using complex numbers.