Tertiary Mathematics Research Articles

Proficiency in the explanation of procedures: A test of the intuitive understanding of teachers of undergraduate mathematics

A discussion of production system approaches to the representation of learned procedures, and of stage models of the acquisition of procedures, yielded four general principles applicable to the construction of effective explanations. The intuitive appreciation of these principles by tertiary teachers was tested in two studies. In the first, separate verisons of an explanation of a standard undergraduate mathematics problem solution procedure were prepared, these versions differing in the extent to which they exemplified the derived principles. Subjects ranked the explanations in terms of their perceived effectiveness. In the second study, subjects of varying experience at teaching tertiary level mathematics were video recorded while they individually explained three standard undergraduate problems. Their explanations were scored for the extent to which some awareness of the general principles was evidenced. In general terms the findings from these two studies suggested that mathematics teachers might be well able to discriminate between explanations which differ in their compliance with the derived general principles, but that they were not well skilled at employing these principles in explanations which they generated themselves.

The 6‐3‐3‐4 education system and tertiary mathematics curriculum—A case for matching the objectives in senior secondary mathematics curriculum with the preparatory stance of the teacher

The National Policy of Education (revised 1981) professes a functional literacy dimension to educational attainments in the Federal Republic of Nigeria. Consequently, obvious and unavoidable steps were adopted by government for the purposes of ensuring the realization of this functional literacy element in the system. One such step bordered on the revision/restructuring of school curricula at the appropriate levels. In this paper, we sought to examine to what extent that teacher preparation at the tertiary levels reflected the attainment of objectives for mathematics education at the senior secondary level. This report centred essentially on the Imo, Bendel and Rivers State School Systems, the result of which guided us to the conclusion that vital elements of teacher preparation seemed lacking in the context of ensuring thorough grounding in mathematics of pupils at the senior secondary level.

Tertiary mathematics without lectures

A number of teaching methods which differ from the standard lecture/tutorial format have been tried with first year undergraduate students. In spite of initial resistance by some staff and students, and institutional restrictions such as funding, rooms and timetables, a more satisfactory format involving more active participation by students is emerging. The most successful format to date is described, as well as its evaluation by students.

Writing in natural language helps students construct algebraic equations

An experiment was conducted to find out whether students’ success in constructing a simple algebraic equation from graphical data would he affected if they described the relation in written English first. The subjects were students in a first-year tertiary mathematics course. It was found that writing sentences helped students to write correct equations. Contrary to expectations, the most successful students were those who used common idiomatic forms of English that could not be directly translated into mathematical notation.

An exploration of gender differences in tertiary mathematics

Data from 400 students in a tertiary mathematics course were analysed to explore gender differences on a number of variables associated with learning mathematics. It was concluded that while differences did occur on variables associated with confidence, self-concept, test anxiety and quantitative ability indicating a detrimental effect for women, compensating behaviour by women, including increased assignment work and tutorial attendance, resulted in comparable final course performance for women and men. These findings are discussed in light of participation rates of women in mathematics.

The Effect of Method of Instruction on Long‐term Retention of Mathematics Concepts

ABSTRACT This paper presents the final report of an extended study which assessed the viability of individualised tertiary mathematics instruction in Australia. Data collected over five years between 1978 and 1984 gave information on three treatments: a personalised system of instruction based closely on the Keller Plan with no final examination, a conventional lecture course with final examination and a modified personalised system including lectures. Long‐term retention of concepts was used as the major criterion for judging success of the methods. Results favouring students taught in the conventional manner have led to a questioning of the original precepts of the personalised system as developed by Keller.

Attitudes to mathematics of beginning undergraduates and prospective teachers: Some implications for education

An acute shortage of mathematics teachers has emerged in the Western world. This article describes a study of the influence of tertiary education experiences on the attitudes of potential mathematics teachers towards their subject. Parallel questionnaires were given to groups of students who were respectively entering university mathematics courses as new undergraduates, and entering postgraduate teacher training courses. Both groups of students answered items pertaining to their experiences within secondary mathematics courses. The undergraduate students were also asked a series of questions about their expectations of tertiary mathematics courses. For the postgraduates a parallel set of questions was provided that required them to rate their actual tertiary experiences. An analysis of responses indicated that the postgraduate students were more positive about their recollection of secondary mathematics than were the undergraduate students with their more recent experience of it. They were also less positive about the reality of their tertiary courses than were the undergraduates about their expectations. Responses of the postgraduates suggested that tertiary mathematics is not merely an extension of secondary mathematics, but a subject with which distinctive and, in general, more negative reactions are associated. Mathematics emerges as a subject which progressively loses its appeal with further study and implications are drawn for both tertiary education and teacher supply.

Student Choice of Assessment in an Individualized Mathematics Course

Abstract This paper describes an individualized tertiary Mathematics course in which students were given a considerable degree of choice in terms of assessment. Covariates were measured at the same time as the choice was made and the relationship of these to the choice made was studied. Student progress through the course was monitored, as was student reaction to the course and long‐term retention of the concepts taught. The relationship of these to choice of assessment and other covariates was considered. It was concluded that students generally chose appropriately to their abilities and achieved accordingly. In addition, students had little hesitation in deserting the end‐of‐course examination for continuous assessment.

A module in mathematics: description and evaluation

This paper describes an approach to the problem of teaching first year tertiary level mathematics students who have widely varying levels of achievement and ability in mathematics. The evaluation of some aspects of the proposed solution to the problem is based on a semantic differential and a Likert‐type questionnaire.

Student and teacher perceptions of the degree of difficulty in a mathematics course

In designing a curriculum and its constituent teaching and learning strategies, it is important to consider the relative difficulties of the various sub‐sections. As single measures of perceived difficulty (from teachers and learners) have been used in some studies, the efficacy of such readily available data has been studied in a tertiary level mathematics course for engineering students. Several approaches (parallel forms, comparison with achievement, and loaded questions) to the reliability and the validity of the measures of perceived difficulty are explored. The results indicate that the findings from such measures need to be interpreted with caution. This was particularly so during the first year of the course when the students have so recently come from a great variety of other mathematics learning environments in secondary schooling. The efficacy of the measures seems to be much improved in the second year of the course and the quite high correlation (0‐753) between staff and student perceptions o...