Sergiy Klymchuk

A Comparison of Teacher and Lecturer Perspectives on the Transition from Secondary to Tertiary Mathematics Education.

The transition from school to tertiary study of mathematics comes under increasing scrutiny in research. This article reports on some findings from a project analysing the transition from secondary to tertiary education in mathematics. One key variable in this transition is the teacher or lecturer. This article deals with a small part of the data from the project–analysing secondary teachers’ and lecturers’ responses to questions on the differences they perceive between school and university and the importance of calculus, a bridging content. The results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the others perspective, and there is a great need for improved communication between the two sectors.

University Students' Difficulties in Solving Application Problems in Calculus: Student Perspectives

This paper reports on the results of an observational parallel study conducted simultaneously at 2 universities — one each in New Zealand and Germany. It deals with university engineering students’ difficulties in the formulation step of solving a typical application problem from a first-year calculus course. Two groups of students (54 in New Zealand and 50 in Germany) completed a questionnaire about their difficulties in solving the problem which was set as part of a mid-semester test. The research endeavoured to find reasons most of the students could not use their knowledge to construct a simple function in a familiar context. It was neither lack of mathematics knowledge nor an issue with the context. The students’ difficulties are analysed and presented along with their suggestions on how to improve their skills in solving application problems.

Paradoxes and Sophisms in Calculus

Introduction Part I. Paradoxes: 1. Functions and limits 2. Derivatives and integrals Part II. Sophisms: 3. Functions and limits 4. Derivatives and integrals Part III. Solutions to Paradoxes: 5. Functions and limits 6. Derivatives and integrals Part IV. Solutions to Sophisms: 7. Functions and limits 8. Derivatives and integrals References.

Modelling of Infectious Disease with Biomathematics: Implications for Teaching and Research

The chapter compares a variety of models from biomathematics and bioinformatics of the spread of severe acute respiratory syndrome (SARS) that hit dozens of countries worldwide in 2003. It also investigates students’ and lecturers’ opinions regarding differences in predictions from three different models. All models were based on the real data for Hong Kong published by the World Health Organization (WHO). Although the models were based on the same data, they gave very different predictions of the spread of the disease. The models were discussed with two groups of people: undergraduate students majoring either in engineering or applied mathematics and university lecturers who teach mathematics or mathematical modelling courses. In this chapter we present, analyze, and compare responses to the same questionnaire given to the two groups.

The influence of attention on mathematical knowledge of teachers and lecturers: a comparison

This article reports on some findings from the project ‘Analysing the Transition from Secondary to Tertiary Education in Mathematics’. One of the key variables in the school to university transition is the teacher/lecturer, and here, we deal with the data analysing secondary teachers’ and tertiary lecturers’ responses to four mathematics questions. Elsewhere, we consider knowledge, preparedness, teaching style, etc., but this article tracks the ability to use mathematical procedures. We hypothesize that this is a function of what we pay attention to, as described in Masons discipline of noticing. The results reveal that many teachers and lecturers fail to notice the necessary conditions for problems that imply that procedures are not always applicable. Possible reasons for this along with implications for student learning are discussed.

20 – Role of Mathematical Modelling and Applications in University Mathematics Service Courses: An Across Countries Study

The aim of this study was to find out what university students, studying mathematics as a service course, think about the role of the mathematical modelling process and application problems in their studies. For this purpose a questionnaire was given to more than 500 students from 14 universities in 9 countries. The research was not a comparison of countries or universities: an across countries study approach was chosen to reduce the affect of differences in education systems, curricula, cultures. The results of the questionnaire were analysed and presented in the paper. In particular, an attempt was made to identify which step of the mathematical modelling process the students found most difficult.

Puzzle-based learning in engineering mathematics: students’ attitudes

ABSTRACT The article reports on the results of two case studies on the impact of the regular use of puzzles as a pedagogical strategy in the teaching and learning of engineering mathematics. The intention of using puzzles is to engage students’ emotions, creativity and curiosity and also to enhance their generic thinking skills and lateral thinking ‘outside the box’. Students’ attitudes towards this pedagogical strategy are evaluated via short questionnaires with two groups of university students taking a second-year engineering mathematics course. Students’ responses to the questionnaire are presented and analyzed in the paper.

Experience with using counterexamples in an introductory calculus class

The paper describes a personal experience with using counterexamples as a pedagogical strategy in the teaching and learning of an introductory calculus course at a university of technology.

Paradoxes and counterexamples in teaching and learning of probability at university

This article is devoted to practical aspects of teaching and learning of probability at university. It presents the difficulties and attitudes of first-year university science and engineering students towards using paradoxes and counterexamples as a pedagogical strategy in teaching and learning of probability. It also presents a students point of view on the effectiveness of this pedagogical strategy.