This study aimed at identifying the difficult concepts in introductory level mathematics as perceived by students, and ascertaining the causes of the identified difficult mathematics topics. The respondents of the study were the first- and second-year undergraduate students, from 2 schools [School of Public Administration (ESAP) and School of Business (ESCE)] and 5 programmes [Computing, Accounting, Marketing, E-Commerce, and Management], of MPI during the first and second semesters of school year 2016-2017. A total of 239 respondents served as the sample for this study.

A survey design was adopted for the study. Two research instruments, the Students’ Perception of Difficult Mathematics Topics Questionnaire (SPDMTQ) and the Factors Causing Difficulties in Mathematics Questionnaire (FCDMQ), were used for collecting data. The two sets of questionnaires were designed by the researchers. Data collected were analysed using frequencies and averages.

SPDMTQ was a questionnaire measured on a 4-rating scale of very easy (VE), easy (E), difficult (D), and very difficult (VD). This was structured to determine the topics perceived to be either easy or difficult by the students. The students’ perception of mathematics topics was scored using a range of one (1) for very easy, two (2) for easy, three (3) for difficult, and four (4) for very difficult. The level of difficulty was based on the criterion mean of 2.5. Topics with mean difficulty level below 2.5 are perceived easy by students and topics with mean difficulty level greater than 2.5 are perceived difficult by the students.

As for FCDMQ, students rated their level of agreement with some given statements regarding the possible factors for contributing difficulties in mathematics on a 4-point Likert scale, namely, 1 = strongly disagree (SD), 2 = disagree (D), 3 = agree (A), and 4 = strongly agree (SA). The agreement or disagreement was based on the criterion mean of 2.5. Factors with mean below 2.5 are grouped as disagree and factors with mean greater than 2.5 are grouped as agree.

The study has revealed that there were no difficult topics in Essential Computer Mathematics. However, it was observed from the findings that “Subgroups from Algebraic Systems” got the highest mean score of 3.30 from the scale of 4, this shows that Subgroups was found to be the most difficult topic in Discrete Mathematics. This study also showed that “The Fundamental Theorem of Integral Calculus from Integration” has the highest level of difficulty (mean = 3.04) in Business Mathematics.

The study has also revealed that hard to connect mathematics to real life (overall mean = 3.08), language of instruction – English (overall mean = 2.99), and abstractness of mathematics (overall mean = 2.89) were the three critical factors of causing difficulties in introductory level mathematics at MPI.

Recommendations were made that teachers try as much as possible to understand their students and their perceptions of difficult topics in mathematics and adopt teaching methods that would be to their benefit.

Author Profile(s)

Dr. L. W. Yip received his MSc in Mathematics from the University of Windsor and his PhD in Mathematics from the University of Alberta. Since 1990 he has been teaching mathematics and computing in the Computer Studies/Computing Programme at the Macao Polytechnic Institute. He has been leading the team for setting the Mathematics Admission Examination papers of Macao Polytechnic Institute since 1995. His current research interest is number theory.

Dr. Edmund Yung received both his BSc in Mathematical Studies and MSc in Operational Research from the University of London and his EdD from the University of Leicester. Since 1989, he has been teaching mathematics and statistics in the Computer Studies/Computing Programme at the Macao Polytechnic Institute. His current research interest is multivariate data analysis like multiple regression and factor analysis.

Natalie Pang is a lecturer in the School of Business at the Macao Polytechnic Institute. She has over 16 years of experience teaching mathematics and statistics to undergraduate students. Her research interests include time series methods, delay differential equations and data analysis.