Mathematics pedagogical content knowledge (MPCK) of teachers cannot be easily defined but is a complex concept integrating generic pedagogical knowledge, mathematics teaching methodology as well as knowledge of the discipline of mathematics. It is the objective of mathematics methodology courses in teacher preparation programmes to begin the development of MPCK in their pre-service teachers. As part of a research study on the development of MPCK in primary school beginning teachers, a 16-item instrument was developed to measure some aspects of the MPCK for teaching mathematics at primary level. The instrument was administered to the 2003 Intake of the Diploma in Education student teachers at the National Institute of Education, Singapore just at the beginning of their programme. As they completed their methodology course in February 2005, the instrument was administered again. This paper will discuss the findings concerning their performance in these two tests, with reference to the overall performance as well as topic-specific and MPCK construct-specific performance. The findings indicate that student teachers at the beginning of their programmes are generally quite weak in their mathematics pedagogical content knowledge, as might be expected. There was significant improvement in some aspects of their MPCK on completion of their mathematics pedagogy course.
The main purpose of this study was to ascertain the students' attitude towards learning calculus. A survey was conducted among the calculus students of the junior colleges, polytechnics, and universities in Singapore. The study indicated th at in general the students have a positive attitude towards calculus. A majority of the 932 students perceived that calculus is interesting and challenging. However, there is cause for concern because students are learning calculus by taking notes , memorizing and applying formulae and procedures and they find difficulty when they encounter more conceptual approaches at university levels. A substantial number also believes that practice is the key to scoring well and thus do not see the need for conceptual understanding. About a third of the students find calculus boring and they suggest that teachers and lecturers use more interesting ways of teaching calculus.
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