Teo, Kok Ming

This study employs Sfard’s (2008) socio-cultural theory of Commognition to analyse student teachers’ thinking and communicating practices. Specifically, we investigate the effectiveness of the student teachers’ communication of a particular mathematical proof with reference of the four features of the commognitive framework, i.e., word use, visual mediators, narrative and routines. In this paper, we can report on the routine of the discourse to analyse the quality of mathematical discourse in two situations of “Expert-to-Novice” and “Novice-to-Novice”.

This paper examines the calculus curriculum in the current Singapore secondary and pre-university levels. Two concepts, (1) increasing and decreasing functions and their derivatives, and (2) the second derivative test for the nature of stationary points, are elaborated. An example of an incorrect calculus item in a national examination is brought up in relation to conditional reasoning involving calculus concepts. We reckon that the current emphasis on procedural knowledge in calculus is useful. However, we argue that formal conditional reasoning should not be introduced prematurely for school students.

The purpose of this study was to examine the effects of a calculus course using the flipped classroom model on undergraduate students’ achievement in mathematics which was measured by their scores on three quizzes, a test, and a final written examination, as well as their overall scores. The scores of a total of 58 second year students, comprising 17 students in the experimental group and 41 students in the control group, enrolled in a university degree programme in Singapore were analysed retrospectively using analysis of covariance (ANCOVA) so as to control for initial differences. The experimental group comprised students who took the flipped calculus course in the August 2016 semester while the control group comprised students who took the same calculus course taught using a lecture-tutorial approach in the August 2013 semester. Results of ANCOVA show that after controlling for initial differences the experimental group scored statistically significantly higher in the test but lower in the final examination than the control group.

The Singapore Mathematics Assessment and Pedagogy Project (SMAPP) is a research project conducted by the National Institute of Education and funded by the Ministry of Education. It aims to make assessment practices an integral part of teaching and learning, and broaden student learning outcomes by using authentic disciplinary tasks. As part of the project, some guidelines are provided for designing disciplinary tasks which have the distinctive features of their emphasis on contextual aspects. One of the criteria of a good disciplinary task is its ability to assess multiple mathematical competencies of students. In this paper, we will present some examples to illustrate how these competencies can be assessed. Another aim is to find out to what extent these tasks serve the purpose of assessing these competencies, by analyzing the students’ performance in a sample SMAPP task.

In recent years, computer-based technology (CBT) has enabled university lecturers to teach their courses using non-traditional pedagogies. One such pedagogy is the flipped learning model. Under this model, students learn the basic content on their own using pre-class tasks and then come to class to engage in more challenging work such as solving difficult problems. CBT can play two important roles in flipped learning, namely to deliver learning materials efficiently and to assess student achievement effectively. This paper describes how these two roles were applied to a flipped Linear Algebra II course in the National Institute of Education (Singapore), taken by a group of student teachers (n = 15) over a 12-week period from January to April 2018. Their perceptions of flipped activities were gathered using weekly surveys, mid-semester survey, end-of-course survey, and end-of-course interviews. They generally agreed that flipped learning using CBT was helpful and enjoyable. As flipped learning becomes more common among university lecturers in Asian countries, it is beneficial to share experiences of utilising CBT to promote active learning of mathematics among university students.

In recent years, computer-based technology has enabled university lecturers to teach their courses using non-traditional pedagogies. One such pedagogy is the flipped learning model. As flipped learning is being used more frequently to teach undergraduate mathematics, instructors need to collect data to identify practices that work well to promote student mathematics achievement and favourable perceptions toward this new learning mode. This paper describes six different types of pre-class tasks for a flipped Linear Algebra II course in a Singapore university, such as short videos narrated by the instructor, synopses, summary sheets, worksheets of problems and activities, and online quizzes. The sample comprised 15 pre-service teachers, who had adequate to good mathematics backgrounds, and their participation in this project would prepare them to implement flipped learning in school mathematics in the future. On average, they spent about one hour to complete these weekly pre-class tasks, but the stronger ones reported spending less time on these tasks than the other students. Almost all the students rated very highly these tasks in terms of helping them to learn and enjoyment at mid-semester and end-of-course surveys. These perceptions had weak correlations with the course grade. Suggestions for practice and future research are discussed.

In this work, we report the emergence of the Hands, Head and Heart framework that arose within the curriculum review for subject knowledge courses for primary school pre-service teachers in the National Institute of Education, Singapore. Through an initial grounded analysis of a survey of pre-service teachers and faculty focus group meeting data, the responses were broadly categorised into hands, head and heart domains and these formed an initial framework for discussions in the review committee meetings. By revisiting the data from the survey, an analysis through a complexity lens revealed the emergence of a characteristic nested self-similarity of the framework. Over the course of several committee meetings, further self-similarity was discovered. We conjecture that the Hands, Head and Heart framework and its self-similarity property provide a potential basis for a holistic approach to curriculum review. We used this framework to revise the learning objectives of the subject knowledge curriculum by resolving perspectives which previously seemed contradictory.