Ng, Wee Leng

In the light of the recent focus on the use of technology in education, a Crucial Factors in the Integration of ICT Survey (CFS) was developed to examine mathematics teachers' perceptions of the degree of importance pertaining to the key factors influencing the integration of Information and Communications Technology (ICT) into the classroom. The purpose of this study was to field-test this instrument which measures secondary school mathematics teachers' perceptions of the positive impact of the following factors on ICT implementation as identified by a review of the literature: (a) usefhlness and worthiness of technology, (b) support from various departments in the school, (c) availability and accessibility of technology, (d)professional development opportunities in technology, (e) leadership, planning and implementation of technology, and ( f ) partnerships with external organisations. In this study, a total of 60 pre-service mathematics teachers were surveyed. The results show that these pre-service teachers rate both professional development opportunities and the availability and accessibility of technology as the most influential factors among the six in determining the extent to which they will employ ICT in the classroom. However, all factors are deemed important in determining whether teachers utilised technology in the classroom.

The purpose of this study was to investigate how the use of TI-Nspire™ could enhance the teaching and learning of calculus. A conceptual framework for the use of TI-Nspire™ for learning calculus in a mathematics classroom is proposed that describes the interactions among the students, TI-Nspire™, and the learning tasks, and how they lead to the learning of calculus. A design experiment was conducted in a class of 35 students from a secondary school in Singapore. Use of TI-Nspire™ was integrated into the teaching and learning of calculus concepts in the classroom with the aid of TI-Nspire™ Navigator, a wireless classroom network system that enables instant and active interaction between students and teachers. It was found that the appropriate use of graphical, numerical and algebraic representations of calculus concepts using TI-Nspire™ enabled students to better visualize the concepts and make generalizations about relevant mathematical properties. In addition, the students were able to link multiple representations, especially algebraic and graphical representations, to improve their conceptual understanding and problem-solving skills. Six roles of TI-Nspire™ in classroom mathematical practice were identified from the findings of the experiment; TI-Nspire™ was used as an exploratory tool, graphing tool, confirmatory tool, problem-solving tool, visualization tool and calculation tool. This suggests that TI-Nspire™ is a multi-dimensional tool that supports mathematics learning. Overall, the findings of the study indicate that TI-Nspire™ is an effective tool to develop mathematical concepts and promote learning and problem solving.

In this paper, it is shown how the Banach-Steinhaus theorem for the space P of all primitives of Henstock-Kurzweil integrable functions on a closed bounded interval, equipped with the uniform norm, can follow from the Banach-Steinhaus theorem for the Denjoy space by applying the classical Hahn-Banach theorem and Riesz representation theorem.

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 purpose of this study is to investigate the effects of an Ancient Chinese Mathematics Enrichment Programme (ACMEP) on pre-university students’ attitudes towards mathematics. A total of 37 students took part in this study and a mathematics attitudes scale was administered prior to and after the ACMEP which consisted of 4 sessions of one hour duration each, held once a week, conducted during curriculum time. Results of statistical analysis revealed that the post-ACMEP mathematics attitudes survey overall mean score was higher (t = 1.99, df = 31, p = 0.06) than that of the pre-ACMEP mathematics attitudes survey, with an effect size of 0.40. Overall, the conduct of the ACMEP appeared to improve pre-university students' attitudes towards mathematics.

Teachers’ judgements of the cognitive demand of mathematical assessment items have implications for the nature of students’ learning experiences. However, existing taxonomies for classifying cognitive demand are often not customised for pre-university or A-level mathematics teachers to use. This paper reports on the development and field-testing of a cognitive demand instrument specifically for helping A-level mathematics teachers to sharpen their judgements of the cognitive demand of A-level mathematical assessment items. Fourteen A-level Mathematics teachers from a junior college and an Integrated Programme school in Singapore participated in this study, where they rated the cognitive demand of assessment items on selected Pure Mathematics topics from the national A-level examinations using the cognitive demand instrument. The instrument was found to be useful to the teachers in providing them with an awareness of how the cognitive demand of A-level mathematical assessment items could be understood through the dimensions of complexity, abstractness, and strategy.

We introduce the notion of an H-primitive being the limit of a sequence of absolutely continuous functions satisfying certain conditions and use it to formulate an alternative definition of the Henstock-Kurzweil integral on a closed bounded interval. Furthermore, the definition provides a characterisation of the primitive of a Henstock-Kurzweil integrable function.

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.

This paper reports on a study on a semester-long flipped university mathematics course (Calculus II) taught to a cohort of pre-service teachers enrolled in the Bachelor of Science (Education) programme at the National Institute of Education, which is the autonomous teacher training institute of Nanyang Technological University, Singapore. The current study is the second phase of a three-phase project which developed a comprehensive framework to guide the design of three stages of flipped learning activities: pre-class tasks; in-class interactions; and post-class consolidation. A mixed methods research design was used to collect quantitative and qualitative data over many occasions, through methods such as weekly surveys, to investigate students’ perceptions of flipped learning activities. Results of the study suggest that the students generally found the flipped learning activities helpful and enjoyable.

The authors of this paper have conceptualized and constructed a tool, using dynamic geometry software, to simulate scenarios of word problems involving speed, and used it to help students acquire the concept of speed and solve speed problems involving two objects moving toward each other. This paper demonstrates how such a tool can be created using GeoGebra, and describes how the use of this tool had improved understanding of speed concept, and ability to solve speed problems for a class of sixth grade students in Singapore.