A study of pre-service teachers' performance on two calculus tasks on differentiation and limit
The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.
Teaching undergraduate mathematics: A problem solving course for first year
In this paper we describe a problem solving course for first year undergraduate mathematics students who would be future school teachers.
Infusing problem solving into mathematics content course for pre-service secondary school mathematics teachers
This paper presents a re-design of an undergraduate mathematics content course on Introductory Differential Equations for pre-service secondary school mathematics teachers. Based on the science practical paradigm, mathematics practical lessons emphasizing problem-solving processes via the undergraduate content knowledge were embedded within the curriculum delivered through the traditional lecture-tutorial system. The pre-service teachers' performance in six mathematics practical lessons and the mathematics practical test was examined. They were able to respond to the requirements of the mathematics practical to go through the entire process of problem solving and to carry out "Look Back" at their solution: checking the correctness of their solution, offering alternative solutions, and expanding on the given problem. The use of Mathematics Practical has altered the pre-service teachers’ approach in tackling mathematics problems in a positive direction.
Preparing mathematics teachers in Singapore: The issue of mathematics content knowledge
Lee Shulman (1986) brought to the forefront the need to distinguish the different dimensions of teacher knowledge that will help guide teacher preparation. Instead of the then prevalent view of ensuring that the student teacher enters teacher education with adequate subject content knowledge and then equipping her with generic pedagogical knowledge, Shulman introduced the dimension at the nexus of subject content knowledge and generic pedagogical knowledge as pedagogical content knowledge. We, as Mathematics educators, are happy to claim Shulman as one of our own, as he based much of his research and writing on the discipline of Mathematics.
Teaching and learning complex numbers through problem solving
With reference to complex numbers, it is argued in this paper that attention should not only be focused on the practical usefulness or the aesthetics of mathematics to make mathematics attractive to students. Teachers could ride on the affordance of the problem solving mathematics curriculum framework in engaging students in activities that reveal the “power” of mathematics in solving mathematics problems and generalizing the results. The paper illustrates how portions of complex numbers, a pre-university mathematics topic, could be introduced through the various stages of mathematical problem solving. The use of complex numbers is a natural progression from basic algebraic manipulation at the secondary level and could be introduced through expanding a problem in the problem solving process; students could be introduced to the power of mathematics in providing an alternative solution or proof to mathematics problems from geometry and calculus. The roots of a complex numbers can be introduced by teaching through problem solving and re-enacting the (simplified) process of how mathematicians discovered complex numbers.
What is spoken in a junior college mathematics lecture?
The dissertation English in Mathematics Discourse highlights for mathematics educators a body of practical knowledge about Junior College mathematics lecture discourse from the linguistic perspective. Although this dissertation is found among the collection of the dissertations done by postgraduate students of linguistic studies, it is of value to mathematics educators, particularly, mathematics teachers at the Junior College level.
Self-directed learning through gamification of mathematics lessons: Literature review and a framework for enactment
Gamification, or the use of game-like elements for classroom instruction, has been the subject of study by educators. Currently there are no frameworks for enacting gamification in the mathematics classroom. In this paper, we propose a framework for facilitating Mathematics teachers to implement gamification in classrooms. Through gamification, we target to nurture self-directed learners of Mathematics. Our proposed framework is based on a systematic literature review conducted by the researchers. In our proposal, we map the use of various elements of gamification at each phase of learning through to Merrill’s First Principles of Instruction and van Hiele’s Model of Geometric Thinking. An exemplar of a lesson on geometry with the use of the framework is also presented.
A regularized logistic regression model with structured features for classification of geographical origin in olive oils
Geographical origin of extra virgin olive oil is a factor that consumers may take into account when making purchasing decisions. Oils that are labelled to be from regions famous for olive cultivation may be assumed to be of higher quality. However, difficulties in the authentication of the geographical origin of olive oils arise due to the similarity in chemical compositions of the oils involved. Fourier-transform infrared (FTIR) spectroscopy has been found to be a viable technology for the classification of oil samples by geographical origin. However, classical methods involving dimension reduction before model fitting usually yield models that are more challenging to interpret. Sparse fused group lasso logistic regression (SFGL-LR) is used with FTIR spectroscopic data to discriminate between Greek and non-Greek organic extra-virgin olive oils. The prediction performance is also compared with that obtained by partial least squares linear discriminant analysis (PLS-LDA). While both methods give comparable good prediction performance, with more than 90% accuracy in classification, the SFGL-LR model demonstrates improvements in the interpretability of the model coefficients.
Use of real-world contexts in instructional materials designed by pre-university mathematics teachers
Pre-university education in Singapore serves as a bridge between secondary and university education. Despite its importance in the Singapore education system, few studies have been conducted on Singapore pre-university mathematics. We also notice that problems in real-world contexts have been increasingly emphasized in the Singapore mathematics curriculum. In this paper, we study the infusion of real-world contexts in the design of instructional materials in a typical pre-university institution, with a focus on the topic of vectors. The real-world contexts used in the instructional materials are categorized into neutral contexts or real-life experiences, where each of these categories has their benefits. These include the potential to raise students’ awareness that mathematics can be used to solve real-world problems and explain real-world phenomena. Their alignment to the Singapore mathematics syllabus and 21st Century Competencies is also discussed.