Asian Journal for Mathematics Education

This commentary paper is a pedagogical reflection on the interplay between variation and invariant. It begins with a brief discussion on the concept of Unity of Opposites as an ancient philosophical theme. Ancient thinking systems regarded the variation and invariant pair as a Unity of Opposites. Next, the use of variation as a pedagogical approach in mathematics education is briefly examined under Marton's variational theory of learning, Gu's bianshi jiaoxue, and the related research done by the author in the context of Dynamic Geometry Environment (DGE). These lead to the formation of the concept of variational thinking, the main contribution of this paper, which is presented and explained. A DGE task design sequence example is presented to illustrate how variational thinking can be used to frame a process of geometrical reasoning and argumentation.

During the COVID-19 pandemic, researchers faced challenges conducting data collection. However, emerging communication technologies, such as web-conferencing platforms, provided an alternative mode of data collection. Among these platforms, Zoom stands out for its functional affordances and unique features that support data collection methods, including screen-capturing, digital photography, drawing, polling, and artifact-based interviews, which attempt to reveal a child's viewpoint and ability. In this article, we explore the feasibility of using Zoom to conduct educational research by investigating the mathematical learning experience among 26 primary 1 and 2 students in Hong Kong on two topics—understanding time and addition and subtraction. Five mathematics teachers were recruited to participate in 2-month online workshops with assessments among three groups of students to understand the suitability for data collection. Based on teachers’ observations and students’ responses, our findings suggest that Zoom is a viable and effective tool for qualitative data collection. It offers a cost-effective method for researchers and educators to examine students’ mathematical performance in an online environment. We also investigate students’ perceptions of online assessment strategies, perceived usefulness of various Zoom functions, and explore the benefits and challenges teachers and students perceived throughout mathematical education using Zoom. However, several technical difficulties were encountered, such as the digital literacy gap and privacy concerns. Therefore, improving students’ digital literacy for remote learning and triangulation is important for online mathematical data collection and assessments.

This study concerns an intervention incorporating the KNOWS strategy (K—Know, N—Need to know, O—Organize, W—Work, and S—Solution), a mnemonic problem-solving tool to improve students’ performance in ratio word problems. Quantitative data through pre- and post-tests were collected from 42 Year 9 students in one of the secondary schools in Brunei Darussalam. Results from a paired-sampled t-test show that the students scored higher in the post-test compared to the pre-test, confirming the effectiveness of the KNOWS intervention in improving students’ performance in ratio word problems. Despite the improvement in students’ performance, this study highlights some misconceptions and common mistakes of students when solving ratio word problems before and after the KNOWS intervention. It also suggests alternative ways of using the KNOWS strategy as an instructional option to improve students’ performance in ratio word problems.

We conducted a cross-cultural experimental study, consisting of Australian students (N = 57) and Malaysian students (N = 75) on learning to solve one-step and two-step linear equations. Central to our research inquiry is the perceived difference between two instructional methods: the balance method of learning vs. the inverse method of learning. The balance method and the inverse method differ in their use of mathematical operations to solve linear equations (e.g., +4 on both sides, balance operation, vs. –4 becomes +4, inverse operation). According to cognitive load theory, the balance operation imposes twice the level of element interactivity (i.e., interaction between elements) than that of the inverse operation. Our findings, ascertained from univariate analysis of variance (ANOVA) testing, show that for the Australian students, the balance group outperformed the inverse group. Such results do not support our hypothesis and contradict with previous findings, where the inverse group outperformed the balance group in a Malaysian context. No statistically significant difference was found between the two groups of Malaysian students. In line with our hypothesis, the Malaysian students outperformed the Australian students with respect to the inverse method. We attributed the results, in part, to the impact of prior knowledge of the balance method (Australian students) and the inverse method (Malaysian students) upon subsequent learning of linear equations. Nonetheless, given that the differential level of element interactivity favors the inverse method, we advocate the exploration of the potentiality of the inverse method for enhancing the learning of linear equations.

This study explored what Ghanaian student teachers value in college mathematics learning. A cross-sectional survey involving 180 student teachers from College of Education in Ghana was conducted using the What I Find Important (WIFI) in mathematics learning questionnaire. The study employed principal component analysis with Oblimin rotation and one-way multivariate analysis of variance in analyzing the data gathered. Among the findings, it was found that student teachers value exploration, connections, understanding, and fluency in their study of college mathematics. Also, the findings of the study revealed a statistically significant difference in what student teachers value in college mathematics learning across college class levels. To facilitate a clearer understanding of valuing in the colleges of education in Ghana, it is considered important to establish through research the values of teacher educators regarding college mathematics learning and teaching, and how these values reflect what student teachers value and those values espoused in the new 4-year Bachelor of Education (B.Ed.) curriculum in Ghana.

This research explores the type of conceptual difficulties that female Saudi students encounter in Introductory Algebra courses at college level and identifies pedagogical practices that might impact students’ learning of algebra. Instructional tasks were designed and implemented for 12 weeks to collect and analyze data. The research sample consisted of a study group of 28 students from an Introductory Algebra class. The findings identified and classified the types of difficulties that the students encountered and suggested instructional models to overcome or minimize them and a theme to teach and learn algebra.