The primary school mathematics syllabuses in Singapore as of the year 2020 reinforces that Big ideas are central to the learning of mathematics. In support of the push to teach for big ideas, a research study is presently underway. A part of it is on the professional development (PD) of primary school mathematics teachers. As part of the PD…

Problem decomposition into sub-problems or subgoals and recomposition of the solutions to the subgoals into one complete solution is a common strategy to reduce difficulties in structured problem solving. In this study, we use a datadriven graph-mining-based method to decompose historical student solutions of logic-proof problems into Chunks. We…

In this study, hypothetical samples of students' work on a task involving pattern generalizations were used to examine the characteristics of the ways in which 154 elementary prospective teachers (PSTs) paid attention to students' work in mathematics. The analysis included what the PSTs attended to, their interpretations, and their suggestions for…

In this paper, we analyse a grade 8 (age 13-14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in…

Nowadays, many education programmes claim to evolve according to present and future skills needed for sustainable development, and one of these skills is inventive problem-solving. Systematic-inventive problem solving (SIPS) is a systematic approach to problem-solving derived from engineering, technology, science, mathematics, and general…

This study aimed to investigate the relative effectiveness of a computer-supported teaching sequence in solving optimization problems in calculus compared to a traditional teaching approach. The participants in the study were 46 first-year prospective mathematics teachers studying in two different classes of a four-year elementary mathematics…

Research suggests that most college and beginning graduate students lack the cognitive complexity required to engage in effective practical and ethical reasoning. Studies on cognitive development support the view that how people approach complex problems varies significantly depending on the underlying epistemic assumptions they use to guide their…

For many decades, problem solving has been a focus of elementary mathematics education reforms. Despite this, in many education systems, the prevalent approach to mathematics problem solving treats it as an isolated activity instead of an integral part of teaching and learning. In this study, two mathematics teacher educators introduced 19 Irish…

3D geometry is an essential concept in mathematics because it relates to real-world experiences and numerous mathematical topics. However, some students still have difficulty understanding this geometry. Therefore, this study aims to identify and describe students' epistemological obstacles to the dimensions of representation, spatial structure,…

While Internet of Things (IoT) devices have increased in popularity and usage, their users have become more susceptible to cyber-attacks, thus emphasizing the need to manage the resulting security risks. However, existing works reveal research gaps in IoT security risk management frameworks where the IoT architecture -- building blocks of the…

Problem-solving is an essential undergraduate learning outcome that also supports students' professional success. The creative problem-solving model (CPS) (Isaksen et al., 2011) facilitates the development of these skills and aligns well with the scope of public relations (PR). The current study investigates student perceptions of an assignment…

Encouraging students' ability to reason can be looked at through the lens of both oral and written representations. In 2022, the author participated in the first intake of the Teacher Excellence Program run by the Victorian Teaching Academy. Being part of an in-depth professional learning program challenged the author's teaching practices to focus…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

Science and art are intrinsically linked. Science requires curiosity, along with skills in observation, problem-solving, and critical thinking. Art is no different; however, the two disciplines are typically presented as opposites to children at a young age and the emphasis on differences lead to a false dichotomy of career paths and even…

Teaching robotics courses online is challenging due to the complexity of the interdisciplinary topics involved. One of the most challenging topics is 3D coordinate transformations. Students often struggle to grasp the concept of 3D coordinate transformations and their relevance to real-world robotic applications. This paper applies the Scholarship…