As an excellent means of improving students' effective learning, knowledge tracking can assess the level of knowledge mastery and discover latent learning patterns based on students' historical learning evaluation of related questions. The advantage of knowledge tracking is that it can better organize and adjust students' learning plans, provide…

This dissertation explores bridge n-sections of knotted surfaces in 4-manifolds by defining invariants that measure the complexity of their topology and by giving geometric constructions that determine Lagrangian surfaces in 4-manifolds under certain conditions. First, we present an elegant geometric construction that generates all triple grid…

Biology is perhaps the most complex of the sciences, given the incredible variety of chemical species that are interconnected in spatial and temporal pathways that are daunting to understand. Their interconnections lead to emergent properties such as memory, consciousness, and recognition of self and non-self. To understand how these…

School-based citizen science (SBCS) provides opportunities for teachers to purposefully integrate mathematics and science content and practices throughout the year. With SBCS projects, students have countless opportunities to apply their mathematics skills within the context of science data collection and sense making. This article details how a…

Research into didactics of calculus has maintained a long-standing interest in students' grasp of the relations between definite integrals and areas. This study comes to contribute to this line of research by unpacking how students use the concept of area to find definite integrals. Specifically, we focus on mathematical situations where the…

This literature review covers 42 years and has two main objectives: to identify the obstacles to learning the polar coordinate system and to explore the teaching proposals suggested to overcome them. These questions are answered by locating and analysing articles related to the topic published in research and practitioner journals specialising in…

One challenging issue in improving the teaching and learning methods in MOOCs is to construct potential knowledge graphs from massive learning resources. Therefore, this study proposes knowledge graphs driving online learning behaviour prediction and multi-learning task recommendation in MOOCs. Based on the knowledge graphs supported by…

Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we…

Graph neural networks (GNN) are vital for analyzing real-world problems (e.g., network analysis, drug interaction, electronic design automation, e-commerce) that use graph models. However, efficient GNN acceleration faces with multiple challenges related to high and variable sparsity of input feature vectors, power-law degree distribution in the…

Functions are an essential concept in mathematics. The studies that have examined functions in advanced contexts have primarily focused on students' reasoning about specific types of functions (such as binary operations and isomorphisms) but not on the core characteristics of well-definedness and everywhere-definedness. Here, we report on a study…

Causal inference is a central topic in education research, although oftentimes it relies on observational studies, which makes causal identification methodologically challenging. This manuscript introduces causal graphs as a powerful language for elucidating causal theories and an effective tool for causal identification analysis. It discusses…

We use a tensile testing machine to create stress-strain plots and determine Young's modulus for some ductile and plastic materials. Supplementary videos are also provided.

The aim of this study is to investigate how students graphically represent qualitative and quantitative aspects of co-varying quantities in an embodied digital learning environment that provides feedback in the form of an animation showing what kind of motion their graph represents and how this feedback helped them to overcome typical graphing…

Misleading data visualizations have become a significant issue in our information-rich world due to their negative impact on informed decision-making. Consequently, it is crucial to understand the factors that make viewers vulnerable to misleading data visualizations and to explore effective instructional supports that can help viewers combat the…

The ability to accurately interpret mathematical functions is crucial for understanding complex physical and mathematical concepts. Differentiating isothermal from adiabatic change of state in p-V diagrams respectively graphs of indirectly proportional functions from graphs of power functions in x-y diagrams presents a common challenge for…