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…

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…

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…

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with…

We describe and evaluate a method to mitigate unwanted student collaborations in assessments, which we recently implemented in a second-year undergraduate mathematics module. The method requires a list of specific pairs of students to be prevented from collaborating, which we constructed based on the results of previous assessments. We converted…

Inferentialism has emerged as a valuable theoretical resource in mathematics education. As a theory of meaning about the use and content of concepts, it offers a fresh perspective on traditional epistemological and linguistic questions in the field. Despite its emergence, important inferentialist ideas still need to be operationalized. In this…

Reading and understanding scientific texts is useful and necessary in many informal collaboration settings, including research or innovation collaborations, or when discussing public science in lay peer groups. In this work, we investigate whether an interactive predefined concept map that builds up gradually while reading a scientific research…

The objective of question generation from knowledge graphs (KGQG) is to create coherent and answerable questions from a given subgraph and a specified answer entity. KGQG has garnered significant attention due to its pivotal role in enhancing online education. Encoder-decoder architectures have advanced traditional KGQG approaches. However, these…

Single-case design (SCD) is frequently utilized in applied contexts, such as schools or clinics, due to its utility in evaluating individual intervention effects of students. Data collected in SCD are often displayed in a linear graph, which can vary drastically in their construction leading to inconsistencies in rater interpretation. This has led…

Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…