Item difficulty and dimensionality often correlate, implying that unidimensional IRT approximations to multidimensional data (i.e., reference composites) can take a curvilinear form in the multidimensional space. Although this issue has been previously discussed in the context of vertical scaling applications, we illustrate how such a phenomenon…

In the boxplot, the box always represents -- regardless of its area -- the middle half of the data and thus a measure of variability (interquartile range). However, when students first learn about boxplots, they are usual already familiar with other forms of statistical representations (e.g., bar or circle graphs) in which a larger area represents…

When describing motion in physics, the selection of a frame of reference is crucial. The graph of a moving object can look quite different based on the frame of reference. In recent years, various tests have been developed to assess the interpretation of kinematic graphs, but none of these tests have specifically addressed differences in reference…

Word-problem features such as text complexity, charts and graphs, position of the unknown, calculation complexity, irrelevant information, and schemas impact word-problem performance. We compared the word-problem performance of typically achieving (TA) students and students with mathematics difficulty (MD). First, we measured the word-problem…

Official communications and media news in Greece about the COVID-19 pandemic very often involve a multitude of numerical concepts and mathematical relationships, which are presented in different forms and in various contexts. This paper reports selected findings of a survey among adults, which had two aims. First, to investigate their subjective…

Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations…

Word-problem features such as text complexity, charts and graphs, position of the unknown, calculation complexity, irrelevant information, and schemas impact word-problem performance. We compared the word-problem performance of typically achieving (TA) students and students with mathematics difficulty (MD). First, we measured the word-problem…

When learning physics, students need more than just an understanding of mathematical and physical concepts. Integrating the two fields is crucial, as research indicates that students often struggle even when they have a strong grasp of both. In this paper, we use the heat equation as an example from higher education. Given the importance of the…

Teachers' ability to accurately judge difficulties of mathematical tasks is an essential aspect of their diagnostic competencies. Although research has suggested that pedagogical content knowledge (PCK) is positively correlated with the accuracy of diagnostic judgments, experimental studies have not been conducted to investigate how PCK affects…

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…

Covariational reasoning and the creation and interpretation of graphs of covariational situations are important skills in math and science. Unfortunately, research shows that students often struggle to make meaningful connections between graphs and the covariational situations they represent. Educational activities designed to help students…

Linear functions are an essential part of school and university education. Nevertheless, this topic is challenging for many students--especially in STEM topics. In this article, we contribute to the understanding of learning difficulties in the context of mathematical and physical problems. Here, we present the results of an eye-tracking study on…

Epistemological obstacle is emphasized in mathematics education. Students often have limited students' context of knowledge in understanding trigonometry. Knowing the epistemology obstacle can help a teacher understand the student's misconception. Therefore, this study aimed to identify students' epistemological obstacles of trigonometry and…

The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that…

The impact of task complexity on integrated writing performance is under-researched. This study purports to investigate the effect of graph complexity and planning time on graph writing performance as well as graph description strategies. Ninety-six EFL learners of English were assigned into three groups to examine the effect of three planning…