Related papers: Visualizing the Matrix Product as a Transformation…
It can be difficult to tell whether a trained generative model has learned to generate novel examples or has simply memorized a specific set of outputs. In published work, it is common to attempt to address this visually, for example by…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
While mathematical creative writing can potentially engage students in expressing mathematical ideas in an imaginative way, some elementary school-age students struggle in this process. Generative AI (GenAI) offers possibilities for…
The quality of mathematics education depends largely on the quality of education in general. The main idea may be summarized as follows: in order to educate the younger generation of people to be able to meet adequately the demands of the…
Coupling of physics across length and time scales plays an important role in the response of microstructured materials to external loads. In a multi-scale framework, unresolved (subgrid) meso-scale dynamics is upscaled to the homogenized…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
Students in Algebra I classrooms typically learn at different rates and struggle at different points in the curriculum---a common challenge for math teachers. Cognitive Tutor Algebra I (CTA1), educational computer program, addresses such…
Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…
Pretrained encoders for mathematical texts have achieved significant improvements on various tasks such as formula classification and information retrieval. Yet they remain limited in representing and capturing student strategies for entire…
We describe the development of a course of quantum mechanics for secondary school designed to address the challenges related to the revision of classical knowledge, to the building of a well-organized knowledge structure on the discipline,…
In this paper, we reflect on the educational challenges and research opportunities in running data visualization design activities in the context of large courses. With the increasing number and sizes of data visualization course, we need…
Objectives: Several studies have focused on the role of working memory (WM) in predicting mathematical and reading literacy. Alternative models of WM have been proposed and a modality-dependent model of WM, distinguishing between verbal and…
Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze,…
We investigated some difficulties that students often face when studying linear algebra at the undergraduate level, and identified some common mistakes and difficulties they often encountered when dealing with topics that require…
Generative models are now capable of producing natural language text that is, in some cases, comparable in quality to the text produced by people. In the computing education context, these models are being used to generate code, code…
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…
We present a motivating example for matrix multiplication based on factoring a data matrix. Traditionally, matrix multiplication is motivated by applications in physics: composing rigid transformations, scaling, sheering, etc. We present an…
Learning product representations that reflect complementary relationship plays a central role in e-commerce recommender system. In the absence of the product relationships graph, which existing methods rely on, there is a need to detect the…
This study, conducted among more than 250 physics and chemistry teachers in Morocco, analyzes the impact of experimentation on student learning and attention in middle and high school. The results show that the majority of teachers favor…
The rapid adoption of generative artificial intelligence (AI) tools in higher education is transforming how students engage with undergraduate mathematics, raising concerns about learning and assessment validity. This study examines the…