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Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…

Problems in probability theory prove to be one of the most challenging for students. Here, we formulate and discuss four related problems in probability theory that proved difficult for first to fourth-year undergraduate students whose…

The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…

Starting from the well-known and elementary problem of inscribing the rectangle of the greatest area in an ellipse, we look at possible, gradually more and more complicated variants of this problem. Our goal is to demonstrate to an average…

For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…

Understanding issues involved in expertise in physics problem solving is important for helping students become good problem solvers. In part 1 of this article, we summarize the research on problem-solving relevant for physics education…

We consider training probabilistic classifiers in the case of a large number of classes. The number of classes is assumed too large to perform exact normalisation over all classes. To account for this we consider a simple approach that…

Some actions must be executed in different ways depending on the context. For example, wiping away marker requires vigorous force while wiping away almonds requires more gentle force. In this paper we provide a model where an agent learns…

Active learning promises to improve annotation efficiency by iteratively selecting the most important data to be annotated first. However, we uncover a striking contradiction to this promise: active learning fails to select data as…

Mathematics is a compulsory subject in Nigerian secondary schools, and the subject plays an important role in the scientific and technological growth and development of the nation. A shortfall in the knowledge of the students in Mathematics…

There is increasing interest in employing large language models (LLMs) as cognitive models. For such purposes, it is central to understand which properties of human cognition are well-modeled by LLMs, and which are not. In this work, we…

Highly successful students, as measured by grades and by scores on the Force Concept Inventory, still struggle with fundamental concepts in mathematics and physics. These difficulties, which turn physics into parrot learning and include…

This paper explores the pedagogical potential of "teacher pre-prompting" as a means of guiding student collaboration in programming education. In particular, we investigate how brief teacher-initiated questions posed before students engage…

In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…

Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…

Helping students become proficient problem solvers is a major goal of many physics courses from introductory to advanced levels. In fact, physics has often been used by cognitive scientists to investigate the differences between the…

In this paper we investigate the extent to which students' problem-solving behaviors change as a result of working on multi-faceted, context-rich problems. During the semester, groups of two to three students work on several problems that…

Many researchers and textbooks have promoted the use of rigid prescribed strategies for encouraging development of expert-like problem-solving behavior in novice students. The University of British Columbia's introductory algebra-based…

One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts.…

Background: Programming skills are advantageous to navigate today's society, so it is important to teach them to students. However, failure rates for programming courses are high, and especially students who fall behind early in…