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This study explores student attitudes to the use of substantive on-line assessments that require mathematical answers. Our goal is to learn what are the important aspects in a design of more effective e-assessments that support learning of…
Many instructors choose to assess their students using open-ended written exam items that require students to show their understanding of physics by solving a problem and/or explaining a concept. Grading these items is fairly time…
In this paper we present the use of Constraint Programming for solving balanced academic curriculum problems. We discuss the important role that heuristics play when solving a problem using a constraint-based approach. We also show how…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
We studied the impact of metacognitive reflections on recently completed work as a way to improve the retention of newly-learned problem-solving techniques. Students video-recorded themselves talking through problems immediately after…
First year calculus is often taught in a way that is very burdensome to the student. Students have to memorize a diversity of processes for essentially performing the same task. However, many calculus processes can be simplified and…
In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on…
Nowadays, learning increasingly involves the usage of search engines and web resources. The related interdisciplinary research field search as learning aims to understand how people learn on the web. Previous work has investigated several…
A hybrid teaching approach that relied on combining Project Based Learning with Team Based Learning was trialled in an engineering module during the past five years. Our motivation was to expose students to real-world authentic engineering…
Investigations related to expertise in problem solving and ability to transfer learning from one context to another are important for developing strategies to help students perform more expert-like tasks. Here we analyze written responses…
The objective of this article is to investigate the effect of active-learning pedagogy on learners' academic achievement and their attitude toward mathematics using both quantitative and qualitative methods. We cultivated sustainable…
When does a course count as 'inverted'? When first faced with a new teaching method, deliberate lectures may want to test it without abandoning the advantages of the established method. Aftes the experiment they have to evaluate additional…
A simple model to help students see the connections between a physics course and their engineering major is described. "Bridging" had positive effects on performance, attitude, and motivation, as measured by grade analyses, surveys, and…
Asking questions during class time is one form of participation not commonly employed by members of underrepresented groups in large enrollment college classrooms, even though the form of participation is highly conducive to student…
Self-reflection on learning experiences constitutes a fundamental cognitive process, essential for the consolidation of knowledge and the enhancement of learning efficacy. However, traditional methods to facilitate reflection often face…
This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…
In the rapidly evolving interdisciplinary field of quantum information science and technology, a major obstacle is the need to understand advanced mathematics to solve complex problems. Current findings in educational research suggest that…
We describe the evolution of a personal non-lecture active learning pedagogy developed in numerous courses at all university levels. A distinguishing feature is its tight integration of pre-class preparation, involving student…
Math is the backbone of any field. Still its a night mare for many. Recent survey proves that many students become dropouts from their higher education due to math courses. ICT is an enchanted word in the contemporary educational…
We show that individual topics and skills can have a dramatic effect on the outcomes of students in various mathematics courses at the University of Illinois. Data from the placement program at Illinois associates a knowledge state, a…