The present paper explores the relationship between attitudes towards mathematics (ATM) and achievement in college calculus in active learning (AL) and lecture-based (LB) classrooms. Previous work on this relationship has mainly been limited to LB instruction, neglecting the impact of innovative approaches such as AL. Less attention has been paid…

When embarking on our journey of learning in mathematics, we may envision a linear path of modules for acquiring mathematical knowledge and understanding to reach a predetermined outcome. However, this is a partial representation since the outcome and path are developing and adapting and our learning is continuously emerging. In this paper, our…

Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate…

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely…

The growing adoption of active learning pedagogical methods has shown significant positive effects in higher education as they promote students' engagement and meeting of learning outcomes. Similarly, problem-based learning and media-based learning allow instructors to model educational experiences that prepare students with knowledge and skills…

As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

The study examines the levels of understanding logarithmic expressions within the frames of a mathematical card game. The game is based on the popular card game Saboteur. In this paper, we analyse the progress of a group of six undergraduate students participating in a remedial course using games for recalling some fundamental mathematical…

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…

This short note discusses how the optimality conditions for minimizing a multivariate function subject to equality constraints have been covered in some undergraduate Calculus courses. In particular, we will focus on the most common optimization problems in Calculus of several variables: the 2 and 3-dimensional cases. So, along with sufficient…

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…

The role of mathematics in secondary-tertiary transition is subject to increasing analysis in several education contexts. We explore the longitudinal relationships among a standardized test used for assessing secondary school mathematics, high school final grades and the academic progress of a sample of Italian undergraduates. Results from…

We report findings from a longitudinal study of students' beliefs about empirical arguments and mathematical proof. We consider the influence of an 'Introduction to Proof (ITP)' course and the consequences of the observed changes in behaviour. Consistent with recent literature, our findings suggest that a majority of the thirty-eight undergraduate…

The decision to undertake undergraduate studies as a mature student poses challenges, especially when service mathematics is part of the programme of study, giving rise to mathematics anxiety. Mathematics anxiety comprises negative feelings pertaining to a person's engagement with mathematics. While much research into mathematics anxiety…

Mathematical modelling is an interlinking process between mathematics and real-world problems that can be applied as a means to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas of science, such as engineering disciplines. This study was designed to investigate the effect…

Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further.