In many countries STEM degree programs face high dropout rates, which are often attributed to insufficient mathematical preparation of incoming undergraduates. However, it is largely unclear which mathematical prerequisites universities expect from their new STEM undergraduates. There are hardly official documents and it is even an open question…

We describe the design and evaluation of an innovative course for beginning undergraduate mathematics students. The course is delivered almost entirely online, making extensive use of computer-aided assessment to provide students with practice problems. We outline various ideas from education research that informed the design of the course, and…

Because of the increasing use of business analytics to improve business processes, it is not difficult to argue the importance that undergraduate business students gain the ability to understand, interpret, and communicate statistics. However, a task that may be difficult for statistics instructors is to quickly demonstrate and convince business…

Project-based learning supports unique and authentic problems in differential equations courses. An intuitive, interesting and deep differential equations project is described. The description illustrates a case study of guiding students through a complex project and the technical and personal rewards gained from it. Valuable advice is provided to…

Mathematics education is highly valued in advanced economies due to its role in developing skilled workforces, economic resilience and social well-being. However, university academics across disciplines regularly bemoan undergraduate students' under-preparedness for the mathematical and quantitative demands of undergraduate degree programmes. In…

Research exploring undergraduates' tool preferences in tertiary mathematics is currently limited. In this paper, we explore the tools mathematics and engineering students use when studying mathematics and the ways undergraduates combine these tools. Results from our survey (N = 628) showed that students in our sample use mostly their notes, the…

A lack of mathematics facility prevents many students from pursuing majors in science, technology, engineering, and mathematics. Research revealed that teaching methodology is crucial for success in any course. This dissertation focuses on learners' experiences in a flipped instructional model and a customized direct instructional model. Although…

Undergraduate students' engagement with mathematical discourse when defining geometric solids is analysed and compared with what their lecturers expect them to do. The theory of commognition is adopted as the theoretical framework, which permits the characterisation and comparison of their discursive activities, and may lead to the identification…

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion…

It has been well documented that active learning (AL) improves student learning outcomes in education. This quasi-experimental study explores the effect of active learning on students' knowledge of calculus concepts, in the form of the Calculus Concept Inventory (CCI), regular assignment scores, and test scores, during an 8-week calculus tutorial…

Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend the "Rule-of-Four," initially used in calculus reform efforts, to a "Rule-of-Five"…

The aim of this study is to investigate the misanalogical construction of undergraduate students in their cognitive conflict in doing a non-routine mathematical task. Qualitative methods were used in this research. Data were collected from 68 seventh semester undergraduate students of Mathematics Education Study Program, Universitas Negeri Malang…

A relative extrema optimization problem is one in which the domain of the objective function (i.e. the function whose maximum or minimum value is to be found) is an open interval. An absolute extrema optimization problem is one in which the domain of the objective function is a closed interval. Analysis of task-based interviews conducted with 12…

Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that…

Teaching determinants poses significant challenges to the instructor of a proof-based undergraduate linear algebra course. The standard definition by cofactor expansion is ugly, lacks symmetry, and is hard for students to use in proofs. We introduce a visual definition of the determinant that interprets permutations as arrangements of…