Mathematics for economics: special issue editorial

1 Introduction

Mathematics courses at university are not only a challenge for students who want to major in mathematics as a scientific discipline or who desire to become mathematics teachers, but also for students of many other disciplines, for instance the natural sciences or engineering fields. It is therefore important to also investigate the teaching and learning of mathematics for students of these disciplines.

Lots of attention has been paid to mathematics in engineering and the natural sciences in the last decades in mathematics education research. For instance, there are several special issues in mathematics education research journals dedicated to the teaching and learning of mathematics in these disciplines (Alpers, 2013; Velichová & Gustafsson, 2017; Velichová, 2019, 2022; Pepin et al., 2021; Goos et al., 2023). The spotlight has, however, been much less focussed on economics, although mathematics is hugely significant for students majoring in economics (Siegfried et al., 1991). In this context, it is not enough merely to teach economics students computational procedures—although these are of course important in economics, e.g., in symbolic derivations of relationships between economic quantities under certain conditions. Economics students also need a profound understanding of the mathematical concepts used in economics, especially regarding what these concepts refer to in the economics sense, and they need to be able to use mathematics in modelling and reasoning within their major discipline. However, there are only a few studies in the mathematics education literature that explicitly focus on the teaching and learning of mathematics for economics thus far. This Special Issue therefore aims to collect previous findings in this field while also providing a wealth of new insights into the teaching and learning of mathematics for and by economics students.

2 Overview of the contributions in this special issue

The Special Issue brings together 11 contributions. One of these is a literature review that collates previous findings on the challenges economics students face as they transition from school to their mathematics courses at university. Three articles focus on the teaching and learning of particular content that is relevant for economics students. And finally, seven articles focus on approaches/interventions to help address economics students’ difficulties in their mathematics courses.

The article by Landgärds-Tarvoll is the first extensive systematic literature review on challenges for economics students when transitioning from school into their tertiary mathematics courses. Summarizing previous studies that examine the teaching and learning of mathematics for economics, she has identified several important difficulties for economics students:

• The institutional culture changes from school to university: the class size is usually very large and the teaching style changes to a ‘transmissionist’ approach, which requires a lot of self-regulation by the students for the mastery of their tertiary mathematics courses.

• There is a great heterogeneity in students’ prior mathematical knowledge and skills, and there is often a mismatch with what teachers of mathematics courses expect.

• Students of economics might not see the relevance of the mathematics taught, and thus may not be able to establish a link to their major discipline.

Three articles in this Special Issue focus on the teaching and learning of certain pieces of mathematical content that are of great relevance in economics. Mkhatshwa studied business students’ knowledge of the concept of elasticity in the context of price and demand, as well as their covariational reasoning abilities related to this concept. He found especially that none of the participants had acquired a deep conceptual knowledge regarding the price elasticity of demand. Hence, this concept is not easy to grasp for economics students. Feudel & Skill focussed on the concept of differential. By means of a textbook analysis, they investigated how this concept is understood in economics. Their analysis showed in particular that there is a discrepancy between the understanding of differentials relied upon in microeconomics and the way these are usually introduced in calculus for economics students. Landgärds-Tarvoll & Göller identified a similar issue, but this time relating to methods for constrained optimization—a topic of enormous relevance in economics. They showed—also by means of a textbooks analysis—that not all techniques for constrained optimization that are used in microeconomics are covered in mathematics courses for economics students. Furthermore, in microeconomics, the techniques used are justified with different kinds of arguments than in the students’ mathematics courses. These two studies provide evidence that there are mismatches between how mathematical content is covered in mathematics courses for economics students and how it is used in the students’ major discipline. This can make it hard for the students to acquire a holistic picture of the respective content.

As already said, seven contributions in this Special Issue focus on possibilities for helping economics students cope with problems in their mathematics courses. Two articles evaluate approaches that aim to foster an active and continuous engagement during the semester, which can help to address the problem of students’ passivity in their mathematics courses at university—one of the challenges highlighted in Landgärds-Tarvoll’s literature review. One such approach is to set optional homework assignments for submission that can provide students with continuous feedback. Büchele & Feiste investigated the influence of such optional assignments on students’ performance in their mathematics course and explored which students derived the greatest benefit from these. Using a regression method, they found particularly that participating in such assignments had a positive impact on the students’ scores in a mid-term test. However, students who were less motivated and—perhaps surprisingly—students who had stronger prior knowledge in mathematics engaged less in the assignments, and hence missed opportunities for practising and chances to receive feedback during the semester. Another approach to fostering students’ engagement during the semester is to offer additional online resources. Barile et al. examined how often students used a variety of optional online resources offered in an econometrics course, such as topic notes, lecture captures, discussion forums, past exams or online quizzes, and how this usage affected their grades. By means of a regression analysis, they found a positive impact on students’ grades when they used the online resources offered, especially for the online quizzes and the topic notes. Hence, providing optional assignments and additional online resources can help economics students in the mastery of their mathematical courses.

Five of the contributions on approaches for supporting economics students in their mathematics courses describe explicitly implemented interventions. Three of these interventions aim to link the mathematical content taught to economics. Trigueros & Martínez-Planell present a possibility to include modelling into a mathematics course for economics students on differential equations, using APOS theory (Arnon et al., 2014). The basis for the modelling activities was the question of how an innovative product would spread in the community. Students were asked to develop models, use data to test the models’ predictions and perhaps suggest modifications to the models to improve their efficacy. In this situation, the course’s participants tended to view the problem through an economics lens when discussing whether the functions and/or equations involved in their model were appropriate. Hence, they made a connection between mathematics and the economics context. Furthermore, the inclusion of the latter also fostered their reasoning abilities relating to the mathematical concepts involved in the task, especially regarding the notions of function and derivative.

Benítez & Parra present an example of how inquiry-based learning in a mathematics course for economics students can help to establish a connection between mathematics and economics—using the study and research paths (SRP) approach (Bosch, 2018), in which new content is discovered by generating questions that the students pose themselves. Based on the initial teacher-given question of how much consumers and producers benefit from a competitive market, the students came up with more detailed sub-questions. In trying to find answers to these, the students came across several calculus concepts that are highly relevant in economics, such as the derivative, elasticity or the integral. Since the questions arose from economics, the link between mathematics and economics was clearly and permanently present.

The focus of the third intervention on fostering a connection between mathematics and economics—presented by Meyer—is slightly different, as this intervention was aimed at students enrolled in a mixed study programme ‘Applied Mathematics with Economics’ at a UK university. Therefore, the emphasis in this intervention lies more on inner-mathematical features of mathematical content used in economics, namely on a theorem that occurs in the modelling of production processes in macroeconomics: the theorem on the solvability of Leontief systems. The intervention consists of a modified version of its proof with small edits at significant positions and a sequence of tasks. The latter explicitly require students to check whether the lines with the edits are true and to either provide counterexamples or correct these lines. Further tasks then focus on the conditions for the applicability of the theorem, so that students become aware of these. This sequence especially aimed at helping students read the formal theorem and its proof. Although the mathematical content in this paper is rather advanced, helping students read symbolic derivations (on a more elementary level) is also a useful support approach in standard mathematics for economics courses, as economics majors are also confronted with such derivations in both basic and intermediate micro- and macroeconomics courses.

The next intervention in this Special Issue, presented by Brendon-Penn et al., is an approach that aims to address the specific problem of heterogeneity in economics students’ prior mathematical knowledge, which is also one of the important transition-related challenges identified by Landgärds-Tarvoll in her literature review. For this, the authors devised a collection of revision resources that they implemented into a virtual learning environment at a UK university. A subsequent investigation of students’ usage of the resources showed a high demand for these.

Finally, Barile proposes a teaching framework for introductory mathematics courses for economics students, which aims to address the mismatch between students’ expectations and course demands, help them in their navigation through the course and recognize the relevance of the mathematics taught for their major discipline. Its main components are the consideration of prior knowledge, scaffolding and integrating practical applications.

3 Short summary and outlook for further research

The articles in this Special Issue contribute to the research in the area of mathematics education for economics students in several respects:

• They summarize important previous findings in the area, especially concerning economics students’ difficulties during the transition from school to their mathematics courses at university.

• They extend the research on the teaching and learning of particular mathematical content that is relevant for economics students by featuring studies that look at the understanding of and practices related to concepts/methods that are of great importance in economics: price elasticity of demand, differentials and constrained optimization.

• They provide valuable suggestions on how to build bridges between mathematics and economics, especially by including and integrating economic contexts and modelling activities into the mathematics courses.

• They provide evidence for a positive effect of certain optional resources offered to help students cope with problems encountered during the transition from school to university, such as optional assignments or virtual learning resources.

Thus, the findings presented in this Special Issue extend on the one hand the knowledge of economics students’ potential and actual difficulties in their mathematics courses. On the other hand, some of its articles provide intriguing approaches for how to address these.

There are of course a host of other important themes that are not addressed in this Special Issue. One of these is assessment in mathematics for economics students, as the content of exams tends to determine much of what is actually taught and what students learn. Another crucial theme is the use of technology within mathematics courses for economics students and its effect on students’ learning. Finally, I would like to emphasize that more research is needed into what kind of mathematics is required by economics students—in their programmes of study and perhaps also in their eventual working lives. Hence, there are many more research avenues to explore in the growing field of mathematics education for economics students in order to understand and address students’ difficulties, thereby helping the latter to achieve a fuller grasp of the mathematics needed in their major discipline.

Teaching Mathematics and Its Applications: An International Journal of the Institute of Mathematics and Its Applications will welcome future contributions that address any aspects of research related to mathematics education for economics students.

References