Undergraduate mathematics education is essential for building a foundation for success in various scientific disciplines. Curriculum reforms in mathematics education have emphasized the need for cultivating learning skills that depend on effective student engagement (SE). Consequently, there has been growing research on the mechanisms that facilitate SE and promote its development. To gain insights into the state of SE research in undergraduate mathematics, the current systematic review addresses the varied research by examining four key aspects: a) theoretical grounding and research aims, b) definitions, c) measurement, and d) learning outcomes. Following the PRISMA guidelines, a literature search identified 1,584 records, with 48 papers meeting the inclusion criteria. The findings reveal three primary research aims and three approaches to grounding SE research, with most studies using an instruction-focused framework to evaluate instructional methods. Nearly half of the papers provided a definition of SE, with analysis showing varied uses of elements like psychological investment and multidimensionality. Studies that used multiple elements offered more concise definitions. Measurement of SE predominantly focused on online learning through log files or course participation via self-reports, with behavioral engagement being the most commonly examined dimension. Less than half of the studies explored the relationship between SE and learning outcomes, using both variable-oriented and person-oriented approaches to examine this connection. Based on the current findings, the review offers recommendations for aligning conceptualizations, definitions, measurement, and context in future research to foster a shared understanding and guide interventions.

In tertiary mathematics education for engineers (hereafter called service mathematics education, SME), there is a long-lasting controversy on what and how to teach. The goal of SME is to provide a base for engineering-specific courses and to develop mathematical competencies needed for academic success and professional practice. A leading question in engineering education is how to take mathematical competencies into account when designing content. Mathematical competencies are employed to understand, judge, do, and use mathematics in a variety of mathematical contexts and situations in which mathematics could play a role [1]. Although mathematical competencies have been introduced for about two decades, Alpers [2] noted that research in engineering higher education had focused chiefly on the modelling competency and less on other competencies. By means of a scoping review, the current study aims to examine how mathematical competencies are investigated in higher education research. The main research question is “To what extent and in what ways have mathematical competencies been examined in higher engineering education research?” Papers were retrieved and qualitatively reviewed using the Preferred Reporting Items for Systematic Reviews and Meta- Analyses (PRISMA) guidelines. A systematic search yielded 166 records, of which, 65 unique records were relevant to engineering education and screened for eligibility. A synthesis of 23 studies reviewed showed that problem-solving and modelling were the most investigated mathematical competencies and were often investigated together or with other mathematical competencies. The inconsistencies in the terminologies used suggest a need for clearer conceptualizations to advance research and inform practice on mathematical competencies.

1.1 Background To educate future competent engineers, it is crucial to adopt teaching and learning approaches that support students in dealing with highly complex problems [1]. One strategy is to enhance service mathematics in higher engineering education by shifting from outcome-centered to competence-centered approaches [2]. This strategy is examined and adopted in a large-scale innovation programme of mathematics education (PRIME) at TU Delft to design effective service mathematics courses in higher engineering education. As mathematics is at the core of engineering education, we will, in this workshop, explore how to create a viable and resilient educational model for developing mathematical competencies, described in the Framework of Mathematics Curricula in Engineering Education [2, 3]. Additionally, we will discuss how the development of mathematical competencies can be facilitated by leveraging technology in blended and remote learning environments. The aim of this workshop is to start a process via a living document which serves to share and create material and expertise in teaching, learning and assessing the mathematical competencies.