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.

Behavioural engagement as a predictor of academic success hinges on the interplay between effort and time. Exploring the longitudinal development of engagement is vital for understanding adaptations in learning behaviour and informing educational interventions. However, person-oriented longitudinal studies on student engagement are scarce. Moreover, online engagement metrics are rarely grounded in theory and often result in simplified descriptions overlooking the complexity of engagement processes. This study applies a theory-based operationalization of behavioural engagement to examine the log data of 236 students in a web-based learning platform. We explored 1) whether weekly profiles based on distinct engagement patterns can be identified and 2) how students transition across profiles over time. Hierarchical clustering yielded one Inactive and six active profiles (Fast-Learners, Regular-Learners, Average-Engagement, Minimalists, Struggling-Learners, and Procrastinators). Results suggest heterogeneity in profile emergence, with effective engagement characterized by alignment with the course deadlines. Process mining revealed changes in profile membership across weeks. Profile transitions revealed relative stability among effective groups and greater fluctuation among low-time profiles. By investigating the complexity and temporality of engagement in online learning, our findings provide insights for developing personalized learning support through training artificial intelligence applications and informing learning analytics dashboards.

The Initiative for Innovation in Engineering Education, IDEE, is a university-wide activity at Delft University of Technology (TU Delft), aiming to strengthen the capacity for evidence-based innovation in engineering education. The goal is to create a more systematic and evidence-informed approach to educational innovation at TU Delft, and to ensure that the knowledge gained is documented and shared with the wider education community. This paper describes the first steps in establishing the structures for the initiative, identifying the educational themes to be addressed, mobilising teams of faculty members and recruiting junior researchers, creating support for these teams, and building a productive community. Through this setup, IDEE has high ambitions for creating both educational innovation and associated scientific gains. It is also intended to create role models for novel kinds of academic careers with an emphasis on teaching.

This article is a reflection of a SEFI workshop on Retention. In the workshop, a SWOT Analysis has been realised of four pedagogical solutions addressing Retention in undergraduate STEM education. The pedagogical solutions are programmatic assessment, micro-credentials for online mathematics (support) learning modules, autonomous and self-regulated learning and mathematical competencies for learning. Results have provided insights into the relevance and feasibility of implementation.

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.

One of the concerns in service mathematics courses, such as calculus for engineering, is students’ interest in these studies. Research suggests that engineering undergraduates’ lack of awareness about the importance of mathematics for their study success and for their careers contributes to their low motivation for mathematics. An approach to increasing student motivation is to take advantage of technological tools to provide students with more engaging learning experiences. Recent studies showed that augmented reality (AR) enhances student engagement, motivation, and knowledge retention. However, implementing AR can be challenging since it can be quite costly and technically complex. The current paper describes a case study in which an AR application was designed and developed using WebXR, in the context of a service mathematics course for teaching calculus. The AR content involves drawing of level curves and the visualization of a volcano and the flow of lava to support students’ learning of directional derivatives. A pilot study was conducted to examine engineering undergraduates’ perceptions of using AR for learning mathematics. Results show that students perceived using AR for learning math as enjoyable and motivating. Students reported that AR content adds value to their classes by making the mathematical concepts clearer and helping them apply what they have learned to real life. However, the AR content did not work well on all mobile phones and all versions of web browsers. Lessons learned from the design and development of AR using WebXR as well as recommendations for future studies are discussed in this paper.

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.

3D anthropometry has created a significant opportunity for designers to improve fit by offering detailed information regarding the shape of the human body. Various researchers have shown the benefit of using 3D anthropometric data in the development or evaluation of head related products for adults. However, detailed 3D anthropometric data of children heads and faces is still lacking. This paper presents up to date descriptive statistics of detailed measurements made of heads and faces of Dutch children. For the purpose of developing ergonomic head and face wear for children, an anthropometric survey was conducted, whereby children aged 6 months to 7 years were measured, utilising both traditional anthropometric measurement techniques and 3D image derived measurements. The traditional measurements were compared with the most recent dataset of Dutch children and, on a more detailed level, with a dataset of North American children.

This project aims to understand Behavioral and Psychological Symptoms of Dementia (BPSD), specifically, identify location-related factors influencing BPSD at the individual level in the nursing home setting by means of a mixed methods approach facilitated by Indoor Positioning System (IPS). The use of a mixed methods approach fits with the “pragmatism” research paradigm in ergonomics. Previous research has identified some factors influencing BPSD by observations, interviews and multidisciplinary meetings; however, the data supporting the previous findings are mainly subjective. IPS will keep track of the location data of each People with Dementia (PwD) and the caregivers over time in this project. Therefore, we could generate objective data for location-related factors, which could influence BPSD for each PwD in the nursing home setting. The caregivers will analyze the data collected by IPS together with the researcher, by reflecting on their own experiences. As such, both quantitative and qualitative data will be generated and analyzed together to identify location-related factors influencing BPSD for each PwD participant. This is the first project to collect objective data for understanding BPSD. This research protocol discusses the rationale behind this project; the mixed methods approach to be applied in this project, and the impact of this project’s outcomes.

Increasing class sizes forces universities to change their education in ways that allow for independent learning for students. This study looks at a case where blended learning was introduced to alleviate some of the educationally negative consequences of large class sizes. Independent learning requires from the students to become more self-regulated while at the same time they need efficient feedback from lecturers to enact these self-regulated learning activities. In this paper we investigate whether at Delft University of Technology (TU Delft) student perceptions of lecturing behaviour is such as to stimulate student’s independent learning and whether self-regulated learning behaviour results in more active engagement with the learning materials.

“Prepare, Participate, Practice”: active learning in designing basic maths courses for engineering students at TU Delft works! The PRoject Innovation Mathematics Education (PRIME) at Delft University of Technology (TU Delft) is all about redesigning mathematics courses for engineers. This paper describes the process of developing, implementing, evaluating and implementing again of three basic courses at TU Delft using a blended learning approach developed by a growing team of teachers from the mathematics department. Our findings suggest that the approach taken enhances students’ learning performance in maths education. The main results show that students have a more active learning experience compared to the traditional setup of these courses, leading to more engagement, more interaction and better results. An important role is played by meaningful examples taken from the engineering faculty where the students are studying, showing students from that faculty what role the mathematics play in their field of interest. This is also used to develop their skills in mathematical modelling.

This study investigated organic micropollutant (OMP) biodegradation rates in laboratory-scale soil columns simulating river bank filtration (RBF) processes. The dosed OMP mixture consisted of 11 pharmaceuticals, 6 herbicides, 2 insecticides and 1 solvent. Columns were filled with soil from a RBF site and were fed with four different organic carbon fractions (hydrophilic, hydrophobic, transphilic and river water organic matter (RWOM)). Additionally, the effect of a short-term OMP/dissolved organic carbon (DOC) shock-load (e.g. quadrupling the OMP concentrations and doubling the DOC concentration) on OMP biodegradation rates was investigated to assess the resilience of RBF systems. The results obtained in this study imply that – in contrast to what is observed for managed aquifer recharge systems operating on wastewater effluent - OMP biodegradation rates are not affected by the type of organic carbon fraction fed to the soil column, in case of stable operation. No effect of a short-term DOC shock-load on OMP biodegradation rates between the different organic carbon fractions was observed. This means that the RBF site simulated in this study is resilient towards transient higher DOC concentrations in the river water. However, a temporary OMP shock-load affected OMP biodegradation rates observed for the columns fed with the river water organic matter (RWOM) and the hydrophilic fraction of the river water organic matter. These different biodegradation rates did not correlate with any of the parameters investigated in this study (cellular adenosine triphosphate (cATP), DOC removal, specific ultraviolet absorbance (SUVA), richness/evenness of the soil microbial population or OMP category (hydrophobicity/charge).

This study investigated relationships between OMP biodegradation rates and the functional groups present in the chemical structure of a mixture of 31 OMPs. OMP biodegradation rates were determined from lab-scale columns filled with soil from RBF site Engelse Werk of the drinking water company Vitens in The Netherlands. A statistically significant relationship was found between OMP biodegradation rates and the functional groups of the molecular structures of OMPs in the mixture. The OMP biodegradation rate increased in the presence of carboxylic acids, hydroxyl groups, and carbonyl groups, but decreased in the presence of ethers, halogens, aliphatic ethers, methyl groups and ring structures in the chemical structure of the OMPs. The predictive model obtained from the lab-scale soil column experiment gave an accurate qualitative prediction of biodegradability for approximately 70% of the OMPs monitored in the field (80% excluding the glymes). The model was found to be less reliable for the more persistent OMPs (OMPs with predicted biodegradation rates lower or around the standard error = 0.77 d−1) and OMPs containing amide or amine groups. These OMPs should be carefully monitored in the field to determine their removal during RBF.

This study investigated sorption and biodegradation behaviour of 14 organic micropollutants (OMP) in soil columns representative of the first metre (oxic conditions) of the river bank filtration (RBF) process. Breakthrough curves were modelled to differentiate between OMP sorption and biodegradation. The main objective of this study was to investigate if the OMP biodegradation rate could be related to the physico-chemical properties (charge, hydrophobicity and molecular weight) or functional groups of the OMPs. Although trends were observed between charge or hydrophobicity and the biodegradation rate for charged compounds, a statistically significant linear relationship for the complete OMP mixture could not be obtained using these physico-chemical properties. However, a statistically significant relationship was obtained between biological degradation rates and the OMP functional groups. The presence of ethers and carbonyl groups will increase biodegradability, while the presence of amines, ring structures, aliphatic ethers and sulphur will decrease biodegradability. This predictive model based on functional groups can be used by drinking water companies to make a first estimate whether a newly detected compound will be biodegraded during the first metre of RBF or that additional treatment is required.

In addition, the influence of active and inactive biomass (biosorption), sand grains and the water matrix on OMP sorption was found to be negligible under the conditions investigated in this study. Retardation factors for most compounds were close to 1, indicating mobile behaviour of these compounds during soil passage. Adaptation of the biomass towards the dosed OMPs was not observed for a 6 month period, implying that new developed RBF sites might not be able to biodegrade compounds such as atrazine and sulfamethoxazole in the first few months of operation.

Our aim is to estimate the volume-weighted mean of the volumes of three-dimensional ‘particles’ (compact, not-necessarily-convex subsets) from plane sections of the particle population. The standard stereological technique is to place test lines in the plane section, and measure cubed intercept lengths with the two-dimensional particle profiles. This paper discusses more efficient estimators obtained by integrating over all possible placements of the test line. We prove that these estimators have smaller variances than the line transect estimators, and indeed are related to them by the Rao-Blackwell process. In the improved estimators, the cubed intercept length is replaced by a moment of the distance between two points in the section profile. This can be computed as a moment of the set covariance function, which in turn is computable using fast Fourier transform.
We also derive an isoperimetric type inequality between the improved estimator and the area-weighted 3/2 th moment of the profile areas. Finally, we present two practical applications to particles of silicon carbide and to synaptic boutons in brain tissue. We estimate the variance of the technique and the gain in efficiency over line transect techniques; the efficiency improvement appears to be as much as one order of magnitude.

We define the ‘linear scan transform’ G of a set in Rd using information observable on its one-dimensional linear transects. This transform determines the set covariance function, interpoint distance distribution, and (for convex sets) the chord length distribution. Many basic integral-geometric formulae used in stereology can be expressed as identities for G. We modify a construction of P. Waksman [Adv. Appl. Math. 8, No. 1, 38-52 (1987; Zbl 0638.60016)] to construct a metric η for ‘regular’ subsets of Rd defined as the L1 distance between their linear scan transforms. For convex sets only, η is topologically equivalent to the Hausdorff metric. The set covariance function (of a generally non-convex set) depends continuously on its set argument, with respect to η and the uniform metric on covariance functions.

In [4] a central limit theorem for the number of vertices of the convex hull of a uniform sample from the interior of a convex polygon is derived. This is done by approximating the process of vertices of the convex hull by the process of extreme points of a Poisson point process and by considering the latter process of extreme points as a Markov process (for a particular parametrization). We show that this method can also be applied to derive limit theorems for the boundary length and for the area of the convex hull. This extents results of Rényi and Sulanke (1963) and Buchta (1984), and shows that the boundary length and the area have a strikingly different probabilistic behavior.

Pohl proved an analogous formula for closed convex plane curves with smooth.