The mathematics in your ears. The role of math in integrated STEM via the modeling of hearing aids

Although the mathematical and scientific education in Flanders is at a high level, the integration of technology with these abstract courses is a large gap in the educational system. This has the consequence that -despite the fact that in secondary education there are quite a lot of pupils taking scientific programs- there is far less choice for or interest in scientific and technical careers in continued education. In order to recognize the importance of mathematical equations and scientific models for everyday problem solving in general and for engineering in particular, students will have to make the connection between math and science and practical applications. In order to use mechanical and electrical devices, students will have to discover the world of technical systems, get insight into basic principles and make stuff work. Thus, there is a need for a new kind of didactic approach that integrates these important domains: STEM - Science, Technology, Engineering and Mathematics. In this context, this project wants to make a first step towards a more STEM integrated view on the mathematical topics 'sines', 'integrals' and 'Fourier series'. It's all about sound: how a physical sound wave can be translated into a mathematical model, how frequencies are important in sound waves, how the biology of the human ear benefits from these mathematical transformations, and how technology steps in to support this functioning, in terms of a hearing aid. Step by step we put the necessary mathematical techniques on the map and relate them to the biological phenomena and the technical principles required in the context of sound and hearing. The material is made such that math teachers can use it with pupils of the 5th and 6th year of the Flemish secondary educational system (17- to 18-year olds). The content remains close to the learning goals within their curricula.status: publishe

A Nonlinear Dynamical System Perspective on Team Learning: The Role of Team Culture and Social Cohesion

This paper examines team learning within a nonlinear dynamical system (NDS) perspective. Research has successfully identified various conditions that promote learning behaviors in teams. In the present study, our focus is on the role played by team culture and by social cohesion as supporting conditions of team learning. Previous studies revealed that a culture oriented to learning tends to promote the adoption of team learning behaviors in the group. Results concerning the role played by social cohesion in team learning is, however, less clear. Indeed, while social cohesion might promote learning behaviors because it increases the willingness to work together and to help each other, high levels of social cohesion could also lead to uncritical acceptance of solutions. The complex relationship between social cohesion and team learning behaviors led us to study it under the NDS framework. Using the dynamic difference equation model, the present research proposes a cusp catastrophe model for explaining team learning, implementing the team culture as the asymmetry variable and social cohesion as bifurcation variable. The sample of the present research is constituted by 44 project workgroups, and data were collected at two moments of the life cycle (half-time and end) of teams, with single-item visual analogue scales. Results reveal that the cusp models are superior to the pre-post linear models by explaining a larger portion of the variance. In addition, the cubic term, the bifurcation effect and the asymmetry term are statistically significant. Social cohesion acts as a bifurcation factor, that is to say, beyond a certain threshold of social cohesion, groups that have the same cultural orientation might oscillate between two attractors, the modes of high and low learning behaviors respectively. These results suggest that a small variation of social cohesion causes the system to enter an area of unpredictability in terms of team learning, where sudden shifts in the outcomes might be expected. Leaders and members need to monitor the levels of social cohesion of the team, to avoid phenomena like groupthink, which jeopardizes the implementation of learning behaviors, such as the exploration of different opinions or error discussion

Co-limitation towards lower latitudes shapes global forest diversity gradients

The latitudinal diversity gradient (LDG) is one of the most recognized global patterns of species richness exhibited across a wide range of taxa. Numerous hypotheses have been proposed in the past two centuries to explain LDG, but rigorous tests of the drivers of LDGs have been limited by a lack of high-quality global species richness data. Here we produce a high-resolution (0.025° × 0.025°) map of local tree species richness using a global forest inventory database with individual tree information and local biophysical characteristics from ~1.3 million sample plots. We then quantify drivers of local tree species richness patterns across latitudes. Generally, annual mean temperature was a dominant predictor of tree species richness, which is most consistent with the metabolic theory of biodiversity (MTB). However, MTB underestimated LDG in the tropics, where high species richness was also moderated by topographic, soil and anthropogenic factors operating at local scales. Given that local landscape variables operate synergistically with bioclimatic factors in shaping the global LDG pattern, we suggest that MTB be extended to account for co-limitation by subordinate drivers