Mathematical modelling of exponential growth as a rich learning environment for mathematics classrooms

Abstract

Mathematical concepts are regularly used in media reports concerning the Covid-19 pandemic. These include growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Our contribution has the aim of showing that basic mental models about exponential growth are important for understanding media reports of Covid-19. Furthermore, we highlight how the coronavirus pandemic can be used as a context in mathematics classrooms to help students understand that they can and should question media reports on their own, using their mathematical knowledge. Therefore, we first present the role of mathematical modelling in achieving these goals in general. The same relevance applies to the necessary basic mental models of exponential growth. Following this description, based on three topics, namely, investigating the type of growth, questioning given course models, and determining exponential factors at different times, we show how the presented theoretical aspects manifest themselves in teaching examples when students are given the task of reflecting critically on existing media reports. Finally, the value of the three topics regarding the intended goals is discussed and conclusions concerning the possibilities and limits of their use in schools are drawn.

Advantages and challenges of using digital technologies in mathematical modelling education – a descriptive systematic literature review

“…In this way, technology can enhance connections between various types of mathematical knowledge (Geiger, 2011). Overall, studies reported that technology offered plenty of opportunities for students and confirmed that technology can be successfully applied at different stages of the modelling cycle, including simplification, mathematization, making connections, evaluation, interpretation, and validation (Siller and Greefrath, 2010;Geiger, 2011;Daher and Shahbari, 2015). In line with our results, Molina-Toro et al (2019) found that studies on modelling used digital tools to visualize the representation of data, make complicated calculations, develop or validate mathematical models and simulate phenomena.…”

“…The black box issue frequently arises when the creator and user are not the same person (Greubel and Siller, 2022). Concerning this challenge, research has shown that the difficulties frequently encountered in solving modelling problems in digital group work appear to be a direct result of the automatic calculation provided by technological tools (Siller et al, 2022). Studies highlighted that for students who avoided necessary validity checks, it might be easy to blindly trust digital technologies, get lost in the modelling process, and disengage from the solution to the modelling problem.…”

“…In the last two decades, the use of digital technologies to improve mathematical modelling education has attracted increased interest among researchers (Siller and Greefrath, 2010;. Recent developments (e.g., the COVID-19 pandemic and recent technological innovations) may accelerate the integration of digital technologies into modelling education, as well as in other fields of mathematics education (Mulenga and Marbán, 2020;Soto-Acosta, 2020;Borba, 2021).…”

“…New technologies can play a significant role in learning and teaching mathematical modelling as they can open new horizons to explore different mathematical situations (Drijvers, 2003;Niss et al, 2007) and foster new ways of understanding, evaluating, and interpreting real-world situations (Molina-Toro et al, 2022). Some researchers have argued that it is possible to integrate digital tools (e.g., dynamic geometry software [DGS], computer algebra systems [CASs]) into different stages of the modelling cycle (Siller and Greefrath, 2010;Geiger, 2011;Daher and Shahbari, 2015). From this perspective, technology can promote learners' modelling processes.…”

Will we ever teach mathematics again in the way we used to before the pandemic?

“…There is also quite a strong focus on developing a public understanding of mathematics that is used by the media to explain and predict trends in the pandemic and other global phenomena. In their study Siller et al ( 2022 ) addressed the way the media present data on the pandemic, referring to growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Since these reports sometimes appeared contradictory or even false to students, they showed that basic mental models about exponential growth are important for understanding media reports of COVID-19.…”