Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

The use and potential of Fermi problems in the STEM disciplines to support the development of twenty-first century competencies

“…Our review of the literature reveals numerous articles highlighting the potential of FPs to introduce and engage students in creating models that describe phenomena or situations specific to science (Cordry 2010;Efthimiou and Llewellyn 2006;Robinson 2008), engineering (Shakerin 2006), or economics (Anderson and Sherman 2010). We have also shown that the literature on FPs promotes problem-solving competencies in contextualized situations in the teaching and learning of mathematics Gorgorió 2014, 2018;Ärlebäck 2009;Czocher 2016Czocher , 2018Ferrando et al 2017;Gallart et al 2017;Keune and Henning 2003;Peter-Koop 2009). All these studies have in common that they confront students with accessible realistic situations and require an analysis using the Fermi method as a first attempt to create a model, allowing the students to develop their methods and solutions by discussing these among themselves.…”

“…Lastly, Czocher (2016) used FPs with engineering students and confirmed that the modeling processes needed to solve a FP are complex even for these students, requiring them to regulate their modeling processes by monitoring how their immediate goals or subgoals are related to the problem statement. In a follow-up study, Czocher (2018) showed that college students do not construct their models independently of validation, but that validating is an integral part of the model construction process.…”

“…Given this recommendation from STEM education research to focus on real world problems, and motivated by recent research carried out on modeling in the field of mathematics education showing that Fermi problems (FPs) can be useful in introducing mathematical modeling at educational levels ranging from primary to tertiary (Albarracín and Gorgorió 2014;Ärlebäck 2009;Czocher 2016;Peter-Koop 2009), we focus our review on what FPs have to offer in relation to STEM education and twenty-first century competences.…”

Precision, Priority, and Proxies in Mathematical Modelling

“…The interdependency of phases of modelling with individuals' knowledge leads to idiosyncratic and non-linear individual modelling routes (Ärlebäck 2009;Borromeo Ferri 2006Czocher 2016). The term idiosyncratic responses means that making sense of, or responding to, student work on modelling tasks, even in tasks purportedly as straightforward as those with intended solutions, is difficult.…”

Students Estimating Large Quantities: From Simple Strategies to the Population Density Model

“…From the perspective of Mathematical Education, Ärlebäck (2011) states that working with Fermi problems may be useful to introduce modelling to the classrooms for several reasons: 1) they are accessible to students of different educational stages and do not require any type of previous mathematical knowledge; 2) they hold a clear relation to the real world; 3) they force the students to define the structure of the relevant information; 4) being open problems that are not associated with any specific knowledge, they require the student to elaborate a resolution strategy; 5) not offering numerical data, the students should estimate several quantities by themselves; and 6) they promote discussion among students. In fact, complex modelling processes have been identified in high school and undergraduate students while solving problems Fermi problems (Ärlebäck, 2009;Czocher, 2016).…”