Modelling in Science Education and Learning - Vol. 15, Núm. 1 (2022)

Tabla de contenidos

Opening Remark
Conception and reflection of a university seminar concerning realistic modelling in mathematics education
Choreographies for musical fountains
Interpreting and validating models of loans
A Mathematical Modelling Unit for First-Year Engineering Students
Autumn School Mathematical Modeling – a cooperation between ZFM and TUDa
Compartment models to study human impact on climate change
Case Study on Students’ Mathematical Modelling Processes considering the Achievement Level
Digital Tools to Enable Collaborative Mathematical Modeling Online
Concept and structure of the Hamburg Modeling Days
Teachers' and students' perspectives on modeling projects

URI permanente para esta colecciónhttps://riunet.upv.es/handle/10251/180403

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Opening Remark
(Universitat Politècnica de València, 2022-01-29) Humenberger, Hans; Siller, Hans-Stefan
[EN] Mathematical modelling is a process in which individuals use mathematics actively in real and meaningful contexts. Dealing with real problems, issues or contexts mathematically important and relevant aspects can be identified, realised and implemented. This approach – starting from the concrete problem – makes mathematical concepts, tools and processes more comprehensible and understandable. In the last decades the topic of mathematical modelling in mathematics education has been discussed exhaustively within science. As a guest editors for MSEL, we report here on mathematical modelling in German speaking countries based on school practice examples or on project related perspectives.
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Teachers' and students' perspectives on modeling projects
(Universitat Politècnica de València, 2022-01-29) Vorhölter, Katrin; Haier, Karoline
[EN] Mathematical modeling can be promoted in regular lessons as well as in project form. Both options have advantages and disadvantages and provide different challenges, but also opportunities for students and teachers. Since 2001, teachers in Hamburg have the opportunity to participate with their students in modeling projects organized by members of the University of Hamburg. In this paper, the perspective of teachers, some of whom have been participating in modeling activities for more than five years, on the opportunities, but also on the difficulties of participation are presented. In addition, the views of over 200 students regarding their participation in the modeling days are outlined.
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Concept and structure of the Hamburg Modeling Days
(Universitat Politècnica de València, 2022-01-29) Vorhölter, Katrin; Freiwald, Janne
[EN] In Germany, there is quite a tradition of modeling projects, carried out by different universities all over Germany. Since 2001, different modeling projects has been conducted by the working group on Didactics of Mathematics of Department of Education of the University of Hamburg. In this paper, the current project, the Hamburg Modeling Days, is described in detail. One goal of this project is to enable students to gain experience in working on modeling problems and to acquire modeling competencies. Furthermore, prospective teachers are supported in their professionalization for teaching mathematical modeling, especially with respect to the supervision of students working on modeling problems. Finally, practicing teachers are in the implementation of modeling problems in mathematics classes.
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Digital Tools to Enable Collaborative Mathematical Modeling Online
(Universitat Politècnica de València, 2022-01-29) Schönbrodt, Sarah; Wohak, Kirsten; Frank, Martin
[EN] To enable collaborative modeling activities online digital tools are essential. In this paper we present a holistic and adaptable concept for the development and implementation of modeling activities – which could especially be fruitful in times of homeschooling and distance learning. The concept is based on two digital tools: Jupyter Notebooks and a communication platform with video conferences.We carried out this concept in the context of two types of modeling activities: guided modeling days, where the students work on previously prepared and didactically developed digital learning material, and modeling weeks, in which the students work on open problems from research and industry very freely. In this paper the usage of Jupyter Notebook in modeling activities is presented and illustrated with the example of the optimization of a solar power plant. On top, we share our experiences in online modeling activities with high-school students in Germany.
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Case Study on Students’ Mathematical Modelling Processes considering the Achievement Level
(Universitat Politècnica de València, 2022-01-29) Ostkirchen, Friederike; Greefrath, Gilbert
[EN] Heterogeneity can be taken into account in the classroom by using self-differentiating tasks. From a mathematical-didactic point of view, modelling tasks are of particular interest in this regard because of this. The paper focuses on the heterogeneity dimension of mathematical achievement and modelling competence of 15-year-old students. First results of a case study will be described in how far the processes of a modelling task vary with regard to the aspect of achievement levels.
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Compartment models to study human impact on climate change
(Universitat Politècnica de València, 2022-01-29) Hattebuhr, Maren; Frank, Martin
[EN] Climate change is subject to lively public discussions. Especially the question of whether climate change is manmade is a central point of contention. Since climatic processes are interleaved and complex, it is difficult to evaluate public, political or scientific statements. In this work, we look at mathematical models behind climate processes on a simplified level. We present a simple model of the Earth?s energy budged developed by high school students themselves during a project week. The model allows the students to compute the global Earth?s surface temperature and effects of varying solar activity and land surface changes. More precisely, the model describing the energy budget of the Earth forms a systems of partial differential equations and can be linked to compartment models. We show how this mathematically challenging question can be didactically reduced in such a way that students can be enabled to develop, solve and extend compartment models independently without having been taught the theoretical background. We implemented this course as an interactive online workshop and present our experiences with gifted student groups. We believe that our material presents an opportunity to demonstrate the power of mathematical modeling, to understand natural phenomena, and to critically reflect on discussions.
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Autumn School Mathematical Modeling – a cooperation between ZFM and TUDa
(Universitat Politècnica de València, 2022-01-29) Kiehl, Martin
[EN] Since 2000 the Zentrum f¨ur Mathematik in Bensheim (ZFM) and the Technical University Darmstadt (TUDa) have organized an annual autumn school for mathematically highly talented pupils in their last year of school. For one week, the participants work in groups on application problems, which first need to be transformed into mathematics and then be solved by mathematical analyzation and numerical approximation and implementation on a computer. Finally, the results are presented. The problems are very realistic. Only minor details may be skipped, to make the problem easier to handle and to focus on the main issue at hand, but only if they do not affect the basic result. For some of the problems there exist similar, but much simpler, counterparts that can be solved in a shorter time period even in a usual school setting. Solving those simple problems opens the outlook to the hard problems if they are mentioned before. This paper examines two applications that led to mathematical problems from analysis and geometry.
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A Mathematical Modelling Unit for First-Year Engineering Students
(Universitat Politècnica de València, 2022-01-29) Durandt, Rina; Blum, Werner; Lindl, Alfred; National Research Foundation, South Africa
[EN] This paper is practice-oriented and reports on a mathematical modelling unit specifically developed for first-year engineering students in a South African context. The main idea with the unit was to foster students’ mathematical modelling competency development. This idea supports an essential goal of mathematics teaching, that is to enable students to solve real - world problems by means of mathematics. The unit consists of five lessons and several tasks, carefully planned to consider students’ mathematical pre-knowledge, the demands of the first-year mathematics (calculus) curriculum and the intended competency development. The unit was linked to the mathematical topic of functions and taught for different groups of students according to two different teaching designs, similar to the designs used in the German DISUM project. 144 first year engineering students from the extended curriculum programme of a large public university were divided in three groups and exposed to the unit. An empirical evaluation of the intervention (with a pre-post-test design) showed a significant competency growth for all groups, with substantial differences, dependent on the teaching design. Some strengths and shortcomings of the unit will be identified and implications for future practice will be discussed.
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Interpreting and validating models of loans
(Universitat Politècnica de València, 2022-01-29) Dorner, Christian
[EN] Due to developments in the financial marketplace, digitalization of finance and easy access to financial products, financial literacy is becoming increasingly important. The paper at hand introduces parts of a learning environment for mathematics classes that focuses on mathematical modelling and financial literacy. After theoretical considerations, two worksheets are presented, which deal with influences of the interest rate on the repayment of loans. Based on the description of a test run, the usability of the worksheets in class is concluded.
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Choreographies for musical fountains
(Universitat Politècnica de València, 2022-01-29) Bracke, Martin; Capraro, Patrick; European Social Fund
[EN] This paper describes different possibilities to answer the question of automatically creating a choreography for musical fountains using mathematical modeling. The possibilities for an implementation range from a short project in the middle school, which has large parts in mathematics, to long-term projects, which deal with the physical background, an implementation with the help of the computer and in the highest expansion stage even a technical realization. In the article different variants are described, supplemented by experiences from practice and extension possibilities are pointed out. All in all, the readers should be enabled to design and practically implement their own project according to the individual local conditions such as time frame, learning level of the target group and possibilities for interdisciplinary cooperation. (This article is a translation and update of the German first edition Bracke, M. & Capraro, P. (2021)).
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Conception and reflection of a university seminar concerning realistic modelling in mathematics education
(Universitat Politècnica de València, 2022-01-29) Ableitinger, Christoph; Humenberger, Hans
[EN] In this article we primarily want to share our experiences and reflections concerning a special course at the University of Vienna (see chapter 2). The topic of this seminar was “modelling and modelling problems”and the aim was twofold: On the one hand student teachers themselves should gain experience in working on a modelling problem (small groups of 3-5 persons), on the other hand they should get first experiences to create modelling problems for students at school (grade 8-11) and to supervise their modelling processes during a modelling day at school. These skills are crucial for prospective teachers if they should implement the idea of “modelling”later in their professional life as teachers in classroom. In order to make clear our personal view on modelling and modelling problems (What are proper modelling problems? What is the difference between modelling problems and dressed-up word problems? Etc.) –which is necessary to properly understand Section 2 –we first outline our corresponding approach in Section 1.

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