Empirical Results in Mathematical Modelling
with a Focus on Competence Measurement
Gabriele Kaiser (University of Hamburg, Germany & Australian Catholic University, Australia); Stanislaw Schukaljow (WWU Münster, Germany)
In the symposium the current state-of-the-art empirical results in mathematical modelling will be discussed focusing especially on modelling competencies, their description and measurement.
Based on a literature review of the most recent empirical studies on mathematical modelling and its teaching and learning by Gabriele Kaiser and Stanislaw Schukaljow, they will introduce the theme of the symposium and provide an overview on the current discussion. Based on the fact that on the one hand there exists a high number of empirical studies on the teaching and learning of mathematical modelling, however, on the other hand, there is a strong need for more studies with clear conceptualisations following rigorous standards, the symposium aims at discussing exemplary studies in this field.
The following selected studies will be described, which discuss specific aspects of the conceptualisation and measurement of modelling competences:
Gloria Stillman (Australian Catholic University, Australia): Mathematical modelling competencies and their measurement in an educational context – an overview
Alina Alwast (and Katrin Vorhölter) (University of Hamburg, Germany): Conceptualisation and measurement of metacognitive competencies as sub-competencies of modelling competencies
Serife Sevinc (Middle East Technical University, Turkey): Assessment of modelling competencies in early years (K-2 Level): a toolkit for teachers and researchers
Corey Brady (Vanderbilt University, USA): Class presentations of modelling solutions: A setting for individual and group modelling competencies
On Mathematical Modeling Contests
Jinxing Xie (Tsinghua University); Solomon Garfunkel (COMAP)
The Consortium for Mathematics and its Applications (COMAP) first organized the Mathematical Contest in Modeling (MCM) in 1985. Now more than thirty years have passed and the contest has expanded and is getting more and more popular all around the world, especially in the United States and China. The aim of the contests is to give students an opportunity for practicing the whole mathematical modeling process; to improve students’ understanding of mathematics, especially mathematical modeling; to enhance students’ motivation for learning and applying mathematics; and to cultivate students’ overall competency (creativity/innovation, collaboration and practice competencies).
The aims of this symposium are:
To introduce the aims, scope, organization and achievements of the most popular mathematical modeling contests all around the world, in particular, for the contests MCM/ICM/HiMCM, CUMCM and IMMC;
To analyze how the unique features of the contests help to improve students’ mathematical modeling competency;
To introduce how the contests influence mathematical modeling education;
To discuss the advantages and disadvantages of the contests;
Tentative schedule of the symposium:
Solomon Garfunkel (COMAP): An introduction to MCM/ICM/HiMCM (20 minutes)
Jinxing Xie (Tsinghua University): An introduction to CUMCM (20 minutes)
Ross Turner (ACER - Australian Council for Educational Research): An introduction to IMMC (20 minutes)
Free discussion (30 minutes)
Learning to Solve Real Life Problems
Through Statistical Models and Modelling
Jonas Bergman Ärlebäck (Linköping University, Sweden); Takashi Kawakami (Utsunomiya University, Japan)
Now more than ever, humans need models to cope with, interpret and make critically sense of data in various forms in their private and professional lives. In particular, when solving real world problems, it is important to develop models and skills that facilitate the ability to critically look beyond the collected or available data. This includes acknowledging and learning to tackle the limitations of different models, diagrams and plots of data as well as how these facilitate what attributes of the data becomes discernible and what attributes are suppressed.
This symposium focuses on aspects involved in solving real life modelling problems using statistical models and modelling in educational contexts. The aim is to initiate a discussion and start to elaborate on the connections, boundaries and boundary crossings between research on mathematical models and modelling to solve real world problems and the use, teaching and learning of statistical models and modelling.
The symposium welcomes more papers and studies to discuss and if you are interested in participating in the symposium please contact Jonas Bergman Ärlebäck (email@example.com). As to date, the following paper will be briefly presented (7-10 minutes each), followed by joint work and an open round table discussion:
Peter Frejd (Linköping University, Sweden): Statistics models and modelling – an ICTMA perspective.
Pauline Vos (University of Agder, Norway): Grade 8 students to visualize and mathematically model industrial processes through Sankey diagrams.
Takashi Kawakami (Utsunomiya University, Japan): Data-based modelling to combine mathematical, statistical, and contextual ideas: Boundary interactions between mathematical modelling and statistical modelling.
Jonas Bergman Ärlebäck (Linköping University, Sweden): The red book activity – a model eliciting activity to introduce and initiate a section on statistics.
Interdisciplinarity In Mathematical Modelling
Angeles Dominguez (Mexico) and Mogens Niss (Denmark)
By its very nature, mathematical modelling deals with aspects of the world outside mathematics itself, and more often than not with other subjects and scientific disciplines to which mathematics is not the primary interest in and of itself but nevertheless a very helpful or even essential companion. This implies that mathematical modelling involves much more than just mathematics.
Now, mathematical models have very different roles in different extra-mathematical domains and disciplines, and the interplay between mathematical modelling and extra-mathematical substance, including extra-mathematical theories, varies greatly amongst and across domains. In some disciplines and contexts, mathematical modelling is fully integrated in and inseparable from the very concepts and theoretical constructs of the domain (e.g. in Newtonian mechanics, thermodynamics, actuarial science, and mathematical economics), whilst mathematical modelling in other disciplines and contexts is a sort of "add-on" to the concepts and theoretical constructs of the domain (e.g. in population dynamics, geography and macroeconomics, but also in, say, solid state physics). Moreover, those who profess disciplines that are "consumers" of mathematics typically have experiences, views and priorities that differ from those of mathematicians and mathematical modellers, which gives rise to very interesting issues and opportunities for interdisciplinarity. These facts are, of course, significant to the teaching and learning of mathematical modelling. Therefore, the spirit of this symposium is to elucidate and discuss the state of affairs with regard to mathematical modelling in different disciplines from different angles and perspectives, with a particular focus on the actual or potential impact on mathematics education.
The structure of the 90-minutes symposium is as follows:
1. Introduction to the symposium by Angeles Dominguez (Mexico)
2. Presentation by Peter Galbraith (Australia)
3. Presentation by Itzel Hernandez-Armenta (Mexico)
4. General discussion of the points and issues raised, moderated by Angeles Dominguez (Mexico) and Mogens Niss (Denmark)
5. Concluding remarks by Mogens Niss (Denmark)