Professor ANG, Keng Cheng (Nanyang Technological University, Singapore)
Ang Keng Cheng is an Associate Professor at the National Institute of Education (NIE), Nanyang Technological University, Singapore. Currently, the Associate Dean for Higher Degrees, Dr Ang was formerly the Head of the Mathematics and Mathematics Education academic group at the NIE. His research interests encompass mathematical modelling in various biological and medical settings (such as blood flow problems, epidemics and tumour growth), numerical and computational methods for partial differential equations, as well as the teaching and learning of mathematical modelling, including teacher education. His most recent work includes the setting up of an online resource centre for teachers of mathematical modelling, and the publication of a book on mathematical modelling for teachers.
Exploring the Nexus Between
Computational Thinking and Mathematical Modelling
Computational thinking has been a subject of much discussion in education in recent times and is considered as one of the key skill sets for the future by educators and policy makers in many countries. This increased interest in computational thinking was probably sparked by Wing, who views computational thinking as a “fundamental skill for everyone” (Wing, 2006). Since then, many schools have introduced coding and programming to students, sometimes very early in their education years, in a bid to help them develop computational thinking. There are also numerous informal “coding schools” that offer lessons in programming to anyone who wants to learn, sometimes for free. Though there have been claims that computational thinking improves and enhances certain cognitive abilities in other domains, its actual impact on raising competencies in these areas has yet to be studied thoroughly (Denning, 2017).
In this paper, we explore and explicate the role of computational thinking in mathematical modelling, and examine the relationship between them. Examples from the different modelling approaches will be used to contextualize this relationship, and to demonstrate that mathematical modelling does indeed provide an excellent platform for the use, practice and development of computational thinking. Some of these examples are drawn from other sources (such as from Ang, 2004, and Ang, 2019), but are now presented from the perspective of employing computational methods in the design of the solution to the modelling problem. In addition, these examples will illustrate how computational thinking fits into mathematical modelling naturally in certain modelling situations. The paper concludes with questions that may lead to further research and exploration into this relatively new but potentially significant area in mathematical modelling.
Ang, K.C. (2004). A simple model for a SARS epidemic. Teaching Mathematics and Its Applications, 23(4), 181–188.
Ang, K.C. (2019). Mathematical Modelling for Teachers: Resources, Pedagogy and Practice, Routledge: London.
Denning, P.J. (2017). Remaining trouble spots with computational thinking. Communications of the ACM, 60(6), 33–39.
Wing, J.M. (2006). Computational Thinking. Communications of the ACM, 49(3), 33–35.
Professor Borromeo Ferri, Rita (University of Kassel, Germany)
Rita Borromeo Ferri studied Mathematics and Geography, received her 1st and 2nd State Exam to be a full teacher for primary and secondary schools. Since 2011 Rita is a Professor of mathematics education at University of Kassel and was a Visiting Professor at University of Hamburg from 2007 to 2011. In 2004 she got her doctoral degree (Dr.phil.) and in 2010 her Habilitation in Mathematics Education at University of Hamburg. She worked as a Guest Professor at Teachers College of Columbia University in New York City in 2013 and 2014. In 2010 Rita got a Teaching Award from the University of Hamburg and in 2018 she won again a Teaching Award from the Ministry of Science and Education of the State of Hesse for the University Seminar “Modelling Days”. In 2016 she was awarded from the Stifterverband and the Daimler Benz Foundation for the project MINTERFACE, because this project encourage university students in STEM-fields to finish their studies by connecting them with industry and internships in companies. Rita was Vice-Chair of ICTMA-14 in Hamburg and gave an invited Regular Lecture at the ICME 12 in Seoul. Her research areas are Mathematical Modelling in school and teacher education, Interdisciplinary Mathematics Education, cognitive processes while learning mathematics and diagnostically competencies of pre- and in-service teachers in secondary and vocational schools.
Mandatory Mathematical Modelling in School –
What Do We Want Teachers to Know?
Defining mathematical modelling as a mandatory content for schools is taking place in more and more countries around the world. Also many educational policy makers recognized in the meantime that mathematical modelling activities can be a fruitful way to prepare and inspire students for their future professional and everyday life and broaden up their view on mathematics and thus for further STEM-fields. As a consequence of this encouraging development of mathematical modelling as an inherent part of school curricula, mathematics teachers who are able to conduct quality modelling lessons are needed. Teacher education in mathematical modelling is the basis and the starting point for modelling lessons to take place in schools. Within the international discussion one can find several best practice examples of teacher education in mathematical modelling, which differ in regional, national and cultural aspects.
So, what do we want the teachers to know? The lecture tries to shed light on this difficult question. It refers, on the one hand, to the state-of-the-art of international research on teacher education in mathematical modelling and, on the other hand, to a current empirical study on measuring teacher competencies for mathematical modelling in Eastern and Western countries. The lecture closes with an outlook for future research in teacher education in mathematical modelling.
Professor Rodriguez-Gallegos, Ruth (Tecnológico de Monterrey, Mexico)
Ruth Rodríguez Gallegos is a Research Professor in the National Graduate School of Humanities and Education at the Tecnológico de Monterrey since August 2014. Ruth Rodríguez Gallegos had worked as an Associated Professor in the Mathematics Department in the same institute, Monterrey Campus since 2007. She is a Math Education Researcher and Member of the National Researcher System and of the Mexican Committee of Educational Researchers. She was the President of the Executive Committee and Member of the Network of Centers for Research in Mathematics Education (2014-2017). Since 2009, she has coordinated the faculty academy of differential equations in the Mathematics Department (Tec de Monterrey). She is a thesis advisor and professor in the graduate programs of Education and Educational Technology and in the PhD program in Education at Tecnológico de Monterrey. Her interests are the teaching and learning of mathematics for future engineers through modeling and technological applications and the construction of a bridge between the discipline of mathematics education and the community of engineering education. She also participates in 2016 as a Mentor at the international Program 1,000 Girls, 1,000 Futures and she collaborates with the Equality Committee at Tecnologico of Monterrey to enhance the women participation in the STEM (Science, Technology, Engineering and Mathematics) fields.
Modelling and Simulation of Complex Problems:
a Dialogue between Math Education and the Community of Engineers
The main goal of this lecture is to show the importance of building communication bridges between two apparently disjoint academic communities: the mathematicians’ and the engineers’. The starting point is an overview of an approach to teach mathematics through modeling and simulation of real phenomena at a private university in the northeastern of Mexico, which mainly focuses on the training of future engineers.
The intention in this conference is to first show some background about the teaching and learning of mathematics through an overview of modeling. Later on, some reflections and limitations of studies conducted from a particular theoretical perspective are presented to undertake more comprehensive studies on engineering education for the 21st century. Several generic skills are required for math colleagues to expand their vision of the first approach on modeling and simulation of complex phenomena and social nature. In particular, the above is exemplified by the introduction of holistic and / or systemic thinking in the training of engineers in a specific course of Differential Equations (sophomore year). Through the introduction of a new language and vision of the phenomena, qualitative studies can give feedback that allow the introduction of a new vision, a new approach and a new language for modeling.
In the context of a change of academic programs in an educational institution, we rethink the need to modify the mathematics courses for future engineers to promote an integrated curriculum with STEM disciplines. The need for building communication bridges between the mathematics and engineering education communities seem to be fundamental in order to rethink the goals of mathematics education to be prepared to face the challenges posed by today's changing situations. The results and experience of mathematics professors that teach engineering students allow to see some advantages of incorporating new ways of visualizing and understanding phenomena. Furthermore, these allow students to have a new vision of mathematics and deeper understanding of several math concepts.
Professor XU, Binyan (East China Normal University, P. R. China)
Binyan Xu is Full Professor in the College of Teacher Education of East China Normal University. She earned a B. Sc. degree in mathematics from East China Normal University in 1986, and a Ph.D. degree in mathematics education from University of Osnabrueck of Germany in 1994. Her research interests focus on the students’ mathematics core competences assessment and design of mathematics project to improve students’ engagement in mathematics activities in classroom. Now she is the co-chair of Local Organizing Committee of the 14th International Congress on Mathematics Education (ICME 14) in 2020 in Shanghai. Since 2017, she is the EC member of the International Commission of Mathematical Instruction (ICMI).
Mathematical Modeling in China Mainland: From Mathematical Modeling Competition to the Development of Mathematical Modeling Competence
Since the 21st century, the mathematics curriculum in mainland China has developed with an increasing emphasis on students’ competence, and the curriculum objectives have evolved from "Two Basics" to "Four Basics". The 2017 version of the high school mathematics curriculum standards promulgated in 2018 clearly proposes six Core Mathematics Competences for Chinese students to achieve “proper values, necessary personalities, and key skills”. This development of mathematics curriculum in mainland China is a reflection of the needs of society and the needs of talent training. My talk begins with a brief introduction to the development of the concept of Chinese mathematics curriculum.
As one of the six Core Mathematics Competences proposed in the new curriculum standards, Mathematical Modeling would be the most challenging in the mathematics teaching practice in schools of China. Teachers or students are no strangers to mathematical modeling, but in their eyes, Mathematical Modeling is one of the mathematical competitions for a small group of students who are talent and good at not only mathematics but also knowledge in many other fields. With Mathematical Modeling appears in the national curriculum standards, it would be learned and applied by every student in their school time.
How to move from mathematical modeling competition to teaching and learning mathematical modeling in schools, so to developing students’ modeling competences? What are the obstacles in the “going forward” process? Are we prepared for ways and resources to overcome these obstacles? Where do we get these methods or resources? My talk will discuss these issues.
First, the talk will analyze and compare the variety of functions of mathematical modeling competence in the mathematics curriculum and the mathematical modeling in the mathematics competition in China. Then the talk will report several investigations of mathematical modeling competence of middle school students or future mathematics teachers, and explore how middle school students perform mathematical modeling tasks, whether future mathematics teachers have a certain level of mathematical modeling competence. My talk will also analyze the confusion encountered in the school's mathematical modeling teaching, and then discuss how to build various resources and methods that contribute to the teaching of mathematical modeling, so that students’ mathematical modeling competence could be achieved in schools practices. Finally, it would lead to such a conclusion that mathematical modeling competition and the development of mathematical modeling competence in schools could complement each other with the same goal of promoting students’ ability/competency in solving real-life problems.