Using Modeling and Simulation to Learn Mathematics

Using Modeling and Simulation to Learn Mathematics

Ruth Rodríguez Gallegos (Tecnologico de Monterrey, Mexico)
DOI: 10.4018/978-1-5225-2026-9.ch002
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Abstract

In this chapter, we present a specific approach on how to teach math through mathematical modeling and simulation. The literature review is presented from the Math Education Community and the advantages for the students using this approach focuses on how to apply Math in their professional lives. We also introduce a framework of reference on using matching technology to help the students make some transitions in the modeling cycle. Several examples from a course in an undergraduate program are shown and we develop some conclusions for basic education and for high school level. Previous research studies developed from a qualitative point of view have helped to demonstrate the potential use of this approach for students to achieve better understanding of this science.
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Introduction

Since the world is changing so quickly, it seems necessary to rethink the working schemes that have been used for a long time. According to different authors (Bourn & Neal, 2008; Fisher, 2011; Rodríguez, 2013; Rodríguez & Bourguet, 2014), the 21st century has brought different demands because we are living in a connected, global world, which needs to build teams with people from different cultures; a natural path follows that leads to rethinking education from various points of view. This paper aims to share an effort being made from the Mathematics Education perspective, especially in the effort of reformulating the intentions of math education to provide training in critical skills that the 21st century citizens require. Thus, it is important to review some key ideas previously pursued on substantially modifying the teaching of mathematics in the classroom by introducing the use of technology and simulation, as well as by incorporating the development of social, communication and teamwork skills in a math course.

From an international perspective, studies such as the Program for International Student Assessment (PISA) report (OCDE, 2009) state the need to train people in developing skills such as mathematical literacy. PISA defines mathematical literacy as the capacity to identify, to understand, and to engage in mathematics and to make well-founded judgments about the role that mathematics plays, as needed for an individual’s current and future private life, occupational life, social life with peers and relatives, and this person’s life as a constructive, concerned, and reflective citizen.

Subsequently, more specific studies (Bourn & Neal, 2008; Jhori 2009) aimed specifically at the population of future engineers, have made explicit the prevailing need that the basic education of an individual considers the fact that they should develop generic skills that complement and reinforce disciplinary skills. In particular, we highlight part of a report (Bourn & Neal, 2008) which aims to develop the global dimension in shaping the future engineer and emphasizes the need and importance of these skills in several areas.

Generic Skills from Bourn and Neal (2008):

  • 1.

    Holistic thinking, critical inquiry, analysis and reflection.

  • 2.

    Active learning and practical application.

  • 3.

    Self-awareness and empathy.

  • 4.

    Strong communication and listening skills.

Hence, the need to develop holistic thinking as an essential skill for students and future citizens of the 21st century is made explicit.

Based on the request of training students of basic education in this area, we decided to explore the importance of the development of the holistic thinking for the future engineers.

Since holistic thinking is also related to Systems Thinking (ST), our proposal is to think how the ST skills can be included from the perspective of math education. Bourn and Neal’s (2008) report mentions the work done by Senge (2006) in this regard and it became the trigger to show the advantages and benefits of incorporating systems thinking in a math class. It is our hope to shed some light on the wealth of integrating the two seemingly disjoint disciplines, Systems Thinking and Mathematics.

Although this study is analyzed from a qualitative paradigm, we have included some quantitative results obtained from an institutional survey. These results are shown only to illustrate the students’ ideas about the course in which we implemented our activity.

Key Terms in this Chapter

System: Isn't just any old collection of things. A system is an interconnected set of elements that is organized coherently in a way that achieves something. A system consists of three kinds of things: elements, interconnections and a function or purpose.

Reality: The world outside Mathematics.

Mathematical Literacy: The capacity to identify, to understand, and to engage in mathematics and to make well-founded judgments about the role that mathematics plays, as needed for an individual’s current and future private life, occupational life, social life with peers and relatives, and life as a constructive, concerned, and reflective citizen.

System Dynamics: A technique que allow to obtain models to explore possible futures or scenarios and ask “what if” questions in complex situations.

Mathematical Modelling: The relationship between Mathematics and the “reality”. Since a specific point of view, a didactical strategy to teach and learn maths showing at the student the application of this Science in their daily life.

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