Design of a Simulation Game for the Learning of Mathematics

This chapter provides the theoretical and methodological background for the design of simulation games; within this context attention will be focused on the teaching model and the characteristics of the games that have been used in the research. Although aware of the fact that the process of acquiring mathematical knowledge is both complex and non linear, we present the guided stages of the work, in each of which we shall describe the teaching materials employed to help further the didactic aims.

A Review of Previous Studies

The chapter presents a critical analysis of the literature on simulation games identifying the research direction along which the studies conducted up until now have been following and the issues that have emerged during the research. On the basis of these considerations, a choice can be made of the most suitable simulation games to employ in a specific learning context.

Theoretical Reflections on the Construction of Simulation Games

With the aim of studying the process of transcoding and identifying the meaning assigned to specific research variables described in the present work, a number of reflections are presented in this chapter that, apart from supplying the methodological background for the teacher, allow researchers to identify the main factors that distinguish the traditional classroom lesson and the experimental method represented by simulandia games. In particular, reference is made to the work of Bloom, Gagné and Gardner and Bandura’s concept of self-efficacy.

Research Results

In this chapter, we present the research process followed in the work from the try out phase for each game, the testing of materials and methods, the definition of research protocols, thus the experimental procedure, the description data analysis and the interpretation of the results. Finally, we present the primary results of our work in the primary school classroom, where we proposed the Cartolandia experiment.

Methodological Proposals for Simulation Games

This chapter introduces the transcoding pattern, used in simulation games, to organize the language, the setting and the learning environment, defining the course of learning on various levels of abstraction. The aim is to facilitate the construction of a language that can be used in the processes of the mathematicization of reality and in math teaching in general. In order to give the reader a better understanding of the ideas and components of this process, an example of the transcoding pattern is provided before going on to describe the objective of our research the simulation game.

Research Outline

This chapter describes how the research was developed: the hypotheses and the decisions taken in the planning stage are explained and the documentation on the carrying out of the project provided along with the research protocols.

Description of Games

The chapter defines the criteria on which the choices for the design and realisation of the simulation games were based as well as the educational goals. Two simulation games are presented, one for geometry the other for arithmetic; these are supplemented by the relevant documentation, a description of the materials and the observation and verification instruments.

Epistemological Framework and Mathematical Learning

The aim of this chapter is to provide some indications on the background of our research regarding the use of simulation games for learning geometry and arithmetic. We reinterpret certain educational goals from the perspective of the anthropology of the virtual. Within this context, a number of important international commissions on math teaching are analyzed with particular reference to the difficulties involved in finding the right balance between the need for a formal mathematical language and teaching solutions to guide learning.

The Conduct of a Simulation Game

The chapter describes the phases of the simulation games presenting the role and functions of the game leader in each phase. The chapter also provides helpful advice on the different ways of conducting the simulation games and discusses the main difficulties that can arise in each phase and how to overcome them.

Simulation Games

This chapter develops a reflection on the theme and the different meanings that simulation can assume in applied research ambits, and deals with the problems connected to the lack of a specific ontology shared by the scientific community. In this context, after the reflections on the interconnections between simulation and reality with a view to integrating rather than superimposing one on the other, we propose a classification for simulation in the educational field that takes the didactic, social and political literature into account and underlines the need to construct an ontology that can overcome the semantic ambiguity and support a scientific debate, with particular reference to simulation games seen from the perspective of the ecology of human development.