Teachers' Struggling in Identifying the Semiotic Potential of Mathematical Board Games

Introduction

Games are often considered means for enhancing student motivation, interest, attention to the content, and content retention (Garris et al., 2002). These and other features of play are considered so relevant that some institutions suggest the use of games in mathematics education. For instance, in the Italian national curriculum for primary school, in the section about methods for the teaching of mathematics, we can read:

Among the different playful activities in which children may engage, we can first distinguish between free play and guided play, the latter consisting of adults structuring the play environment but leaving control to the children within the environment (Weisberg et al., 2013). Here we will consider games as guided playful activities. There is a large body of research about game-based learning, but not all the possible types of games received the same attention by educational researchers. For instance, literature about video-games is getting larger and larger (e.g., Yong et al., 2021), while board games are included in a small amount of studies (Ramani & Siegler., 2008). In this contribution, we define board games as those games that are played on a printed surface by one or more people usually sitting around a table (Parlett, 2018); they usually include the use of cards or dice. As testified by the available literature, board games can play an important role in the processes of teaching and learning mathematics (see next section) both from the affective and cognitive points of view. Researchers have noticed the opportunities provided by these kinds of games to offer an inclusive context allowing participation for students with different levels of mathematical competence (Stebler et al., 2013; Vogt et al., 2018). Also, specific board games have shown an impact in developing early number sense (e.g., Ramani & Siegler, 2008; Whyte & Bull, 2008). However, the introduction of board games in mathematics classes may require an attentive analysis of the affordances provided by the game in relation to the mathematical content that is the goal of the teaching intervention. There are empirical results showing that primary teachers can struggle in analyzing the potential of a given mathematical board game and then they may find difficulties in employing the game in their classes (Dorier & Maréchal, 2009). The aim of this chapter is to contribute to this stream of research by realizing an a priori analysis of the semiotic potential of the game ‘Shut the Box’ in respect to the development of foundational number sense (Andrews & Sayers, 2015). This analysis will be then compared with the results from two research cases. The studies refer about the analysis provided both by primary teachers who did not use the game and by teachers who used this same game in their classroom for a semester. We will contrast and discuss the results of the two research cases in terms of completeness of the teachers’ analysis in comparison to our a priori analysis.

Board Games In Mathematics Education

Potentialities of board games for mathematics education are as many as the different representations of numbers, geometrical shapes, calculation algorithms, and so on. There are several publications concerning the design and testing of board games for primary and secondary students (e.g. Campos & Moreira, 2016). Here we circumscribe our discussion to how board games can contribute to the development of foundational number sense (in the sense of Andrews & Sayers, 2015, as it will be better explained below).

Game-based learning is recognized as effective in promoting a positive disposition to the content (e.g. Garris et al., 2002) and this sound as an important affordance since students’ attitude towards mathematics is often influenced my several affective factors including emotions and self-efficacy (e.g. Di Martino & Zan, 2011). This is true also for other subjects, but there are features of some board games that appear to sustain abilities that are specifically mathematical; while we do not deny the importance of affective and meta-cognitive factors, here we focus on these cognitive aspects of learning.