Abstract
This work offers some insights coming from the use of the application Fractio Quest, which was developed in the Project Gamifying CLIL within a Mathematics Context, within the mathematics classroom. The app was conceptualized in principle for a CLIL approach to fraction learning. Focus is put on two complementary dimensions of usage: a pilot experiment conducted in Italy in 2020, which involved a grade 7 class and its mathematics teacher in using a preliminary English version of the app, and the development of supplementary materials for teachers. The chapter first discusses the challenges posed for teachers and students when the app is used in a foreign language and explores the language/content interplay fostered by the activity. Then, reflections on methodological aspects considered for the design of supplementary materials for teaching are presented. These aspects are framed into the CLIL framework and by following research trends in mathematics education.
TopTheoretical Background
Wide interest in the learning of fraction is shared among researchers in mathematics education and mathematics teachers. From an epistemological point of view, fraction is one possible representation and one crucial meaning of rational numbers among others (Kieren, 1976). Students commonly experience rational numbers in the real world as they deal with measurements or sales receipts, but they usually encounter fractions at school after being mainly acquainted with natural (whole) numbers, and this might create inconsistencies and misconceptions. Whole-number schemes can interfere with the learning of fractions to the extent to which children can apply whole number strategies to fraction problems: they sometimes view fractions as two separate whole numbers and deal with them accordingly (Hart, 1989) and this problematic can be tackled differently (Sun, 2019). More generally, the different ways in which rational numbers can be represented are a considerable source of misconceptions among students, together with the fact that many rules that are consistent within the natural number system are no longer applicable to rational numbers (like the existence of a successor for each natural number). Hart (1980) studied secondary school students at work with fractions and highlighted that, even though most of them could name the fraction which is represented by a region and dominated the initial ideas of the subject, more than a half of the students did not work on fractions as numbers, for example with dimensions expressed as fractions in a geometric problem that asks to calculate the surface of a figure. Other studies in mathematics education pointed out a gap between the use of signs and symbols in mathematics learning and the understanding of the associated concepts, often taking years for learners to grasp the functioning of the number representation system (e.g., Duval, 2006). As noted by Marmur et al. (2020) even the historical development of fractions (which existed for centuries as ideas connected to symbolic representations, before being fully legitimated as numbers) points out an ancient difficulty with the concept, which is not restricted to learners but touches upon teachers too (e.g., Osana & Royea, 2011).
Key Terms in this Chapter
Game-Based Learning: Learning that is facilitated by the use of a game taking advantage of its playful engagement (Whitton, 2012).
Fraction Literacy: Mathematical skills and knowledge about fractions.
CLIL: Acronym for Content Language Integrated Learning.
Content Language Integrated Learning: Dual-focused educational approach in which an additional language is used for the learning and teaching of content and language with the objective of promoting both content and language mastery to predefinite level (Maljers et al., 2010).