Textbooks for Bilingual Mathematics Classrooms: Analyzing the Cognitive Demand of Mathematical Tasks

Introduction

This research work focuses on the analysis of bilingual and non-bilingual mathematical textbooks of secondary education, from the perspective of types of tasks and cognitive demand. The study is developed in Andalusia (Spain), a monolingual region which holds the highest ratio of bilingual educative centres in the country. In bilingual schools in Andalusia, English predominates as the second/foreign language of choice and most of these schools have adopted the Content and Language Integrated Learning (CLIL) approach. This is an educational concept where the focus is on content and non-native language in an intertwined way (Coyle et al., 2010). The European Commission (Eurydice, 2006) expresses itself in similar terms by defining CLIL as an approach that goes beyond the mere learning of a language; it is more a question of language and non-language subject matter constituting objects of learning without there being a predominance of one over the other. This approach implies a more integrative methodology based on what is known as the 4Cs (Coyle et al., 2010): subject content, communication (language use and learning), cognition (learning and thinking processes) and culture (developing intercultural understanding and global citizenship).

The report on the management, competences and organization of bilingual education in Andalusia (Lorenzo, 2019) states the following findings about the Bilingual Program: it promotes the learning of the foreign language (English), benefits the learning of the Spanish language, does not affect the learning of the other subjects at the stage of Primary Education, does not affect the learning of the subjects at the stage of Secondary Education, and the measurements between the different socioeconomic and cultural index (SCI) levels in bilingual groups tend to homogenise.

In addition to the above, Lorenzo et al. (2010) claimed in previous research that bilingual programmes modify the school functioning and organisation, generating a more cohesive and interdisciplinary group work between teachers to update themselves in planning. Moreover, bilingual students who had joined a bilingual programme for the first time at the stage of Secondary Education, reached resemblant proficiency levels compared to the classmates who had previously performed a bilingual programme at the Primary Education stage. Assessments of the same bilingual programmes in the regions of Madrid, Extremadura and the Canary Island yielded similar results for, at least, the last year of Primary Education (García-Centeno et al., 2020).

In relation to Mathematics, research has shown that bilingual students display a higher mental activity and adaptability (Salekhova & Tuktamishov, 2020; Van Rinsveld et al., 2017), facing ambiguous or even unknown words in problem statements. In fact, bilingual students are more selectively attentive throughout the problem-solving processes than their non-bilingual partners, who tend to recognise specific elements to perform a direct execution of the operation without having understood or even read the whole statement. In general terms, bilingual students produced more detailed answers, fewer mistakes, and a more in-depth understanding of the task statement (Ambrose & Molina, 2014; Fernández-Ahumada et al., 2020).

Concerning academic literacy in mathematics, Moschkovich and Zahner (2018) defined this construct as the integrated view of three components: ‘mathematical proficiency’, ‘mathematical practices’ and ‘mathematical discourse’. The latter integrates a sociocultural conception to the traditional, from which it can be assumed that the teaching learning process occurs out of a static and established mathematical course. Therefore, mathematical discourses are conceived by the union of the perspectives of ‘vocabulary acquisition’ and ‘constructing multiple meanings’, employing the notion of discourses, and the situated perspective of learning mathematics, which adds the notion about what mathematical classes should foster in lessons.

Through discourses, learners participate in exchanging their own ideas and negotiating others by being immersed in a contextualised practice (Moschkovich, 2002), encouraging them to get involved, to reflect and to verbally engage in the given situation. An effort has been made towards the approach of this conception of mathematics in different educational contexts, which is upheld by its positive results, via legislation, given that the context of mathematics problems is now fundamentally understood as part of a sociocultural sphere.