Comparative didactic analysis of the teaching of calculus concepts in textbooks using the modeling eliciting activity (MEA) approach

Textbooks play a central role in mathematics education, structuring learning, guiding teachers, and influencing teaching practices (Remillard, 2005; Ball & Cohen, 1996).

This paper presents an analysis of secondary school textbooks using the theory of Modeling Eliciting Activities (MEA) and semiotic register theory (Duval, 1993). The MEA approach, created by Lesh et al. (1987), aims to develop open-ended, contextualized activities that encourage students to construct mathematical models applicable in various contexts.

The analysis of textbooks is conducted using the evaluation criteria proposed by Lesh and Doerr (2003), which examine authenticity and contextual relevance, openness and cognitive complexity, construction of mathematical models, transferability of models, communication and collaboration, and evaluation and feedback.

This study adopts a comparative qualitative approach focusing on the following textbooks from three countries (Morocco, Italy, and the Philippines):

• "Al Mofide en Maths", edition : DAR ATTAKAFA, 2018.
• "Manuale blu 2.0 di matematica", third edition, 2020.
• "Matematica blu 2.0", third edition, 2020.
• "Basic Calculus Learner’s Material", Department of Education, Republic of the Philippines. First Edition, 2017.
• "Precalculus Learner’s Material", Department of Education, Republic of the Philippines, First Edition, 2016.

To analyze these textbooks, an evaluation grid based on the six criteria proposed by Lesh and Doerr (2003) was developed and used to identify the presence and quality of modeling activities. Additionally, another grid was used to analyze the types of frameworks and semiotic registers employed in these textbooks.

Preliminary results show that most analyzed textbooks emphasize procedural exercises and offer limited opportunities for authentic modeling consistent with the MEA framework. Moreover, the use of semiotic registers is mainly restricted to symbolic representations, with limited coordination between graphical, tabular, and verbal registers, which may constrain students’ understanding and engagement in mathematical modeling processes.