JEE ISSN 2146-2674 Volume 8 Issue 2 2018 Contreras, Slisko, Rebollar 1 PRESENCE OF SITUATIONAL AND MATHEMATICAL MODELS IN MEXICAN MATHEMATICS TEXTBOOKS FOR MIDDLE SCHOOL: AN INITIAL CATEGORIZATION AND QUANTIFICATION Eugenia Hernández Contreras 1 Josip Slisko 2 Lidia Aurora Hernández Rebollar 3 Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla Puebla, Mexico eugene_he@hotmail.com 1 jslisko@fcfm.buap.mx 2 lhernan@fcfm.buap.mx 3 (Received: 08.06.2018; Accepted: 26.06.2018) Abstract Problem solving and, since recently, mathematical modeling are of a crucial importance in processes of learning and teaching school mathematics. Both processes are greatly influenced by the ways mathematics textbooks treat problem solving and mathematical modeling. Main objective of this documental research was to determinate basic features and quantify presence of situational and mathematical models in 480 problem formulations proposed by authors of Mexican of 29 mathematics textbooks for middle school (IX grade). The results show that students are not informed about (1) the differences between situational and mathematical models and (2) their role and importance in learning and practice of mathematical modeling. In addition, in many examples, complete or incomplete mathematical models are inserted into situational models (drawing or photograph). Finally, three selected problems with different visual complements were given to 43 students in order to explore which type of drawings (situational, mathematical or mixed) students carry out when asked to make them. Students’ performances were analyzed and compared with the common images (drawings and/or photographs) provided by mathematics textbooks to complement problems formulations. Keywords: Situational model, mathematical model, mathematical modeling, mathematics textbooks INTRODUCTION To promote deeper learning and 21st century skills, educators have to design and implement successfully those learning sequences that foster a cluster of cognitive competences: critical thinking, non-routine problem solving, and constructing and evaluating evidence-based arguments (Pellegrino & Hilton, 2013). Solving problems in mathematics education had always two related roles. One was to give students opportunities to learn mathematics through problem solving and the other one was to use mathematical problems as an evaluation tool to measure students’ learning progresses in formative and summative assessments. As many students weren’t successful in learning to solve problems, there was a big need to give them a few general ideas and steps that can be used strategically in solving almost any problem in school mathematics. The first systematic approach to solving mathematical problems, with a clear teaching purpose on mind, was given by Gerge Polya in his famous book “How to solve it. A new aspect of mathematical method” (Polya, 1945). Polya’s ideas were later elaborated, extended and popularized by Schoenfeld (1985) and became main focus of world