Patterns and generalization: the influence of visual strategies 1 Ana Barbosa LIBEC, School of Education of Viana do Castelo, Portugal Pedro Palhares LIBEC, Universidade do Minho, Portugal Isabel Vale LIBEC, School of Education of Viana do Castelo, Portugal This paper gives a description of an ongoing study focused on pattern exploration and generalization tasks and justifies that study with respect to the literature. It promises to make a contribution to appreciation of the ways in which visual strategies can be used to enhance and enrich learners’ experience of generalization. The main purpose is to analyse the strategies and difficulties presented by grade 6 students when solving these activities, along with the role played by visualization in their reasoning. Preliminary results indicate that, in general, students prefer analytic approaches over visual ones and that, among the group of students that are most successful, the majority chooses a mixed strategy. THEORETICAL FRAMEWORK A quarter of a century ago, problem solving became a focus of school mathematics. According to recent curricular guidelines of several countries, one of the main purposes of mathematics learning is the development of the ability to solve problems. In spite of the growing curricular relevance of this theme over the last few years, several international studies (SIAEP, TIMSS, PISA) have shown that Portuguese students have low results when solving problems is required (Ramalho, 1994; Amaro, Cardoso & Reis, 1994; OECD, 2004). Pattern exploration tasks may contribute to the development of abilities related to problem solving, through emphasising the analysis of particular cases, organizing data systematically, conjecturing and generalizing. The Principles and Standards for School Mathematics (NCTM, 2000) acknowledges the importance of working with numeric, geometric and pictorial patterns. This document states that instructional mathematics programs should enable students, from pre-kindergarten through grade 12, to engage in activities involving the understanding of patterns, relations and functions. On the other hand, Geometry is considered a source of interesting problems that can help students develop abilities such as visualization, reasoning and mathematical argumentation. Visualization, in particular, is an important part of mathematical 1 Artigo publicado em Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, 2007, pp. 844-851.