AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES

This paper is a product of a research that investigates the presence of Geometry in textbooks, that is part of project of a Theorem – Reflection on Geometry and Mathematics Education research group. The focus here is to present results of the international study: how textbooks present the concept of similarity? For this, a qualitative research were developed and textbooks of three collections from Brazil and three from United States were examined. A synthesis of the literature related to the search for textbooks and the teaching and learning of the concept of similarity is presented, and the theoretical framework explores similarity as positioned at the crossroads of geometry and number to describe the ways in which different textbooks approach it. Sequence of topics and tasks presented in each textbook are described and then comparisons are made. There were theorems and problem types that were presented consistently across all textbooks, but differences in expectations related to proof and the use of coordinates and geometric transformations were identified. Only textbooks in the US included the use of transformations and coordinates and placed more emphasis on formal proof. Implications for the teaching and learning of similarity are provided.