Developing Mathematical Thinking and Attitudes through Geometry along Secondary School or College Verónica Hoyos and Harry Silfverberg Universidad Pedagógica Nacional (Mexico) and University of Tampere (Finland) vhoyosa@upn.mx and harry.silfverberg@uta.fi Introduction Many mathematicians share Hawking’s view that “Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.” (Hawking, NCTM, 1989, p. 35. Cited in Clements and Battista 1992, p. 420). In that way they contrast those branches of math that use strategies for procedures or algorithms against those more related to developing mathematical intuition, particularly geometry. They consider geometry to be one of the branches of math least contaminated by rules, formulas, or algorithms in discovering and solving problems. Yet Math itself recognizes this feature, problematic if we ponder the teaching and learning of Geometry. In effect, more evidence has probably come out on low student performance in solving geometry tasks, compared with other areas in the math curriculum such as algebra or arithmetic. It is also likely that classroom teachers leave geometry subject matter at the end, and finally not reaching it (see for example Hoyos 2004). Although great efforts are made to compile, systematize, and disseminate research on the teaching and learning of geometry, such as what the NCTM does (NCTM 2000), it is probably time to guarantee a stronger impact and cap them off with proactive results (see Blair 2004, Gawlick 2004, Yevdokimov 2004) or contemporary alternative approaches. Finally, looking to replicability or coverage of an approach, it might be apropos to bring in the notion of mathematical literacy as Gellert (2004) does to clarify the pertinence and completeness in the deployment of specific teaching materials. Gellert has identified “fundamental tensions between the development of new didactic material and the cognitive style and daily routines of practicing teachers” (ibid 163), and “discusses whether the emphasis on mathematical literacy affects conceptions of didactic material and how didactic material for the development of mathematical literacy can look like.” (ibid 164) Curriculum for School Geometry Some modifications are notable between NCTM’s 1989 curriculum standards and its most recent edition in 2000 of Principles and Standards for School Mathematics. Now, the geometry standard for grades 6-8 and 9-12 call for students to - Analyze characteristics and properties of two –and three—dimensional geometric shapes and develop mathematical arguments about geometric relationships; - Specify locations and describe spatial relationships using coordinate geometry and other representational systems; - Apply transformations and use symmetry to analyze mathematical situations;