Irina Lyublinskaya

Symbolic Geometry Software and Proofs

1 IntroductionPrinciples and Standards for School Mathematics (National Council of Teachers ofMathematics [NCTM] 2000) advocates a unified approach to mathematics educationincorporating multiple strands in coherent focused elements. Special place in the NCTMstandards is provided for a reasoning and proof strand, emphasizing its place across themathematics curriculum:‘‘Reasoning and proof are not special activities reserved for special times or specialtopics in the curriculum but should be a natural, ongoing part of classroom discus-sions, no matter what topic is being studied. In mathematically productive classroomenvironments, students should expect to explain and justify their conclusions.’’(NCTM 2000)Dynamic Geometry software (Cabrilog 2007; Key Curriculum Press 2007) has facili-tated an inductive approach to geometry. These technologies have been widely adopted inthe last 20 years and a vast amount of creativity has been brought to bear on applying it tothe educational process. (Kunkel et al. 2007; Scher et al. 2004; Gaulik 2002; King andSchattschneider 1997). However, this technology is not without its shortcomings. First it is