GEOMETRIC CALCULATIONS ARE MORE THAN JUST THE APPLICATION OF PROCEDURAL KNOWLEDGE

Calculations are often viewed as the application of procedural knowledge or algorithms. In this paper, I argue that geometric calculations can be more than that. To prove this assumption, firstly I analyze a geometric calculation using the theoretical framework of proof schemes proposed by Harel and Sowder (1998). The theoretical analysis shows that solving a geometric calculation can provide the opportunities to learn transformational observations just as geometric proofs do. Secondly, by analyzing instruction data, I report how a teacher conveys the opportunities to learn transformational observations in terms Of scaffolding students in recognizing the geometric properties the diagram possesses and in inferring new measurements inside the diagram. In doing so, the teacher expects students to see the need for using transformational observations to form a solution.