Increasing insightful thinking in analytic geometry using frequent visualisation and a synthetic approach

Increasing insightful thinking in analytic geometry using frequent visualisation and a synthetic approach Theoretical background and practical implementation As of 2014, synthetic geometry will not be part of the Dutch 'VWO – Mathematics B' programme anymore. Instead, the focus will be more on analytic geometry. Mark Timmer explored possibilities to connect the two disciplines in order to have students look at analytical exercises from a more synthetic point of view. 1. Introduction Although analytic geometry is a wonderful technique to prove a variety of theorems in Euclidean geometry in a convincing and easy manner, it rarely provides many insights. Secondary school students often apply it without any consideration of what they are actually doing. We conjecture that this leads to fragmented understanding. Rather than developing an overall picture of the geometric concepts the students are working with, the analytic and synthetic geometry remain isolated domains. This results in limited understanding of the mathematical structures at hand, and a limited set of techniques and strategies for solving exercises from these different domains. Analytic geometry becomes