Wiskundig actief: het ondersteunen van onderzoekend leren in het wiskunde onderwijs

Within mathematics education a distinction can be made between a more procedural oriented approach and an approach in which concepts and their relations take a central place. Inquiry environments offer students the opportunity to investigate a domain and to focus on conceptual aspects. In this research we developed a learning arrangement that has a set of guided simulations in mathematics as its core. These guided simulations are linked to a (standard) book and, in addition, classroom conversations and subject matter overviews supported the learning process. We emphasized six core activities which are central within mathematics and mathematical problem solving: abstracting, structuring, evaluating, interpreting, reasoning, and communicating. The learning materials, especially the simulation environment, were iteratively developed over a series of design experiment. These iterations led to a structure in the series of assignments which was as follows: - The starting point is a well-known situation for learners - Looking at the well-known context with ‘mathematical eyes’ - Generalising the newly derived mathematics - Looking at the general form with ‘mathematical eyes’ The support for the assignments was shaped according to the following step-by-step plan: Step 1: Consider which variable(s) you’re going to change and at which output you’re going to look at. Step 2: What are the different possibilities? Step 3: Try these possibilities. Step 4: Look back at the process. What can you conclude? The final version was evaluated against a standard classroom situation. A total of 11 schools, 20 classes and 418 students participated. Due to differences between the conditions on pre-test scores, post-test scores were corrected for pre-test scores. Results show that the traditional classroom condition outperformed the inquiry class on near transfer and procedural items. The inquiry condition acquired better scores on far transfer and conceptual (insight) items but these differences did not reach significance. Overall, it appeared that girls perform better in the traditional classroom setting, whereas boys seem to profit from an inquiry setting. It also appeared that the implementation of the inquiry (computer based) learning arrangement was hampered by many organizational and practical problems.