Fra mekanisk procedure til forståelse: GeoGebra som ressource til udvikling af matematisk ræsonnement

Mathematical reasoning is recognized as one of the most important competencies in mathematics education. Not only, is it in itself, an important learning target, also it is fundamental as a means for learning and understanding of mathematics in general.
Experimental studies show that GeoGebra, an extensively used program by primary and lower secondary school mathematics teachers, has great potential to help foster students’ mathematical reasoning. However, teachers miss this potential, as they tend to use GeoGebra as a tool for substituting paper and pencil work with drawing and calculation rather than as a didactical tool for challenging and supporting students’ mathematical reasoning. The latter being perceived as particularly challenging for teachers to deal with.
This thesis is a product thesis, whose purpose is to investigate the didactic potentials and challenges of using GeoGebra to support the development of lower secondary pupils’ reasoning competency. The product, accessed through IT’s Reason, is designed in order to scaffold mathematics teachers in their work with reasoning and offer them professional development that enables them to support the students acquiring the competency in focus.
This thesis builds primarily on the theoretically oriented, interventionist and collaborative dimensions of design-based research. The qualitative data is collected in a co-learning process through three iterations of design, testing, and design adjustments in collaboration with three lower secondary school mathematics teachers and their 7th graders. This thesis uses data from qualitative participant observations, short video observations, and interviews.
The main finding is that the use of GeoGebra’s functions, specifically dragging and measuring, do have a positive effect on students' development of mathematical reasoning. Observations of classroom activity show compelling examples of students enhancing and promoting their mathematical understanding when working with GeoGebra. In addition, many students find the whole experience working with GeoGebra rewarding. However, the analysis of the qualitative data shows that the above-mentioned positive effect of using GeoGebra can only be achieved through the teacher’s intervention. This essential role of the teacher is emphasised throughout this thesis. It is proposed that the teacher can fulfil such a role using expectation and prediction games by asking the students to explain their constructions in GeoGebra and thereby shifting their focus from how to why in the process.
Analysis of the collected data also states that it is too late to introduce reasoning competency as late as at lower secondary level. It is important that focusing on reasoning is present throughout primary and lower secondary level, as developing reasoning takes time and requires great effort on the part of both teachers and students.
Therefore, it is essential that teachers raise their ambition regarding fostering mathematical reasoning and become more aware of how to embrace the challenges related to reasoning competency. Thus, it is crucial that teachers are supported and prepared for this work through professional development, where they gain knowledge and are offered strategies as well as didactic activities. Which should take place in an environment that encourages collective collegial reflection and with a predominant focus on practice, where co-teaching, professional and collegial sparring is offered as a path towards professional development.
Materials from workshops for teachers, tasks for students with examples and explanations have been organised in the above-mentioned product that is designed as an introduction to the topic “Mathematical reasoning through GeoGebra” and as a companion website for initiatives of professional development.