Michiel Doorman

Digital Technology and Mid-Adopting Teachers’ Professional Development: A Case Study

The integration of digital technology into secondary mathematics education is not yet a widespread success. As teachers are crucial players in this integration, an important challenge is not only to attract early adopters, but also to support mid-adopting teachers in their professional development on this point. The questions addressed in this Chapter are: which practices such mid-adopting teachers develop when starting to use technology in their mathematics classroom; and how these practices change over time while engaging in a project with colleagues and researchers. To answer these questions, theoretical notions of instrumental orchestration, TPACK and community of practice underpin the case study of two mathematics teachers from a group of twelve, who engaged in a project on technology-rich teaching. The data includes lesson observations, blogs and results from questionnaires. The results show the type of teaching practices the teachers develop and the changes in these practices. Even if these changes are modest and the impact of the community is limited, the teachers clearly became more confident in integrating technology in their teaching.

The Interaction Between Multimedia Data Analysis and Theory Development in Design Research

Mathematics education researchers conducting instruction experiments using a design research methodology are challenged with the analysis of often complex and large amounts of qualitative data. In this paper, we present two case studies that show how multimedia analysis software can greatly support video data analysis and theory development in design research. The software can (a) act as a type of mould for organising large amounts of data; (b) contribute to improving the trackability and reliability of the research; and (c) support theory generation and validation. We propose an integrated model that elucidates the complex process of data analysis by showing how each of the components that are involved in the data analysis procedures feeds into the emerging local instruction theory. The model combines the intricate cycles of coding and analysing raw video data with the cumulative cyclic process that characterises design research in mathematics education. Our experiences with this model may support other mathematics education researchers in the development of thorough and empirically supported local instruction theories from complex qualitative analyses.

The Effect of Online Tasks for Algebra on Student Achievement in Grade 8

Online resources are widely used for educational purposes, such as the training of skills. For algebra education in particular, online resources are expected to contribute to skill mastery in an efficient and effective way. However, studies that underpin these claims through a randomized experiment are scarce. To experimentally investigate the effect of online tasks for algebra, sixteen teachers each taught two grade 8 algebra classes, one randomly assigned traditional teaching and the other using an online algebra environment. In total, 842 students took part in a pretest, two posttests, and a retention test. Results show that the experimental group scored slightly below the control group on these tests. The main factors involved are students’ pretest scores and the schools’ experience with ICT. Possible explanations include a spill-over effect and a more superficial type of learning than expected in the experimental condition. These results do not confirm the hypotheses on the effectiveness of using online resources for algebra.

Algebra in Function

The function is a special kind of dependence, that is, between variables which are distinguished as dependent and independent. (…) This – old fashioned – definition stresses the phenomenologically important element: the directedness from something that varies freely to something that varies under constraint. (Freudenthal, 1983, p. 496).