Peter Boon

Algebra and Technology

An algebra curriculum that serves its students well in the coming century may look very different from an ideal curriculum from some years ago. The increased availability of computers and calculators will change what mathematics is useful as well as changing how mathematics is done. At the same time as challenging the content of what is taught, the technological revolution is also providing rich prospects for teaching and is offering students new paths to understanding. (Stacey & Chick, 2000, p. 216)

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 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.

Fine-Grained Cognitive Assessment Based on Free-Form Input for Math Story Problems

We describe an approach to using ICT for assessing mathematics achievement of pupils using learning environments for mathematics. In particular, we look at fine-grained cognitive assessment of free-form answers to math story problems, which requires determining the steps a pupil takes towards a solution, together with the high-level solution approach used by the pupil. We recognise steps and solution approaches in free-form answers and use this information to update a user model of mathematical competencies. We use the user model to find out for which student competencies we need more evidence of mastery, and determine which next problem to offer to a pupil. We describe the results of our fine-grained cognitive assessment on a large dataset for one problem, and report the results of two pilot studies in different European countries.