Christian Bokhove

Digital Tools for Algebra Education: Criteria and Evaluation

In the Netherlands, as in many other countries, the algebraic expertise of students graduating from secondary education is an issue. The use of digital tools for algebra education is expected to change epistemologies, activity structures and student achievement. Therefore, a study was set up to investigate in what way the use of ICT in upper secondary education might enhance the algebraic expertise of students. One of the first decisions to be made concerned the choice of appropriate digital tools. This paper describes the process of designing and using an instrument for evaluating digital tools. The conceptual framework guiding this process includes notions on symbol sense, instrumental genesis and formative assessment. The evaluation instrument is designed through a Delphi method and provides a blueprint of tool features that are relevant for the purpose of this study. The results show that such an evaluation instrument is valuable both for choosing appropriate digital tools and for making concrete the aims and expectations that researchers have on the issue of integrating technology in algebra education. The final instrument is presented and illustrated through examples implemented in different digital algebra tools.

Effects of Feedback in an Online Algebra Intervention

The design and arrangement of appropriate automatic feedback in digital learning environment is a widely recognized issue. In this article, we investigate the effect of feedback on the design and the results of a digital intervention for algebra. Three feedback principles guided the intervention: timing and fading, crises, and feedback variation. The intervention aims at improving algebraic expertise and is deployed in fifteen grade 12 mathematics classes in nine secondary schools. Results show that the use of feedback timing and fading, the creation of crises and feedback variation facilitates the acquisition of algebraic expertise, and that relevant feedback fosters algebra learning by decreasing the number of attempts needed for a task while improving the scores. We conclude there is potential in applying these design principles in an online algebra education design.

The problem of identifying misogynist language on Twitter (and other online social spaces)

Misogynist abuse has now become serious enough to attract attention from scholars of Law [7]. Social network platform providers have been forced to address this issue, such that Twitter is now very clear about what constitutes abusive behaviour, and has responded by updating their trust and safety rules [16].

Exploring classroom interaction with dynamic social network analysis

ABSTRACT This article reports on an exploratory project in which technology and dynamic social network analysis (SNA) are used for modelling classroom interaction. SNA focuses on the links between social actors, draws on graphic imagery to reveal and display the patterning of those links, and develops mathematical and computational models to describe and explain those patterns. Dynamic SNA extends SNA and builds on previous research on network change. Utilizing data from six videos from the TIMSS video study and a convenience sample of five observations of one teacher in a secondary school in the south of England, a methodology for dynamic SNA was applied to classroom interaction data. The results are in two ways relevant for this journal. Firstly, they show that recent developments in SNA might be usefully applied to furthering knowledge about the dynamics of classroom interaction. Secondly, the results provide an example of the use of tablet technology for fieldwork data collection.

Mapping Changes in Support: A Longitudinal Analysis of Networks of Pre-Service Mathematics and Science Teachers.

Abstract In England teachers of secondary school mathematics and science are in short supply and it is important to understand how pre-service teachers develop and maintain networks of support during their training year and the impact these networks can have on their training outcomes. The purpose of this study is to examine how changes to the size and composition of these support networks during the training year are associated with programme outcomes. The paper draws on social network theory to examine the nature of the support networks that develop around each pre-service teacher, and examines how supportive ties were initiated, maintained, and broken over the course of the training year. A survey design was utilised to collect data at four time points across the 2014–2015 academic year from a total cohort of more than 75 pre-service teachers. At all four time points, participants were asked to nominate those peers and others to whom they had turned during the previous month for different aspects of support. Results showed that the size and composition of support networks changed over time with significant differences in the development of the networks between pre-service teachers on school-led and university-led programmes.

Augmenting mathematics with mobile technology

This chapter describes two case examples of the use of mobile technology for mathematics. Building on the assumption that mobile learning has a positive effect on student attitudes and academic outcomes including STEM subjects (Hsi, 2007; Wu et al., 2012) we develop a theoretical lens for future studies for ‘mobile mathematics’. The two case examples describe how mobile technology could provide opportunities for ‘mathematics outside the classroom’. The first example describes a dynamic Ferris wheel, the second a static cathedral. Both examples demonstrate how ‘geo-location’ and ‘augmented reality’ features allow mobile technologies to bridge formal and informal mathematics learning (Lai et al., 2016).

Automated generation of “good enough” transcripts as a first step to transcription of audio-recorded data

In the last decade, automated captioning services have appeared in mainstream technology use. Until now, the focus of these services have been on the technical aspects, supporting pupils with special educational needs and supporting teaching and learning of second language students. Only limited explorations have been attempted regarding its use for research purposes: transcription of audio recordings. This article presents a proof-of-concept exploration utilising three examples of automated transcription of audio recordings from different contexts; an interview, a public hearing and a classroom setting, and compares them against ‘manual’ transcription techniques in each case. It begins with an overview of literature on automated captioning and the use of voice recognition tools for the purposes of transcription. An account is provided of the specific processes and tools used for the generation of the automated captions followed by some basic processing of the captions to produce automated transcripts. Originality checking software was used to determine a percentage match between the automated transcript and a manual version as a basic measure of the potential usability of each of the automated transcripts. Some analysis of the more common and persistent mismatches observed between automated and manual transcripts is provided, revealing that the majority of mismatches would be easily identified and rectified in a review and edit of the automated transcript. Finally, some of the challenges and limitations of the approach are considered. These limitations notwithstanding, we conclude that this form of automated transcription provides ‘good enough’ transcription for first versions of transcripts. The time and cost advantages of this could be considerable, even for the production of summary or gisted transcripts.

Supporting Variation in Task Design Through the Use of Technology

This chapter describes a digital intervention for algebraic expertise that was built on three principles, crises, feedback and fading, as described by Bokhove and Drijvers (Technology, Knowledge and Learning. 7(1–2), 43–59, 2012b). The principles are retrospectively scrutinized through Marton’s Theory of Variation, concluding that the principles share several elements with the patterns of variation: contrast, generalisation, separation and fusion. The integration of these principles in a digital intervention suggests that technology has affordances and might be beneficial for task design with variation. The affordances in the presented technology comprise (i) authoring features, which enable teacher-authors to design their own contrasting task sequences, (ii) randomisation, which automates the creation of a vast amount of tasks with similar patterns and generalisations, (iii) feedback, which aids students in improving students’ learning outcomes, and (iv) visualisations, which allow fusion through presenting multiple representations. The principles are demonstrated by discussing a sequence of tasks involving quadratic formulas. Advantages and limitations are discussed.

Designing Technology that Enables Task Design

Although there is considerable interest in the use of technology in mathematics teaching and learning, there has been little focus within mathematics education on the design of the technology itself, or on how technology design might facilitate task design. In this chapter, we address the question of how technology has been designed to enable task design through interviews with four developers of technology environments designed to facilitate the learning of mathematics. Questions ranged from more general ones concerning the purposes and challenges faced in designing the environments to more specific aspects concerned with task design, such as the management of instrumental genesis and the provision of feedback. We found that all designers are facing technical challenges due to rapid hardware and software changes which make it important to identify the crucial aspects of the technology to conserve and develop. Such aspects include maintaining an appropriate balance between flexibility and constraint as well as addressing issues such as the way in which the environment responds to student actions.

The Web Practice of Mathematicians on the Web: An Insight into Significant but Neglected Web Groups

In this paper, we describe the findings from a three-year multi-phased investigation into the Web practice of online mathematics communities. Our results indicate that the equivalent technologies that enable text-input or image-uploads without the need to understand programming languages have not been made available for the mathematics/ scientific communities to enable fluid communications. Given the global importance of mathematical and scientific collaborations, we argue that the mathematical and scientific communities are significant but neglected groups, and that more attention should be given to the user-interface designs to support fluid online mathematics communications.