Design considerations for facilitating mathematical learning online

This paper presents a graduate student’s reflections on the design of learning opportunities using the Desmos tool for carrying out mathematical activities and the online Zoom platform for facilitating mathematical learning. Using the theory of instrumental orchestration as our interpretative framework, we discuss the different types of orchestrations when a digital tool is used to support mathematical learning not in the familiar face-to-face classroom-based environment, but online instead. The contribution of this paper lies in the discussion of the design considerations and orchestrations to overcome the challenges of online learning and at the same time to capitalise on the opportunities it offers for mathematical learning

Students’ Justification Strategies on the Correctness and Equivalence of Computer-Based Algebraic Expressions

This volume emphasizes the role of effective curriculum design, teaching materials, and pedagogy to foster algebra structure sense at different educational levels

A case study of an expert in computational thinking in the context of mathematics education research

We conducted semi-structured interviews with three experienced mathematics education researchers with great expertise in the design and use of digital technologies, including programming skills, to investigate their views and perceptions on computational thinking (CT) and its impact on mathematical learning. In this paper we report on our findings from one of them, Mark, and we suggest ways for adapting the very recent Mathematical Digital Competency (MDC) framework to encompass CT practices and dispositions. Our aim is to offer insights into how CT is perceived and understood by him, by prompting him to reflect on his own CT practices and competencies. We offer suggestions for an MDC framework for mathematics teacher educators that encompasses CT

An exploratory study on mathematics teacher educators’ beliefs and understandings about computational thinking

This paper reports an investigation of mathematics teacher educators’ views and perceptions on computational thinking (CT) and its impact on mathematical learning. We conducted semi-structured interviews with experienced mathematics teacher educators, all of whom have extensive experience with the use of digital technologies for mathematical teaching and learning and report on data from two of them. Our aim is to offer insights into how CT is perceived and understood by them, to support them in self-assessing their possession of CT practices, and how to support mathematics teachers and students in gaining CT. We offer ideas regarding the promotion of CT and its integration in mathematics teaching and learning

Primary school teachers meet learning analytics dashboards: from dispositions to situation-specific digital competence in practice

This paper looks into teachers’ use of Learning Analytics Dashboards, visualization tools that present data regarding students’ learning progress in and out of lessons. Based on data of two studies conducted in Belgium and England, we discuss primary school teachers’ dispositions and performance regarding the use of learning analytics dashboards in the classroom. We argue on the importance of looking into specific elements of teacher competence in using such dashboards in their practice but also understanding the broader educational context and the teachers’ goals. We conclude by suggesting further research into the relationship between teachers’ dispositions and how they make sense of the information presented on dashboards in practice, to inform future dashboard design and teacher training opportunities

Preservice teachers’ beliefs about mathematical digital competency – a “hidden variable” in teaching mathematics with digital technology?

Recently the construct of mathematical digital competency (MDC) was put forward in which mathematical competency and digital competency are seen as a connected whole. This entails that student understanding of mathematical concepts may be almost inseparable from digital tools. We report on a quantitative study with n=238 preservice teachers (PSTs) from Germany that investigates PSTs’ beliefs about such a “connected position” of MDC. Results show that a large group of PSTs believe in the potential of digital technology but at the same time opposes the notion of MDC and rather believe that mathematical and digital competency should be separated. Furthermore, PSTs’ beliefs about MDC are largely independent from epistemological beliefs. We hypothesize, that beliefs about MDC may be an overlooked variable which may influence how teacher think about and use digital technology in the mathematics classroom

STACKification: automating assessments in tertiary mathematics

In this paper, we report on four university lecturers’ first-time experiences with computer-aided assessments. They were required to automate a significant proportion of the pre-existing weekly coursework for modules in first- or second-year undergraduate mathematics using STACK. We consider lecturers’ perspectives on the role of computer-aided assessments in course design for undergraduate mathematics; the knowledge of technical aspects required to implement STACKbased assessments; and the perceived merits of automated assessment for different aspects of mathematical study. We conclude with a series of reflections upon our departmental practice and the process of enculturating mathematicians into the realm of automated assessment

Authoring your own creative, electronic book for mathematics: the MC-squared project

The EU-funded ‘MC-squared’ project is working with a number of European communities to develop digital, interactive, creative, mathematics ‘textbooks’ that the project calls ‘cBooks’. The cBooks are authored in a Digital Mathematics Environment in which participants can construct books with various interactive ‘widgets’. This paper provides an outline of the MC-squared project illustrating an interactive storyboard of the Digital Mathematics Environment architecture. This includes examples of how authoring by cBook designers of interactive ‘widgets’ is possible. The workshop that relates to this paper is augmented, of course, by suitable ‘hands-on’ materials aimed at two possible cBooks: one focusing on aspects of geometric and spatial thinking using building blocks, the other on aspects of number and fractions

On mathematical digital competency for teaching: The case of an expert teacher

In this paper, we present a mathematics teacher’s reflections on the design and experimentation of an activity sequence involving transitions from ‘pen-and-paper’ mathematical explorations to mathematical explorations within three different digital environments, GeoGebra, the Scratch programming environment and Excel. We look at her arguments for supporting students’ development of Mathematical Digital Competency (MDC) and reflect on her instrumental orchestration approaches. We then argue and discuss the idea of MDC for teaching (MDCT) using this expert teacher’s case as an exemplar for such practice

Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology

This working group (WG), which met for the second time in June 2021, was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted as a result of the COVID-19 pandemic. Following a brief introduction to the aims for the WG, we offer three further case studies of teachers’ practices and an emerging synthesis of the cases according to three pedagogic activities that are proving to be particularly challenging