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

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

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

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

A Department-Wide Transition to a New Mode of Computer-Aided Assessment Using STACK

We focus on the integration of STACK—a Computer-Aided Assessment (CAA) technology—in the mathematics department of a high-ranking University in the United Kingdom. We study a department-wide project where instructors were expected to implement STACK into continuous assessment tasks for (nearly) all core modules across the first two years of undergraduate study. We present this work as a departmental case study, drawing on semi-structured interviews with six novice STACK assessment designers (and module leaders), supplemented by students’ responses to an open-response feedback questionnaire, and the reflections of a co-project lead (also first author). Our thematic analysis identified four themes related to the design of STACK-based assessments by novice to STACK tutors: the process of ‘STACKification’, technical challenges, users’ perspectives on the role of CAA, and finally, variations in assessment designers’ approaches to the role of feedback. In presenting our results, we are guided by Sangwin’s (2013) design principles for mathematics assessment. We consider various technical aspects of implementing STACK-based assessments as a first-time user, and the knowledge required to do so effectively and coherently. We conclude with a series of reflections on the role of CAA in undergraduate mathematics, and the ways in which such technology can be productively integrated with established practice