The use of programming in mathematics education is undergoing a renaissanceand, in this paper, we analyse students’ handling of programming in mathematicsusing the Instrumental approach as a theoretical lens. We are especially interestedin analysing the development of mental schemes using two analytical frameworkswhich are compared and contrasted according the idea of networking theories. Thestudy illustrates that the frameworks’ detail of richness can have both advantagesand disadvantages and that one of the frameworks are more customed to be appliedwhen analysing students’ instrumental genesis concerning the use of a programmingenvironment as a mathematical artefact.

This paper relates to an ongoing project using design-based research as a methodol- ogical approach in which students with no prior experiences of using programming as a mathematical tool are observed trying to solve mathematical problems with the help of programming. The Instrumental Approach is used as conceptual framework in which the concept of instrumental genesis describes the process where the programming environment as an artefact together with student-developed mental schemes forms an instrument in order to solve mathematical problems. The development of schemes is of special interest in this paper where Vergnaud’s components of a scheme provide a framework for analysing transcripts of talk between student pairs and the programming code that they generate.

There is a recognized need in mathematics teaching for new kinds of task which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study conducted by the authors in collaboration with four upper secondary school teachers. A task sequence was trailed with four 10^th grade classes, involving a total of 85 students. The research process pinpointed key didactical variables that proved crucial in designing these tasks. As well as being useful in the task design process, the didactical variables were found to be valuable in the processes of analysis and revision. While the didactical variables identified a priori were informed by the research literature concerning reasoning and functions, those identified a posteriori deal mainly with scaffolding issues that emerged.  

Logic reasoning and communication are general competencies, important in all areas of mathematics. We think that one of the major advantages of GeoGebra is the possibility to create favorable learning situations for these competencies. We would like to investigate these possibilities. Our main interest is to find out how students use logic reasoning and how they communicate when they work in pairs with GeoGebra. We think that investigating the validity of certain geometrical statements is a kind of task appropriate for this purpose

Research points out the importance of following up students’ work on computerbasedtasks with whole-class discussions in which students play a central role.However, at the same time, research highlights the challenge for teachers in orchestratingsuch follow-up discussions. This paper examines whether an establishedmodel developed as guidance for teachers to orchestrate mathematical whole-classdiscussions (Stein, Engle, Smith & Hughes, 2008) could be useful in this educationalsetting. Students’ written responses to two different tasks are the main data used toexamine the model. The results indicate that the model has great potential to guidethese follow-up discussions

This paper reports on a pilot study with the focus on (re)design of a digitized task environment utilizing two types of technology – a dynamic mathematics software and a computer-aided assessment system. The data consist of responses from 256 first year engineering students, taking their first Calculus course, on two different types of task. The results are discussed in relation to (re)design of tasks as well as possible feedback design options to enable a formative assessment approach.

In the poster, we will present a planned study focusing on the design of DMS tasks and elaborated feedback within a CAA system. The study will be conducted in a first year engineering mathematics course during autumn 2020.

This thesis concerns the challenge of integrating dynamic software environments into the teaching of mathematics. It investigates particular aspects of the design of tasks which employ this type of computer-based system, with a focus on improvement, both of the tasks themselves and of the design process through which they are developed and refined.

The thesis reports two research projects: a small initial one preceding a larger main project. The initial case study, involving two graduate students in mathematics, develops a task design model for geometrical locus problems. The main study constitutes the first iteration of a design-based study, conducted in collaboration with four upper-secondary school teachers and their classes. It seeks to identify task design characteristics that foster students’ mathematical reasoning and proficient use of software tools, and examines teachers’ organisation of ‘follow-up’ lessons.

The findings concern three particular aspects: features of tasks and task environment relevant to developing a specific plan of action for a lesson; orchestration of a particular task environment to support the instrumental genesis of specific dynamic software tools; how to follow up students’ work on computer-based tasks in a whole-class discussion.

It is recognized that the process in which an artefact becomes an instrument for a user, denoted as instrumental genesis, is a complex process. The aim of this paper is to identify elements of the process of instrumental genesis when students are dealing with scales and scaling issues in a dynamic mathematics software environment. This study involves four upper secondary school teachers and their classes. By observing the students’ instrumented techniques while working with tasks designed with a hypothetical instrumental genesis in mind, some key elements are identified.

In recent decades, there has been rapid development in digital technologies for automated assessment. Through enhanced possibilities in terms of algorithms, grading codes, adaptivity, and feedback, they are suitable for formative assessment. There is a need to develop computer-aided assessment (CAA) tasks that target higher-order mathematical skills to ensure a balanced assessment approach beyond basic procedural skills. To address this issue, research suggests the approach of asking students to generate examples. This study focuses on an example-generation task on polynomial function understanding, proposed to 205 first-year engineering students in Sweden and 111 first-year biotechnology students in Italy. Students were encouraged to collaborate in small groups, but individual elements within the tasks required each group member to provide individual answers. Students’ responses kept in the CAA system were qualitatively analyzed to understand the effectiveness of the task in extending the students’ example space in diverse educational contexts. The findings indicate a difference in students’ example spaces when performing the task between the two educational contexts. The results suggest key strengths and possible improvements to the task design. 

The increasing availability of new technologies in schools provides new possibilities

for the integration of technology in mathematics education. However, research

has shown that there is a need for new kinds of task that utilize the affordances provided by

new technology. Numerous studies have demonstrated that dynamic geometry environments

provide opportunities for students to engage in mathematical activities such as

exploration, conjecturing, explanation, and generalization. This paper presents a model for

design of tasks that promote these kinds of mathematical activity, especially tasks that

foster students to make generalizations. This model has been primarily developed to suit

the use of dynamic environments in tackling geometrical locus problems. The model was

initially constructed in the light of previous literature. This initial model was used to design

a concrete example of such a task situation which was tested in action through a case study

with two doctoral students. Findings from this case study were used to guide revision of the

initial model.

This paper reports a study of teachers’ use of Connected classroom technology to prepare for whole-class discussions building on students’ computer-based work in mathematics. The study investigates four upper secondary school teachers’ management of time and progression during the phase of the lesson where students are working in pairs. The findings highlight various didactical choices made by the teachers. These choices and some related challenges are discussed

This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students’ mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined use of a dynamic mathematics software environment and a computer-aided assessment system. In example-generating tasks, students are asked to generate examples that fulfil certain conditions. Based on data in terms of examples generated by 491 first-year engineering students, taking a first course in calculus, the paper examines patterns of student response to three example-generating tasks. As a theoretical lens, the notions of dimensions of possible variation and associated ranges of permissible change are used. In light of the observed patterns, the paper provides some guiding principles for designing example-generating tasks and associated formative feedback to foster students’ mathematical understanding by enriching their example spaces. For example, this paper illustrates occasions where it might be instructive to start by asking for two examples, followed by adapted feedback before requesting a third example.

Based on the patterns of response to an example-generating task, this paper provides suggestions onhow the task could be redesigned to enrich students’ example spaces in relation to the key ideasaddressed by the task. The participants are 236 first-year engineering students

Task design is a central issue in mathematics education, not least in relation to digital technology. This paper reports how a smal lbut significant change in wording affects students’ explanatory responses. The study is comparative and involves 229 10th grade students working on tasks designed for a dynamic mathematics software environment. The findings indicate that inclusion of the word ‘mathematical’ prompted students to use algebraic symbols and algebraic arguments, to a higher degree.

This paper reports on the planning of a pilot study where the aim is to develop and investigate teaching practices, using connected classroom technology (CCT), to support formative classroom practices in mathematics. The focus is on the design of a teaching unit including a whole-class discussion drawing on students’ computer-based work. The paper outlines both generic and topicspecific theories underpinning the design. Moreover, findings from a previous study, in terms of student responses to a task developed for a dynamic mathematics software environment, are used in the planning. One important issue addressed in this paper is the sequencing of student responses to display and use as a basis for whole-class discussions.

This paper reports a study of four upper secondary school teachers’ use of Connected Classroom Technology to select student responses to computer-based activities, and to use these responses to launch successive stages of a planned whole-class discussion. Although the preparation for the class discussion was quite successful, it was a challenge for the teachers to conduct the whole-class discussion, particularly in posing specific questions based on appropriate student responses.

This paper reports on the planning of a design-based research (DBR) study, where the main aim is to develop principles in designing technology-enhanced learning environment utilizing a combination of a dynamic mathematics software (DMS) and a computer-aided assessment (CAA) system. The focus is on the design of tasks and automated feedback of high quality so as to enhance first year engineering students’ engagement in and conceptual understanding of mathematical contents. The paper outlines the rationale for the project and highlights theoretical aspects that will be considered in the study. Moreover, some findings from a pilot study that will inform the first cycle of the DBR study are presented.

The paper examines the quality of digitized tasks designed by 10 (small) groups of prospective upper secondary school teachers as part of a geometry course assignment. The results indicate that a small instructional intervention, addressing the planning and implementation of tasks in digitized task environments as well as how to stimulate students to make mathematical generalizations, led to a relatively high proportion (8 out of 10) of high-quality tasks designed by the prospective teachers.

In this poster, we present an ongoing study about prospective mathematics teachers' conceptions about the relationship between mathematics, problem-solving and GeoGebra. The context of our study is a curriculum reform in Sweden that emphasizes the use of digital tools in mathematics education. In that respect, we will investigate prospective upper-secondary teachers´ conceptions when participating in a geometry course at the university level. During the course, participants will construct mathematical activities for pupils by using GeoGebra.

The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.