An activity theory investigation of tool-use in undergraduate mathematics

This mixed methods study investigates a number of aspects related to tool-use in undergraduate mathematics as seen from an Activity Theory perspective. The aims of this study include: identifying the tools that undergraduates use; seeking for an empirically-based typology of these tools; examining how undergraduates themselves can be profiled according to their tool-use; and finally identifying the factors influencing students tool preferences. By combining results from survey, interview and diary data analyses, it was found that undergraduates in the sample preferred using mostly tools related to their institution s practice (notes, textbooks, VLE), other students and online videos. All the tools students reported using were classified into five categories: peers; teachers; external online tools; the official textbook; and notes. Students in the sample were also classified into five distinct groups: those preferring interacting with peers when studying mathematics (peer-learning group); those favouring using online tools (online-learning group); those using all the tools available to them (blended-learning group); those using only textbooks (predominantly textbooks-learning group); and students using some of the tools available to them (selective-learning group). The main factor shaping students tool choices was found to be their exam-driven goals when examined from an individual s perspective or their institution s assessment related rules when adopting a wider perspective. Results of this study suggest that students blend their learning of mathematics by using a variety of tools and underlines that although undergraduates were found to be driven by exam-related goals, this is a result of the rules regulating how Higher Education Institutions (HEI) function and should not be attributed entirely as stemming from individuals practices. Assigning undergraduates exam- driven goals to their university s sociocultural environment, was made possible by combining two versions of Activity Theory (Leontiev and Engestrøm s) and analysing data at two different levels (individual and collective respectively)

Students as partners in complex number task design

We report on a collaborative project at university level involving students as partners in task design for a bridging mathematics module (known in the UK as a Foundation module) which is part of gaining access to first year degree studies. Three teacher-researchers met regularly with four student partners who developed a set of tasks on matrices and on complex numbers which were trialled with students on this Foundation module. We show the mediational processes by which the tasks developed from ‘static’ designs to more ‘dynamic’ designs using the software Autograph. Our analyses highlighted various tools in the mediation of the learning of mathematics, in the mediation of task development and in the mediation of the engagement of all team members in collaboration

Collaborative task design with student partners in a STEM foundation mathematics course: visual support for the multiplication of matrices

This paper concerns part of a collaborative project involving ex-students from a university Foundation Studies Programme working with teacher-researchers and analytic assistants in designing computer-based tasks for Foundation level tutorial sessions. This paper focuses on the design and use of a GeoGebra file to assist with students becoming proficient with matrix multiplication. The visual support of highlighting particular rows and columns of two matrices which are to be multiplied together proved helpful for students to develop success with carrying out matrix multiplication but also had a negative effect as well. A particular issue arose concerning the lack of variation in the size of matrices within the first set of questions. This led to difficulties with later questions involving matrices of different sizes

Student Partners in Task Design in a computer medium to promote Foundation students’ learning of mathematics

A team consisting of three mathematics education teacher-researchers, four former Foundation students (called Student Partners, SPs), and two analytic assistants worked together to produce mathematical tasks in a computer medium for the mathematical learning of current Foundation students (FSs). We have explored the collaboration between the SPs and researchers, the processes and outcomes of task design, and the contribution of the collaboration to tutorial teaching of FSs. We seek insight into the learning of all concerned of mathematics, mathematics teaching, task design and personal-professional development. The project is ongoing. Here we introduce the project and present early findings – specifically related to task design and the contribution of SPs

Links between students' goals and their choice of educational resources in undergraduate mathematics

© The Author 2017. Currently, there is a dearth of studies exploring the kind of tools that undergraduates use when studyingmathematics with previous approaches focusing mostly on digital or institutionally provided resources. In this article, we present and discuss the results from our investigations into the different types of tools that a cohort of second year engineering undergraduates uses. Our survey (N= 201) showed that although to some extent students use resources external to their university, their practices are dominated by tools that their institution provides to them. Analysis of six follow-up interviews revealed that when students use the most popular resources they aim mostly for exam-related goals. This suggested that students in our sample choose to use certain tools because these enable them to pursue their exam-driven goals

Using imagery with GeoGebra to assist with matrix multiplication: a collaborative project

Using imagery with GeoGebra to assist with matrix multiplication: a collaborative projec