Introduction

In the areas of both second and third level Mathematics Education, the topic of Transposition has repeatedly been flagged as one of the most problematic. Recognition of the issues surrounding this topic led to the Teaching and Learning Unit funded Transposition Project that ran during the second semester of the 2017/2018 academic year. The positive response to the project was far greater than anticipated and we were able to form a project team of ten members of staff from the Department of Mathematics. Due to the large number of staff engaged in the project, the initial first phase produced a greater number of outputs than expected, including:

• Staff workshop within the Department of Mathematics
• Staff workshop for staff from the Faculties of Science and Engineering and Business and Humanities
• Student interviews
• Analysis of errors from sample questions
• Exploration of current teaching practices
• Exploration of potential teaching tools
• Outline of research plan to measure the impact of chosen teaching tool
• End of semester seminar to bring together the different research strands

The two most striking findings from the staff workshops were first, the lack of understanding surrounding the topic of Transposition is widespread, affecting many students across all disciplines and second, the negative impact of this on other modules is large and affects a vast number of modules throughout many course programmes in CIT. It was noted by (non-Mathematics) lecturers that the difficulties students have with the topic of transposition confounds the teaching and assessment of key concepts within subject areas.

Having established that the topic of Transposition is not well understood but is extremely important for many modules and disciplines, we are now very enthusiastic about entering Phase 2 of the project and hope to get your support with this. We plan to develop resources for students, staff in the Department of Mathematics and staff in other departments who use Transposition within their modules. To keep the momentum of the project up, we hope that some team members will attend conferences nationally and internationally disseminating what we have done in Phase 1 and also networking and learning. We see this as key in keeping the energy of the team up.

 Outline of work to be undertaken

• Create a guide for non-Mathematics lecturers who come across using transposition in their courses (suggestion from Non-Maths staff workshop in Phase 1)
• Create a resource of discipline related formulae from each department so maths lecturers can easily use formulae that students would meet in other modules in the future. (suggestion from Maths staff workshop in Phase 1)
• Attend national and international conferences sharing our work from The Transposition Project – Phase 1
• Develop a valid and reliable diagnostic test
• Create a set of lesson plans based on Peer Instruction using concept questions
• Run a study to quantify the impact of the Peer Instruction teaching tool
• Develop an online module on Transposition to fit into MathsOnline using Numbas and other ed-tech tools

Types of outputs

• Lecturer guide on teaching transposition
• Booklet of discipline related formulae
• Diagnostic test
• Transposition teaching tool for use in the classroom (Peer Discussion using concept questions)
• Online transposition learning module
• National and international dissemination of The Transposition Project Phase 2.
• Strengthened and energized community of practice in Department of Mathematics