






MATHEMATICS EDUCATION










As Lecturer in Mathematics at the Department of Mathematics of the University of Sussex, I attended the 2year parttime Masterlevel course “Postgraduate Certificate Learning and Teaching in Higher Education (PGCertHE)” from October 2007 to August 2009 and became subsequently a Fellow of the Higher Education Aacdemy.
Motivated by the PGCertHE course, I became interested in practicerelated problems of mathematics education and, since then, have much learned about the problems of learning and teaching mathematics. This research interest caused me to attend several conferences on mathematics education (for higher education) and to start my own projects in mathematics eduaction.










A. RESEARCH and DEVELOPMENT PROJECTS

Online tests for evaluating learning success in HM A:
Multiplechoice questions are a popular assessment method, since they can be easily marked. The debate, whether multiplechoice questions can test deeper knowledge or even comprehension and understanding, goes back many years. In the development part of my project I developed “online tests for evaluating learning success” with understandingoriented multiplechoice questions for seven of the ten topics of the course “Höhere Mathematik A für Elektrotechniker” (HM A). Each multiplechoice question has five given choices for the answer, and exactly one of these choices is appropriate. An unterstandingoriented multiplechoice question means that, for answering the question correctly, it is necessary to investigate each of the five possible answers and that this requires an understanding of the mathematical content as well as problem solving. An important educational aspect are the explanations that are shown to the students, once they have selected an answer. These explantions give hints, how the five different possible choices have to be analysed, so that all students can now work out the solution process with this help.
The aim of the online tests for evaluating learning success is to give the students formative feedback on their learning, after each topic of the course has been completed. In particular, I hoped that those students who invest too little time and effort for their studying will, with the help of the online tests for evaluating learning success, realise early enough that they need to invest more time for the lecture course HM A.

In a pilot project, I developed 95 multiplechoice questions for the first five course topics and implemented these with Moodle in five online tests for evaluating learning success. There was a test run of the online tests with volunteers from electrical engineering, mechanical engineering and physics. The Project was presented at the khdm conference with a poster presentation, and an extended abstract (8 pages) has appeared online as a contribution to the khdm conference 2015.

In Wintersemester 2016/17, based on the multiplechoice questions from the pilot project, online tests for evaluating learning success were developed for seven of the ten topics of HM A and were used in addition to conventional exercise sheets. Since the HM A has no prerequisites for taking part in the final exam, participation in the online tests was on a voluntary basis. Because of the lack of sufficient student participation the project was terminated after Christmas.

During the project, a variety of different types of multiplechoice questions have already been developed. A classification of these multiplechoice questions, as well as the investigation of a representative selection of these questions with respect to the literature on mathematical misconceptions, offer interesting research topics in mathematics education.

The project is of interest for online examinations and online testing in large lecture courses.

The project can be transferred to other mathematics lecture courses (e.g. introductory mathematics lecture courses for prospective teachers for the "Gymnasium") and even to lecture courses in different subjects.

Remodelling of HM A, B and C: Coordination with electrical engineering and development of comprehensive teaching materials (jointly with Dr. Cornelia Kaiser, WS 2013/14  WS 2015/16)
When my colleague Cornelia Kaiser took over the lecture courses “Höhere Mathematik A, B und C für Elektrotechniker” (Higher Mathematics A, B and C for Electrical Engineers), abbreviated HM A, HM B and HM C, she coordinated the topics and their ordering and timing with electrical engineering and provided handwritten lecture notes. As the next lecturer of the MH A, B and C lecture courses cycle, I further developed and expanded these handwritten lecture notes into comprehensive latexed lecture notes that contained also further explanations and examples. Since the solving of exercise problems plays a central role in learning mathematics, during the two cycles of the HM A, B and C lecture courses we developed a comprehensive collection of about 450 exercise problems with detailed solutions. Naturally the new teaching materials will be improved and developed further over the next years. The lecture notes are available for download on Teaching and Teaching Materials.

Evaluation of the new teaching materials and the learning in HM A and HM B:
I developed a questionaire to investigate the use of the new teaching materials and the learning behaviour in “Höhere Mathematik A and B für Elektrotechniker” (Higher Mathematics A and B for Electrical Engineers), abbreviated HM A and HM B. The questionnaire was handed out at the beginning of winter semester 2015 after the students had taken part in the combined written examination for HM A and HM B. The collected data confirmed the high educational value of the new teaching materials and provided interesting insights in the use of these teaching materials and the learning behaviour of the students. A paper on this and the previous project has been published in a conference proceedings.






B. FORMER PROJECTS in MATHEMATICS EDUCATION

Supporting Student Learning in Mathematics (autumn 2008):
The project aimed to evaluate the learning behaviour of first year mathematics students at the
University of Sussex and to improve it through a learning intervention.
Abstract of the Project Report:
This research project was concerned with two objectives:
(1) to investigate the mathematics students' learning and studying
habits, and (2) to provide learning support for the first
year mathematics students through an intervention,
with the aim to improve student learning, in particular,
problem solving skills.  The mathematics students' learning
and studying habits were investigated through a
questionnaire distributed to the first year mathematics students
in Week 4 of Autumn Term 2008. The data collected supports
the impression that many students do not learn in
an appropriate way.  The learning support intervention “Incorrect
Solutions” was a 2hour session in Week 5 of Autumn Term 2008 for
all first year mathematics students. “Incorrect Solutions” focussed
on a problem solving activity, namely, the students discussed
and critically analyzed in small groups sets of 8 problems
with given usually incorrect solutions. Data collected at the end of
the activity and at the end of term, via two questionnaires,
indicates that the intervention “Incorrect Solutions”
did not have the desired positive impact of improving
problem solving skills and student learning. Possible
reasons for this lack of impact are discussed.







