Helsinki University of Technology, Espoo, Finland
(Main building, Otakaari 1, hall G)
October 26th, 2009
Teaching mathematics is always a challenging task. Recent advances in didactics and technology offer new opportunities in advanced mathematics teaching. A number of national and international experts share their views in a seminar organised by the Department of Mathematics and Systems Analysis, TKK. The purpose of the seminar is to discuss the implementation of new teaching methods at technical universities.
I present some theoretical and empirical results from my study about students? encounters with proof at a mathematics department in Sweden as well as mathematicians? views of proof in the teaching of mathematics. I also discuss the renewed emphasis on mathematical proof in the ongoing revisions of the school curricula in many countries. Finally, I present some main concerns of mathematics educators in Sweden regarding the students? difficulties in mathematics when moving from secondary to tertiary level.
I'll consider in my presentation are there structural reasons in the Finnish education system why the very good students in school mathematics may have problems in university mathematics. There is also other point of views to the problem: student's view of mathematics, working culture, learning materials, teachers etc. If we recognize roots of problems in students' mathematical proficiency we could find effective means to help students in their mathematics study.
In 1988, provincewide data on the math skill levels of high school graduates entering Memorial University in Newfoundland, Canada, was collected. This data showed that 44% of these students graduating from an academic math stream in high school, had a math skill level appropriate to a 12year old, and 38% had a math skill level appropriate to a 14year old. Furthermore, in followup studies of students? performance in a university precalculus course, it was discovered that their pass rate in that course was only 20% and 50%, respectively.
In 1988 in response to this situation, the Mathematics Learning Centre (MLC) at Memorial University was founded to investigate why this was so and how to correct it. The work of the founder, Dr. Sherry Mantyka, focused on the students with the lowest skill levels because initially the university allowed students to selfselect to participate in the program at the MLC. But as failure rates in first year courses continued to be unacceptably high, the university imposed compulsory placement for students. At this time (1999), enrollment at the MLC went from 125 students per semester to over 450.
The program that has been developed at the Mathematics Learning Centre can reverse this situation for these students. In a study of all current matriculants entering Memorial University between 1990 and 1993, it was discovered that for students who needed the MLC program but did not complete it, compared to those who needed it and did, the percentage of university math courses passed went from 49% to 67% (compared to 72% for students who did not need the MLC program); the average grade in firstyear English went from 53% to 60% (compared to 61% for students who did not need the MLC program); and the graduation rate from university went from 17% to 27% (compared to 36% for students who did not need the MLC program).
Dr. Mantyka will speak about the methods used at the MLC for universityaged mathematics underachievers.
STACK is an open source computer aided assessment system for mathematics. The use of computer algebra provides a suite of tools with which a teacher may establish mathematical properties of the student's final answer. On the basis of these properties outcomes are assigned in the form of a numerical mark (including partial credit as appropriate), text based feedback to the student and a "note" for later analysis. These three outcomes correspond broadly to the summative, formative and evaluative purposes of assessment. This is much more sophisticated than multiple choice formats, but falls short of being able to automatically assess chains of related mathematical expressions, i.e. a full "worked solution".
The talk reports a cycle of development in STACK which has aimed to increase reliability and scalability of the system.
STACK is now fully integrated into Moodle, including question authoring. The display of mathematics is now client side  increasing, we hope, accessibility. We expect this to produce quality mathematics rendering in a consistent way that reduces processing load on the server.
STACK is, however, still logically separate to Moodle, being linked by a SOAP protocol jointly developed by the Open University. This would certainly allow STACK to be included in other content management systems. A "minimal client" will be demonstrated.
Mathematical questions now have builtin test cases support. Similar to unit tests in software development, these allow the question author to verify the outcome of items for student answers in terms of any random parameters. By including this information within the item, the author can test questions and furthermore, when the question is shared, other teachers can more easily understand the intensions of the original author.
STACK now optimizes its use of computer algebra with a dynamic caching layer. This shifts future optimization and scaling work to database design where it can more effectively be addressed. The record of attempts references this layer which can be analyzed for evaluative feedback on a question.
The system will be demonstrated with example questions suitable for first year courses.
For more information:
