The 4th Workshop of Mathematical and Scientific eContent was a great opportunity for me to get an introduction into the mathematical eLearning community. I had the chance to talk to many researchers in mathematical education, system designer of educational software, and math/ physics teachers (on secondary and university level).
(1) I received many pointers to existing online materials and courses that we might be able to integrate or allow ours students to use. For example, Patrick Johnson (Postgraduate Student at the University of Limerick) pointed me to the material of their math center. Valentyna Pikalova, Kharkiv National Pedagogical University, Ukraine pointed to me to a corpus of problems that she created to educate math teachers. Valentyna also mentioned the pool of problems she created during her stay in the US. Moreover, Zsolt Lavicza (University of Cambridge) pointed me to his survey on mathematical practice, which I am eager to read as it is a further state of the art contribution I want to list in my Ph.D. thesis.
(2) I was able to try out and get to know many different systems such as the GeoGebra, DME, the MathDox system, and the learning tool presented by Matti Pauna. All of these system support interesting aspects in math education. Reimplementing these features from scratch seems to be very tedious, rather we will analyse whether we can build on the existing approaches.
- DME: The applet generator could be used to generate interactive problems for our precourse and course system. But the system is not open source, so we need to verify whether we can effort a license.
- GeoGebra: First I thought that GeoGebra can only be used for secondary school and in particular Geometry. But Patrick Johnson pointed out that he is also using it in his university math lecture. We need to verify whether we can provide our student with useful material in GeoGebra
- MathDox: We will be in contact with the MathDox group to analyse their interactive exercises. Maybe we can establish a collaboration to produce more English material, alternative strategies for the same problem as well as a tracking of the user’s problem solving path. The latter two would be very interesting from a research-perspective as I am interested in understanding and analyzing mathematical practice and problem solving is indeed an important practice. The former can potentially help to improve our precourse system.
- Matti’s presentation: We need to get in touch with the project manager (Mika Seppala) to evaluate whether we can point our students to the existing infrastructure and problem pool used at the University of Helsinki. I believe that this system could be helpful to our students.
(3) Talking to the community allowed me to better distinguish the background and focus of my own research group (KWARC). I realized that we are providing basic technology (still in prototypical states) that might be of interest to this community at some point of time but is still at a far too prototypical, technical, and abstract level (which might be necessary for some of our research project and not suited for others). Our group has so far not focused on the particular need of a specific group of users, also we have started to establish first collaboration with real users. Please don’t get me wrong as you read along, I think that my group is doing an excellent job. We have a lot of potential and very existing projects. The following only presents our work from the perspective of this event and my personal opinions on the requirements of this community.
Before our technologies can be used by the workshop participants we need to revise our services and interfaces. For example, the preliminaries we currently expect our users to fullfill do not fit to the background of most participant of the workshop. Most educational researchers use MS Word or specific education software to store their materials. They are not used to formats/ technologies such as LaTeX, OpenMath, MathML, or even semantic Markup format such as our OMDoc. Consequently, suited editors and converters are needed that support the user-friendly transformation/ import of existing eLearning resources into our formats (and to be accepted by the community this would require us to build on existing eLearning standards such as SCORM).
Moreover, the services we provide in our precourse/ course system are not analogously to features of the presented educational software (GeoGebra, DME, …). In contrast to our system, the focus seems to be the (automatized) creation of suited problems, the management of materials, and on interactive technologies that allow the visualization and animation of mathematical concepts/ problems. Teachers do not have the time to help improving a research prototype, they want to use software that has proved to improve the student’s learning experience. Consequently, many participants of the conference are interested in exchanging experiences and news on running, user-friendly, and (more or less) established SW as well as evaluations and guidelines on the use of education technologies.
Our precourse/ course system relates most to the presented tools at the workshop. However, due to limitation of time and budget, we could not consult teachers, mathematicians, or education researchers. Instead, we have been trying to implement this system from scratch, without considering any existing work in the field of mathematical education software. We have not build on any standards, evaluations, or technologies of this community.
Moreover, we did not have the time and skills to run prior studies before the implementation, such as an observation of the student’s situation (tools they have used, methods the know, topics they have covered, prior knowledge they bring along). All we had was a first need assessment from the Academic Affairs Committee of the Undergraduate Student Government. Consequently, we designed the system based on our assumptions and experiences what features/ content the students might need. Problems and contents have been created by former students, based on their perspective on the course. Evaluation of the content is still in progress. Moreover, the usability of all features of the system is not clear, they have not been based on any concrete requirements of our students.
Nevertheless, we share features with the presented eLearning systems: For example, ICT Teacher also provides a chat and forum to communicate with students. Our forum is widely used by the students, as all our TAs are answering the students question and this seems to help them in solving their weekly assignments as well as preparing for the midterm and finals. We provide a questionnaire infrastructure, which will prove its usability within the next week. However, the usability of the libary, slide, and multiple choice section is not clear – as it strongly depends on the quality of the presented material.
However, I am sometimes wondering whether we should rather stop all implementation and rather fully focus on the improvement and extension of our problem pool, i.e. to provide many more examples and solutions for our students. And if resources are available, rather provide additional human support. Using ICT successfully seems to be a very interesting but challenging topic, and has attracted several researchers with much wider backgrounds.
One point I have to make is that the system is also used as case study for my work on mathematical practice. I was hoping that the system would allow me to better understand and support the student’s practice and that I could apply these findings on mathematical practice in general. But the system did not really help me. Instead, I have based my assumptions on literature reviews (on mathematical practice) and understandings/ possibilities/ focus of my research group. For example, as our group has been working on the representation and rendering of notations we are now support a context-aware rendering of mathematical concepts. But we are not sure whether this feature can reduce the discrepancies between the students’ background or speed up their understandings. The second feature that is of interest to some members of the group are examples and their dependencies – but again we are not even sure what services we want to provide and whether this can have any impact on our students. For this we need to start evaluations. Unfortunately, we do not have the required skills and competencies for such studies. But, we have very good competences on the backend side, e.g. the storing, sharing, interlinking, maintenance and mark up of mathematical content. Nevertheless, our technological foundations and (backend) services should also be applied to concrete use cases. At least we should have an idea where we are aiming at, at which point we think we are successful, and how we can evaluate our success.
(4) Some participants have been asking me about my project and further career plans, which very much helped me to reflect on my Ph.D. topic and future plans. They reported on their backgrounds and paths, their hints and experiences will be very helpful. I was very impressed about the openness of the community, I did not feel to be excluded at any moment. Besides the participants, the great atmosphere was also due to an excellent organization and very impressing events/ excursions in the evenings. Thank you all!
As you can see from my above report, the workshop has been tremendously helpful for reflecting on my current work and gathering new ideas. As this is a yearly event, I recommend anyone involved in mathematical software and tools to join this or other events of the mathematical eLearning community. All participants have been open and very enthusiastic about investing time and efforts to improve mathematical education and to eventually countervail the more and more declining numbers of mathematical students and increasing difficulties of students in High School and at university.