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software e.g. (Moodle, 2013; OLAT, 2013) provides
interactive (self-)tests, which allow students to prac-
tice and evaluate their skills. Thus, obtaining feed-
back on their learning progress. Unfortunately, giv-
ing automatic feedback for mathematical exercises is
difficult. Responses may not only involve numeric
values, but expressions may also include functions or
mathematical sets which have many equivalent repre-
sentations (e.g. x(x +1) is equivalent to x
2
+x). These
mathematic expressions cannot be handled properly
by state-of-the-art learning management systems.
For a meaningful feedback an interactive learning
tool needs to better “understand” these mathemati-
cal expressions. As a first step in this direction we
therefore propose an automatic feedback and evalua-
tion system tailored to mathematical exercises. Our
system leverages existing computer algebra software
in order to evaluate student responses and to provide
immediate individual feedback. It allows teachers to
easily create custom content with the granularity of
feedback of their choice.
With the automatic feedback functionality turned
off, the system can also be used for efficient assess-
ment and grading of large numbers of students.
2 ELECTRONIC SUPPORT FOR
MATH TEACHING
In abstract subjects such as mathematics feedback
plays an important role in the learning process. While
self-studying from a book or video is important, stu-
dents require much more support compared to facts-
based subjects (e.g. history).
Traditionally, this support is to a large extent
provided through face-to-face communication with
teachers, teaching assistants or fellow students. When
teaching online, we need to replace this valuable form
of feedback using different means.
2.1 Virtual Classrooms
Virtual classroom software has gained widespread ac-
ceptance in recent years. Universities use commer-
cial services like Adobe Connect or Google Helpouts
1
for live sessions between students and teachers. Vir-
tual classroom software provides real-time audio and
video communication. With the included whiteboard
and screen sharing capabilities this setup can mimic
the lecture style of large on-campus lectures. That is,
a professor is explaining and students are listening.
1
http://www.adobe.com/products/adobeconnect.html,
http://helpouts.google.com
Student questions in these virtual classrooms are
often tedious due to organizational issues (who is al-
lowed to talk at which point?) and technical problems
(microphone setup, network delays etc.). More over,
the software or network often only allows for a lim-
ited number of participants. When groups are small,
virtual classroom can, however, be a decent tool to
provide feedback. Particularly, since touchscreens of
today’s notebooks and tablets make it easy to write
mathematical equations and formulas.
2.2 Forums
Forums are another popular tool for online learning.
Communication is asynchronous and thus does not
provide immediate feedback. Students may ask a
question and a member of the teaching staff responds
later on. While in some cases this might result in stu-
dents working harder to solve a problem all by them-
selves, the delayed feedback often also disrupts and
postpones the learning process.
Forums require the teaching staff to spend a large
amount of time formulating written answers to stu-
dent questions, which is tedious and does not scale
well to large amount of students.
2.3 Learning Management and
Tutoring Systems
Existing learning management systems e.g. (Moo-
dle, 2013; OLAT, 2013) and tutoring systems e.g.
(Koedinger and Corbett, 2006; Melis and Siekmann,
2004) offer the functionality to create electronic ex-
ercise sheets. This allows students to practice and to
obtain immediate feedback to their solutions. These
systems may also display context-sensitive informa-
tion, hints and instruction to guide students towards
reasonable next steps.
LMS: Learning Management Systems. Gener-
ally, teachers are required to reformulate mathemat-
ical problems in a way, that is supported by the LMS.
That is, in order to allow automatic feedback, exer-
cises have been in the form of multiple choice or fixed
answer questions.
Since these systems do not understand mathemat-
ical expressions and their equivalent representations
it is impossible to use more complex expressions as a
solution. Exercise questions allowing free-text fields
are of course possible, but they require manual inter-
vention, which leads to a delayed feedback.
Overall, current LMS limit the selection of possi-
ble exercises considerably, which is why most math
teachers avoid using these systems.
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