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Mathematical learning environments give domain-specific and immediate feedback
to students solving a mathematical exercise. Based on a language for specifying
strategies, we have developed a feedback framework that automatically calculates
semantically rich feedback. We offer this feedback functionality to mathematical
learning environments via a set of web services. Feedback is only effective when
it is precise and to the point. The tests we have performed give some confidence
about the correctness of our feedback services. To increase confidence in our
services, we explicitly specify the properties our feedback services should
satisfy, and, if possible, prove them correct. For this, we give a formal
description of the concepts used in our feedback framework services. The
formalisation allows us to reason about these concepts, and to state a number of
desired properties of the concepts. Our feedback services use exercise
descriptions for their instances on domains such as logic, algebra, and linear
algebra. We formulate requirements these domain descriptions should satisfy for
the feedback services to react as expected.
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Paper, accepted at
IWS 2010
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Project website