Presentation by Johan Jeuring (Open Universiteit Nederland) at the JEM Symposium on “math tutoring: tools and feedback” in Heerlen, Netherlands.
Johan Jeuring presented his work on exercise strategies presented at the MKM conference. The presentation was followed by three talks on feedback tools that make use of the exercise web service (by Bastiaan Heeren, Hans Cuypers (MathDox), and Rick van der Meiden)
For me the introduction of Johan’s talk was extremely interesting as it reflects scientific practice for solving problems in different scientific areas. It would also be interesting to look at the different types of strategies that the project has identified as well as concrete instances of these strategies for concrete exercises (e.g. created for the feedback tools).
A web service is available. Only for own personal testing purpose a GUI has been implemented. A potential system using the web service should interpret/ wrap the feedback of the service. Users are not intended to directly use it. For example in the GUI, the numbers of steps are displayed and the user’s progress. Users can solve more then one step with one interaction, thus the progress and feedback should be wrapped by a system using this web service.
The flexibility of the problem solving depends on the strategies. Very strict strategies reduce the number of possible paths; non-specified steps cause complaints. Again, the feedback needs to be re-interpreted for the end-user.
Following Johan’s talk, Bastiaan Heeren illustrated the interaction with the web service, showing some very nice examples.
Hans Cuypers introduced the services of the MathDox system. Among others he mentioned that back engines such as mathematics return typical notations and solutions; here typicality refers to the specific syntax/ characteristics of the back end service. That’s an interesting point for us in the discussion on typical exercises and examples, as the concrete system can be a potential context parameter for typicality. The MathDox material has been integrated intof Moodle (a SCORM package has been created for the import) and will be used next semester.
Rick van der Meiden (Technische Universiteit Delft) presented the direct feedback in an eLearning system for linear algebra.
Further Details
Procedural Skills in different scientific areas
- Mathematics: calculate the value of an expression
- Computer Science:
- Physics
- Biology
- …
Tutoring Systems for procedural skills (providing feedback)
- Wisweb (Freudenthal Institute)
- LeActiveMath
- MathXPert
- Aplusix
Strategies types:
- Expert Strategy
- Arithmetic Strategy
- ….
Use of Strategies for error diagnosis and feedback; embedding in other systems.
- Strategy unfolding
- hints, feedback, …
Further Readings
- Anderson: Rules of the mind
- VanLehn: Mind bugs – the origins of procedural misconceptions; specify requirements for strategy language
- ideas
- Recognizing Strategies
- technical report on the topic; MKM springer link
- Feedback Services for Exercise Assistants
- protocol for communicating with Eindhoven
- Documentation to the Online Exercise Assistant
- code of the online tools, services, and strategy descriptions is online available: download
[...] which seems an important condition of tutoring systems. This includes basic technologies and services, interfaces (partly making use of these services), and evaluations. Most of the participants of the [...]
[...] strategies cannot be created or modified by the author of exercises (in contrast to the approach by Johan Jeuring), but are created and maintained by the developer of the system. Technically, strategies are [...]
[...] Jeuring mentioned that their worked out examples (in their exercise web service) are actually (hopefully/ ideally/ potentially) typical examples to illustrate a problem. The study [...]
Johan Jeuring recommend me to look at the following references for further news on the “Procedural Skills in different scientific areas” as well as the different “Strategy types”.