Ideas: interactive domain reasoners

Domain reasoners help students solving interactive exercises in learning environments, such as ActiveMath, MathDox, and the Digital Mathematical Environment from the Freudenthal Institute.

Ideas is a framework for developing domain reasoners that give intelligent feedback. Using Ideas, we have developed domain reasoners for solving linear, quadratic and higher-degree equations, gaussian elimination, and many other domains.

 

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Feedback

The distinguishing feature of our tools is the detailed feedback that they provide, on several levels. They support a student using an interactive learning environment for solving exercises by:

• giving a hint for the next step
• showing a worked-out solution to an exercise
• reporting a common error (or buggy rule)
• reporting a correct but suboptimal step
• decomposing an exercise into subexercises, etc.

We offer our feedback services as webservices. For a complete list of services see our documentation pages. Examples of most of some our services can be found on Math-Bridge (select Ideas exercises collection).

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Exercises

We have developed domain reasoners that can deal with many kinds of exercises:

• At the Open Universiteit Nederland, we use our domain reasoners in a learning tool for rewriting logical expressions to disjunctive normal form (login with any number).
• Together with the Freudenthal Institute, we have incorporated our domain reasoners in the Digital Mathematical Environment, to support solving linear, quadratic, and higher-degree equations and inequations, to simplify and evaluate fractions, expressions using powers and square roots, etc.
• We have developed domain reasoners for linear algebra, in particular for gaussian elimination, gram-schmidt, solving systems of linear equations, in cooperation with the TU/e, accessible via MathDox.
• Our domain reasoners are used within the Math-Bridge project, to support interactive exercises in ActiveMath in bridging courses all over Europe.
• Ask-Elle (introductory movie), our functional programming tutor, supports developing small functional programs.

For a complete list of the kind of exercises we offer see our documentation pages.

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More information

The ideas framework uses rewrite strategies for specifying how to solve exercises. The main ideas are described in our paper Specifying Rewrite Strategies for Interactive Exercises.

Several other aspects of our domain reasoners are described in the various publications about our work.

Information about our framework, documentation, etc, is available on our trac.

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Projects

• Onbetwist, 2011-2013, Surf-funded. We will make a small contribution towards assessing mathematical exercises.

Finished:

• Math-Bridge, 2009-2012, EU eContentPlus-funded. Domain reasoners for many mathematical domains, such as equations and inequations, differentiation, etc, and a binding to ActiveMath.
• Automatic assessment of mathematics exercises, 2012, funding from Sprint within Utrecht University. We have performed an experiment to automatically correct derivations of exercises in Freudenthal Institute's DME.
• Programming tutors. 2007-2012, OU-funded.
• Nationale Kennisbank Basisvaardigheden Wiskunde 2, 2008-2010, Surf-funded. Domain reasoners for many mathematical domains, and a binding to Digital Mathematical Environment.
• Intelligent Feedback, 2007-2008, Surf-funded. Defining the strategy language for our domain reasoners, domain reasoners for linear algebra, a binding with MathDox.

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People

Our work on domain reasoners is performed at the Faculty of Computer Science of the Open Universiteit Nederland and the department of Information and Computing Sciences of Utrecht University, by

• Alex Gerdes, now working on at Quviq, the main developer of Ask-Elle projects.
• Bastiaan Heeren, lecturer, working on the NKBW, Onbetwist, Math-Bridge, and Ask-Elle projects.
• Johan Jeuring, professor, theme-leader, working on the NKBW, Math-Bridge, and Ask-Elle projects.
• Josje Lodder, lecturer, working on e-learning tools for mathematics and the Math-Bridge project.

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Contact

Recent Updates

[19/05/2013] We organise a symposium on How do students make progress in simple mathematics exercises? on May 24. Partially funded by the Utrecht University Research Impulse Educational and Learning Sciences.

[23/11/2012] Alex' work got quite some attention: tweakers, Computable, Trouw, Channelweb, Facility wereld.

[23/11/2012] Alex Gerdes got his PhD! His thesis, Ask-Elle: a Haskell Tutor, is online available. Here is the video registration of the event.

[9/07/2012] Our paper Feedback genereren in leeromgevingen voor algebra. (in Dutch, Johan Jeuring and Bastiaan Heeren) has been accepted for the Nieuw Archief voor Wiskunde, 2012.

[9/07/2012] Our paper Teachers and students in charge - Using annotated model solutions in a functional programming tutor (Alex Gerdes, Bastiaan Heeren, and Johan Jeuring) has been accepted for the 7th European Conference on Technology Enhanced Learning, EC-TEL 2012.

[9/07/2012] Our paper Ask-Elle: A Haskell tutor - Demonstration - (Johan Jeuring, Alex Gerdes and Bastiaan Heeren) has been accepted for the 7th European Conference on Technology Enhanced Learning, EC-TEL 2012.

[27/02/2012] Our paper An Interactive Functional Programming Tutor (Alex Gerdes, Johan Jeuring and Bastiaan Heeren) has been accepted for the 17th Annual Conference on Innovation and Technology in Computer Science Education, ITICSE 2012.

[31/01/2012] Our paper Probability estimation and a competence model for rule based e-tutoring systems (Johan Jeuring, Diederik M. Roijers and Ad Feelders) has been accepted for the Second International Conference on Learning Analytics and Knowledge.

[01/10/2011] We have started a cooperation with the DFKI and the University of Saarland to set up a common laboratory in CelTech. We will particularly study interactive tutoring systems, such as Math-Bridge for mathematics, and for other sciences. See the press release (in Dutch).

[01/09/2011] We released version 1.0 of our ideas framework. The services have been further improved, and more exercises and buggy rules are included.

[01/06/2011] We finished our lecture notes on a programming tutor for Haskell (Johan Jeuring, Alex Gerdes, and Bastiaan Heeren) for the Central European School on Functional Programming, which will be held this summer.

[09/05/2011] The camera-ready version of our paper about A Teaching Tool for Proving Equivalences between Logical Formulae is now available online, and will be presented at the Third International Congress on Tools for Teaching Logic (TICTTL).

[06/05/2011] Our paper Interleaving strategies (Bastiaan Heeren and Johan Jeuring) has been accepted for publication in the proceedings of the Conference on Intelligent Computer Mathematics, 2011, to be held in Bertinoro, Italy, this summer.

[13/12/2010] The Dutch Surf foundation has decided to fund the `Onbetwist' proposal, the purpose of which is to improve mathematics education using assessments. We will continue our work on feedback partly in the context of this proposal.

[13/11/2010] Our paper Properties of exercise strategies (Alex Gerdes, Bastiaan Heeren, and Johan Jeuring) has been accepted for publication in the Proceedings of IWS 2010: 1st International Workshop on Strategies in Rewriting, Proving, and Programming.

[16/10/2010] Our work is used as an example of validation of research in the Annual report 2009 of the Dutch research universities (pdf english, pdf dutch).

[10/6/2010] Johan Jeuring presented our research on domain reasoners for interactive learning environments, together with an overview of the projects we have worked on in the last five years on the symposium on Computer Science, education and innovation (in Dutch) at the Open Universiteit.

[10/6/2010] The association of Dutch research universities VSNU describes our research on domain reasoners as an excellent example of applying science in day-to-day life, in their description of the power of knowledge.