Canonical Forms in Interactive Exercise Assistants

Authors:
Bastiaan Heeren;Johan Jeuring
Affiliations:
School of Computer Science, Open Universiteit Nederland, Heerlen, The Netherlands 6401 DL;School of Computer Science, Open Universiteit Nederland, Heerlen, The Netherlands 6401 DL and Department of Information and Computing Sciences, Universiteit Utrecht,
Venue:
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Year:
2009

Citing 8
Cited 2

Views: a way for pattern matching to cohabit with data abstraction

POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
MATHPERT: a computerized learning environment for algebra, trigonometry, and calculus

Journal of Artificial Intelligence in Education
Term rewriting and all that

Term rewriting and all that
Non-Trivial Symbolic Computations in Proof Planning

FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
There and back again: arrows for invertible programming

Proceedings of the 2005 ACM SIGPLAN workshop on Haskell
A lightweight approach to datatype-generic rewriting

Proceedings of the ACM SIGPLAN workshop on Generic programming
Specifying Strategies for Exercises

Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Interactivity of Exercises in ActiveMath

Proceedings of the 2005 conference on Towards Sustainable and Scalable Educational Innovations Informed by the Learning Sciences: Sharing Good Practices of Research, Experimentation and Innovation

Adapting mathematical domain reasoners

AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
A programming tutor for haskell

CEFP'11 Proceedings of the 4th Summer School conference on Central European Functional Programming School

Quantified Score

Hi-index	0.00

Visualization

Abstract

Interactive exercise assistants support students in practicing exercises, and acquiring procedural skills. Many mathematical topics can be practiced in such assistants. Ideally, an interactive exercise assistant not only validates final answers, but also comments on intermediate steps submitted by a student, provides hints on how to proceed, and presents worked-out examples. For these purposes, fine control over the symbolic simplification procedures of the underlying mathematical machinery is needed. In this paper, we introduce views for mathematical expressions. A view defines an equivalence relation by choosing a canonical form of mathematical expressions. We use views to track and recognize intermediate answers, to help in presenting expressions to a user, and to control the granularity of the steps in worked-out examples. We develop the concept of a view, discuss the laws it satisfies, and show how views are composed, which means that they can be used for multiple exercise classes.