Using a constraint-based expert model to provide step-level feedback for user-inputted mathematics equations

Abstract

Studies across a variety of educational fields have shown the efficacy of feedback on student performance and learning. Web-based homework is a common feature of secondary and collegiate mathematics courses to provide such feedback. While web-based homework provides often instantaneous feedback to students as they complete assignments, the feedback is limited to the correctness of the final answer or to a limited number of pre-programmed common mistakes. Intelligent Tutoring Systems have the ability to provide step-by-step feedback and guidance tailored to individual students, however authoring content for such systems is generally considered a huge barrier to their wider use. This paper presents an alternative system, called SANYMS (Show and Name Your Math Steps), which combines the wide-scale usability of web-based homework with a Constraint-Based Intelligent Tutoring System Expert Model based on the open-source computer algebra system Maxima. With the integration of Maxima, SANYMS can provide step-by-step feedback to students constructing their own solutions to a wide variety of algebraic equations of their choice without the need for extensive content authoring inherent in many Intelligent Tutoring Systems.

KEYWORDS:

• Intelligent Tutoring Systems
• web-based homework
• constraint-based model
• computer algebra system
• maxima
• expert model

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 https://mlm.pearson.com/northamerica/mymathlab/educators/features/index.html

2 https://www.wileyplus.com/platforms/wileyplus/

3 https://webassign.com/instructors/features/

4 https://webwork.maa.org/index.html

5 https://goformative.com/

6 https://new.assistments.org/

7 https://www.wolframalpha.com/examples/pro-features/step-by-step-solutions/

8 Desmos website: https://www.desmos.com/

9 Desmos scientific calculator: https://www.desmos.com/scientific

10 Python language website: https://www.python.org/

11 Maxima website: http://maxima.sourceforge.net/

12 YAMWI: http://maxima.cesga.es/

13 YAMWI project website: http://yamwi.sourceforge.net/

14 http://maxima.sourceforge.net/docs/manual/maxima_9.html