Limitations
Other Pathways in a mathematical Proof
The current version of the iMathAS e-Proof Environment allows a semi-automated assessement. Deviations from a pre-defined graph for a given proof might be correct, but the are marked as false, expecially when student can enter arbitrary proof steps in the e-proof environment. A manual re-assessment might be necessary if the automated assessement of the student's e-proof contains some errors. The manual assessment will be necessary, if students use other pathways for the mathematical proof, that are not covered by the pre-defined solution of the author.
So one main limitation of the e-Proof is, that it is designed to support the students in learning proof steps by checking the student's proof against the predefined steps of the proof implemented by the author/instructor. Creative mathematical thinking could lead to other pathways of the proof that are not considered or predefined by the instructor or author of the e-Proof.
Creative mathematical Thinking
The predefined solution limits the Learner to reproduce a predefined solution of a proof. The consequence is that the e-Proof environment in iMathAS is recommended to use predominantly in the very beginning of learning to prove a theorem (e.g. in Calculus). The open paper & pencil proofs are more appropriate for Creative mathematical Thinking. Furthermore own proof step can be possible in the e-Proof Environment, so students can introduce their own proof steps mixed with pre-defined proof steps in the e-proof environment.
Points for the e-Proof Solution of Stundents
The automated assessment and points for a single proof step might lead to a sum of points that differ from a manual assessement. Communicate this limitation to the students. The points scored automatically might be incorrect, due to other correct solutions that are possible with the provide options in the e-Proof Environment.
Nevertheless the proof of concept helps to develop the e-Proof Environment further until an advanced support for students is possible.
The current version of the iMathAS e-Proof Environment allows a semi-automated assessement. Deviations from a pre-defined graph for a given proof might be correct, but the are marked as false, expecially when student can enter arbitrary proof steps in the e-proof environment. A manual re-assessment might be necessary if the automated assessement of the student's e-proof contains some errors. The manual assessment will be necessary, if students use other pathways for the mathematical proof, that are not covered by the pre-defined solution of the author.
So one main limitation of the e-Proof is, that it is designed to support the students in learning proof steps by checking the student's proof against the predefined steps of the proof implemented by the author/instructor. Creative mathematical thinking could lead to other pathways of the proof that are not considered or predefined by the instructor or author of the e-Proof.
Creative mathematical Thinking
The predefined solution limits the Learner to reproduce a predefined solution of a proof. The consequence is that the e-Proof environment in iMathAS is recommended to use predominantly in the very beginning of learning to prove a theorem (e.g. in Calculus). The open paper & pencil proofs are more appropriate for Creative mathematical Thinking. Furthermore own proof step can be possible in the e-Proof Environment, so students can introduce their own proof steps mixed with pre-defined proof steps in the e-proof environment.
Points for the e-Proof Solution of Stundents
The automated assessment and points for a single proof step might lead to a sum of points that differ from a manual assessement. Communicate this limitation to the students. The points scored automatically might be incorrect, due to other correct solutions that are possible with the provide options in the e-Proof Environment.
Nevertheless the proof of concept helps to develop the e-Proof Environment further until an advanced support for students is possible.