We envisaged a future where online content would be brimming with interactive models, lettings students explore and tinker with problems alongside AI that would guide students in their thinking.
In the early 2000s, colleagues and I developed The Intelligent Book – a suite of technologies for adaptive materials, that let students work with smart graphical exercises as if the AI was their partner rather than their marker. Our new algorithm has further applications in grading Parson's Problems, as well as any other kind of homework or exam problem where the solution space may be modeled as a directed acyclic graph. We benchmark our algorithm on thousands of student submissions from Fall 2020, showing that our novel algorithm can perform over 100 times better than the naive algorithm on real data. We propose a novel algorithm for finding the edit distance from an arbitrary student submission to some correct solution of a Proof Blocks problem. Because of the large solution space, it is computationally expensive to calculate the difference between an incorrect student solution and some correct solution, restricting the ability to automatically assign students partial credit. In this paper, we address the problem of assigning partial credit to students completing Proof Blocks problems.
UNC LIBRARY TEXMACS SOFTWARE
Proof Blocks is a software tool which allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. Some users were able to complete proofs with much less training than is usual for the automated proof assistant itself, but there remain significant usability issues to overcome. We performed a user study and qualitative analysis of the system. The exercises take place within the context of an Intelligent Book.
Also, the tile syntax does not need to match the underlying Isar syntax exactly, and dierent tiles can be used for dierent questions. Unlike traditional syntax-directed editors, MathsTiles allow students to keep many answer fragments on the canvas at the same time, and do not constrain the order in which an answer is written. Proofs are written using MathsTiles: composable tiles that resemble written mathematics. To ensure students cannot "game the system" the exercise avoids tactic-choosing interaction styles, but asks the student to write out the proof. We examine whether, by providing a very specialised interface, it is possible to build something that is usable enough to be of educational value. Automated proof assistants are generally considered to be dicult for novices to learn. In this paper, we investigate using an automated proof assistant, particularly Isabelle/HOL, as the model supporting first year undergrad- uate exercises in which students write proofs in number theory.
The Intelligent Book project aims to improve online education by designing materials that can model the subject matter they teach, in the manner of a Reac- tive Learning Environment.
0 kommentar(er)
