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Efficient Feedback and Partial Credit Grading for Proof Blocks Problems
Artificial Intelligence · Submitted 8 Apr 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We benchmark our algorithm on thousands of student submissions from multiple courses, showing that the baseline algorithm is intractable, and that our proposed algorithm is critical to enable classroom deployment.
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The abstract, sentence by sentence
Proof Blocks is a software tool that allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. Proof Blocks offers the capability of assigning partial credit and providing solution quality feedback to students. This is done by computing the edit distance from a student's submission to some predefined set of solutions. In this work, we propose an algorithm for the edit distance problem that significantly outperforms the baseline procedure of exhaustively enumerating over the entire search space. Our algorithm relies on a reduction to the minimum vertex cover problem. We benchmark our algorithm on thousands of student submissions from multiple courses, showing that the baseline algorithm is intractable, and that our proposed algorithm is critical to enable classroom deployment. Our new algorithm has also been used for problems in many other domains where the solution space can be modeled as a DAG, including but not limited to Parsons Problems for writing code, helping students understand packet ordering in networking protocols, and helping students sketch solution steps for physics problems. Integrated into multiple learning management systems, the algorithm serves thousands of students each year.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Proof Blocks is a software tool that allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. | background 1.00 | 0.08 | 0.02 | asserted 1.00 |
| s1 | Proof Blocks offers the capability of assigning partial credit and providing solution quality feedback to students. | background 0.84 | 0.14 | 0.05 | asserted 0.97 |
| s2 | This is done by computing the edit distance from a student's submission to some predefined set of solutions. | method 0.80 | 0.19 | 0.04 | asserted 1.00 |
| s3 | In this work, we propose an algorithm for the edit distance problem that significantly outperforms the baseline procedure of exhaustively enumerating over the entire search space. | contribution 0.98 | 0.93 | 0.53 | asserted 1.00 |
| s4 | Our algorithm relies on a reduction to the minimum vertex cover problem. | method 0.97 | 0.86 | 0.06 | asserted 1.00 |
| s5 | We benchmark our algorithm on thousands of student submissions from multiple courses, showing that the baseline algorithm is intractable, and that our proposed algorithm is critical to enable classroom deployment. | result 0.95 | 0.95 | 0.60 | asserted 1.00 |
| s6 | Our new algorithm has also been used for problems in many other domains where the solution space can be modeled as a DAG, including but not limited to Parsons Problems for writing code, helping students understand packet ordering in networking protocols, and helping students sketch solution steps for physics problems. | contribution 0.65 | 0.74 | 0.07 | asserted 1.00 |
| s7 | Integrated into multiple learning management systems, the algorithm serves thousands of students each year. | result 0.82 | 0.64 | 0.13 | asserted 1.00 |
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The paper
Original abstract
Proof Blocks is a software tool that allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. Proof Blocks offers the capability of assigning partial credit and providing solution quality feedback to students. This is done by computing the edit distance from a student's submission to some predefined set of solutions. In this work, we propose an algorithm for the edit distance problem that significantly outperforms the baseline procedure of exhaustively enumerating over the entire search space. Our algorithm relies on a reduction to the minimum vertex cover problem. We benchmark our algorithm on thousands of student submissions from multiple courses, showing that the baseline algorithm is intractable, and that our proposed algorithm is critical to enable classroom deployment. Our new algorithm has also been used for problems in many other domains where the solution space can be modeled as a DAG, including but not limited to Parsons Problems for writing code, helping students understand packet ordering in networking protocols, and helping students sketch solution steps for physics problems. Integrated into multiple learning management systems, the algorithm serves thousands of students each year.
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