Automated Grading Engine for Quantitative Constructed-Response Problems
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Solution Overview
Problem
Current systems lack an efficient method for automatically grading quantitative constructed-response problems (QCRPs), which are unstructured and yield unstructured answers, making it difficult to determine accurate scores in STEM education and other fields.
Innovation Solution
A computer-implemented testing system with a graphical user interface that allows users to drag-and-drop elements to construct scorable response models, which are then evaluated against rubric models using a grading engine that implements a grading algorithm to assign partial or full credit, enabling fine-grained, weighted scoring.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If automated grading is implemented for unstructured QCRP answers, then grading efficiency and productivity are improved, but the complexity of the grading system increases due to the need to handle unstructured answers
Solution Approach 1:
The patent segments the unstructured answer into multiple structured components (equations, variables, operators, constants) that can be individually identified and evaluated. The grading system divides the complex grading task into smaller sub-tasks: parsing the answer, identifying components, matching against solution pathways, and assigning partial credit for each correct element found.
Solution Approach 2:
The patent introduces an intermediary parsing and analysis layer between the unstructured answer input and the grading decision. This intermediary system converts free-form text into a structured representation that can be systematically compared against solution pathways, using natural language processing and mathematical expression parsing as mediator technologies.
2Adaptability or versatility
If multiple solution pathways are allowed for QCRP answers, then adaptability and versatility of the grading system are improved, but the difficulty of detecting and measuring correct answers increases
Solution Approach 1:
The patent implements a dynamic grading approach where the system adaptively processes answers through multiple potential solution pathways. Instead of a fixed single-correct-answer model, the system dynamically evaluates whether the student's answer follows any valid solution pathway, allowing the grading logic to flexibly adapt to different correct methods and approaches.
Solution Approach 2:
The patent changes the parameter of answer evaluation from exact matching to equivalence checking. The system recognizes that different mathematical expressions can represent the same solution (e.g., 2+2 vs. 4, or different algebraic manipulations leading to the same result), and uses parameter transformations and mathematical equivalence rules to verify correctness across multiple valid forms.
3Measurement precision
If fine-grained partial credit scoring is implemented, then measurement precision of student understanding is improved, but the device complexity and grading algorithm complexity increase
Solution Approach 1:
The patent implements partial credit scoring by evaluating and rewarding correct intermediate steps, components, or sub-solutions within an otherwise incomplete or partially incorrect answer. The system identifies and scores individual correct elements (such as correctly identified variables, proper equation setup, or accurate intermediate calculations) without requiring the entire solution to be correct, thus providing fine-grained measurement of student understanding.
Solution Approach 2:
The patent segments the scoring process into discrete evaluable units, where each correct component or step can be independently identified and assigned a specific credit value. This segmentation allows the complex task of evaluating partial understanding to be broken down into manageable scoring decisions, with each segment contributing to the overall precision measurement of student knowledge.
Data Source
AI summary
An exemplary testing system and method are disclosed to provide (i) computerized testing of unstructured questions such as quantitative constructed-response problems (QCRP) configured as words problems and (ii) a corresponding grading engine and computerized grading platform to determine partial or full credit or score for the problem.