Equation Grading via Syntax Tree Structural Normalization
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Solution Overview
Problem
Current participant response systems are inadequate for grading equation-based assessments accurately, as they rely on simple string comparison, leading to errors due to multiple valid solutions not being recognized.
Innovation Solution
A computerized grading method that creates syntax trees for both the response and the solution, comparing them to determine equivalence, allowing for grading based on the structural and algebraic normalization of equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If simple string comparison is used for grading, then the grading process is simple and fast, but grading accuracy deteriorates due to inability to recognize multiple valid solutions
Solution Approach 1:
The patent introduces syntax trees as an intermediary data structure between the participant's response string and the solution string. The syntax tree parser converts both strings into standardized tree representations that capture mathematical structure, enabling accurate comparison while maintaining automated processing. This intermediary structure resolves the contradiction by providing both speed (through automated parsing) and accuracy (through structural normalization).
Solution Approach 2:
The patent changes the representation parameter from raw string form to normalized syntax tree form. By transforming both responses and solutions into a common structural representation where equivalent mathematical expressions map to identical tree structures, the system achieves accurate recognition of multiple valid solutions while maintaining efficient automated grading.
2Device complexity
If string comparison is used, then the system complexity is low, but the ability to detect mathematical equivalence deteriorates
Solution Approach 1:
The patent segments the mathematical expression into constituent parts (operators, operands, parentheses) and organizes them into a hierarchical syntax tree structure. This segmentation allows the system to compare mathematical equivalence at multiple levels of the tree structure, reliably detecting equivalent expressions while maintaining manageable system complexity through modular parsing logic.
Solution Approach 2:
The patent replaces the mechanical string-matching approach with a symbolic parsing and normalization system. Instead of directly comparing character sequences, the system uses syntax tree construction and traversal algorithms to detect mathematical equivalence, significantly improving reliability while keeping the system computationally manageable.
3Loss of time
If automated grading is implemented, then grading time is reduced, but grading accuracy deteriorates due to inability to handle multiple valid solutions
Solution Approach 1:
The syntax tree serves as an intermediary that enables automated systems to accurately handle multiple valid solutions. By converting both responses and solutions into normalized tree structures, the automated grader can reliably compare mathematical equivalence without time-consuming manual review, simultaneously achieving speed and accuracy.
Solution Approach 2:
The patent changes the data representation parameter from raw strings to normalized syntax trees, enabling automated grading to accurately recognize multiple valid mathematical solutions. This parameter transformation allows the system to maintain both rapid automated processing and high grading accuracy.
Data Source
AI summary
A computerized assessment grading method comprises creating a syntax tree for a received equation-based response to at least one assessment question and a syntax tree for at least one solution to the at least one question, comparing the syntax trees, and grading the response based on the results of the comparison.