Automated Grading of Handwritten Math Expressions
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Solution Overview
Problem
Current grading systems are inadequate for automatically assessing subjective problems with mathematical expressions, particularly in STEM fields, as they require human intervention and lack efficient methods for evaluating intermediate steps and providing feedback, while also being resource-intensive in terms of data and computational power.
Innovation Solution
A system and method that converts hand-written mathematical expressions into digital format using LaTeX for grading, employing machine learning and state estimation to check derivations, suggest corrections, and identify matching handwriting via a Siamese Neural Network, allowing for automated grading and feedback without requiring extensive data or computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If current grading systems are used for subjective problems with mathematical expressions, then human intervention is required for grading, but this increases instructor workload and time consumption
Solution Approach 1:
The patent replaces the mechanical system of manual grading with an automated computer-based system that uses optical character recognition (OCR) to capture handwritten mathematical expressions, converts them to digital format, and automatically grades them by comparing against solution keys, thereby eliminating the need for instructor intervention in the grading process
Solution Approach 2:
The system enables students to submit their handwritten assignments digitally, which are then automatically processed and graded by the computer system without requiring instructor time, allowing the grading function to serve itself through automation
2Extent of automation
If scantron or simple software programs are used for grading, then objective problems can be graded automatically, but intermediate steps and subjective problems cannot be assessed
Solution Approach 1:
The patent segments the grading process into distinct components: capturing individual handwritten expressions, converting each to digital format, storing them in sequence, and comparing each against corresponding solution steps, enabling granular assessment of intermediate work rather than only final answers
Solution Approach 2:
The system creates a universal grading platform that can handle multiple types of problems (objective and subjective), multiple formats (handwritten and typed), and multiple grading levels (intermediate steps and final answers) through a single integrated system using OCR and digital expression processing
3Extent of automation
If AI models like Gemini or ChatGPT are used for math grading, then automated grading is possible, but vast amounts of data and computational power are required
Solution Approach 1:
The patent uses lightweight, simple algorithms for comparing mathematical expressions against solution keys rather than deploying large, resource-intensive AI models, achieving adequate grading functionality with minimal computational resources by using straightforward pattern matching and expression comparison techniques
Data Source
AI summary
A system and method for the automatic grading of mathematical expressions includes importing a hand-written answer, converting the hand-written answer to a LaTeX formula, creating a model with noise to compare one or more mathematical expressions, checking the correctness of derivations between the mathematical expressions, applying machine learning and/or state estimation theory to determine the mistakes, and suggesting correct coefficients for the derivation. The system and method may further include identifying the handwriting of students using machine learning to determine whether cheating or copying has occurred.