Handwritten Graph Regression Selection for Online Math Assessment
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Solution Overview
Problem
In online tests, particularly in mathematics, it is challenging for students to accurately draw graphs by handwriting on a computer, and teachers struggle to assess the understanding of such hand-drawn graphs.
Innovation Solution
A system that uses a computer-readable storage medium and server to acquire plot points from handwriting inputs, apply regression models to calculate multiple graph data, determine graph data within predetermined coordinate ranges, and select the best regression result for drawing a graph.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a graph is automatically drawn based on an input graph formula, then the graph drawing accuracy is improved, but the ability to assess student understanding deteriorates
Solution Approach 1:
The system creates a standardized copy of the hand-drawn graph by applying regression analysis to the handwritten plot points. This generates a clean, accurate graph representation that preserves the student's original drawing intent while eliminating handwriting imperfections, thus maintaining assessment capability while improving visual accuracy.
2Loss of information
If a student draws a graph by handwriting on a computer, then the ability to assess student understanding is improved, but the graph drawing accuracy deteriorates
Solution Approach 1:
The system introduces regression analysis as an intermediary process between the student's hand-drawn graph and the final presentation. The regression model acts as a mediator that transforms the imperfect handwritten input into an accurate graph representation, preserving the student's original work while improving its visual quality for assessment.
3Manufacturing precision
If multiple regression models are used to calculate graph data, then the graph drawing accuracy is improved, but the device complexity increases
Solution Approach 1:
The system segments the graph generation task by applying multiple different regression models (e.g., linear regression, polynomial regression) to the same set of plot points. Each model provides a different interpretation of the underlying pattern, and the system compares these segmented results to determine the most appropriate graph representation, thereby improving accuracy through diversified analysis.
Data Source
AI summary
A non-transitory storage medium stores a graph drawing program for causing a computer to execute acquiring a plot point of a first graph by a handwriting input, regressively calculating a plurality of graph data by a plurality of regression models, based the acquired plot point, performing first determination to determine, in regard to each of the graph data, whether at least a partial data element is included in a predetermined range of coordinates, performing second determination to determine graph data having a good regression accuracy among the plurality of graph data, selecting one of the graph data, based on a result of the first determination and a result of the second determination and drawing a second graph in place of the first graph, based on the selected graph data.