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Estimating Student Competence in Engineering Statics From a Lexical Analysis of Handwritten Equations


We present a technique that examines handwritten equations from a student's solution to an engineering statics problem and estimates the correctness of the work. The solution is recorded with a smartpen that digitizes the writing with time stamps. Our technique first separates equation pen strokes from other content, such as diagrams. Then the equation pen strokes are grouped first into individual equations, then into individual characters. A character recognizer is used to recognize each character, and then a Hidden Markov Model is used to correct recognition errors. The equation text is characterized by a set of features. Some of these describe the frequency of various symbols and symbol combinations, such as a letter following a mathematical operator. One feature describes the frequency with which units of measure (e.g., "kg") appear, while another describes inter-character pauses. This set of features is used to construct SVM regression models to predict the correctness of the work. We tested our approach on a corpus of solutions to exam problems from an undergraduate statics course. The SVM models predicted the grade assigned by the instructor with an average coefficient of determination of 36%. We also combined our features with an existing set of features that describe the temporal and spatial organization of a handwritten solution a statics problem. Using both sets of features, the SVM models predicted the grade on the exam problems with an average coefficient of determination of 56%. This is a surprising result given that none of the features consider the semantic content of the writing, or even the correctness of a student's final answer.

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