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Objective Scoring Partial Credits by Tracking Failure Cascade in Mechanics Problem Solving

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2020 ASEE Virtual Annual Conference Content Access


Virtual On line

Publication Date

June 22, 2020

Start Date

June 22, 2020

End Date

June 26, 2021

Conference Session

Grading and Feedback Models in Mechanics

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Paper Authors


Andrew Dongjin Kim Georgia State University

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Andrew Dongjin Kim is an Assistant Professor of Computer Science and Engineering at Georgia State University.

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Consistent and objective grading open-ended questions for mechanics course problems is a challenge, especially in terms of offering partial credits to failures arising from mistakes. In general, there is no standard grading rubric for failures, and in most cases, it solely depends on each instructor’s decision as well as each question’s level of difficulty and the length of its solution. This study aimed at finding an alternative way that assesses students’ integrative interpretation-planning-execution level in solving the open-ended questions as well as objectively tracks students’ failures that cascade incorrect results. One method proposed here is using a variable-based question set. Differently from traditional open-ended questions, the proposed model consists of a sub-question set - the sub-questions are listed in a sequence of suggested solving procedure such that if a student successfully solves the sub-questions s/he will be able to reach the final answer that was ultimately requested to be determined by the main question statement. This indicates that if a student could not solve the previous sub-question correctly, that error will cascade toward the following sub-questions. The variable-based sub-question sequence was designed as it was considered as the possible finest level of the question set. Error cascade was tracked by plugging student’s answers from the previous steps in the equation for the current step. A MATLAB script was used to repeat this failure tracking for all sub-questions. If the student’s answer for the current step was the same as the result from the failure tracking subroutine, it was considered as the student has obtained the incorrect answer due to the calculation error that occurred during the previous step, and thus the deducted points were returned. Otherwise, the failure was considered as an individual calculation error or the result of misconception. Collected two years assessment results at Georgia State University’s engineering courses were examined, and the statistics revealed that average 60% (± 22%) of students were at the risk of losing points due to error cascade; average 10% points (± 6% points) were detected as deducted points due to the effect of failure cascade, and more number of the sub-questions set could detect more cascaded errors. The algorithm applied in this study can also be deployed to automatic grading along with providing standardized feedback messages.

Kim, A. D. (2020, June), Objective Scoring Partial Credits by Tracking Failure Cascade in Mechanics Problem Solving Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--35005

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