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Representing Student Performance with Partial Credit

Inproceedings

Representing Student Performance with Partial Credit

1. Example of different Partial Credit. We conducted two analyses on 52,529 data records from 72 students in order to evaluate the predictive power of partial credit in comparison to traditional binary performance. The first analysis compares the predictive power of the mean value of all the previous performances. As a baseline we used a logistic regression model with binary performance as the dependent, and student id as an independent. We then compare using mean previous partial credit vs. mean previous binary performance as independents in the model. The results are shown in Table 2. The model with mean previous partial credit gets a 0.0019 better R-squared than the one with mean previous binary credit. The absolute numerical improvement is small, which indicates that it is difficult to substantially improve student modeling. On the other hand, because knowing mean previous binary performance only brings 0.0046 better R-squared over baseline, knowing mean previous partial credit brings a relative 41.3% better R-squared compared to it. Table 2. Comparison between partial credit and binary performance. In the second analysis, instead of the mean value of previous performances, we compare the predictive power of the trends of these two measures of performance. We choose data in which students have 5 opportunities in one skill and use the previous 4 performances to create a trend line to predict the value of the 5th performance. To smooth the result and generate a bounded prediction between 0 and 1, we also apply a logistic regression model to this prediction. The result is shown in the fourth and fifth column of Table 2. Using partial credit improves R-squared by about 0.002 compared to using binary performance. This result is consistent with analysis 1. 3 Conclusions and Future work. In this paper we present a naïve algorithm to assign partial credit given detailed student responses. Partial credit performance contains much more information than binary performance, which is currently used in almost all researchers in the educational data mining field. Evaluations show that partial credit improves student model fitting by only a small absolute value but a high relative value compared to the binary performance. One question we are interested in is how to refine the algorithm to better fit student data and infer student knowledge. Also, we are interested in finding out in which situations partial credit does better than binary performance, so we can use it as an efficient complement to all the current models that use only the binary performance.

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