TitleUsing Computerized Adaptive Testing to Detect Students’ Misconceptions: Exploration of Item Selection
Publication TypeConference Paper
Year of Publication2017
AuthorsShen, Y, Bao, Y, Wang, S, Bradshaw, L
Conference NameIACAT 2017 Conference
Date Published08/2017
PublisherNiigata Seiryo University
Conference LocationNiigata, Japan
KeywordsCAT, incorrect answering, Student Misconception

Owning misconceptions impedes learning, thus detecting misconceptions through assessments is crucial to facilitate teaching. However, most computerized adaptive testing (CAT) applications to diagnose examinees’ attribute profiles focus on whether examinees mastering correct concepts or not. In educational scenario, teachers and students have to figure out the misconceptions underlying incorrect answers after obtaining the scores from assessments and then correct the corresponding misconceptions. The Scaling Individuals and Classifying Misconceptions (SICM) models proposed by Bradshaw and Templin (2014) fill this gap. SICMs can identify a student’s misconceptions directly from the distractors of multiple-choice questions and report whether s/he own the misconceptions or not. Simultaneously, SICM models are able to estimate a continuous ability within the item response theory (IRT) framework to fulfill the needs of policy-driven assessment systems relying on scaling examinees’ ability. However, the advantage of providing estimations for two types of latent variables also causes complexity of model estimation. More items are required to achieve the same accuracies for both classification and estimation compared to dichotomous DCMs and to IRT, respectively. Thus, we aim to develop a CAT using the SICM models (SICM-CAT) to estimate students’ misconceptions and continuous abilities simultaneously using fewer items than a linear test.

To achieve this goal, in this study, our research questions mainly focus on establishing several item selection rules that target on providing both accurate classification results and continuous ability estimations using SICM-CAT. The first research question is which information criterion to be used. The Kullback–Leibler (KL) divergence is the first choice, as it can naturally combine the continuous and discrete latent variables. Based on this criterion, we propose an item selection index that can nicely integrate the two types of information. Based on this index, the items selected in real time could discriminate the examinee’s current misconception profile and ability estimates from other possible estimates to the most extent. The second research question is about how to adaptively balance the estimations of the misconception profile and the continuous latent ability. Mimic the idea of the Hybrid Design proposed by Wang et al. (2016), we propose a design framework which makes the item selection transition from the group-level to the item-level. We aim to explore several design questions, such as how to select the transiting point and which latent variable estimation should be targeted first.

Preliminary results indicated that the SICM-CAT based on the proposed item selection index could classify examinees into different latent classes and measure their latent abilities compared with the random selection method more accurately and reliably under all the simulation conditions. We plan to compare different CAT designs based on our proposed item selection rules with the best linear test as the next step. We expect that the SICM-CAT is able to use shorter test length while retaining the same accuracies and reliabilities.


Bradshaw, L., & Templin, J. (2014). Combining item response theory and diagnostic classification models: A psychometric model for scaling ability and diagnosing misconceptions. Psychometrika, 79(3), 403-425.

Wang, S., Lin, H., Chang, H. H., & Douglas, J. (2016). Hybrid computerized adaptive testing: from group sequential design to fully sequential design. Journal of Educational Measurement, 53(1), 45-62.

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