In the TIMSS (the Trends in International Mathematics and Science Study) 2023 computer-based assessment, student process data was provided along with other achievement and context questionnaires data. Process data (e.g., response time) provide empirical evidence about the cognitive states and behaviors that occur while working on a test item and that influence how the measured construct(s) translate into item performance (Goldhammer & Zehner, 2017). By revealing underlying response mechanisms beyond the test score, these processes provide evidence supporting the validity of intended interpretations of test scores. This source of validity evidence is emphasized in the Standards for Educational and Psychological Testing (American Educational Research Association, American Psychological Association, and National Council on Measurement in Education, 2014). Examining response processes in TIMSS, as a large-scale assessment, provides valuable insights into the cognitive processes underlying item responses and contributes to a better understanding of the meaning and interpretation of test scores.

There are various approaches to examining response processes, but mixture item response theory (IRT) models have been widely used due to their strengths. Mixture IRT models combine features of traditional IRT models with latent class analysis (LCA) and assume the presence of hidden subpopulations in the data (Sen & Cohen, 2019), which makes them especially useful for examining students’ distinct response strategies. Huang, Luo, and Jeon (2025) reviewed previous models within the mixture IRT framework for studying item-response strategies and proposed a new response time-based mixture IRT model. They grouped existing approaches into two categories: examinee-level mixture models (e.g., Jeon & De Boeck, 2019) and examinee-by-item-level mixture models (e.g., Nagy & Robitzsch, 2021). While examinee-level models assume that test-takers employ the same response strategy throughout the assessment, examinee-by-item-level models allow test-takers to switch between response strategies (Huang et al., 2025). The examinee-by-item-level mixture model proposed by Huang et al. (2025) assumes the presence of multiple latent classes, including one regular ability-based class (modeled using a two-parameter logistic [2PL] IRT model) and one or more non-ability-based secondary classes (e.g., rapid guessing, knowledge retrieval), and incorporates response times to predict examinee-by-item class membership. This modeling approach allows examinees to switch between response strategies across items, which is likely in practice, as they may use different strategies depending on item properties (e.g., difficulty, complexity) or other factors (e.g., fatigue, lack of motivation).

In this study, we aim to explore which response strategies eighth-grade students use when responding to TIMSS 2023 mathematics items in Türkiye and Finland, two countries with similar average mathematics achievement. We apply a response time-based mixture IRT model proposed by Huang et al. (2025) to both easy and difficult item groups to examine potential differences in response processes across item difficulty levels.

The study uses a subset of Finland and Türkiye TIMSS 2023 eighth-grade mathematics achievement and process data, which are publicly available from the International Association for the Evaluation of Educational Achievement (IEA) (https://www.iea.nl/data-tools/repository/timss). In TIMSS 2023, each student is randomly assigned to one of 14 test booklets, each consisting of two mathematics and two science item blocks. Each item block appears in two booklets and is paired with different item blocks (Mullis, Martin, & von Davier, 2021). Because each student receives a different set of items, we focus on item blocks to maintain a consistent item sequence and enable clearer interpretation of response processes. The assessment booklets are divided into two levels of difficulty: less difficult and more difficult (Mullis et al., 2021). We select two mathematics item blocks: one from the less difficult set (ME1) and one from the more difficult set (MD3). The ME1 block appears in Booklets 8 and 9, whereas the MD3 block appears in Booklets 2 and 5. The ME1 item block contains 14 items (scored 0/1), while the MD3 block contains 15 items (scored 0/1). TIMSS 2023 provides student process data files that include three types of variables related to students’ on-screen navigation during the assessment: total time on screen, time on first screen visit, and number of screen visits (Fishbein, Taneva, & Kowolik, 2025). To meet the requirements of response time-based modeling, we use total time on screen as the response time variable. For the analysis, we will estimate two models separately for each item block and each country: (1) a 2PL model (DeMars, 2010) as baseline model and (2) a two-class examinee-by-item mixture IRT model proposed by Huang et al. (2025). The mixture IRT model will include two latent classes: an ability-based class and a secondary (i.e., non-ability-based) response class. The latent class variable will be regressed on double-centered, log-transformed response times as suggested. All models will be estimated using maximum likelihood with robust standard errors (MLR). Analyses will be conducted using Mplus Version 9 (Muthén & Muthén, 1998–2017).

We expect that the two-class examinee-by-item mixture IRT model will fit the data better than the standard two-parameter logistic (2PL) IRT model, suggesting the presence of a secondary response process in addition to the regular ability-based one. Response time deviations are anticipated to be associated with these response processes. In particular, shorter response times accompanied by a high probability of correct answers may reflect rapid knowledge retrieval strategies, whereas longer response times with a high probability of correct answers may reflect more effortful knowledge retrieval strategies (Huang et al., 2025). Through cross-country and cross-item-block comparisons, the results are expected to offer deeper insights into the underlying cognitive processes employed by students in the TIMSS 2023 mathematics assessment. Overall, the findings are expected to contribute to understanding how students engage with assessment tasks of varying difficulty and how response processes relate to score interpretation.

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