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There is little empirical research related to how elementary students develop computational thinking (CT) and how they apply CT in problem-solving. To address this gap in knowledge, this study made use of learning trajectories (LTs; hypothesized learning goals, progressions, and activities) in CT concept areas such as sequence, repetition, conditionals, and decomposition to better understand students’ CT. This study implemented eight math-CT integrated lessons aligned to U.S. national mathematics education standards and the LTs with third- and fourth-grade students. This basic interpretive qualitative study aimed at gaining a deeper understanding of elementary students’ CT by having students express and articulate their CT in cognitive interviews. Participants’ ( n = 22) CT articulation was examined using a priori codes translated verbatim from the learning goals in the LTs and was mapped to the learning goals in the LTs. Results revealed a range of students’ CT in problem-solving, such as using precise and complete problem-solving instructions, recognizing repeating patterns, and decomposing arithmetic problems. By collecting empirical data on how students expressed and articulated their CT, this study makes theoretical contributions by generating initial empirical evidence to support the hypothesized learning goals and progressions in the LTs. This article also discusses the implications for integrated CT instruction and assessments at the elementary level. 

For K-8 computer science (CS) education to continue to expand, it is essential that we understand how students develop and demonstrate computational thinking (CT). One approach to gaining this insight is by having students articulate their understanding of CT through cognitive interviews. This study presents findings of a cognitive interview study with 13 fourth-grade students (who had previously engaged in integrated CT and mathematics instruction) working on CT assessment items. The items assessed four CT concepts: sequence, repetition, conditionals, and decomposition. This study analyzed students' articulated understanding of the four CT concepts and the correspondence between that understanding and hypothesized learning trajectories (LTs). We found that 1) all students articulated an understanding of sequence that matched the intermediate level of the Sequence LT; 2) a majority of students' responses demonstrated the level of understanding that the repetition and decomposition items were designed to solicit (8 of 9 responses were correct for repetition and 4 of 6 were correct for decomposition); and 3) less than half of students' responses articulated an understanding of conditionals that was intended by the items (4 of 9 responses were correct). The results also suggested questioning the directional relationships of two statements in the existing Conditionals LT. For example, unlike the LT, this study revealed that students could understand "A conditional connects a condition to an outcome'' before "A condition is something that can be true or false.''