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  1. Evans, T ; Marmur, O ; Hunter, J ; Leach, G ; Jhagroo, J (Ed.)
    This case study of one first grade student involves the analysis of three interviews that took place before, during, and after classroom teaching experiments (CTEs). The CTEs were designed to engage children in representing algebraic concepts using graphs. Using a knowledge-in-pieces perspective, our analysis focused on identifying students’ natural intuitions and ways of thinking algebraically about a functional relationship represented using graphs. Findings reveal four seeds, two of which were identified in prior studies, and how the activation and coordination of these seeds results in students' production of function graphs. 
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    Free, publicly-accessible full text available July 21, 2025
  2. Lindgren, R ; Asino, T I ; Kyza, E A ; Looi, C K ; Keifert, D T ; Suárez, E (Ed.)
    This study involved a 7-lesson generalized arithmetic classroom teaching experiment (CTE) with kindergarten students. We interviewed four students individually before and after the seven weeks to explore their understandings and representations of arithmetic properties. Here, we report on students' responses to questions on the additive inverse property. Using Skemp’s framework of relational and instrumental understandings (2006), our analysis revealed that most of the interviewed kindergarteners could understand the additive inverse relationally by the end of the CTE. Our interviews revealed that tables and number lines enabled students to articulate more sophisticated understandings of the additive inverse. 
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    Free, publicly-accessible full text available June 14, 2025
  3. Gestures are one of the ways in which mathematical cognition is embodied and have been elevated as a potentially important semiotic device in the teaching of mathematics. As such, a better understanding of gestures used during mathematics instruction (including frequency of use, types of gestures, how they are used, and the possible relationship between gestures and student performance) would inform mathematics education. We aim to understand teachers’ gestures in the context of early algebra, particularly in the teaching of the equal sign. Our findings suggest that the equal sign is a relatively rich environment for gestures, which are used in a variety of ways. Participating teachers used gestures frequently to support their teaching about the equal sign. Furthermore, the use of gestures varied depending on the particular conception of the equal sign the instruction aimed to promote. Finally, teacher gesture use in this context is correlated with students’ high performance on an early algebra assessment. 
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    Free, publicly-accessible full text available May 8, 2025