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1. Introducing An RME-Based Task Sequence to Support the Guided Reinvention of Vector Spaces

   Plaxco, D.; Andrews-Larson, C.; Smith, J.; Kim, M.; Mauntel, M.; Watford, M. (January 2021, 2021 Research in Undergraduate Mathematics Education Reports)

   Karunakaran, S.; Higgins, A. (Ed.)

   In this paper, we introduce an RME-based (Freudenthal, 1991) task sequence intended to support the guided reinvention of the linear algebra topic of vector spaces. We also share the results of a paired teaching experiment (Steffe & Thompson, 2000) with two students. The results show how students can leverage their work in the problem context to develop more general notions of Null Space. This work informs further revisions to the task statements for using these materials in a whole-class setting. 

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2. Introducing An RME-Based Task Sequence to Support the Guided Reinvention of Vector Spaces

   Plaxco, D. (January 2021, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   S. S. Karunakaran, & A. (Ed.)

   In this paper, we introduce an RME-based (Freudenthal, 1991) task sequence intended to support the guided reinvention of the linear algebra topic of vector spaces. We also share the results of a paired teaching experiment (Steffe & Thompson, 2000) with two students. The results show how students can leverage their work in the problem context to develop more general notions of Null Space. This work informs further revisions to the task statements for using these materials in a whole-class setting. 

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3. Analyzing Children’s Spatial Reasoning Using an Existing Learning Progression: Insights from Interviews and Task Performance

   https://doi.org/10.1007/s10643-025-01862-6  

   Pinilla, Robyn K; Wellberg, Sarah; Castro-Faix, Moraima; Ketterlin-Geller, Leanne R (February 2025, Early Childhood Education Journal)

   Spatial reasoning comprises a set of skills used to mentally visualize, orient, and transform objects or spaces. These skills, which develop in humans through interaction with our physical world and direct instruction, are strongly associated with mathematics achievement but are often neglected in early grades mathematics teaching. To conceptualize ways to increase the representation of spatial reasoning skills in the classroom, we examined the outcomes of cognitive interviews with kin- dergarten through grade two students in which they engaged with one spatial reasoning task. Qualitative analyses of students’ work samples and verbal reasoning responses on a single shape de/composition task revealed evidence of a continuum of sophistication in their responses that supports a previously articulated hypothetical learning progression. Results suggest that teachers may be able to efficiently infer students’ skills in spatial reasoning using a single task and use the results to make instructional decisions that would support students’ mathematical development. The practical implications of this work indicate that additional classroom-based research could support the adoption of such practices that could help teachers efficiently teach spatial reasoning skills through mathematics instruction. 

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4. Characterising Individual-Level Collaborative Learning Behaviours Using Ordered Network Analysis and Wearable Sensors

   Yan, L; Swiecki, Z; Gašević, D; Zhao; L; Li, X; Martinez-Maldonado; R; Tan; Y; et al (October 2023, Springer, Cham)

   Irgens, G; Knight, S (Ed.)

   Wearable positioning sensors are enabling unprecedented opportunities to model students’ procedural and social behaviours during collaborative learning tasks in physical learning spaces. Emerging work in this area has mainly focused on modelling group-level interactions from low-level x-y positioning data. Yet, little work has utilised such data to automatically identify individual-level differences among students working in co-located groups in terms of procedural and social aspects such as task prioritisation and collaboration dynamics, respectively. To address this gap, this study characterised key differences among 124 students’ procedural and social behaviours according to their perceived stress, collaboration, and task satisfaction during a complex group task using wearable positioning sensors and ordered networked analysis. The results revealed that students who demonstrated more collaborative behaviours were associated with lower stress and higher collaboration satisfaction. Interestingly, students who worked individually on the primary and secondary learning tasks reported lower and higher task satisfaction, respectively. These findings can deepen our understanding of students’ individual-level behaviours and experiences while learning in groups. 

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5. Using Collaborative Interactivity Metrics to analyze students’ Problem-Solving Behaviors during STEM+C Computational Modeling Tasks

   Snyder Caitlin; Hutchins, Nicole; Cohn, Clayton; Fonteles, Joyce; Biswas, Gautam (September 2023, Learning and individual differences)

   Grieff, S. (Ed.)

   Recently there has been increased development of curriculum and tools that integrate computing (C) into Science, Technology, Engineering, and Math (STEM) learning environments. These environments serve as a catalyst for authentic collaborative problem-solving (CPS) and help students synergistically learn STEM+C content. In this work, we analyzed students’ collaborative problem-solving behaviors as they worked in pairs to construct computational models in kinematics. We leveraged social measures, such as equity and turn-taking, along with a domain-specific measure that quantifies the synergistic interleaving of science and computing concepts in the students’ dialogue to gain a deeper understanding of the relationship between students’ collaborative behaviors and their ability to complete a STEM+C computational modeling task. Our results extend past findings identifying the importance of synergistic dialogue and suggest that while equitable discourse is important for overall task success, fluctuations in equity and turn-taking at the segment level may not have an impact on segment-level task performance. To better understand students’ segment-level behaviors, we identified and characterized groups’ planning, enacting, and reflection behaviors along with monitoring processes they employed to check their progress as they constructed their models. Leveraging Markov Chain (MC) analysis, we identified differences in high- and low-performing groups’ transitions between these phases of students’ activities. We then compared the synergistic, turn-taking, and equity measures for these groups for each one of the MC model states to gain a deeper understanding of how these collaboration behaviors relate to their computational modeling performance. We believe that characterizing differences in collaborative problem-solving behaviors allows us to gain a better understanding of the difficulties students face as they work on their computational modeling tasks. 

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