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Paper presentation at the Utah Council of Teachers of Mathematics Conference 

The paper describes an intervention to support teachers and paraprofessionals to integrate mathematics and computer science. Expansive Framing is the theoretical framework used to support transfer. It might help to communicate clearly the connections between mathematics and computer science and how EF supports in making these connections. A couple of examples might help the reader understand what expansive framing means in the context of the problems and communicate the efficacy of the approach and limitations if any. It does add value to the discussions. This paper describes the engagement of teams to co-design of curriculum, drawing on Expansive Framing theory to encourage transfer of learning. Preliminary results are reported on the value of EF when clearly explicated in the lesson plans. This paper will be a valuable inclusion in this TSG. In reviewing this paper, check word and page length to adhere to template; if possible, it would be good to consider implications of your work with reference to scalability and sustainability. 

The learning sciences community is currently exploring new ways to enact productive and equitable co-design research-practice partnerships that are sensitive to all the concerns and needs of stakeholders. The paper contributes to that still-growing literature through an interaction analysis of a co-design discussion involving school district partners that unfolded about cultural relevance and sensitivity in relation to the use of a specific image in an elementary school coding lesson. The episode involved looking moment-by-moment at how district educators recognized and acknowledged that a specific design decision could be harmful for a minoritized population of students enrolled in the district. However, once a key change was made to be more culturally responsive and considerate, new and unexpected pedagogical challenges appeared. This case serves to illustrate some of the unexpected tensions that can appear in real-time when unanticipated questions about cultural relevance are foregrounded during lesson and materials co-design. 

The learning sciences community is currently exploring new ways to enact productive and equitable co-design research-practice partnerships that are sensitive to all the concerns and needs of stakeholders. The paper contributes to that still-growing literature through an interaction analysis of a co-design discussion involving school district partners that unfolded about cultural relevance and sensitivity in relation to the use of a specific image in an elementary school coding lesson. The episode involved looking moment-by-moment at how district educators recognized and acknowledged that a specific design decision could be harmful for a minoritized population of students enrolled in the district. However, once a key change was made to be more culturally responsive and considerate, new and unexpected pedagogical challenges appeared. This case serves to illustrate some of the unexpected tensions that can appear in real-time when unanticipated questions about cultural relevance are foregrounded during lesson and materials co-design. 

This study examines how a rural-serving school district aimed to provide elementarylevel computer science (CS) by offering instruction during students’ computer lab, a class taught by paraprofessional educators with limited background in computing. As part of a researchpractice partnership, cross-context mathematics and CS lessons were co-designed to expansively frame and highlight connections across – as opposed to integration within – the two subjects. Findings indicate that the paraprofessionals teaching the lessons generally reported positive experiences and understanding of content; however, those less comfortable with the content reported lower student interest. Further, most students who engaged with the lessons across the lab and classroom contexts reported finding the lessons interesting, seeing connections to their mathematics classes, and understanding the programming. In contrast, students who only learned about mathematics connections within the CS lessons (thus not in a cross-context way) reported significantly lower levels of interest, connections, and understanding. 

Planning a path from an origin to a destination is a common task for studying children’s spatial thinking and a foundational part of many early programming environments. This paper examines children’s means of abstraction between the grid space and the program domain through an exploration of the strategies they used to plan a robot’s routes in 2-D space. Qualitative analysis focused on ways children used materials to aid in spatial planning and programming, advancing previous work on material anchors for concepts (Hutchins, 2005). Through an elaboration of several path planning strategies, we illustrate how children varied in their use of materials in space to represent a path-program relationship. We argue that these strategies represent multiple ways of contextualizing and abstracting in a programming task, with implications for design of equitable CT assessments in early childhood. 

Many coding environments for young children involve using navigational arrow codes representing four movements: forward, backwards, rotate left, and rotate right. Children interpreting these four, seemingly simple codes encounter a complex interaction of spatial thinking and semantic meaning. In this study of how children interpret directional arrows, we found that they interpret each of the arrows as encoding many meanings and that the orientation of the agent plays a critical role in children’s interpretations. Through iterative rounds of qualitative coding and drawing on two examples, we unpack some common interpretations. 

With growing interest in supporting the development of computational thinking (CT) in early childhood, there is also need for new assessments that serve multiple purposes and uses. In particular, there is a need to understand the design of formative assessments that can be used during classroom instruction to provide feedback to teachers and children in real-time. In this paper, we report on an empirical study and advance a new unit of observational analysis for formative assessment that we call an indicator of a knowledge refinement opportunity or as a shorthand , KRO indicators . We put forth a new framework for conceptualizing the design of formative assessments that builds on the Evidence Centered Design framework but centers identification and analysis of indicators of knowledge refinement opportunities. We illustrate a number of key indicators through empirical examples drawn from video recordings of Kindergarten classroom lessons. 

In this chapter, we share observations from a multiyear design-based research project exploring how to teach developmentally appropriate coding concepts and skills in kindergarten. We focus on coding toys that fit within a genre we call “grid- agent” robot coding toys. These are robots that are specifically for early childhood, commercially available, screen-free, tangible, moveable and programmable. Grid- agent robot toys invite children to explore mathematics through precise movements across a grid space.