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1. Teachers' initial responses to high leverage instances of student mathematical thinking

   Stockero, S. L. ; Peterson, B. E. ; Ochieng, M. A. ; Ruk, J. R. ; Van Zoest, L. R. ; & Leatham, K. R. ( July 2019 , Proceedings of the 43rd Annual Conference of the International Group for the Psychology of Mathematics Education)

   We investigate teachers’ initial in-the-moment responses to instances of high-potential student mathematical thinking (SMT) during whole-class discussion to understand what it means to productively incorporate SMT into instruction. Teachers’ initial responses were coded using the Teacher Response Coding scheme, which disentangles the teacher action, who the response is directed to, and the degree to which the SMT is honored. We found that teachers incorporated students’ actions and ideas in their response, but tended to address the SMT themselves and did not fully take advantage of the SMT. We consider the productivity of teachers’ initial responses in relation to principles of productive use of SMT and compare the results to those of a previous study of teachers’ hypothetical initial responses to SMT in an interview setting. 

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2. Teachers' Initial Responses to High Leverage Instances of Student Mathematical Thinking

   Stockero, Shari L. ; Peterson, Blake E. ; Ochieng, Mary A. ; Ruk, Joshua R. ; Van Zoest, Laura R. ; Leatham, Keith R. ( July 2019 , Proceedings of the 43rd Annual Conference of the International Group for the Psychology of Mathematics Education)

   We investigate teachers’ initial in-the-moment responses to instances of high-potential student mathematical thinking (SMT) during whole class discussion to understand what it means to productively incorporate SMT into instruction. Teachers’ initial responses were coded using the Teacher Response Coding scheme, which disentangles the teacher action, who the response is directed to, and the degree to which the SMT is honored. We found that teachers incorporated students’ actions and ideas in their response, but tended to address the SMT themselves and did not fully take advantage of the SMT. We consider the productivity of teachers’ initial responses in relation to principles of productive use of SMT and compare the results to those of a previous study of teachers’ hypothetical initial responses to SMT in an interview setting. 

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3. Teachers’ responses to instances of student mathematical thinking with varied potential to support student learning

   https://doi.org/10.1007/s13394-020-00334-x  

   Stockero, Shari L. ; Van Zoest, Laura R. ; Freeburn, Ben ; Peterson, Blake E. ; Leatham, Keith R. ( January 2020 , Mathematics Education Research Journal)

   null (Ed.)

   Teacher responses to student mathematical thinking (SMT) matter because the way in which teachers respond affects student learning. Although studies have provided important insights into the nature of teacher responses, little is known about the extent to which these responses take into account the potential of the instance of SMT to support learning. This study investigated teachers’ responses to a common set of instances of SMT with varied potential to support students’ mathematical learning, as well as the productivity of such responses. To examine variations in responses in relation to the mathematical potential of the SMT to which they are responding, we coded teacher responses to instances of SMT in a scenario-based interview. We did so using a scheme that analyzes who interacts with the thinking (Actor), what they are given the opportunity to do in those interactions (Action), and how the teacher response relates to the actions and ideas in the contributed SMT (Recognition). The study found that teachers tended to direct responses to the student who had shared the thinking, use a small subset of actions, and explicitly incorporate students’ actions and ideas. To assess the productivity of teacher responses, we first theorized the alignment of different aspects of teacher responses with our vision of responsive teaching. We then used the data to analyze the extent to which specific aspects of teacher responses were more or less productive in particular circumstances. We discuss these circumstances and the implications of the findings for teachers, professional developers, and researchers. 

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4. Cogenerative Dialogues and Development of the Culturally Relevant Pedagogical Guidelines for Computational Thinking and Computer Science.

   Sirrakos, G. ( January 2023 , American Association for the Advancement of Curriculum Studies Annual Meeting)

   In this proposal, we will share some initial findings about how teacher and student engagement in cogenerative dialogues influenced the development of the Culturally Relevant Pedagogical Guidelines for Computational Thinking and Computer Science (CRPG-CSCT). The CRPG-CSCT’s purpose is to provide computer science teachers with tools to enhance their instruction by accurately reflecting students’ diverse cultural resources in the classroom. Additionally, the CRPG-CSCT will provide guidance to non-computer science teachers on how to facilitate the integration of computational thinking skills to a broad spectrum of classes in the arts, humanities, sciences, social sciences, and mathematics. Our initial findings shared here are part of a larger NSF-funded research project (Award No. 2122367) which aims to better understand the barriers to entry and challenges for success faced by underrepresented secondary school students in computer science, through direct engagement with the students themselves. Throughout the 2022-23 academic year, the researchers have been working with a small team of secondary school teachers, students, and instructional designers, as well as university faculty in computer science, secondary education, and sociology to develop the CRPG-CSCT. The CRPG-CSCT is rooted in the tenets of culturally relevant pedagogy (Ladson-Billings, 1995) and borrows from Muhammad’s (2020) work in Cultivating Genius: An Equity Framework for Culturally and Historically Responsive Literacy. The CRPG-CCT is being developed over six day-long workshops held throughout the academic year. At the time of this submission, five of the six workshops had been completed. Each workshop utilized cogenerative dialogues (cogens) as the primary tool for organizing and sustaining participants’ engagement. Through cogens, participants more deeply learn about students’ cultural capital and the value of utilizing that capital within the classroom (Roth, Lawless, & Tobin, 2000). The success of cogens relies on following specific protocols (Emdin, 2016), such as listening attentively, ensuring there are equal opportunities for all participants to share, and affirming the experiences of other participants. The goal of a cogen is to reach a collective decision, based on the dialogue, that will positively impact students by explicitly addressing barriers to their engagement in the classroom. During each workshop, one member of the research team and one undergraduate research assistant observed the interactions among cogen participants and documented these in the form of ethnographic field notes. Another undergraduate research assistant took detailed notes during the workshop to record the content of small and large group discussions, presentations, and questions/responses throughout the workshops. A grounded theory approach was used to analyze the field notes. Additionally, at the conclusion of each workshop, participants completed a Cogen Feedback Survey (CFS) to gather additional information. The CFS were analyzed through open thematic coding, memos, and code frequencies. Our preliminary results demonstrate high levels of engagement from teacher and student participants during the workshops. Students identified that the cogen structure allowed them to participate comfortably, openly, and honestly. Further, students described feeling valued and heard. Students’ ideas and experiences were frequently affirmed, which served as an important step toward dismantling traditional teacher-student boundaries that might otherwise prevent them from sharing freely. Another result from the use of cogens was the shared experience of participants comprehending views from the other group’s perspective in the classroom. Students appreciated the opportunity to learn from teachers about their struggles in keeping students engaged. Teachers appreciated the opportunity to better understand students’ schooling experiences and how these may affirm or deny aspects of their identity. Finally, all participants shared meaningful suggestions and strategies for future workshops and for the collective betterment of the group. Initial findings shared here are important for several reasons. First, our findings suggest that cogens are an effective approach for fostering participants’ commitment to creating the conditions for students’ success in the classroom. Within the context of the workshops, cogens provided teachers, students, and faculty with opportunities to engage in authentic conversations for addressing the recruitment and retention problems in computer science for underrepresented students. These conversations often resulted in the development of tangible pedagogical approaches, examples, metaphors, and other strategies to directly address the recruitment and retention of underrepresented students in computer science. Finally, while we are still developing the CRPG-CSCT, cogens provided us with the opportunity to ensure the voices of teachers and students are well represented in and central to the document. 

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5. Teacher-Responses: Highlight characteristics of low response process validity for item(s) measuring teachers' pedagogical content knowledge

   Epstein, M. L. ( January 2022 , Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lischka, A. E. (Ed.)

   Response Process Validity (RPV) reflects the degree to which items are interpreted as intended by item developers. In this study, teacher responses to constructed response (CR) items to assess pedagogical content knowledge (PCK) of middle school mathematics teachers were evaluated to determine what types of teacher responses signaled weak RPV. We analyzed 38 CR pilot items on proportional reasoning across up to 13 middle school mathematics teachers per item. By coding teacher responses and using think-alouds, we found teachers' responses deemed indicative of low item RPV often had one of the following characteristics: vague answers, unanticipated assumptions, a focus on unintended topics, and paraphrasing. To develop a diverse pool of items with strong RPV, we suggest it is helpful to be aware of these symptoms, use them to consider how to improve items, and then revise and retest items accordingly. 

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