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1. Student inquiry in interesting lessons

   Nieves, Hector I. ; Singh, Rashmi ; Dietiker, Leslie ( January 2020 , Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Sacristán, A. I. ; Cortés-Zavala, J. C. ; Ruiz-Arias, P. M. (Ed.)

   What impact, if any, do interesting lessons have on the types of questions students ask? To explore this question, we used lesson observations of six teachers from three high schools in the Northeast who were part of a larger study. Lessons come from a range of courses, spanning Algebra through Calculus. After each lesson, students reported interest via lesson experience surveys (Author, 2019). These interest measures were then used to identify each teachers’ highest and lowest interest lessons. The two lessons per teacher allows us to compare across the same set of students per teacher. We compiled 145 student questions and identified whether questions were asked within a group work setting or part of a whole class discussion. Two coders coded 10% of data to improve the rubric for type of students’ questions (what, why, how, and if) and perceived intent (factual, procedural, reasoning, and exploratory). Factual questions asked for definitions or explicit answers. Procedural questions were raised when students looked for algorithms or a solving process. Reasoning questions asked about why procedures worked, or facts were true. Exploratory questions expanded beyond the topic of focus, such as asking about changing the parameters to make sense of a problem. The remaining 90% of data were coded independently to determine interrater reliability (see Landis & Koch, 1977). A Cohen’s Kappa statistic (K=0.87, p<0.001) indicates excellent reliability. Furthermore, both coders reconciled codes before continuing with data analysis. Initial results showed differences between high- and low-interest lessons. Although students raised fewer mathematical questions in high-interest lessons (59) when compared with low-interest lessons (86), high-interest lessons contained more “exploratory” questions (10 versus 6). A chi-square test of independence shows a significant difference, χ2 (3, N = 145) = 12.99, p = .005 for types of students’ questions asked in high- and low-interest lessons. The high-interest lessons had more student questions arise during whole class discussions, whereas low-interest lessons had more student questions during group work. By partitioning each lesson into acts at points where the mathematical content shifted, we were able to examine through how many acts questions remained open. The average number of acts the students’ questions remained unanswered for high-interest lessons (2.66) was higher than that of low-interest lessons (1.68). Paired samples t-tests suggest that this difference is significant t(5)=2.58, p = 0.049. Therefore, student interest in the lesson did appear to impact the type of questions students ask. One possible reason for the differences in student questions is the nature of the lessons students found interesting, which may allow for student freedom to wonder and chase their mathematical ideas. There may be more overall student questions in low-interest lessons because of confusion, but more research is needed to unpack the reasoning behind student questions. 

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2. Student interaction discourse moves: characterizing and visualizing student discourse patterns

   https://doi.org/10.1186/s43031-022-00068-9  

   Nennig, Hannah T. ; States, Nicole E. ; Montgomery, Marika T. ; Spurgeon, Sidney G. ; Cole, Renée S. ( January 2023 , Disciplinary and Interdisciplinary Science Education Research)

   Student-centered instruction allows students to take ownership over their learning in the classroom. However, these settings do not always promote productive engagement. Using discourse analysis, student engagement can be analyzed based on how they are interacting with each other while completing in-class group activities. Previous analyses of student engagement in science settings have used methods that do not capture the intricacies of student group interactions such as the flow of conversation and nature of student utterances outside of argumentation or reasoning. However, these features are important to accurately assess student engagement. This study proposes a tiered analytical framework and visualization scheme for analyzing group discussion patterns that allow for a detailed analysis of student discourse moves while discussing scientific topics. This framework allows a researcher to see the flow of an entire conversation within a single schematic. The Student Interaction Discourse Moves framework can be used to extend studies using discourse analysis to determine how student groups work through problems.

    

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3. Teachers' framing of argumentation goals: Working together to develop individual versus communal understanding

   https://doi.org/10.1002/tea.21530  

   González‐Howard, María ; McNeill, Katherine L. ( January 2019 , Journal of Research in Science Teaching)

   For students to meaningfully engage in science practices, substantive changes need to occur to deeply entrenched instructional approaches, particularly those related to classroom discourse. Because teachers are critical in establishing how students are permitted to interact in the classroom, it is imperative to examine their role in fostering learning environments in which students carry out science practices. This study explores how teachers describe, or frame, expectations for classroom discussions pertaining to the science practice of argumentation. Specifically, we use the theoretical lens of a participation framework to examine how teachers emphasize particular actions and goals for their students' argumentation. Multiple‐case study methodology was used to explore the relationship between two middle school teachers' framing for argumentation, and their students' engagement in an argumentation discussion. Findings revealed that, through talk moves and physical actions, both teachers emphasized the importance of students driving the argumentation and interacting with peers, resulting in students engaging in various types of dialogic interactions. However, variation in the two teachers' language highlighted different purposes for students to do so. One teacher explained that through these interactions, students could learn from peers, which could result in each individual student revising their original argument. The other teacher articulated that by working with peers and sharing ideas, classroom members would develop a communal understanding. These distinct goals aligned with different patterns in students' argumentation discussion, particularly in relation to students building on each other's ideas, which occurred more frequently in the classroom focused on communal understanding. The findings suggest the need to continue supporting teachers in developing and using rich instructional strategies to help students with dialogic interactions related to argumentation. This work also sheds light on the importance of how teachers frame the goals for student engagement in this science practice.

    

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4. Cognitive agency and computer-based tasks

   Riling, M. ( January 2018 , Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   As computer-focused policies and trends become more popular in schools, more students access math curriculum online. While computer-based programs may be responsive to some student input, their algorithmic basis can make it more difficult for them to be prepared for divergent student thinking, especially in comparison to a teacher. Consider programs that assess student work by judging how well it matches pre-set answers. Unless designed and enacted in classrooms with care, computer-based curriculum materials might encourage students to think about mathematics in pre-determined ways. How do students approach the process of mathematics while using online materials, especially in terms of engaging in original thought? Drawing on Pickering’s (1995) dance of agency and Sinclair’s (2001) conception of students as path-finders or track-takers, I define two modes of mathematical behavior: trail-taking and bushwhacking. While trail-taking, students follow an established approach, often relying on Pickering’s (1995) disciplinary agency, wherein the mathematics “leads [them] through a series of manipulations” (p. 115). The series of manipulations can be seen as a trail that a student may choose to follow. Bushwhacking, on the other hand, refers to actions a student takes of their own invention. It is possible that, unknown to the student, these actions have been taken before by others. In bushwhacking, the student possesses agency, which Pickering (1995) describes as active (rather than passive) and as hallmarked by “choice and discretion” (p. 117). In this study, students worked in several dynamic geometric environments (DGEs) during a geometry lesson about the midline theorem. The lesson was originally recorded as part of a larger study designing mathematically captivating lessons. Students accessed both problems and online addresses for corresponding DGEs via a printed packet. Students interacted with the DGEs on individual laptops, but were seated in groups of three or four. Passages of group conversations in which students transitioned between trail-taking and bushwhacking were selected for closer analysis, which involved identifying evidence of each mode and highlighting the curricular or social forces that may have contributed to shifts between modes. Of particular interest were episodes in which students asked one another to share results, which led to students reconsidering previously set approaches, and episodes in which students interacted with DGEs containing a relatively high proportion of drag-able components, which corresponded to some students working in bushwhacking mode, spontaneously suggesting and revising approaches for manipulating the DGE (e.g., “unless you make this parallel to the bottom, but I don’t think you... yes you can.”). Both types of episodes were found in multiple groups’ conversations. Further analysis of student interactions with tasks, especially with varying levels of student control and sharing, could serve to inform future computer-based task design aimed to encourage students to productively engage in bushwhacking while problem-solving. 

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5. Teachers’ Vocabulary Talk in Early-Elementary Science Instruction

   https://doi.org/10.1177/1086296X231163117  

   Anderson, Blythe E. ; Wright, Tanya S. ; Gotwals, Amelia Wenk ( March 2023 , Journal of Literacy Research)

   The purpose of this study was to examine the ways in which teachers use language to promote vocabulary development (i.e., vocabulary talk moves) during science instruction in early-elementary classrooms. Twenty-four total science lessons were recorded by eight teachers, providing 894.27 min of observational data across three timepoints. Discourse analysis was used to identify specific research-aligned vocabulary talk moves. Findings revealed that the cohort of teachers used considerably more moves for building students’ knowledge of word meanings than for building students’ awareness of words and word learning or for interesting students in words and word learning. Likewise, the cohort used more authoritative moves (teacher telling) than dialogic moves (inviting student exploration and engagement). This study contributes to the field's understanding of the ways that science instruction supports literacy learning and literacy instruction supports science learning in the early-elementary grades. The findings from this study have implications for teacher professional development and policy.

    

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