In this influential book from collaborative authors Megan L Franke, Elham Kazemi, and Angela Chan Turrou, explores ways in which two routines -- Choral Counting and Counting Collections -- can ...transform your elementary math classroom, your students' math understanding, and your partnerships with families.
Background: Current efforts to promote reasoning, problem solving, and discussion are often framed as advancing equity, but scholarship suggests individual students' opportunities to learn can vary ...considerably in classrooms that attempt to take up these approaches to teaching mathematics. Noticing students' mathematical strengths and positioning their contributions as competent is among aspects of instruction associated with more equitable learning outcomes for students from marginalized groups, but research has yet to comprehensively examine the range and nuance of this aspect of teachers' practice in classrooms that feature broad distributions of participation. Purpose: The purpose of this study was to examine teachers' instructional practice with respect to assigning competence in two mathematics classrooms that demonstrated high levels of student participation. We investigated the kinds of situations in which teachers positioned students as competent, and the ways assigning competence opened opportunities to participate. Setting: Data were collected at a public elementary school in a culturally, linguistically, and economically diverse neighborhood in southern California. Participants: Participants included two teachers and 45 students from two third-grade classrooms. Teachers had participated in ongoing professional development focused on leveraging children's mathematical thinking in instruction. Research Design: We drew from qualitative methods for analyzing video to investigate classroom interactions from 12 mathematics lessons. Data sources included video recordings, transcripts, and student work. We used Studiocode software to parse each lesson into phases and episodes. Drawing from previous studies, we identified a subset of episodes in which teachers explicitly positioned a student's contribution as competent. An iterative process of coding and discussion was used to analyze patterns with respect to student participation, teacher support, and the unfolding of rights and obligations related to participating in mathematical activity. Findings: Analyses revealed different kinds of situations in which students participated in mathematically substantive ways (in terms of providing detailed explanations of their ideas or engaging with the details of a peer's idea) and teachers positioned their contributions as competent. These situations included highlighting, clarifying, and amplifying contributions; supporting the specificity of student contributions; recognizing emergent ideas; and validating unprompted attention to mathematical details. Assignments of competence emerged in ways that were integrated into teachers' ongoing efforts to surface and make explicit the details of their mathematical ideas, while also broadening the kinds of contributions students could make to joint mathematical work. Conclusions: Helping students to know what it could look and sound like to participate in the moment while recognizing a wide range of contributions as competent created openings for students who in many classrooms might be excluded or relegated to the periphery of conversations. Making competence explicit was a contingent, relational practice that required teachers to find specific ways of leveraging student strengths to support their participation. Recommendations for advancing mathematics teaching must attend to the nuances with which particular practices unfold to open or constrain individual students' opportunities to learn.
Cognitively Guided Instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students’ mathematical thinking, they struggle with how to follow up on student ...ideas. This study examines the classrooms of three teachers who had engaged in algebraic reasoning CGI professional development. We detail teachers’ questions and how they relate to students’ making explicit their complete and correct explanations. We found that after the initial “How did you get that?” question, a great deal of variability existed among teachers’ questions and students’ responses.
Understanding how learning environments productively mobilize children's ideas as resources for participation in joint activity is an ongoing focus of research on classroom instruction. We ...investigated whole-class mathematics conversations in which multiple students participated in ways previous research suggests are consequential for learning. We found that in such conversations, students rarely presented the entirety of their solutions before other students engaged. Rather, incomplete explanations and written representations that emerged over time created entry points for other students to contribute in mathematically substantive ways. These aspects of student participation operated in combination with teachers' in-the-moment responses to create opportunities for, and publicly recognize, different kinds of contributions as resources for collective work. Our findings suggest that, rather than challenges to communication that must be overcome, students' vague, unfinished, and ambiguous ideas present productive contributions that can be leveraged to support collective mathematical work.
► Student participation in classroom conversations predicted student achievement. ► Achievement was best predicted by student engagement with each other's ideas. ► Teachers used multiple ...instructional practices to encourage student engagement. ► Teacher follow-up to initial moves had important effects on student engagement.
This paper explores the relationships between student participation in classroom conversations, teacher practices, and student learning in elementary school mathematics classrooms. Six teachers and 111 children aged 8–10 participated in the study. Students and teachers were videotaped as they discussed how to solve mathematical problems during whole-class and small-group discussions. The results show that the level of student engagement with each other's ideas and the incidence of students providing detailed explanations of their problem-solving strategies were positively related to student achievement. While teachers used a variety of instructional practices to encourage students to attend to and engage with each other's thinking, how teachers followed up on their initial moves was important for whether students engaged with others’ ideas at a high level.
Educators, researchers, and policy makers increasingly recognize that participation in classroom mathematics discussions, especially engaging with others’ ideas, can promote students’ mathematics ...understanding. How teachers can promote students’ high-level engagement with others’ ideas, and the challenges teachers face when trying to do so, have not often been studied, however. Using coding of videotaped whole-class and small-group discussions in 12 elementary school classrooms, we analyzed the level at which students engaged with each other’s mathematical ideas and the moves teachers used—both moves to invite student engagement and follow-up moves to encourage deeper engagement—to support student engagement. Teachers used a wide variety of invitation and follow-up moves to encourage student engagement and combined them in multiple ways in the moment to address the challenges students faced when trying to engage with others’ ideas. We show the limitations of teachers’ initial moves to stimulate engagement and the power of their follow-up moves to foster productive student struggle with the mathematics.
Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one's own thinking and engaging with others' ideas, can ...promote students' mathematics learning. However, precisely how participating in these ways supports learning has not often been examined in detail. Using in-depth analyses of videotaped whole-class discussions, small-group collaborative work, and private partner conversations in two third-grade mathematics classrooms on six occasions over a five- month period, we show advances that students made in their mathematical thinking or mathematical work in the context of explaining their thinking and/or engaging with others' ideas. The detailed analyses focus on students who had previously scored low on standardized tests of mathematics proficiency. The results show how students not considered to have extensive mathematics knowledge can forge new connections between mathematical ideas and representations, and extend their problem-solving strategies in ways that are directly related to their participation.
Accountability mandates linked to state education standards and assessments have largely replaced play in early childhood classrooms. This approach limits educators' opportunities by preventing them ...from using play as a means of identifying and expanding children's diverse range of competencies. In this ethnographic case study, we explore how young children living in a multilingual, new immigrant community use literacy and numeracy practices in play. Drawing from sociocultural theory and ethnomathematics, and highlighting their voices and perspectives, we show how three kindergarten-aged children draw on a broad repertoire of symbolic practices to make meaning as they work together in their play-based afterschool programme. By examining how children use literacy, numeracy and language through their play, we detail how the children collaboratively demonstrate and build knowledge as they build a castle and represent it through a blueprint. We offer implications for how teacher education can better prepare teachers to recognize the diverse range of skills and understandings children bring to school.
Engaging students as active participants in mathematics classroom discussions has great potential to promote student learning. Less well understood is how teachers can promote beneficial student ...participation, and how teacher-student interaction relates to student achievement.This study examined how the kinds of teacher practices that may encourage beneficial student participation relate to student achievement in elementary school mathematics classrooms. Using videotaped recordings, we examined the extent to which students explained their own ideas and engaged with others' ideas and how teachers supported these kinds of student participation. Linking teacher practices, student participation, and achievement all at the individual student level, we found that student achievement was best predicted by the combination of teacher practices and student participation. The results show that taking into account student participation is necessary for understanding how teaching practices relate to student mathematics learning.
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