Conceptualizing routines of practice that support algebraic reasoning in elementary schools: a constructivist grounded theory

There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research on elementary school students' algebraic reasoning, there is a scarcity of research on how elementary school teachers implement algebraic reasoning curriculum and how their practices support algebraic reasoning. The purpose of this study therefore was to discover practices that promote algebraic reasoning in elementary classrooms by studying elementary school teachers' practices and algebraic reasoning that the practices co-constructed. Specifically, the questions that guided the study included (a) what were the teachers' routines of practice, and (b) in what ways did the routines of practice support algebraic reasoning. I sampled On Track Learn Math project and worked with six teachers to explore their routines of practice and students' algebraic reasoning. As a participant observer, I analyzed video data of the classroom activities, memos, field notes, students' written transcripts and interview data using constructivist grounded theory approach and descriptive statistics. Member checking, data triangulation, and data coding by multiple raters ensured consistency and trustworthiness of the results. Descriptive analysis of students' written generalizations showed that about 74% of the generalizations were explicit and about 55% of the generalizations included names of variables indicating that students were learning how to reason algebraically. Data analysis also revealed five routines of practice. These routines are; (a) maintaining open-endedness of the tasks, (b) nurturing co-construction of ideas, (c) fostering understanding of variable, (d) creating a context for mathematical connections and (e) promoting understanding of generalizations. Teachers maintained open-endedness by giving minimal instructions when launching the tasks and providing students with workspaces. They nurtured co-construction of ideas by creating opportunities for students to collaborate, fostering collaboration, and balancing the support of discourse and content. They fostered understanding of variable as a changing quantity and as a relationship. Teachers created a context for mathematical connections between On Track tasks and students' everyday experiences, between student strategies, between different tasks, between On Track tasks and other curriculum ideas, and between different representations. Teachers promoted understanding of generalizations by encouraging students to justify their conjectures, to apply and evaluate peers' generalizations among other practices. These practices were dependent and informed each other

Fostering Inquiry and Creativity in Early Years STEM Education: Policy Recommendations from the <i>Creative Little Scientists</i> Project

Creative Little Scientists was a 30-month (2011-2014) EU/FP7-funded research project focusing on the synergies between early years science and mathematics education and the development of children’s creativity, in response to increasing interest in these areas in European educational policy. Using a variety of methods, including desk research, a teacher survey and classroom-based fieldwork, the research provided insights into whether and how children’s creativity is fostered and appropriate learning outcomes, including children’s interest, emerge. Based on these and ongoing collaboration and dialogue with participants and other stakeholders the project proposed recommendations for policy and teacher education. This paper presents these recommendations and the research on which they were based. Throughout the study, mixed methods were employed, combining quantitative approaches used in surveys of policy and teachers’ views based on a list of factors, alongside qualitative approaches employed in case studies of classroom practice. A strong conceptual framework developed at the start of the project guided data collection and analysis, as well as the presentation of findings and the development of policy recommendations, thus ensuring the latter’s strong and consistent relationship with the relevant theoretical knowledge, the comparative research, analysis of classroom practices and the production of guidelines for teacher education

Exploring the Impact of Teacher Collaboration on Student Learning: A Focus on Writing

In this yearlong case study, six English teachers in an urban high school in Northern California engaged in sustained collaboration focused on developing and enacting strategies to improve the writing skills of their culturally and linguistically diverse freshmen. The study was conducted between August 2018 and June 2019, to determine the connections, if any, between teacher collaboration and student learning. Qualitative data were analyzed from teacher collaboration and observation of classroom practices, focus groups and teacher-created artifacts. Students’ on-demand writing assessments in fall and spring were compared with instructionally supported writing. Student surveys were analyzed in a mixed methods approach. Findings suggest that students’ writing skills improved and students reported increased confidence in writing and other literacy practices. The lessons developed in the collaboration meetings and observed in practice, in tandem with student and teacher self-reports suggest a positive relationship between teacher collaboration and student learning outcomes

Investigating scaffolding strategies for promoting reasoning-based, collaborative discourse with linguistically diverse learners in the mainstream classroom

The Common Core State Standards (CCSS, 2012) call for shifts in teaching and learning, emphasizing diverse students’ complex uses of language and skilled articulation of reasoning in collaborative discussion settings. Concurrently, it is becoming increasingly common for English Learners (ELs) to be educated in mainstream classrooms alongside their English-proficient peers, raising the challenge for teachers to effectively mediate these new standards into practice for all students. This design-based research study, grounded in sociocultural theory, was carried out in collaboration with two classroom teachers. The study focused on the implementation of discussion scaffolding strategies, including academic language functions (e.g., language used by students to tell, restate, build on, or challenge). The analysis investigated shifts in both whole class discourse and the discourse of four English learners in the classroom over a seven-month period. Qualitative and quantitative analyses of eight audio-recorded discussion transcripts examined shifts in student talk, with particular attention to (a) participation, (b) reasoning, (c) collaborative talk, and (d) use of academic language for engaging in dialogue with peers. Analyses revealed that as teachers successively introduced the four categories of talk moves, students engaged in significantly more reasoned, collaborative talk. Over time, students also used the academic language stems with greater frequency and exhibited increased autonomy in reasoned-focused, collaborative talk. Additionally, collective reasoning (prompted by instructional moves designed to have students think with others) appeared to promote individual reasoning, as shown by higher instances of reasoning words used by students. Shifts in talk for EL students were similar to those of the whole class, with key differences being how ELs were afforded additional opportunities for second language development in the context of discussion: ELs had a chance to listen to and express complex reasoning, extended discourse, and relevant language functions in contextualized ways. They engaged in meaningful and sustained interactions with English-proficient peers. Finally, ELs connected new learning with their prior knowledge and experience. These findings pose important considerations for implementing standards in ways that support reasoning-based, collaborative discourse for all students—while simultaneously affording ELs learning opportunities for developing language proficiency and disciplinary knowledge in an equitable learning environment

Review of the Literature on Speaking and Listening Skills

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Reading for Idea Advancement in a Grade 4 Knowledge Building Community

This study looks into the reading practice in a Grade 4 knowledge building community that involved 22 students and a veteran teacher. The students investigated light over a threemonth period supported by Knowledge Forum, a networked collaborative knowledge-building environment. The classroom designs encouraged the students to take on high-level responsibility for advancing the community’s knowledge, as represented in their online discourse in Knowledge Forum. The tracing of student conversations in Knowledge Forum and content analysis of their portfolio notes demonstrate productive advancement of scientific understanding. Qualitative analyses of classroom videos, online discourse, and the teacher’s reflection journal characterize student reading practice along four themes: reading for the purpose of advancing community knowledge; as progressive problem solving; embedded in sustained knowledge-building discourse; and as dialogues between local understanding and knowledge in the larger world. These results contribute to elaborating the possibility and processes of integrating reading with creative knowledge work in content areas. Classroom strategies are identified and discussed in relation to the role of collaborative online technologies

a Review of Instructional Approaches

UIDB/00183/2020 UIDP/00183/2020 DL 57/2016/CP1453/CT0066 PTDC/FER-FIL/28278/2017Over the past 20 years, a broad and diverse research literature has emerged to address how students learn to argue through dialogue in educational contexts. However, the variety of approaches used to study this phenomenon makes it challenging to find coherence in what may otherwise seem to be disparate fields of study. In this integrative review, we propose looking at how learning to argue (LTA) has been operationalized thus far in educational research, focusing on how different scholars have framed and fostered argumentative dialogue, assessed its gains, and applied it in different learning contexts. In total, 143 studies from the broad literature on educational dialogue and argumentation were analysed, including all educational levels (from primary to university). The following patterns for studying how dialogue fosters LTA emerged: whole-class ‘low structure’ framing with a goal of dialogue, small-group ‘high structure’ framing with varied argumentative goals, and studies with one-to-one dialectic framing with a goal of persuasive deliberation. The affordances and limitations of these different instructional approaches to LTA research and practice are discussed. We conclude with a discussion of complementarity of the approaches that emerged from our analysis in terms of the pedagogical methods and conditions that promote productive and/or constructive classroom interactions.publishersversionepub_ahead_of_prin

Bridging between Research and Practice

This book presents a fresh approach to bridging the perceived gap between academic and classroom cultures. It describes a unique form of research partnership whereby Cambridge University academics and school teachers together grappled with and reformulated theory—through in-depth case studies analysing practice using interactive whiteboards in five subject areas. The inquiry exploited the collaborators’ complementary professional knowledge bases. Teachers’ voices are particularly audible in co-authored case study chapters. Outcomes included deeper insights into concepts of sociocultural learning theory and classroom dialogue, more analytical mindsets, sustained new practices and ways of working collegially.; Readership: The book will interest academic and teacher researchers, initial teacher educators, professional development leaders, mentors, plus practitioners interested in using interactive whiteboards and dialogic teaching. It explores widening approaches to collegial development to reach educators working in other contexts (with and without technology). This could involve intermediate theory building or shortcutting by sharing and adapting the outcomes—springboarding teachers’ further critique and professional learning