Developing early algebraic reasoning in a mathematical community of inquiry

This study explores the development of early algebraic reasoning in mathematical communities of inquiry. Under consideration is the different pathways teachers take as they develop their own understanding of early algebra and then enact changes in their classroom to facilitate algebraic reasoning opportunities. Teachers participated in a professional development intervention which focused on understanding of early algebraic concepts, task development, modification, and enactment, and classroom and mathematical practices. Design research was employed to investigate both teaching and learning in the naturalistic setting of the schools and classrooms. The design approach supported the development of a model of professional development and the framework of teacher actions to facilitate algebraic reasoning. Data collection over the school year included participant observations, video recorded observations, documents, teacher interviews, and photo elicitation interviews with students. Retrospective data analysis drew the results together to be presented as cases of two teachers, their classrooms, and students. The findings show that the integration of algebraic reasoning into classroom mathematical activity is a gradual process. It requires teachers to develop their own understanding of algebraic concepts which includes understanding of student reasoning, progression, and potential misconceptions. Task implementation and design, shifts in pedagogical actions, and the facilitation of new classroom and mathematical practices were also key elements of change. The important role which students have in the development of classrooms where algebraic reasoning is a focus was also highlighted. These findings have significant implications for how teachers can be supported to develop their understanding of early algebra and use this understanding in their own classrooms to facilitate early algebraic reasoning

Teachers’ questions matter : exploring the attributes of mathematics teachers’ questions within the Lesson Study context

Thesis (PhD (General))--University of Pretoria, 2023.Questions and questioning remain central to classroom conversations. Classroom interactions are mostly dominated by teachers’ questions and responses offered by learners. If used properly, questions can become tools that inspire deep intellectual thought in mathematics. Quality questions cultivate the habit of reflective inquiry and tend to transform learners into active participants during teaching and learning. Important as they are, questions and questioning appear to be neglected narratives within Lesson Study contexts. Against this background, this study was conducted to explore the attributes of questions developed and used by teachers as they engage in Lesson Study activities. In this study, I used Lesson Study as a context to learn how mathematics teachers incorporate questions during the three of the five stages of LS, i.e., collaborative lesson planning, lesson presentation and observation, and post-lesson reflection. The conceptual framework which guided the study was an amalgam of LS (the context), Variation Theory (theoretical lens) and Emanuelsson’s categories of classroom interactions. Extensive review of literature has shown that there is very little research conducted to explore how LS communities incorporate oral questions (questions they intend to use to facilitate learning) in their plans and how such questions filter into the lesson presentation and observation, and how they are eventually reflected upon during the post-lesson reflection stage. This study is an interpretive qualitative case study which involved five participants from four different schools and a single class of Grade 9 learners. Data were generated through observation, document analysis and informal conversational interviews. The findings show that although teachers were able to give consideration to questions they intend to use to facilitate learning, dorminant questions were those that mainly stimulated interactions in the topical zone. Evidence reported in this study also revealed that there is a policy implementation gap regarding the guidance teachers need when planning questions for informal assessment. This study has also contributed to extending the body of knowledge on how an LS team plan, implement and reflect on the questions.Science, Mathematics and Technology EducationPhD (General)Unrestricte

How Do Teachers Experience Lesson Study?

For the past 20 years, an increasing number of American educators have employed the Japanese model of lesson study as a process to structure their professional development experience. This study endeavored to understand how teachers experienced this relatively new and foreign process in their local contexts, using the overall research question, “How do teachers experience lesson study?” Leveraging hermeneutic phenomenology, the research was based on semi-structured phone interviews of 15 educators. These educators were from various regions in America, two from the Far East, and one from Europe. In describing their professional development experiences prior to lesson study, participants overlapped their terms, which signaled confusion. This was emblematic of their overall experiences with professional development. In general, participants found their professional development to be inapplicable, ineffective, and random. Additionally, they experienced issues sustaining their new learning even when they felt their professional development events were effective. Overall, participants believed their professional development time prior to lesson study was squandered. Participants experienced lesson study as an effective approach to professional development. Out of the 15 participants, 14 stated lesson study was the best form of professional development they experienced in their careers. They felt confident in the formal, yet flexible process. Lesson study offered the participants practice based, shared experiences learning about standards, curriculum, materials, and content fueled by structured collaboration. It changed their dispositions towards professional development. They contended lesson study assisted them in learning more about their students. Participants reported increased feelings of efficacy and professionalism after completing lesson study cycles. However, participants also described how their lesson study work was impeded by systemic obstacles including time, competing initiatives, misconceptions about lesson study, principal turnover, and interpersonal complications. This study adds information about lesson study obstacles in relation to school climate. They were frustrated by the local facilitation of their lesson study professional development. The participants found that the American system was ill-suited to support their lesson study experiences in the way that it is supported in Japan. This research informs those interested in using lesson study as a professional learning community. Further, it adds information to the discussion about professional development in general and the role of collaboration in this regard

Vodenje reševanja problemov pri pouku

We report on the results of a professional development programme involving four Hungarian teachers of mathematics. The programme aims to support teachers in integrating problem solving into their classes. The basic principle of the programme, as well as its novelty (at least compared to Hungarian practice), is that the development takes place in the teacher’s classroom, adjusted to the teacher’s curriculum and in close cooperation between the teacher and researchers. The teachers included in the programme were supported by the researchers with lesson plans, practical teaching advice and lesson analyses. The progression of the teachers was assessed after the one-year programme based on a self-designed trial lesson, focusing particularly on how the teachers plan and implement problem-solving activities in lessons, as well as on their behaviour in the classroom during problem-solving activities. The findings of this qualitative research are based on video recordings of the lessons and on the teachers’ own reflections. We claim that the worked-out lesson plans and the self-reflection habits of the teachers contribute to the successful management of problem-solving activities. (DIPF/Orig.

Teacher Learning in Lesson Study

This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students’ autonomous problem‐solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among the teams’ composition, leadership, and content foci

Understanding Pre-Service Elementary Mathematics Teacher Learning In An Early Lesson Study Experience

As the most important in-school factor in student learning, elementary school teachers must be able to offer all students the quality mathematical learning experiences that they deserve; and the opportunities to learn that pre-service teachers (PSTs) encounter during their preparation programs impact their ability to do so. Content courses are crucial components of the mathematical education of elementary teachers and can be sites for the early development of Mathematical Knowledge for Teaching (MKT) (Ball, Thames, & Phelps, 2008). These courses, often taken early in their preparation programs, can provide PSTs opportunities to create a new vision of mathematics, build new knowledge for action, engage in the complexity of instruction, and prepare to learn in and from their own practice. In this study, PSTs participated in a modified form of lesson study in a mathematics content course. Lesson study has become an important lever for improving teaching and learning. More common in inservice contexts, teacher educators have begun to use lesson study in pre-service preparation programs—typically in methods courses. This study sought to add to the knowledge base by examining the learning afforded and occluded by a modified lesson study activity at an early stage of a university preparation program. This mixed-methods interpretive case study (n=11) analyzed the learning that occurred within the modified lesson study activity. While PSTs’ scores on the Learning Mathematics for Teaching—Teacher Knowledge Assessment System (Hill, Sleep, Lewis, & Ball, 2007) showed little gain, significant changes in PSTs’ beliefs regarding teaching efficacy were observed on the Mathematics Teaching Efficacy Belief Instrument (Enochs, Smith, & Huinker, 2000). Additionally, discussion transcripts and written reflections of PSTs indicated that the lesson study cycle acted as a powerful focusing lens that allowed PSTs to see their previous and current experiences with mathematics instruction juxtaposed with that of elementary students during the research lesson. This lens also allowed them to focus and activate their new MKT (Ball et al., 2008) as they prepared for and observed student thinking made visible through the more equitable and validating instruction that they designed in collaboration with an established lesson study teacher team

Teaching Mathematics: Using research-informed strategies

AER 59 reviews research into aspects of mathematics teaching, focusing on issues relevant to Australian mathematics teachers, to those who support them, and also to those who make policy decisions about mathematics teaching. It was motivated by and draws on the proceedings of the well-attended and highly successful ACER Research Conference Teaching mathematics? Make it count: What research tells us about effective mathematics teaching and learning, held in Melbourne in August 2010. Section 2 describes the goals of teaching mathematics and argues that a practical orientation should be the focus of mathematics teaching in the compulsory years, and outlines the contribution numeracy-based perspectives can make to schooling. Section 3 uses assessment data to evaluate how well those goals are being met in Australia and introduces the challenge of seeking equity of opportunity in mathematics teaching and learning. Section 4 expands on the importance, to individuals and society, of achieving the mathematics goals; and Section 5 discusses six research-based principles of mathematics teaching. Section 6 argues for the importance of well-chosen mathematical tasks in supporting student learning, and models tasks and particular teaching strategies. Sections 7 and 8 analyse research which provides insights into a key issue facing Australian mathematics teachers, that of finding ways to address the needs of heterogeneous groups of students. Section 9 describes and recommends particular emphases and strategies for education programs for both prospective and practising teachers.https://research.acer.edu.au/aer/1022/thumbnail.jp

Collaborative Lesson Study: A Qualitative Case Study of Elementary Teachers’ Professional Learning Experience

Teacher collaboration practices in schools have impacted how teachers work together to prevent professional isolation. The mandate of collaborative practices has resulted in some teachers expressing frustration and a lack of benefit from their current experiences. The purpose of this qualitative case study, conducted in the Southeast region of the United States, was to determine if lesson study provided a more meaningful collaborative approach during focused group sessions. Using New London Group’s (1996) designs of meaning concept encapsulated in the Pedagogy of Multiliteracies Theoretical Framework to gauge the relevance of lesson study, I sought to explore a deeper understanding of the attitudes and perceptions of elementary educators practicing this method. The participants in this study, the kindergarten collaboration team, consisted of three kindergarten teachers, one special education teacher, one media specialist teacher, and one technology specialist teacher. The individuals’ teaching experience ranged from 17 to 30 years. Data collected included field notes, focus group reflections of team lesson observations, transcriptions from semi-structured individual interviews, and a focus group interview. The overarching research question that drove this study was: What were the attitudes and perceptions of elementary educators towards practicing lesson study and its influence on the quality of teaching? Findings from this investigation revealed that participants going through the lesson study were appreciative from acquiring a unique collaborative experience. A new team dynamic, introspective analyses, and transformation of teacher learning contributed to a meaningful collaborative process. Furthermore, maximizing colleagues’ skillsets, preparation, and learning-by-doing heightened the quality of instructional math practices. vi Table o

Using an online forum to mentor secondary mathematics student teachers toward standards-based instruction.

Student teaching is the fundamental field experience where pre-service teachers have the opportunity to conceive and develop standards-based instructional practices under the guidance of mentors. Yet, research reveals that mentoring for novice teachers is most often focused on providing technical and emotional support rather than supporting teachers learning to teach with standards-based instructional practices (Wang and Odell, 2002). In addition, university supervisors’ efforts to mentor mathematics student teachers toward standards-based instructional practices are hindered by their limited opportunities to meet with their assigned student teachers (Borko & Mayfield, 1995; Frykholm, 1996). Online social networking provides an opportunity for consistent communication between university supervisors and student teachers about student teachers’ daily experiences. This study investigated the potential of online social networking as a venue for a university supervisor to mentor secondary mathematics student teachers’ toward the following standards-based instructional practices: (a) elevating conceptual understanding and surfacing “big” mathematical ideas, (b) eliciting and attending to students’ mathematical thinking, (c) connecting mathematics to real-life contexts, (d) using and connecting a variety of representations, (e) facilitating active discovery and mathematical investigations, and (f) promoting student collaboration and mathematical discourse. The online mentoring conversations between a university supervisor and four secondary mathematics student teachers were analyzed for content related to standards-based instruction. Qualitative analysis of the online mentoring content revealed that online social networking was an effective venue for a university supervisor to mentor student teachers toward some aspects of standards-based instruction. In addition, online social networking proved to be a site for tracking and documenting student teacher’s developing conception and implementation of standards-based instruction