An investigation of supporting teacher learning in the context of a common decomposition for leading mathematics discussions (original) (raw)

CONTENT AND CONTEXT: PROFESSIONAL LEARNING COMMUNITIES IN Mathematics

2009

This is a case study of a mathematics professional learning community. It illustrates the experience of eight Grade 2 teachers as they collaborate to improve their students' understanding of mathematics. In this inquiry, I worked as a participant-observer with the teachers over the course of five months as a witness to their expanding understanding of mathematics and learning. The case study describes two manifestations: the experiences of the teachers as they develop their knowledge of the mathematical learning of young children; and secondly, the teachers' growth as a professional learning community committed to improving the mathematical understanding of their students and of themselves. Collectively, the findings from this study extend other conversations on both professional learning communities and the development of teachers' knowledge about mathematical learning (often called pedagogical content knowledge). This work shows that opportunities for professional l...

The challenge of mathematical discussions in teachers' professional practice

Didacticae, 2017

We seek to identify patterns of action in mathematics teachers' classroom practice regarding class discussions and to determine how these actions provide learning opportunities for students. The study is based on a framework that focuses on two key elements of teaching practice: 1) the tasks that teachers propose to their students and, 2) the way they handle classroom communication. Qualitative methodology is used with data collected from video recordings of a grade 6 class that is studying rational numbers. We conclude that challenging situations usually require teacher preparation and follow-up with supporting/ guiding and informing/suggesting actions so that the students can learn what is involved in the teacher's motivations.

Teacher Learning in Mathematics: Using Student Work to Promote Collective Inquiry

Journal of Mathematics Teacher Education, 2004

The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout the year. Prior to each workgroup, they posed a similar mathematical problem to their students. The workgroup discussions centered on the student work those problems generated. This study draws on a transformation of participation perspective to address the questions: What do teachers learn through collective examination of student work? How is teacher learning evident in shifts in participation in discussions centered on student work? The analyses account for the learning of the group by documenting key shifts in teachers' participation across the year. The first shift in participation occurred when teachers as a group learned to attend to the details of children's thinking. A second shift in participation occurred as teachers began to develop possible instructional trajectories in mathematics. We focus our discussion on the significance of the use of student work and a transformation of participation view in analyzing the learning trajectory of teachers as a group.

TEACHER LEARNING IN MATHEMATICS TEACHER STUDY GROUPS

Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education, 24, (vol 3, pp. 1439-1450). Columbus, OH: ERIC Clearinghouse. , 2002

In this paper I explore the challenges and possibilities for teacher learning in study groups by examining the typical discourse generated in one particular group. Special attention was paid to the teachers’ talk when doing mathematics together and when talking about their teaching practices and students’ work. When doing mathematics together, the examined group’s talk can be described as exploratory talk, that is talk characterized by speakers seeking and showing intellectual involvement; public disclosure of disagreements and confusion; and talk that is generative and collaborative. In contrast, the teachers' talk about their teaching and students' work can be categorized as expository talk, which can be characterized by the use of monologues; speakers seeking and giving approval; and the non-analytical or unproblematic narration of events. These are features of study group talk that seem important to attend to and study as these affect the participants’ learning opportunities and impact the design and leadership of teacher groups.

Teachers’ professional practice conducting mathematical discussions

Educational Studies in Mathematics, 2016

This paper seeks to identify actions that can be regarded as building elements of teachers' classroom practice in mathematical discussion and how these actions may be combined to provide fruitful learning opportunities for students. It stands on a framework that focuses on two key elements of teaching practice: the tasks that teachers propose to students and the way teachers handle classroom communication. Tasks are appraised concerning their level of challenge. Teachers' actions in discussions are classified as informing/suggesting, guiding, and challenging. The methodology is qualitative with data collected from video recording of the classroom. The analysis of classroom episodes dealing with rational numbers but with different agendas, such as providing students opportunities for learning about representations, concepts, connections, and procedures and for developing reasoning suggests that some degree of challenge promotes fruitful learning situations. However, such situations tend to require preparation and follow-up with guiding and even informing/suggesting actions so that the students can learn what has been set in the teacher's agenda.

Researching mathematics leader learning: Investigating the mediation of math knowledge needed for teaching on leaders' collective work in mathematics

This research report examines the resources leaders access as they engage in collective mathematical activity. By examining resources we explore how leaders' participation in the collective work looks and sounds different across groups. Furthermore, through our mixed-method research design we investigate possible linkages between leaders' resources and a group's mathematical knowledge for teaching. This novel use of MKT is central in our exploratory study to raise questions and hypotheses about what leaders need to know to lead. Background The data for this paper were drawn from Researching Mathematics Leader Learning (RMLL) 2 investigating how leaders learn to cultivate mathematically rich learning environments for teachers. Two key assumptions under gird our work. First, to improve children's mathematical learning, teachers need to develop deep understandings of mathematics (Ball & Bass, 2000; Hill et al., 2005; Ma, 1999). Second, leaders of mathematics PD need to learn to create and nurture PD climates where teachers have rich opportunities to grapple with and understand mathematics more deeply (Wilson & Bern, 1999). There is widespread agreement that improving teaching and learning requires that teachers participate in high-quality PD (Darling-Hammond & McLaughlin, 1999; Loucks-Horsley et al., 2003). However, what leaders need to know in order to construct high quality PD is under-defined (Even, 2004; Stein et al., 1999). We have chosen, with sound theoretical support, to focus on developing leaders' understandings of norms for mathematical reasoning or sociomathematical (SM) norms. These are the norms that guide the ways people interact mathematically (Yackel & Cobb, 1996). Our work is informed by the classroom research on SM norms where norms are established and cultivated in students' mathematical activity (Kazemi & Stipek, 2001; Yackel & Cobb, 1996). We extend this work, focusing on how leaders may engage teachers in mathematically rich environments where productive SM norms are essential in supporting mathematical discussion and debate 3. This paper examines the mathematical resources leaders bring to mathematical activity to understand what might be entailed in leaders developing an understanding of productive SM norms and putting these norms into practice in mathematics PD. We recognize that leaders' collective mathematical activity is not the same as leaders working with teachers on mathematics. We conjecture that if we know what resources leaders have access to, and how the resources are taken up by leaders when collectively engaged in productive mathematical activity, then we may better understand what resources are available to leaders and perhaps needed to cultivate mathematically rich PD environments.

Teachers’ leading whole-class discussions in a mathematics lesson study: From initial understanding to orchestration in practice

European journal of science and mathematics education, 2024

This study aims to identify how mathematics teachers understand whole-class discussions and to know the influence of lesson study on the way they orchestrate these discussions. This is a qualitative study, conducted with two groups of middle school teachers. We analyze data concerning three teachers, Patrícia, Marta, and Diana, collected through initial individual interviews and observation of three research lessons. Data are analyzed by discourse analysis, establishing a relationship between the discourse about the teachers' understanding of wholeclass discussions in the initial interview and their subsequent orchestration of this lesson moment. From this relation, we consider the influence of the lesson studies on the teachers' orchestration practice. The teachers' discourse in the interviews suggest the existence of a tension between their understanding of the goals of a whole-class discussion and their practice in orchestrating the discussion, causing several challenges. The lesson study contributed to lower these tensions and challenges through the definition of a fluid lesson structure and the appreciation, selection and recording of the students' activity, enriching the discussion. However, carrying out effective questioning and managing time proved to be complex challenges that deserve attention from further research.

The centrality of culture and community to participant learning at and with The Math Forum

Designing for virtual communities in the service of learning, 2004

Our chapter relates to an ongoing and continuously evolving research and development project that has as its goal the design of a socio-technical system (a technical environment and related social structures and activities) that will constitute a good model for distributed teacher professional development programs conceptualized as knowledge-building communities. We focus primarily on a part of our work that is situated within the Secondary Teacher Education Program at the University of Wisconsin-Madison. We begin by describing the original ambitious vision for this program that we set out to implement, including its theoretical basis. Then we discuss how both our initial failures and the theoretical framework itself led us to more carefully consider how the historical and institutional contexts of such community-building efforts might influence the social processes of learning and teaching within the community. To illuminate this idea, we present a contextual analysis of the program as a prelude to an interaction analysis of a representative discourse from a group learning activity within the program. Throughout our chapter, we consider lessons learned from studies such as these and from our immersion in the experience of designing a socio-technical environment for supporting community-based teacher education. Drawing on these lessons, we describe our modified goal and the latest results of our efforts to develop an online system for structuring and supporting group learning, including the online mentoring of such learning, within teacher education programs.