Showing papers in "Journal of Mathematics Teacher Education in 2004"

Teacher learning in mathematics: using student work to promote collective inquiry

Abstract: 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 partici- pation 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.

The Pedagogical Content Knowledge of Middle School, Mathematics Teachers in China and the U.S.

Abstract: This study compared the pedagogical contentknowledge of mathematics in U.S. and Chinesemiddle schools. The results of thiscomparative study indicated that mathematicsteachers' pedagogical content knowledge in thetwo countries differs markedly, which has adeep impact on teaching practice. The Chineseteachers emphasized developing procedural andconceptual knowledge through reliance ontraditional, more rigid practices, which haveproven their value for teaching mathematicscontent. The United States teachers emphasizeda variety of activities designed to promotecreativity and inquiry in attempting to developstudents' understanding of mathematicalconcepts. Both approaches have benefits andlimitations. The practices of teachers in eachcountry may be partially adapted to helpovercome deficiencies in the other.

Initiating change in prospective elementary school teachers' orientations to mathematics teaching by building on beliefs

Abstract: Many mathematics educators have found thatprospective elementary school teachers' beliefsinterfere with their learning of mathematics.Often teacher educators consider these beliefsto be wrong or naive and seek to challengethem so prospective teachers will reject themfor more generative beliefs. Because of theresilience of prospective teachers' beliefs inresponse to these challenges, teacher educatorscould consider alternative ways of thinkingabout and addressing beliefs, particularly thepotential of building on rather than tearingdown pre-existing beliefs. Data from anearly-field experience linked to amathematics-for-teachers course provideevidence that when prospective teachers workintimately with children, in this case tryingto teach 10-year-olds about fractions, theexperience has the intensity from which beliefscan grow. Most of the prospective teachers inthe study were surprised that mathematicsteaching was more difficult than they hadanticipated. They began to consider theimportance of providing children time to thinkwhen solving mathematical problems. The changedescribed in the study is incremental ratherthan monumental, suggesting that building uponprospective teachers' existing beliefs will bea gradual process.

Professional Development of Mathematics Teacher Educators: Growth Through Practice

Abstract: In this paper we present a study conductedwithin the framework of an in-serviceprofessional development program for junior andsenior high school mathematics teachers. Thefocus of the study is the analysis of processesencountered by the staff members, as members ofa community of practice, which contributed totheir growth as teacher educators. We offer athree-layer model of growth through practice asa conceptual framework to think about becominga mathematics teacher educator, and illustratehow our suggested model can be adapted to thecomplexities and commonalities of theunderlying processes of professionaldevelopment of mathematics teacher educators.

Inquiry into Children's Mathematical Thinking as a Means to Teacher Change

Abstract: In the context of U.S. and world wide educational reforms that require teachers to understand and respond to student thinking about mathematics in new ways, ongoing learning from practice is a necessity. In this paper we report on this process for one teacher in one especially productive year of learning. This case study documents how Ms. Statz's engagement with children's thinking changed dramatically in a period of only a few months; observations and interviews several years later confirm she sustained this change. Our analysis focuses on the mathematical discussions she had with her students, and suggests this talk with children about their thinking in instruction served both as an index of change, and, in combination with other factors, as a mechanism for change. We identified four phases in Ms. Statz's growth toward practical inquiry, distinguished by her use of interactive talk with children. Motivating the evolution of phases were two sorts of mechanisms: scaffolded examination of her students' thinking; and asking and answering questions about individual students' thinking. Processes for generating and testing knowledge about children's thinking ultimately became integrated into Ms. Statz's instructional practices as she created opportunities for herself, and then students, to hear and respond to children's thinking.

Pre-service Mathematics Teaching in the Context of Schools: An Exploration into the Constitution of Identity

Abstract: This paper engages withpoststructural ideas for a discussion on whatit means to engage in pedagogical work in thecontext of elementary/primary schoolmathematics classrooms. Central to the analysisare the pre-service student and the part thatthe teaching practicum plays in the `making' ofa teacher. Drawing on insights from the work ofFoucault on power and subjectivity, instancesof teaching knowledge in production, asinterpreted by pre-service teachers, areexamined. The view is towards developing theoryfrom readings of specific regulatory strategiesthat impact powerfully on pre-service teachers'constructions of themselves as mathematicsteachers.

Mathematics Teaching as a Deliberate Practice: An Investigation of Elementary Pre-service Teachers' Reflective Thinking During Student Teaching

Abstract: In this case study I examine the reflectivepractices of two elementary pre-serviceteachers during their student teachinginternship. I extend current views ofreflective practice to create a framework for a`deliberate practitioner'. With this framework,I investigate the pre-service teachers'thinking with regard to reflective processesand how they use their pedagogical contentknowledge in their practices. My findingsindicate that the pre-service teachers usetheir pedagogical content knowledge inanticipating problematic events, and inreflecting on problematic events ininstruction. However, limits in pedagogicalcontent knowledge and lack of confidence impedethe pre-service teachers' reflection while inthe act of teaching. They were more likely toreflect on their practices outside of the actof teaching. Implications for teacher educatorsand pre-service teachers are discussed.

Teachers' Knowledge of Children's Mathematics after Implementing a Student-Centered Curriculum

Abstract: Our study investigated the knowledge 13elementary teachers gained implementing astudent-centered curriculum in the context ofdistrict-wide reform. Participants comprisedall the teachers in grades three, four and fiveat a single elementary school. We believed thatinvestigating teachers' responses to fictionalpedagogical scenarios involving nonstandardalgorithms would yield insights into criticalcomponents of their knowledge base. We lookedin particular at teachers' knowledge of children's mathematics. We found that teacherswere in the midst of creating a knowledge basefocused on children's mathematics and groundedin knowledge about alternative conceptualtrajectories through the elementary curriculum.Teachers' knowledge of nonstandard strategiessupported by the curriculum materials wasstronger and more coherent than their knowledgeof students' novel nonstandard strategies.Strong mathematical knowledge was notnecessarily associated with strong knowledge ofchildren's mathematics. Teachers' thinkingvaried by a topic's treatment in the writtencurriculum materials used, suggestingimplementation of the curriculum as a source oflearning.

"Confidence Is Everything"--Perspectives of Teachers and Students on Learning Mathematics.

Abstract: This paper problematises ‘confidence’ as a frequently used explanation for performance in the mathematics classroom. I report on an interview-based study of how some English ‘Advanced’ level (16+) students who have chosen to study mathematics, and their teachers, speak about confidence with respect to the learning of mathematics. I outline what constitutes confident learners for these teachers and, differently, for their students and what the students feel teachers could do to improve the students’ confident state. I discuss the implications of this for the education of prospective teachers of mathematics.

Connecting Teacher Beliefs to the Use of Children's Literature in the Teaching of Mathematics.

Abstract: This article presents examples that illustrate how teachers use children’s literature in the teaching of mathematics. The examples are related to four curriculum ideologies that have influenced mathematics education in the USA for the last 75 years. It discusses why it is relevant to help teachers understand the ideological positions that influence their use of children’s literature during mathematics instruction, summarizes the four ideological positions, and presents results of a study of how teachers’ ideological positions relate to their use of children’s literature in the teaching of mathematics. The study examines two research questions

Understanding Teacher Educators and Their Pre-Service Teachers through Multi-Media Case Studies of Practice

Abstract: The challenges facing those who seek to prepare mathematics teachers are well established in the literature. Most of the research to date has focused on the perceptions and understandings of pre-service teachers, but not on the perceptions and understandings of teacher educators. In this study, we explore how four teacher educators understand their pre-service secondary teachers as the pre-service teachers attempt to make sense of teaching through the investigation of a multimedia case study of practice. We found that the teacher educators adopted two different implementation strategies: one strategy tended to be open-ended and exploratory; the other was more focused on the teacher educators' goals of anticipating student understanding and developing mathematical content knowledge for teaching. We also found that, in using the case study, teacher educators elicited pre-service teachers' thinking about the complexities of the teacher's role in small group work, about the value of explicitly revealing the teacher's reflections on the lessons, about the role of planning and preparation, and about the limits of pre-service teachers' abilities to understand and appreciate students' thinking and to extend lesson ideas. Both teacher educators and their pre-service teachers gained perspectives on the role of a teacher's mathematical content knowledge. These results imply that multimedia case studies of practice can serve as vehicles for revealing the knowledge and practice of teacher educators, as they engage in supporting the professional development of pre-service teachers.

evolving research of mathematics teacher educators: the case of non-standard issues in solving standard problems

Abstract: This study describes the learning of researchers who engage in mathematics teacher education as an integral part of their practice. As teacher educators working with teachers on the subject of proportional reasoning, the authors reflected on teachers’ solutions to a standard problem and analyzed answers that would conventionally be considered incorrect. This exploration showed that some incorrect answers made sense, were based on problem situation analysis, and brought attention to the fact that conventional formal answers were given without much deliberation on their meaning in the situation. This insight prompted a second research phase in which teachers discussed and explained alternative solutions, and developed deeper analysis of problem situation in solutions that had been correct in the first place. The importance of making teachers aware of the nature of alternative solutions was further exhibited in a third research phase in which teachers evaluated children’s answers to the same problem. The pedagogical insight that emerged stressed the importance of making teachers aware of the tension between an almost automatic application of a mathematical model, and of analyzing problem situation during problem solving. In addition, the researchers developed better understanding of the mathematical challenge associated with the proportional reasoning problem, a stronger awareness of the role of sensitivity to their learners (the teachers), and of the role of reflection.