Karen B. Givvin

Teachers’ beliefs and practices related to mathematics instruction

Abstract Beliefs and practices related to mathematics were assessed for 21 fourth- through sixth-grade teachers. At the beginning and the end of the school year teachers’ beliefs about (1) the nature of mathematics (i.e., procedures to solve problems versus a tool for thought), (2) mathematics learning (i.e., focusing on getting correct solutions versus understanding mathematical concepts), (3) who should control students’ mathematical activity, (4) the nature of mathematical ability (i.e., fixed versus malleable), and (5) the value of extrinsic rewards for getting students to engage in mathematics activities were assessed. (6) Teachers self-confidence and enjoyment of mathematics and mathematics teaching were also assessed. Analyses were conducted to assess the coherence among these beliefs and associations between teachers’ beliefs and their observed classroom practices and self-reported evaluation criteria. Findings showed substantial coherence among teachers’ beliefs and consistent associations between their beliefs and their practices. Teachers’ self-confidence as mathematics teachers was also significantly associated with their students’ self-confidence as mathematical learners.

Mathematics Teaching in the United States Today (and Tomorrow): Results From the TIMSS 1999 Video Study:

The Third International Mathematics and Science Study (TIMSS) 1999 Video Study examined eighth-grade mathematics teaching in the United States and six higher-achieving countries. A range of teaching systems were found across higher-achieving countries that balanced attention to challenging content, procedural skill, and conceptual understanding in different ways. The United States displayed a unique system of teaching, not because of any particular feature but because of a constellation of features that reinforced attention to lower-level mathematics skills. The authors argue that these results are relevant for policy (mathematics) debates in the United States because they provide a current account of what actually is happening inside U.S. classrooms and because they demonstrate that current debates often pose overly simple choices. The authors suggest ways to learn from examining teaching systems that are not alien to U.S. teachers but that balance a skill emphasis with attention to challenging mathematics and conceptual development.

Teachers' analyses of classroom video predict student learning of mathematics: Further explorations of a novel measure of teacher knowledge

This study explores the relationship between teacher knowledge and student learning in the area of mathematics by developing and evaluating an innovative approach to assessing teacher knowledge. This approach is based on teachers’ analyses of classroom video clips. Teachers watched 13 video clips of classroom instruction and then provided written comments on the interactions of the teacher, students, and content. The quality of teachers’ analyses, coded using an objective rubric, are shown to be reliable and valid, relating both to another widely used measure of teacher knowledge and to teachers’ own students’ learning (from pre- to posttest).

Measuring Usable Knowledge: Teachers’ Analyses of Mathematics Classroom Videos Predict Teaching Quality and Student Learning

This study explores the relationships between teacher knowledge, teaching practice, and student learning in mathematics. It extends previous work that developed and evaluated an innovative approach to assessing teacher knowledge based on teachers’ analyses of classroom video clips. Teachers watched and commented on 13 fraction clips. These written analyses were coded using objective rubrics to yield a reliable and valid indicator of their usable teaching knowledge. Previous work showed this measure to correlate with another measure of teacher knowledge and to predict students’ learning from the teachers’ fraction instruction. In this study, the authors replicated those findings and further showed that the effect of teacher knowledge on student learning was mediated by instructional quality, measured using video observations of teachers’ lessons.

Are There National Patterns of Teaching? Evidence from the TIMSS 1999 Video Study

Why do teachers today teach as they do, and why has teaching evolved in the way that it has evolved? In order to improve teaching, it is important to understand why teaching looks the way that it now does and how its general form can be explained. One way to address this question is at the classroom level. This approach has been found in the ethnographic work of anthropologists and has been skillfully applied in the recent work of such researchers as Robin Alexander and Kathryn Anderson-Levitt. In this article we build on ethnographic research by using the 1999 Third International Mathematics and Science Study (TIMSS) video archives. Here we consider two possible explanations for the general patterns that have developed in school teaching. One explanation is that there are universal elements in most schools today that shape teaching practice. These elements include the physical environment, the social dynamics of classrooms, and the content to be learned. If

In the eyes of the beholder: students’ and teachers’ judgments of students’ motivation

Abstract This study was designed to examine the nature and accuracy of teachers’ judgments about students’ motivation related to mathematics. Seventeen fourth- through sixth-grade teachers and 100 of their students participated in this study. Teachers were asked to rate six target students’ motivation four times during the school year. At each of these times students also rated their own motivation. Teachers’ ratings were more stable over time and across mathematics topics and were less differentiated across motivation dimensions than were students’ ratings. The findings suggest that teachers need to pay careful attention to evidence related to childrens motivation that might contradict their perceptions and therefore support more effective interventions.

Problem Implementation as a Lever for Change: An Experimental Study of the Effects of a Professional Development Program on Students’ Mathematics Learning

Abstract This study investigates, through an experimental design, the effectiveness of a professional development program on teacher knowledge and practices and on student learning. The program consisted of a series of video-based modules designed to respond to needs of U.S. teachers, as highlighted by findings from the 1999 Third International Mathematics and Science Video Study. Sixty-four 6th-grade teachers from five low-performing inner-city schools participated in the study and were randomly assigned to treatment and control groups. Measures included fidelity of implementation, teacher knowledge and practice, and student mathematics learning. The program did not impact significantly teacher knowledge or practices as measured in the study. An effect was found on mathematics learning for students whose teachers reached a certain level of mathematics content knowledge. Discussion of findings includes lessons learned about conducting and studying professional development, particularly in low-performing schools.

Goal Orientations of Adolescents, Coaches, and Parents: Is There a Convergence of Beliefs?.

The relations between the goal orientations of adolescents and those of their coaches and parents were examined in this study. Ninety swimmers, 12 through 15 years of age, coaches (N = 10), and parents (N = 71) completed the Task and Ego Orientation in Sport Questionnaire (TEOSQ) with regard to the adolescents’ participation in swimming. Adolescents completed the TEOSQ two additional times: once as they thought their coaches would respond and again as they thought their parents would respond. The self-reported goal orientations of adolescents were correlated highly with their perceptions of the goal orientations of their significant adults but not with the self-reports of significant adults. Adolescents believed that the way they thought and felt about their swimming was more affected by their coaches than by their parents. Comparisons of goal orientations across gender and suggestions for further studies are discussed.

Understanding and Improving Mathematics Teaching: Highlights from the TIMSS 1999 Video Study

portion of the TIMSS 1999 Video Study included Australia, the Czech Republic, Hong Kong SAR, Japan, the Netherlands, Switzerland, and the United States. In this article, we focus on the mathematics lessons; the science results will be available at a later date. Stimulated by a summary article that appeared in the Kappan and by other reports, interest in the TIMSS 1995 Video Study focused on its novel methodology and the striking differences in teaching found in the participating countries. In particular, the sample of eighth-grade Understanding and Improving Mathematics Teaching: Highlights from the TIMSS 1999 Video Study

Video-Based Research Made "Easy": Methodological Lessons Learned from the TIMSS Video Studies

In this article, the authors share some of the methodological lessons learned from the Third International Mathematics and Science Study (TIMSS) 1995 and TIMSS 1999 Video Studies. They focus on their experiences overseeing these large-scale, video-based, cross-national surveys of teaching. The article documents some of the progress the authors made, as well as some of the obstacles they encountered. The authors hope that the ideas shared here help prevent possible missteps, enhance the quality of projects, and encourage researchers to advance the use of video as a methodology.