Rossella Santagata

Studying the Impact of the Lesson Analysis Framework on Preservice Teachers’ Abilities to Reflect on Videos of Classroom Teaching

This study investigates the impact of an observation framework on preservice teachers’ abilities to engage in productive video-based reflections on mathematics teaching. The Lesson Analysis Framework draws from research on expert—novice teacher differences. Its central element is the analysis of the impact of teachers’ instructional decisions on students’ learning of mathematics. Through an experimental design, the effects of this framework on preservice teachers’ abilities to reflect on teaching are compared to the effects of an alternative framework focused on the evaluation of separate elements of instruction. Findings suggest that the Lesson Analysis Framework facilitates preservice teachers’ learning to elaborate on what they observe and to propose alternative teaching strategies. In addition, the framework provides a structure for evidence-based evaluation of observed instruction.

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.

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.

Teaching Mathematics: Italian Lessons From a Cross-Cultural Perspective

The video component of the Third International Mathematics and Science Study (TIMSS) provided national-level descriptions of 8th-grade mathematics teaching in 3 countries: Germany, Japan, and the United States. Based on these data, Stigler and Hiebert (1999) argued that teaching is a cultural activity, varying more across cultures than within. This study extends their work, on a small scale, to investigate 8th-grade mathematics teaching in yet another country, Italy. Eleven Italian lessons, from urban and rural schools in northern Italy, were videotaped, translated, transcribed, and analyzed following the same procedures used in TIMSS. They were then compared with German, Japanese, and U.S. lessons videotaped in TIMSS. Analyses revealed Italian lessons to be relatively homogeneous among themselves, yet distinct from those in the other cultures. In particular, Italian lessons were found to include a unique activity, not observed in other countries, in which students and teachers interact at the blackboard, with the rest of the class as the audience. Interviews with Italian education professionals investigated the roots of this activity and supported the cultural nature of Italian teaching. Cross-cultural studies of teaching are useful for revealing practices hidden within a culture and for finding alternative ways of teaching.

Preservice Teachers’ Learning to Generate Evidence-Based Hypotheses About the Impact of Mathematics Teaching on Learning

This study examines the development of a specific sub-skill for studying and improving teaching—the generation of hypotheses about the effects of teaching on student learning. Two groups of elementary preservice teachers (PSTs) were compared: one group that attended a typical mathematics-methods course and one that attended a course integrating analysis skills for learning from teaching. Data consist of PSTs’ comments on video clips of mathematics instruction administered before and after course completion. Findings reveal that PSTs at the beginning of the program struggled to generate hypotheses with relevant evidence, often equating teacher behavior or student correct answers as evidence of student understanding. After course participation, PSTs who attended the course with integrated analysis skills significantly improved in their ability to generate hypotheses based on student evidence whereas their counterparts continued to display difficulties. Implications for teacher education and future research are considered.

Mathematics Teaching in Italy: A Cross-Cultural Video Analysis

This study investigates the cultural nature of teaching. It compares a sample of 39 videotaped Italian mathematics lessons to German, Japanese, and U.S. lessons videotaped in TIMSS. This study expands on earlier work that was based on a smaller sample; analysis is also extended to the nature of the mathematical content presented. The results confirm the existence of an Italian cultural pattern for mathematics teaching, whose features we outline here. Italian teachers prefer whole-class instruction to individual seatwork; they engage in teacher talk/demonstration to transmit information; and they often call on students to solve problems at the board before the rest of the class. Italian lessons are characterized by the inclusion of a large number of mathematical principles and properties. These are explained 50% of the time, and simply stated the rest of the time. This study adds yet another perspective from which mathematics teaching can be studied, and, by acknowledging the difficulty to change cultural practices, it offers practical implications for teacher learning.

Toward a common language for discussing the features of effective professional development: the case of a US mathematics program

The focus of this paper is on detailing the decisions made when we created, implemented and studied a mathematics professional development (PD) program in low‐performing, urban schools. Our program held many characteristics espoused by researchers as critical for effectiveness. We begin by reviewing the characteristics of quality PD programs that guided our work. For each, we detail our interpretation and how that interpretation played out in the design and implementation of the PD. We also evaluate our level of success with respect to using that characteristic to positively impact teachers’ learning experiences and, where possible, the subsequent learning experiences of their students. We close with suggestions for the development of PD programs.

Professional development processes that promote teacher change: the case of a video-based program focused on leveraging students’ mathematical errors

This study examined processes at the core of teacher professional development (PD) experiences that might positively impact teacher learning and more specifically teacher change. Four processes were considered in the context of a PD program focused on student mathematical errors: analysis of students’ mathematical misconceptions as a lever for changing practice; review and discussion of images of existing and innovative teaching practices; video-enhanced reflection and detailing of new practices; and cycles of examination/implementation and feedback/revision. Participants were four US elementary school teachers, whose engagement in the PD program was studied through video observations and interviews. Findings revealed several positive shifts in teachers’ interests and classroom practices. Challenges involved teacher content knowledge and counteracting cultural beliefs and practices on the role of errors in learning. The conclusions discuss implications for PD scale-up.

Keeping the Mathematics on the Table in Urban Mathematics Professional Development: A Model that Integrates Dispositions toward Students

Which types of teacher knowledge are most important in shaping instructional practice and student learning opportunities in the urban mathematics classroom? Researchers in the field of mathematics education assure us of the role of mathematics content knowledge and pedagogical content knowledge (Hill, Rowan & Ball, 2005; Ball, Thames & Phelps, 2008; Ma, 1999). This work has pushed the field to reconceptualize the types of knowledge needed to provide effective mathematics instruction.

Preparing Elementary School Teachers to Learn from Teaching: A Comparison of Two Approaches to Mathematics Methods Instruction

Teacher preparation programs face a significant challenge in determining how to design learning experiences that develop the combination of knowledge, practices, and dispositions needed for effective classroom teaching. Time constraints and the theory–practice divide are two well-documented concerns. We introduce the conceptual framework and design elements of a video-enhanced mathematics methods course that targets these concerns. The course centers on systematic reflection and analysis of practice intended to foster career-long learning. We then examine the impact of this course on several facets of learning-from-teaching competencies, including teacher knowledge, beliefs, and practices. Sixty-two preservice teachers enrolled in a one-year post-bachelor elementary teacher preparation program were randomly assigned to attend this course or a more typical mathematics methods course. Findings suggest that teacher preparation experiences centered on systematic reflection and analysis create opportunities to develop certain aspects of learning-from-teaching competencies that remain otherwise underdeveloped. Implications for the design of teacher preparation include the integration in mathematics methods courses of cycles of analysis through video-enhanced discussions; collaborative planning, implementation, and reflection on teaching; and live observation and co-constructed interpretations and considerations of next steps.