Ruhama Even

Weizmann Institute of Science | weizmann · Department of Science Teaching

The seven articles that comprise this Special Issue examine the professional growth of mathematics and science teacher educators across different contexts and different foci of who is the teacher educator being studied. Despite these differences, a common thread running throughout these seven articles is the need for learning to be situated in coll...

This introductory paper first reflects the genesis of research in mathematics and science teacher education. The analyses show a movement from foci of research in mathematics and science education from students to teachers, and then to teacher educators. Next, an overview of research in mathematics and science teacher education and its development...

This chapter examines potential opportunities and challenges associated with giving teachers the opportunity to edit the textbooks they use in class. It draws on a set of studies for which the M-TET (Mathematics Teachers Edit Textbooks) project served as research setting. The unique aspects that characterize the work environment offered to teachers...

This working group paper introduces a new initiative to bring together research on proof and proving and research on international comparison. While the past two decades has seen a strong increase in research into proof and proving in mathematics education, much has been conducted in single national and cultural contexts. There are four areas in wh...

This study examined the changes that a group of nine Israeli 7th grade mathematics teachers, who collaborated on editing the textbook they used in class, chose to make in the textbook. Data sources included the project website (using a modified wiki-book platform), the group meetings, interviews with the teachers, individual papers written by the t...

The Rothschild-Weizmann Program is a uniquely crafted master's program at the Weizmann Institute of Science, especially designed for practicing secondary school teachers of mathematics, physics, chemistry, and biology. The chapter describes the rationale and structure of the two components of the mathemat ics strand of the program: Mathematics and...

The Integrated Mathematics Project (Mathematica Meshulevet) is a comprehen sive middle school mathematics curriculum program developed in response to the introduction of a new national curriculum. The chapter presents and discusses two salient aspects of the curriculum program: (1) integrating procedural knowledge and higher order thinking skills,...

This commentary chapter focuses on two main issues related to the challenge of classroom teaching and learning of proofs and proving: (1) classroom-based interventions , and (2) teacher interventions in students’ argumentation. The chapter uses these two issues to comment on the four chapters included in Theme 2 of the monograph, and concludes by s...

This chapter examines what might be the relevance of a unique abstract algebra course to teaching secondary school mathematics. The course was especially designed for experienced Israeli secondary school teachers of mathematics. One of its aims was to make the course relevant to the teachers’ work, for which we defined several modes of relevance. A...

The article summarizes the results of the discussions and the program of TSG 46 on the ICME 13 conference 2016 in Hamburg. The program of TSG 46 focused on three themes: 1. Conceptualization and theorization of knowledge in/for teaching mathematics at the secondary level. 2. Methods for measuring, assessing, evaluating and comparing knowledge in...

The M-TET (Mathematics Teachers Edit Textbooks) project invites mathematics teachers to collaborate in editing the textbooks they use in their classes as a means of transforming conventional connections among teachers, curriculum developers, and mathematicians into more productive connections. The unique aspects that characterize the work environme...

This study focuses on the changes teachers suggest making in math textbooks. The study addresses this issue by investigating the changes the first year participants in the M-TET project suggested to make in the math textbook they used in class, adopting Activity Theory as a theoretical framework. The participants, nine 7th-grade teachers, worked in...

This chapter examines the interplay of several key factors involved in shaping students’ opportunities to learn mathematics. It draws on studies conducted as part of the research program Same Teacher—Different Classes, all of which use the same novel research methodology: multiple case studies, where each case includes a teacher who teaches mathema...

This commentary paper focuses on challenges associated with the professional development of a particular group of mathematics educators: mathematics educators who work in the field of teaching development with practicing teachers. This group is termed in this themed issue didacticians. The paper offers a conceptual framework for addressing the chal...

The aim of this study is to examine how the conventional relationships between teachers and textbooks may be expanded so that teachers become more genuine participants in the process of textbook development. The study uses the Integrated Mathematics Wiki-book Project to examine how this challenge might be addressed. The Integrated Mathematics Wiki-...

This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in tw...

This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem....

This study examines how students’ opportunities to engage in argumentative activity are shaped by the teacher, the class, and the mathematical topic. It compares the argumentative activity between two classes taught by the same teacher using the same textbook and across two beginning algebra topics—investigating algebraic expressions and equivalenc...

This is a case study of a highly regarded high-school mathematics teacher in Israel. It examines the kinds of responses to students’ talk used repeatedly by the teacher, directing and shaping the classroom discourse, during different parts of the lesson. The main data source included 21 h of observations in two of this teacher’s classrooms. Analysi...

This study investigates the different ways by which secondary school mathematics teachers view how advanced mathematics studies are relevant to expertise in classroom instruction. Data sources for this study included position papers and written notes from a group interview of 15 Israeli teachers who studied in a special master’s program, of which a...

The aim of this study was to examine how teachers enact the same written algebra curriculum materials in different classes. The study addresses this issue by comparing the types of algebraic activity (Kieran, 2004) enacted in two 7th grade classes taught by the same teacher, using the same textbook. Data sources include lesson observations and an i...

This aim of this project is to enable teachers to edit the textbook they use for teaching. The rationale for the project is multi-faceted: to expand the connection between curriculum developers and teachers from one to two-way connection, to encourage the use of technological tools in school mathematics, and to support the development of a professi...

This study examines the views of people involved in mathematics education regarding the commonly stated goal of using mathematics learning to develop deductive reasoning that is usable outside of mathematical contexts. The data source includes 21 individual semi-structured interviews. The findings of the study show that the interviewees ascribed di...

This paper (1) presents a conceptual framework for analyzing the mathematics addressed in probability lessons and (2) uses the framework to compare the mathematics that two teachers with contrasting teaching approaches addressed in class when teaching the topic of probability. One teaching approach aimed to develop understanding; the other emphasiz...

This study examines a commonly held view that teachers tend to focus less on developing understanding and more on mechanistic answer-finding when teaching in classes of lower-achieving students. The study investigates this by analyzing actual practices of teaching mathematics and of classroom interactions in classes having different levels taught b...

The focus of the 15th Study, led by the International Commission on Mathematical Instruction (ICMI), was the professional education and development of mathematics teachers around the world. The study was designed to investigate practices and programs of mathematics teacher education in different countries and to contribute to an international disco...

This Study brought together 147 scholars and practitioners from 35 countries to discuss the professional formation of teachers of mathematics. Their individual contributions have been assembled to create a volume filled with descriptions of programs and projects, as well as concepts and data. Readers interested in the development of teachers of mat...

This study examines ways of approaching deductive reasoning of people involved in mathematics education and/or logic. The data source includes 21 individual semi-structured interviews. The data analysis reveals two different approaches. One approach refers to deductive reasoning as a systematic step-by-step manner for solving problems, both in math...

Teachers are expected today to assess student understanding as an integral part of instruction, using a combination of various assessment methods and tools, among which are observing students solve problems in class and listening to their mathematical discussions. The aim of our study is to explore what it might mean for a teacher to hear students...

In this article, two problems associated with the expectation that teachers use contemporary assessment techniques are examined. The first problem relates to teachers’ sense-making of assessment data. Illustrative cases revealed that teachers’ processes of interpretation of students’ understanding, knowledge and learning of mathematics draws on a r...

The overriding aim of MANOR – a national mathematics teacher center – in the last decade has been to provide a theoretically sound, research-based and practically feasible framework to support Professional Development (PD) for teachers of mathematics at a time of curriculum reform in Israel. This paper focuses on the preparation of, and support for...

This paper examines the problematic associated with the current expectation that teachers assess their students’ mathematics learning and understanding by listening to their talk and observing their actions. The paper suggests that the problems are of two different kinds. One kind involves difficulties that could be overcome; the other kind is rela...

Our discussions of the plenary lectures, and of the short presentations, as well as our continued probing of the group’s core questions led to a greater appreciation of the following: 1. Some contemporary researchers are designing projects that aim to develop both knowledge and practice. This is different from developing theory and then “putting...

In this paper we explore the issue of interdependency of theory and research findings in the context of research on the practice of mathematics teaching and learning at school. We exemplify how analyses of a lesson by using two different theoretical perspectives lead to different interpretations and understandings of the same lesson, and discuss th...

This paper is an initial investigation into the practice of providers of professional development for teachers of mathematics. The study examines the work of two providers of professional development for teachers of mathematics. Both provided professional development while working with teachers on implementing a new mathematics curriculum for seven...

In this chapter we consider what it takes to learn to conduct research in mathematics education. We argue that learning any complex practice requires opportunities to unpack its components in order to see what underlies competence performance. Many of the components of successful research remain implicit and are left to new researchers to glean fro...

The implementation of new standards in science and mathematics education necessitates an intensive and comprehensive professional development of science and mathematics teachers. Israel, which currently is in the process of reforming school science and mathematics, constructed a continuous lifelong framework for such professional development. This...

Mathematics classroom situations (MCS) are real or hypothetical classroom situations involving mathematics, in which the teacher has to respond to a student's hypothesis, question or idea. This study investigates the use of one such situation, the decimal point situation, in an in-service course for 20 elementary teachers. Data sources include: wri...

This study examines an attempt to encourage integration of knowledge learned in the academy with knowledge learned in practice as a means to challenge educational practitioners' — teacher leaders and inservice teacher educators — existing conceptions and beliefs, and promote intellectual restructuring. The article centers on two components of the M...

This article discusses the development of teacher leaders and inservice teacher educators whose role it is to promote teacher learning about mathematics teaching in the process of changing school mathematics. The Manor Program for the development of teacher leaders and teacher educators is used as a vehicle for addressing this issue. The article fo...

This article focuses on the intertwining between the flexibility in moving from one representation to another, and other aspects of knowledge and understanding. During the first phase of data collection, 152 college mathematics students who were also prospective secondary mathematics teachers completed an open-ended questionnaire. In the second pha...

This study investigates four seventh-grade teachers' awareness of students' tendency to conjoin or 'finish' open expressions. It also investigates teachers' ways of coping with this tendency. Three types of data were collected: 1) lesson plans, 2) lesson observations, and 3) post-lesson interviews. The analysis showed that the two experienced teach...

This paper discusses two possible approaches to (-8)1/3. The first is that (-8)1/3 = 3(-8) = -2. The second is that (-8)1/3 is undefined. The pros and cons of each of these approaches are considered and some implications to teacher education are specified.

Teachers’ ability to help students learn mathematics requires an understanding of student thinking. No less important is what teachers do with this knowledge; i.e. the nature of their decisions and actions which are based on this knowledge. Two interviews were conducted: one with two junior‐high school teachers, and the other with two eleventh grad...

Pedagogical content knowledge is made up of several components. In this paper we concentrate on one of these: teachers' planned presentations of the subject-matter. We deal with two main sources of this component of pedagogical content knowledge: knowledge about the subject-matter and knowledge about students. Illustrations are given in two mathema...

This study examines differences in connectedness in instruction between two novice teachers and an expert teacher. Three types of data related to lessons on equivalent algebraic expressions were collected: lesson plans, lesson observations, and post-lesson interviews. Although connectedness is an important characteristic of mathematics teaching and...

This article investigates teachers' subject-matter knowledge and its interrelations with pedagogical content knowledge in the context of teaching the concept of function. During the first phase of data collection, 152 prospective secondary teachers completed and open-ended questionnaire concerning their knowledge about function. In the second phase...

This article investigates teachers' subject-matter knowledge and its interrelations with pedagogical content knowledge in the context of teaching the concept of function. During the first phase of data collection, 152 prospective secondary teachers completed and open-ended questionnaire concerning their knowledge about function. In the second phase...

This study investigates prospective secondary mathematics teachers’ knowledge and understanding of the inverse function. It draws on analyses of questionnaires and interviews with subjects from eight universities in the USA. The paper illustrates naive conception of the essence of inverse function and lack of adequate relationships between conceptu...

Interest in teachers' subject matter knowledge has arisen in recent years. But most of the analysis has been general and not topic-specific. This paper shows how one may approach the question of teachers' knowledge about mathematical topics. It demonstrates the building of an analytic framework of subject matter knowledge for teaching a specific to...

This paper discusses the development of the mathematical experiences which make up the three-term sequence of mathematics courses taken by participants in the Elementary Mathematics Project (EMP), a longitudinal study of change in preservice teachers' perceptions and beliefs about mathematics. For the mathematics courses, both content and teaching...

Includes bibliographical references (leaves 236-244). Photocopy. Author's name on photocopy title page: Even, Ruhama Dalia. Thesis (Ph. D.)--Michigan State University, 1989.

Simila rity is an important topic in geometry, basic to understanding the geometry of indirect measurement, proportional reasoning, scale drawing and modeling, and the nature of growing. When United States’ teachers were asked to rate the importance of this topic for the Second International Study of Mathematics, they rated similarity of plane figu...

To teach the arithmetic-driven curriculum of the past, one needed little more than computational skill with the standard algorithms and a text to provide practice. That is no longer the case. To prepare a teacher dedicated to helping children think mathematically requires a very different experience with mathematics than the traditional college cou...

It is widely accepted today that teachers should be aware of, and knowledgeable about, stu- dents' mathematical learning. It is believed that such awareness and knowledge signifi cantly contribute to various aspects of the practice of teaching. In this chapter, we critically examine this commonly held belief. We begin this chapter by interpreting w...

Teachers are expected today to assess student understanding by using a combination of various assessment methods and tools. Among them, observing students solve problems in class and listening to their mathematical discussions. Yet, not much attention has been given to the question whether teachers need to learn these practices. This study begins t...

This paper analyzes the ways proof ideas in an algebra lesson were offered to stu-dents (1) by two different teachers, and (2) in two different classes taught by the same teacher. The findings show differences between the two teachers, and between the two classes taught by the same teacher, regarding the proof ideas made available to learn in the l...

It is widely accepted today that teachers should be aware of and knowledgeable about students' mathematical learning, as this significantly contribute to various aspects of the practice of teaching. We begin this paper by interpreting what one might mean by students' mathematical learning. Then we examine the validity of the assumption that teacher...

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