K-12 Mathematics Education in Israel

The following sections are included:

• List of Authors^*
• Editor’s Preface
• Foreword
• Acknowledgments
• Contents

This chapter provides a timeline for what the authors consider to be the most significant and influential events in mathematics education from 1900 until today, with special emphasis on the years since the establishment of the State of Israel in 1948. Commentary corresponding to each date in the timeline is also given.

This chapter describes an educational reform aimed at increasing the number of students studying advanced level mathematics in high schools. The reform was initiated in view of the deteriorating number of students choosing to study mathematics at the advanced level: between 2006 and 2013, there was a decrease of 30%. This decrease reflected on the level of students who studied engineering and science in the universities. These phenomena could have a negative influence on academia, industry, security, and education. Thus, the Ministry of Education initiated a “Program for the Promotion of Mathematics and Scientific Excellence” which is discussed here.

Israel experienced a sharp decline in the number of its high achievers in mathematics in high schools between 2006 and 2012. The steep falloff placed the “start-up nation” at risk and was cause for alarm. This paper tells the story of how Israel awoke to this trouble and articulates the strategy that enabled it to reverse and restore its performance within five years.

Current major roles of the supervision of mathematics teaching are described. These include developing and implementing the national curriculum and national assessment; supporting mathematics teachers and improving instruction via mathematics instructors; teachers’ professional development; working with the advisory committee; supervision and approval of mathematics textbooks and other teaching materials.

The religious population in Israel is heterogeneous; consequently, there are several kinds of high schools catering to this population. We give a schematic description of the population and of the schools, then present trends at the different levels of study. We relate briefly to outstanding and gifted students, using yeshiva high school for gifted students at JCT as an example.

In this chapter, we describe the current ultra-Orthodox (Haredi) education system, with special emphasis on mathematics studies. We then illuminate some of the recent transformations in this regard, both within the Yeshivot of the Haredi men, as well among the Haredi women’s education system, predominantly the Beit-Ya’akov schools. We conclude by forecasting, cautiously, an imminent shift towards excellence in mathematics among various sections in the U-O society.

This chapter describes mathematics education for Arabic speakers (about 21% of the total population) in Israel. Mathematics education among Arabic speakers is derived from, and directly related to, the mathematics education of the majority of Hebrew speakers. We discuss mathematics education outcomes (MEITZAV, secondary school exams, PISA, and TIMMS) and examine the new mathematics curricula and mathematics teacher training (in-service and pre-service) in primary school, middle schools, and high school. The overall picture is not encouraging given the disparity between Hebrew and Arabic speakers. However, since 2013 there has been a positive change in terms of the M.Ed. in mathematics education curriculum in Arab-sector teacher training institutions and an increase in the number of students enrolled in the advanced-level track in mathematics.

This is an overview of preschool mathematics education in Israel through a description of the triangular relationship between: (a) theory and academic research, (b) policy and teacher training, and (c) the practice of teaching and learning mathematics. Underlying the preschool mathematics curriculum and professional development programs is the accumulated academic knowledge of early mathematical thinking and pedagogical approaches, adapted to the age and cognitive capabilities of preschoolers (3–6 years of age). Two examples of authentic, extended mathematical practices of preschool teachers and their preschoolers are presented.

New opportunities are being researched and examined for teaching geometry in preschool (ages 4–6) and primary school (grades 1–6). Israeli preschool and primary school mathematics curricula have been historically viewed as preparation for the formal teaching of geometry in high school. Our understanding that spatial awareness and geometrical thinking develop at a very early age has led us to build a dynamic learning environment based on the techniques of paper folding, together with digital technologies using animations. The chapter will describe the elements of the Origametria program and its implementation in kindergartens and schools in Israel. Additionally, it will describe the changing attitudes of teachers with respect to teaching geometry, together with the increased motivation of pupils to use their intuitive spatial reasoning for fostering geometric thinking to reach higher levels of abstraction.

Although visual thinking contributes to the development of basic skills in many domains, this subject is neglected in preschool and primary school. The Agam Program is a structured curriculum of 36 units that teaches visual skills, visual vocabulary and visual thinking to young children. Research shows that this approach has many positive effects for young children from diverse backgrounds, in areas such as mathematical thinking, school readiness, and general intelligence.

In Israel, there is a mandatory preschool mathematics curriculum. Yet, most preschool teachers have little preparation for teaching mathematics to young children. In this chapter, we present the Cognitive Affective Mathematics Teacher Education (CAMTE) framework that was developed at Tel Aviv University and used to investigate different elements of preschool teachers’ knowledge and self-efficacy for teaching mathematics. The framework was also used to plan and enact professional development for preschool teachers. The chapter offers a theoretical rationale for the framework and then demonstrates how the framework was used within the context of teaching repeating patterns.

This chapter describes the Time to Know (T2K) Initiative. T2K created a digital teaching platform and interactive core curriculum for one-to-one classrooms. The platform was designed to empower the teacher in conducting different instructional practices based on the socio-constructivist approach. The T2K platform will be presented and discussed by going through a typical lesson.

During the years 2000–2010 we led a national project called Mitzui u-Metzuyanut in Mathematics (the meaning of which is “Exhausting Students’ Mathematical Potential”) that began as an experimental project in 56 middle schools and developed into a nation-wide mandatory program in every middle school in Israel. The project aimed at implementing a special program in mathematics for low achieving students, hand in hand with a special program for high-achieving students. The project’s main goal was to enhance the mathematics learning opportunities for middle school students (7th–9th grades) at both ends—both promising students who are mathematically capable and struggling students who are mathematically disadvantaged. Participating schools were required to implement the program in full — for both ends. The project was launched and supported by the Ministry of Education, and was conducted as a unique collaboration between the Ministry of Education and two academic institutes (The Technion — Israel Institute of Technology in Haifa, and The Hebrew University in Jerusalem). In this chapter we describe the design and implementation of the project as well as its impact on students, teachers, and the school system.

This chapter uses the CompuMath project as an example of a comprehensive curriculum development project to integrate technological tools into everyday school mathematics. After sketching its border lines, we provide a glimpse from the classroom. We end with some longer term implications of the project.

In September 2012, the Center for Educational Technology together with the Israeli Ministry of Education and the Trump Foundation, launched the first Israeli Virtual High School (VHS). The goal was to increase the number of students who study advanced-level mathematics and physics by addressing a two-tiered problem in Israel’s periphery: the shortage of qualified teachers who can teach advanced-level mathematics or physics, and the low numbers of students who opt for these studies — too low to justify funding dedicated classes for them at their home schools. This chapter describes the design, instruction, and support mechanisms of the VHS and presents its growth since its inception in 2012. It then presents preliminary findings gathered from a questionnaire disseminated in 2015 among the first graduating cohort of the VHS and their teachers about their experience.

In this chapter, we describe different types of programs for students with high mathematical potential in Israel. Nurturing mathematically advanced students requires solving complex problems associated with making decisions about the scope of the programs and the choice of appropriate educational approaches. We focus our attention on classes for students with high mathematical potential, university programs for mathematically advanced school students, mathematics Olympiads and competitions. We provide some representative examples of such programs.

This chapter describes the Bar-Ilan University — ICAMS Program for the Advancement of Mathematically Talented Youth. It gives the rationale and a general description of the program, a quantitative summary of the program’s outcomes, as well as some pedagogical details of the program. It also gives an overview of the development of the program over the years.

This chapter introduces the Mofet Network. Starting with its history, it continues with the description of the findings obtained in a research on Mofet’s achievements. The various pedagogical departments of Mofet are presented, focusing on the Mathematics Department. Our vision and goals are defined, along with some examples of tasks we give our students in order to achieve our stated goals.

ORT Israel is the country’s leading network of comprehensive schools geared to teaching advanced technology and sciences. Its Research, Development, and Training Administration works with and for the ORT schools, to create innovative pedagogical projects that develop teachers, enhance students’ skills to raise their matriculation eligibility and achievements, and contribute to bridging gaps between different population groups. ORT Israel’s educational policies are implemented in all its schools, including for the study of mathematics. The policy for mathematics focuses on developing a nurturing environment, enabling students to persevere with their mathematics and science studies at the advanced level throughout grades 10–12, and attain higher scholastic achievements. The change in ORT’s mathematics education policy involves pedagogical aspects which strengthen motivation, and organizational aspects highlighting the importance of the department chair and leading teachers in the guidance and professional development of the teaching staff. The goal of this policy is to support the aspirations of principals, teachers and students for a high-quality secondary school graduation certificate that will pave the way to tertiary education in advanced fields suited to the 21st-century employment environment.

This chapter focuses on how the Amal Educational Network, a leader in promoting scientific and technological excellence, responds to the needs of students and teachers, both as groups and as individuals. This is accomplished through the implementation of three programs: a program to encourage girls to pursue advanced studies in STEM subjects, while raising teachers’ awareness gender-specific aspects of learning; a program to tap the potential of high-achieving students in intermediate-level mathematics, while educating teachers on how to respond to students’ individual needs on the emotional, functional, and learning levels; and a program to improve teaching in the Bedouin sector in southern Israel by recruiting local teachers, providing individualized support for each teacher based on the their needs, and partnership in the unique community of mathematics teachers employed in the Bedouin sector. Each of these programs has served as a model for implementation in additional Amal schools.

We present three examples of online problem-solving forums that accompany the learning of mathematics in Israeli high schools. The first example introduces a Facebook forum intended to prepare students from different schools for the secondary school graduation exam in mathematics. The second example concerns a WhatsApp asynchronous forum opened by a novice mathematics teacher for her 10th grade. The forum has gradually developed into a multifunctional space for students seeking assistance and sharing solutions to homework problems. The third example is a synchronous Google+ forum in an 11th grade initiated by an experienced mathematics teacher. This forum functioned as a platform for collaborative problem solving after school hours. Trends in development of self-organized online activity are discussed by the end of the chapter.

The Integrated Mathematics Project (Mathematica Meshulevet) is a comprehensive 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, and (2) addressing the diverse needs of the Israeli student population within the track for which the program is intended.

This chapter describes an on-going attempt at decreasing the gap between the ordinary school mathematics curriculum and contemporary mathematics, in order to give all high school students a taste of what contemporary mathematics is about.

In this chapter, we present a brief overview of changes that have taken place in the nature and status of Israeli colleges of education over the past 50 years and the controversy these changes have introduced into the discussion of mathematics teacher preparation. We then present data regarding students in the various programs for mathematics teacher training in colleges of education, and conclude by pointing out some current trends that may be the cause for the rising number of students who apply for mathematics teaching certificates in Israeli education colleges, which may have implications on future plans.

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 mathematics strand of the program: mathematics and mathematics education studies, and presents the view of a program graduate on her studies in the program.

This chapter describes the program for prospective secondary school mathematics teachers held at Tel Aviv University. At the university, prospective teachers already have a bachelor’s degree in mathematics or a mathematically rich field of study. The main aim of the program is to promote their mathematical knowledge needed for teaching. Prospective teachers attend courses at the university and comply with field work requirements at local schools. The challenge is to bridge coursework with fieldwork, bringing the courses into the field as well as bringing the field into the university. This chapter focuses on the use of cases as tools in fostering this bridging. The chapter begins by describing the rationale and general outline of the teacher education program. It then describes two specific courses, and in particular, how cases were used in those courses. For each course, we offer some findings on what prospective teachers gained from the analysis of cases, as well as their perspectives on the use of cases as learning tool.

In this chapter, we focus on the training of prospective mathematics teachers who study at the Technion in a program called Views. Views invites Technion graduates back to the Technion Faculty of Education in Science and Technology, to study towards an additional bachelor’s degree that includes a high school teaching certificate. Graduates can choose among the eight tracks of STEM education offered by the program, one of which is mathematics education. In this chapter, we introduce the Views program and, in particular, its mathematics education track, and present the unique characteristics of the students studying in this track. Specifically, we identify their motivational factors for joining the program as a second career, and present how they perceive their unique contribution to the education system in Israel, both as engineers and scientists and as parents.

Increasing number of individuals are entering the field of mathematics education as second career teachers (SCTs). Coming from successful careers in industry, accounting and in the IDF, the SCTs bring with them a range of experiences that makes their teaching qualitatively different from their first career peers. This chapter presents a survey conducted among ten second-career mathematics teachers, all are successfully teaching mathematics in secondary schools. Here we present the main perceptions and themes that came up during the interviews: (1) Inner drive for meaningful action; (2) the gap between the naive initial vision and actual job scope; (3) the unique contribution they bring to school; and (4) common perceptions regarding classroom management.

This chapter describes a nation-wide project—Club-5—aimed at improving the quality of mathematics teaching in high school through management of teachers’ communities of practice. Club-5 aims to create a comfort zone for project participants and enhance the inquiry components in school mathematics teaching. Mutual support, shared experiences, and professional conversations within the communities, along with implementation of challenging mathematical tasks, educational technologies, and collaborative learning in the classes, are core elements of Club-5. Special attention is paid to the professional development of community leaders.

In this chapter we describe two National Centers of Mathematics Teachers: the Primary School Teachers’ Center and the Secondary School Teachers’ Center. The centers are managed by a team from the Department of Mathematics Education in the University of Haifa and are monitored by the Israeli Ministry of Education. In line with their dual affiliation, the centers construct firm bridges between academic research in the field of mathematics education and pedagogical practice in schools across the country. We portray the structure and the activities which are central to the two centers and provide some examples of activities suggested by the centers.

The Teach First Israel science, technology, and mathematics track (TFI STEM) addresses the very large gaps in academic achievement between students from high and low socioeconomic backgrounds. Established in partnership with the Trump Foundation (which promotes excellence in science and mathematics teaching in Israel), the track recruits high-quality candidates with a degree in STEM subjects and a strong commitment to social engagement, gives them intensive teacher training, and places them in schools in Israel’s socio-geographical periphery. These teachers receive long-term professional development and support, including individual mentoring provided by TFI STEM Leading Teachers. Interviews with teachers indicate high levels of social commitment, continued learning, and dedication to achieving excellence in their teaching and in their students’ results.

This chapter describes four secondary school mathematics teacher-preparation practice-based programs established in Israel at four colleges of education during 2013–2014 with the support of the Trump Foundation. The chapter focuses on the clinical aspects of the programs and ends with a discussion of the programs’ strengths and the challenges faced by program developers and graduates.

VIDEO-LM is a professional development project for secondary school mathematics teachers, designed for enhancing mathematical knowledge and supporting reflection on practice. Using six “viewing lenses”, teachers watch authentic mathematics lessons of unknown colleagues and collectively reflect on the teaching practices observed. We describe the rationale, tools, and implementation of the project.

The increasing use of Wikipedia, social networks like Facebook, and databases with search engines such as Google, inspired us to consider a suitable computer-based platform for preserving, accumulating, and continuously improving mathematics teachers’ practice, through collaborative efforts, aiming at empowering the mathematics teachers’ community of practice. This chapter describes a continuing effort invested in the software development and in its assimilation.

The roots of the modern mathematical Hebrew lexicon are found in the Haskalah movement at the end of the 19th century. The next important stages are found in the context of the efforts of Eliezer Ben Yehuda and the institutions he developed for fostering modern Hebrew in general in Palestine. Of particular importance was the contribution of Avraham Baruch Rosenstein in Tel Aviv.

Technological environments have become an integral part of the learning-teaching process. We discuss here the advantages of such environments—full courses and content repositories—and present examples from CET’s repository of interactive books, courses, and activities.

Teachers face challenges when conducting lessons built on student-designed solution strategies. The work we describe here is part of an effort to explore how technological support for classroom formative assessment may play a role in attempts to reform mathematics instruction. We focus on the challenges involved in teachers’ attempts to design and experience a new genre of formative assessment with an automated formative assessment platform in mathematics (STEP).

This chapter describes several projects deriving from Sfard’s Commognitive Theory. After providing a brief outline of its major tenets and concepts, we describe implications of this theoretical framework in four areas of practice: preservice teacher preparation, in-service professional development, introduction of mathematical texts to high school students and diagnosis of mathematical learning difficulties. We end with a discussion of the affordances and challenges of linking the Commognitive Theory with practice.

The chapter presents the story of mathematics education in the Kibbutz Movement. It starts with a description of the kibbutz way of life and its unique educational system. Then the evolution of the education system up to the 1940s follows, focusing on mathematics education for different age groups. Subsequent sections focus on mathematics education in various levels (pre-school, primary, middle, and high school) in the Kibbutz Movement from the 1940s until today, with emphasis on the meaningful changes that led to increasing number of students who study intermediate and advanced-level mathematics and pass the secondary school graduation exams in these levels.

This chapter focuses on Israeli students’ performance in mathematical literacy as assessed by PISA. It discusses the PISA definition of mathematical literacy, and describes how it is assessed by PISA. The chapter then reviews the results of PISA assessment, showing low performance on all four mathematical content areas (quantity, space and shapes, change and relationships, and uncertainty and data), extremely large variations between and within schools, and difficulties in students’ ability to handle certain mathematical processes. The general picture was not new to the Israel people, but the detailed analyses, the depth of the variations, and the very fact that Israel lagged so much behind the OECD average were not anticipated.

“Kidumatica” is an extra-curricular program that, for 20 years, has worked to identify and develop the potential of mathematically talented students in Israel’s geographic and socio-economical periphery. It is built on a cyclic model: its sound theoretical foundation shapes the implementation of Kidumatica experience, which in turn is a platform for generating new research. Every year, approximately 550 students come to the Ben-Gurion University campus to participate in the program, some for up to 5 years. Kidumatica demonstrates how, through a specially designed structure and tailor-made materials and methods, we can help talented students break through social barriers and attain great academic and professional heights.

The chapter describes ideas examining the interweaving of ethnomathematical approach into preservice mathematics teachers education and mathematics school curriculum in Israel. Appraised are the advantages ethnomathematics offers teachers in accommodation of pedagogical skills for effective coping with the cultural diversity of the classroom population, and understanding the perspective of multicultural mathematics with its pedagogical implications.

Understanding the etiology of mathematical learning disability (MLD) has implications for assessments and remedial mathematics education. Diverging opinions regarding the source of the difficulty underlying MLD have slowed progress for new interventions and diagnostic testing in Israel and around the world. Traditional approaches suggest that the source is impaired quantity representation, while others propose skills that support mathematical learning, such as working memory. Currently, there is no normed assessment for MLD in Israel. We propose the establishment of a new test that includes basic numerical processing, mathematics curriculum-based tasks and cognitive tasks. In addition to assessment, educational and cognitive interventions are reviewed. Further progress is needed to establish a normed diagnostic tool, create personalized interventions and greater inclusion of children with MLD in mathematics classrooms.

This chapter focuses on the first five years of the Jerusalem Conference for Research in Mathematics Education. Specifically, the paper examines the development of the conference during that period and presents findings regarding the span of research in mathematics education conducted in Israel as reflected at the first five conferences.

The following sections are included:

• Appendix: Israeli Mathematics Curricula (K-12): A Concise Form Based Upon the Hebrew Original Published by the Ministry of Education (See References Below)
• Glossary