Shocked by the abysmal level of math instruction in the country, a group of math professors is now challenging the Education Ministry and trying to implement the Singapore method.
When Prof. Ron Aharoni of the mathematics department of the Technion - Israel Institute of Technology volunteered to participate in a project to improve math education in Ma'alot-Tarshiha, he never imagined how shocking the experience would be for him. The textbooks used in the first and second grades, he says, described in fact a kind of new math that no one - children, teachers or parents - understood.
"When I came to Ma'alot," says Aharoni, "the teachers explained to me that there are two equivalent approaches to teaching math that compete with one another: the structural approach and the environmental approach. It took me a whole year to realize that it's all a fraud. There is no `environmental math' - there is normal math and there is delusional math, which is unique to Israel. You have to have a distorted mind to invent something like that."
Distorted mind or not, the achievement level of Israeli children in math is low. On an international mathematics test administered in 1999 by Trends in International Mathematics and Science Study (TIMSS), Israeli children placed 28th. In May of this year, TIMSS will once again conduct the test. However, following the deplorable results of last time, the Education Ministry has rolled up its sleeves, and at record speed - over a period of six months instead of years - it has published two new books for the development of quantitative thinking. It then sat seventh- and eighth-grade students down to prepare for the test at full steam.
Boston-based TIMSS is an international organization for the assessment and measurement of math and science achievements. Other sponsors of the study include the World Bank, the National Center for Educational Statistics, the International Science Fund and research groups in Europe and Canada. In the 1999 test, students from 38 countries participated. Israel's placement in the bottom third - after Cypress, Romania, Moldavia and Thailand - launched a heated debate, which has reverberated as far as the United States.
Who is to blame for the fact that Israeli children fell from first place in the same test in 1964 to 28th, 25 years later? The Center for Educational Technology (CET) blames the level of teaching - or, in other words, the teachers. The Ministry of Education believes that perhaps the teaching materials developed by the CET (with the approval of the ministry) are problematic. Mathematicians point an accusing finger at the schools of education, and the educators say that the mathematicians do not know anything about teaching.
Not everyone was asleep on the job: Some teachers and mathematicians sounded the alarm years ago. Israeli children, they said, in sharp contrast to the high self-image of the students and the educational system, are not only failing at reading comprehension, they do not know simple math either. Children in the first and second grades know to say that 3 + 5 is the same as 5 + 3, but they don't know how much 5 + 3 is. A number of parents, teachers, high-tech professionals and math professors are sick of this situation.
Desperate situation
A few months ago, the Israeli Association for Excellence in Mathematics was established. A few dozen of its members succeeded since the beginning of the current school year in introducing math textbooks from Singapore, which have been translated into Hebrew, into 20 schools, as an experiment. Next year, they have been promised that the experiment will be expanded to 50 schools. Beginners' luck? Not really. The Ministry of Education is so desperate because of the situation that almost anyone coming up with some kind of rational curriculum for math can convince Prof. Yaakov Katz, chair of the ministry's pedagogical administration, to experiment. What has not been done for 30 years is now receiving favorable attention.
Five experimental programs in math have been launched this year in the first and second grades. The rights to the Singaporean book were donated to the organization by entrepreneur David Garbasz, an Israeli-born mathematician who lives in New York.
Why Singapore? "They consistently place first in international competitions," says Garbasz, who wanted to donate the rights to use the texts to the ministry for free, but did not encounter any enthusiasm there for his idea. "The minister's bureau told us that if the ministry agreed, it would take a few years to translate the books. I took the books to a firm called Quality Translations and in six weeks, everything was translated. The people from the association worked day and night and printed 20,000 copies."
The Singapore textbooks for the first and second grades are colorful and user-friendly. The "spokesmen" in the books are illustrated figures of children, who explain what is going on. The environment is natural - the home, family, objects from real life, cats, butterflies and apples. The concept behind the method is known as "Back to Basics."
"This is the beginning of a popular protest movement," says Prof. Shimon Schocken, the dean of the Efi Arazi School for Computer and Media Sciences in the Interdisciplinary Center (IDC) in Herzliya, and a member of the Association for Excellence in Mathematics.
"The educational establishment is currently controlled by a culture that is known as `New Math,' which has its source in California of the 1960s. It was imported into Israel and since then, has taken over all the learning materials. I see the catastrophe in this system as a father of young children. I open up their textbooks and I cannot understand what they are being taught in school. As the dean of a computer science faculty, I see the results of math instruction done according to this method on the students that come here to study. They lack basic understanding of mathematics, something they didn't learn in grade school."
The method was brought to Israel in the early 1970s by Prof. Pearla Nesher. She returned from Harvard University with a doctorate in education and began to work as a consultant to the Ministry of Education and in CET in the development of new curricula for elementary schools.
Of rods and patterns
The result was a series of math textbooks called "One, Two ... Three" for the first and second grades, which have dominated the educational system ever since. The method used in the books is called the investigational or structural method, at the center of which is use of the celebrated Cuisenaire rods. "One, Two ... Three" was supposed to create a revolution in thinking. Each rod has a different color and size. Two rods placed side by side are not two. Instead, they represent a particular number, depending on the color and length of the rod. The child reaches the result not using the intuitive method of counting items, as he is used to doing in his natural environment, but rather by means of trial and error. He puts the rods down lengthwise, one after the other, and looks for a pattern that fits them. Their combined length, if it fits exactly into the pattern, is the result.
Those who do not understand will find themselves in the distinguished company of numerous parents, teachers, math professors and, of course, the pupils themselves. The idea is to teach first-grade children to investigate the "pure number." The authors of the book explain in the teacher's guide that the right way to teach math in the lower grades is to disconnect the students from their natural environment and from reality, and to teach them in a pure, clean environment that has nothing to do with prior knowledge. Further along, pupils learn concepts invented by the CET that have no parallel anywhere else in the world, such as Zanavgufim ("Tailbodies"), imaginary creatures that are used to teach the decimal system.
"The idea of the rods doesn't make sense," says physicist Dr. Mira Ofran of the Science Teaching Center at Hebrew University in Jerusalem. "What the child in the first grade learns is that green + yellow = purple. But he doesn't really know how much it is. That is a terrible thing - basing math on something that is not on math. It is not difficult to see that this entire method is groundless from beginning to end. I have written articles on this, spoken about this with everyone and anyone willing to listen. The most terrible thing is that there was no choice. The Ministry of Education decided to follow this program and only this program all these years."
Systemic failure
About two years ago, after the results of the TIMSS test became known, the Ministry of Education formed the Ben-Zvi committee (headed by Prof. Nava Ben-Zvi, currently the president of the Hadassah College of Technology) to examine the state of math in the lower grades. The committee completed its work 10 months ago and from its conclusions, it is clear that there has been an overall systemic failure in math instruction in Israel. Three months ago, the Knesset Education Committee held a special debate on the subject and formed a subcommittee to deal with the subject. During the debate, the chair of the Education Committee, MK Zevulun Orlev, asked why Israel doesn't emulate the teaching methods of countries whose students excel in the international tests.
"I don't understand why we don't sit committees down and search," said Orlev. "I propose not to reinvent the wheel. If we buy our F-16s from the United States, we can just as well import a method to teach math from Singapore. It's not something to be ashamed of."
One of the first signs of revolt against the accepted teaching method came from Telma Gavish of Haifa, a member of the association for excellence in math, an instructor in schools that teach in accordance with the Singapore method. (Like all members, her work is voluntary and she receives only traveling expenses from the association.)
"I began to fight many years ago," she says, "but four years ago, when I retired and they couldn't fire me any more, I got involved with it on all fronts. I went to anyone who would agree to listen to me - from university professors to taxi drivers - and I asked them to help me. I could see mistakes in thinking among the students. A child learns that 3 + 4 is not 5 because that does not fit his structure, but not because he counts and understands that 3 + 4 = 7. After that, there was a terrible decline in the junior-high schools and the percentage of pupils joining the advanced math classes in high school dropped over the years.
"In France, 20 percent of students do the advanced five matriculation units in math and here it is only 7 percent; if there has been a rise, it is only because of the Russian immigration. Even those who complete the advanced math studies, when they reach the university, don't know the basics. It affects all areas of mathematics. One day, I was visiting the chief scientist of the Ministry of Education, Prof. Mira Mevorach, and she asked me how long it would take me to fix the situation. I told her that if the ministry helps out, it will take 25 years. If it doesn't help, it will never be fixed."
Prof. Ron Aharoni of the Technion was invited two years ago by the Karev Foundation to voluntarily join a project to improve math education in Ma'alot-Tarshiha. During his work with the students, he was exposed to the teaching methods in the first and second grades.
"This method has been a colossal failure in America and in the late 1970s, they decided to stop using it there completely," he says. "But people doing their doctorate at the time in the U.S., from numerous countries and not only Israel, came back to their own countries and brought the method back with them."
Aharoni realized that a part-time volunteer effort would not resolve the math problems of Israel's children and today he devotes every free moment to the subject. And he is angry, very angry.
"In Ma'alot, the teachers showed me how, using the Cuisenaire rods system, they forbade the children to count and described how the kids would count using their fingers and toes under the desk. One of the teachers said they did it surreptitiously, `like the Crypto-Jews in Spain.' It is a crime. This method did not leave a single concept to be taught directly in grade school. Someone dared to invent a new math. All over the world, pupils learn the decimal system and in Israel, they learn Zanavgufim. Children don't understand it, I sometimes don't understand it, the parents never understood it. I once heard a parent bragging, `My kid in the first grade studies things that I don't understand.'
"I have shown it to mathematicians, and they don't understand it either. The greatest blunder was that no one understood how unique and bizarre it is, that there is nothing remotely similar to it anywhere else in the world, and certainly that no one would dare to try to impose it on an entire country. In Ma'alot, we replaced all the books with a rational Israeli text called Math 10." This book is now being used experimentally in other local schools.
Shalit's pendulum
The experience in Ma'alot lead Aharoni to open a broad front against the Ministry of Education. One of the articles he wrote appeared in Haaretz, and Garbasz read it in New York and contacted Aharoni. He donated $250,000 and the rights to the Singaporean books, which he had purchased, and encouraged Aharoni to form the association for excellence in math. Prof. Dan Amir, a mathematician and former rector of Tel Aviv University, is the chairman of the organization.
"Through the years, I was always concerned by the level of math education in Israel and I sent letters to ministers of education, but I never received an answer. Somehow, I assumed that someone was taking care of the situation and I dropped it. Now that I have retired, I have decided to pitch in."
Amir was not satisfied with the level of his students. He felt that the problem was the result of a postmodernist approach to life that undermines education.
"They said that you have to take the students' happiness into account, to understand them, not to pressure them, not to ask, not to demand and not to harass them. No more learning by heart and no more homework. Even so, the standard is not particularly high. In the view of ministers of education, everyone should have a matriculation certificate, and that creates a conflict between excellence and egalitarianism. It is an international trend that is beginning to be reversed today, and is particularly salient in two subjects: reading and math.
"Suddenly you realize that we have an entire generation of illiterates. In mathematical research, Israel is in the absolute third or fourth place, thanks to the previous generation and the immigration from Russia, but down below, the branches are drying up and I don't want to think what will happen in the coming generations."
Prof. Ehud de Shalit of Hebrew University's Einstein Institute of Mathematics says that it is a huge mistake to concentrate on a single educational approach: "I like to illustrate this by using the image of a pendulum. Once everything was boring and children learned like robots. Then along came the education experts and they said, `That's horrible. We have to let children discover the beauty of the world and let them be creative.' Then the pendulum moved all the way to the other side, and now they are so creative that they don't know how to add and subtract. The best ones, the ones that go on to study math in the university, will get there no matter what. I am talking about the others, everyone else. Everyone wants to know how to invest in the stock market, how to use a computer, how to understand an accounting trick. Once, all you had to know to run a grocery store was arithmetic. Now it's not enough."
Troubled by the situation, the Ministry of Education together with the CET came up with a new math curriculum, called Program 2000. The committee that prepared the program was headed by Prof. Nesher, and it was supposed to be introduced into schools at the beginning of the current school year. But De Shalit, Gavish, Aharoni and others who read the program stormed the office of Prof. Yaakov Katz to prevent it from being implemented.
Gavish: "After seeing Program 2000, I couldn't sleep for two weeks. It is shocking. It represents three votes of nonconfidence in people. First, children cannot be taught because they are not intelligent, the material is too difficult and the teachers are bad, and the worst part - they wrote that the express goal of the program is that the child should feel good about math - not that he should know math."
Aharoni and the others translated the program into English, and sent it to Garbasz, who passed it on to a number of senior math professors in the U.S. for assessment.
"The program got a failing grade," says Garbasz.
Its implementation was delayed, and Prof. Katz takes credit for this: "When the program arrived on my desk for approval, I stopped it. I passed it on to math professors and they told me that its weaknesses should be reexamined before approval. In some of the chapters, they recommended a cosmetic revision and in others, a complete overhaul. They are now meeting with Pearla Nesher and, based on Program 2000, they are building a new, revised program and we are moving ahead.
Who needs math anyway?
Moshe Rein, a computer expert, made a revolutionary career move four years ago and became a teacher. He had a dream and is now making it come true: Today he is training teenagers to teach math to younger children. He is the one that brought Aharoni to Ma'alot. Now he is an instructor of the Singapore method in three schools in the north of the country - in Tiberias, and in the kibbutzim of Gesher Haziv and Givat Haim.
"The children are taught that 3 x 2 is the same as 2 x 3," he says. "In abstract terms, that's true, but when you attach meaning to it, it's not the same thing at all. Because if you go to the doctor and he tells you to take three pills twice a day, it's not the same thing as taking two pills three times a day. The meaning can be very different, even crucial."
The Singapore books were distributed free of charge this year in the schools participating in the experiment. The Ministry of Education insisted that next year, a token sum be collected from each student for the books in order to guarantee fair competition with other textbooks.
Dr. Ilan Efrat, a mathematician who works for Elbit and is a member of the association for excellence in math, participated in the translation of the books into Hebrew. He joined in the efforts not as a mathematician, but as an Israeli and the father of three children that learned according to the Cuisenaire rods method.
"At a meeting with teachers that we had in the framework of the association, we told them that they would have to learn the new method and to stand in front of the class and teach," he recalls. "It was very difficult for them because in the `One, Two ... Three' method, the teachers don't teach - they hand out work sheets, sit the children down in groups and move among the groups. In this way, for years, a situation was created in which teachers taught less and less and became more and more afraid of math. And suddenly, the same teachers that were afraid are now managing quite well with the new books and are proud to teach. A large proportion of the teachers are really quite happy now."
Why do we need math at all?
Efrat: "It is part of our culture, like languages, literature, history. Some of the children will eventually work in engineering professions. There is no reason for people to hate math or be afraid of it. As a mathematician, I can tell you that it is one of the summits of human philosophy and the fact that our achievements are constantly falling is preventing the next generation from being exposed to this beautiful thing."
Not everyone agrees. "It is a myth to say that in the modern age everyone has to know math," says Prof. Shlomo Weiner, the head of the Science and Technology Teaching Program at Ben-Gurion University of the Negev. "There is no need for everyone to learn mathematics. It is convenient to use the math tests as a filter for higher education, but in principle, mathematics is a subject that most people don't know, and even in previous generations, the situation was no different. There was always a small group that knew mathematics and that is definitely enough."
The post-Cuisenaire era is already here, says Weiner: "We have returned to simple, natural things from which basic arithmetic began. The children are finally being taught to reckon. Those who know how to reckon, concentrate on it and discover their intellectual abilities and start thinking."
Killing the messenger
Prof. David Nevo became chief scientist of the Ministry of Education a year ago and does not view himself as having any commitment to the old system.
"In recent years, Israel went a little too far to please math teachers," maintains Nevo. "They say the children have to learn by means of investigation and discovery, so that they remain interested and happy. And I say that you have to know the basics, too. The mathematicians say that there is no need to rediscover the multiplication tables each time anew, just to learn them, that there are laws and rules and they have to be learned by heart, too. In my view, the explanation for the failure is that with all the involvement in the method, the message was lost. Now there is a clear message coming from the system - that children must be required to have achievements."
Because of the failure in 1999, voices were heard demanding that Israel stop participating in the TIMSS test.
Nevo: "Not to participate in these tests is tantamount to killing the messenger, which is an ancient Greek tradition. It is unthinkable that Israel not participate in international studies, even if it costs us a NIS 250,000."
Prof. Katz is also relatively new to the system (about 18 months) and from this vantage point, he can say that he always thought that the current system needed to be completely overhauled.
Why did you have to wait 25 years to realize that the system didn't work?
Katz: "I am not responsible for what happened before me. I screamed and shouted and came to Education Ministry officials over the years and they knew my opinion of the method. I never liked it."
So why did you introduce the book on quantitative thinking now into eighth-grade classes?
"That is a result of drawing conclusions. I formed a team to examine what it means to be in 28th place in TIMSS, and they reached the unequivocal conclusion that the students do not have a mastery of quantitative thinking. It may well be that the Cuisenaire rods don't teach this, so I formed a steering committee, which proves that the ministry can work efficiently. In February, I formed a team from three universities, I published two books with eight chapters on quantitative thinking, which is the basis for mathematics, and in September-October, the books were already printed. That is a record of the speed of light for the ministry."
Why is it being taught in the eighth grade? Why didn't they learn it in the first grade?
"I admit that that was a mistake. Quantitative thinking is a basic of mathematics and those who do not know quantitative thinking don't know mathematics."
In self-defense
Pearla Nesher says that yes, she brought the knowledge from the U.S., but the textbooks in the "One, Two ... Three" series were written in Israel, and were not influenced, she maintains, by what was being done in America. On the contrary: "My doctorate is about the `New Math,' but it is a critique of it," she says. "And the method we developed here was a reaction to the methods used in America."
Apparently, the system was not that good because the students here are having difficulty in math.
Nesher: "The system is intended for elementary schools and they are having difficulty in the upper classes. They know the material for the first grade. They know it. That is not what they are failing at."
So why are the mathematicians saying just the opposite?
"It is their right to claim whatever they want and they have the right to disseminate the Singapore program. Mathematicians in the U.S. started the war and our mathematicians are jealous and decided they want a little noise and publicity. The Singapore books are very similar to ours, the same approach, the same structures. Except that they have an economic interest in distributing the Singapore books and those nice mathematicians don't know anything about teaching math. They don't understand it and it is not what they do. If they are now proposing that we get back to basics, then they don't know what is going on in the world. When they suggest going back to teaching the way we taught in the 1960s, when only 9 percent of the students passed the matriculation exams and today 50 percent pass, then they are completely cut off from the world of education."
But at that time, we were No. 1 in the world.
"When only 9 percent do the matriculation exams and only the top classes are tested, then of course we made first place. Twenty-eighth place now is not the right picture either because the students didn't take the tests seriously and didn't prepare. And the sample was not suitable and testers included weak schools as well as the Arab sector, which previously had not been tested. But there are people that wanted to be able to point to a terrible catastrophe so that they can push forward some program that someone has the rights to."
Today, even the Ministry of Education admits that the "One, Two ... Three" books are not good.
"They say that because of all the noise the mathematicians have made. In my view, it is a good book and it can still be used to teach. The purpose is to teach children math on a high level and it is suitable for children at this time learn differently than their parents. Otherwise, we will never progress.
Haaretz.com, the online edition of Haaretz Newspaper in Israel, offers real-time breaking news, opinions and analysis from Israel and the Middle East. Haaretz.com provides extensive and in-depth coverage of Israel, the Jewish World and the Middle East, including defense, diplomacy, the Arab-Israeli conflict, the peace process, Israeli politics, Jerusalem affairs, international relations, Iran, Iraq, Syria, Lebanon, the Palestinian Authority, the West Bank and the Gaza Strip, the Israeli business world and Jewish life in Israel and the Diaspora.
