On October 4, 1957, an alarm was heard in the United States. It originated in space. Every radio ham could hear the broadcast that emanated from Sputnik, the satellite sent by Russian into orbit around Earth. The series of beeps sent out by the innovative satellite sowed panic in the United States, which until then had derided Russian technology. The Sputnik crisis generated a genuine revolution in the American education system, notably a rethinking of how to teach mathematics.
The focus on math and the sciences stemmed from positive intentions, but in retrospect had negative results. The big mistake was the “New Math” curriculum, with its group theory and non-decimal number bases. In his memoir “Surely You’re Joking, Mr. Feynman!,” the Nobel Prize-winning physicist Richard Feynman described the textbooks of that era: “Every child had to learn another base! And then the usual horror would come: ‘Translate these numbers, which are written in base seven, to base five.’… If you can do it, maybe it’s entertaining; if you can’t do it, forget it. There’s no point to it.”
The New Math program was eventually forsaken in the United States, but versions of it were imported to Israel. They fomented two upheavals: the “structural approach” (the Cuisenaire rods system) and the so-called exploration revolution of the 1980s and 1990s. Both were harmful to the teaching of mathematics. Ron Aharoni, a mathematics professor from the Technion – Israel Institute of Technology in Haifa, who volunteered in 2000 to teach in a primary school in the northern town of Ma’alot for two years, wrote at length about his classroom experiences. He noted the danger inherent in the attempt to create shortcuts intended to spare the students work by forgoing systematic learning, avoiding precise formulas and trying to skip stages of learning how to solve a given problems.
The proportion of high-school students who take the matriculation exam in mathematics at the level of five units (the highest) plunged by about 30 percent between 2006 and 2014. Former Education Minister Naftali Bennett was right when he stated that reinforcing mathematics studies should be a strategic goal. The challenge could have been met by means of a reform in mathematics teaching – which probably, just as the United States, would have led to serious problems. Instead, Bennett had the sense to present a national program to advance the teaching of mathematics in the country, without changing the curriculum per se. The goal was to double within four years the number of students doing the five-units curriculum.
The underlying concept of Bennett’s plan was that in order to improve high-school math instruction, it wasn’t necessary to change the curriculum or the level of the exams, but simply to heighten motivation in the schools. Systems tend to operate according to the criteria that are invoked to check them. Because the criterion for judging the schools was the number of students obtaining matriculation certificates as such, they had no interest in increasing the number of five-units-level students – just the opposite. Math teachers preferred that only good students to take the five-units program – i.e., those who needed no special investment. Those less talented in the subject were urged to do the less challenging three- or four-unit programs.
Responding to this situation, Bennett’s plan rewarded the schools according to their number of five-unit math students and also launched new training programs for teachers. The rationale was that there was a large pool of students capable of succeeding in the five-unit program, but that some preferred the four-unit level because it was safer and would allow them to get a high grade without having to make a special effort. Some schools didn’t even offer the five-unit option.
The advantages of studying math at a high level are obvious. A five-unit certificate can open doors in the army and subsequently in a broad range of fields at the university level; it also facilitates entry into the world of high-tech. The Central Bureau of Statistics has found that, on average, graduates with five units in mathematics earn a higher salary than those who did not study at that level.
Mathematics is not a simple field. It’s interesting to compare studying math and studying English. English is a universal language, without which it’s hard to get along. Like math it, too, must be learned from the basics upward. Why did a crisis develop in learning math that doesn’t exist when it comes to English?
The general public associates math with one’s thinking ability, or at least with analytical thinking ability. The perception is, either you’ve got it or you don’t. In regard to this discipline, at least, awareness of the importance of doing exercises and putting in effort is sometimes not recognized. Clearly, not everyone is endowed with the skill to learn mathematics at a high level – but what keeps those who have the ability from doing so? The root of the matter would seem to lie in the emotional baggage that accompanies the field. For the majority of high-school students, math study constitutes a serious challenge. They need reinforcement and encouragement to persevere, and a teacher who will encourage them to believe they can do it.
A large pool of “passed over” students who choose not to take five-units mathematics, or don’t even have the opportunity to choose, exists in the Israeli periphery. This was exemplified by Zohar Maliniak, a teacher who decided he would work in the outlying area and offered his students the possibility for the first time of taking four- or five-unit mathematics. At the end of five years, about 40 percent of the seniors at his school were successful in the matriculation exams at those levels. Like many others, he, too, believes that good teachers should be given incentives to encourage them to teach in these far-flung areas, where residents are often at a lower socioeconomic level.
But is there any point to making such an effort in the age of online learning? Would it not be enough to create courses comprised of recorded lectures, or online courses to replace frontal teaching? Teaching methods have changed a great deal in recent years. Excellent websites, such as Etgar 5, exist today for math teaching, covering all the material required for the matriculation exam, in the form of high-quality presentations and video clips. Nonetheless, the answer to the question is apparently negative, especially in weaker communities. In the absence of support from the surrounding environment, a teacher is still needed who will imbue his or her students with motivation and self-confidence.
The margins of Jewish society are not the only place where Bennett’s program – which did not address problems in schools that did not have high-level programs at all, or try to motivate good teachers to work in “problematic” high schools – caused gaps to open up. The results of the OECD’s international student assessment tests also point to huge disparities between Jews overall and Arabs in Israel. This too should be a significant warning bell. The low level of achievement in mathematics among Arab students derives from reasons similar to those that affect the Jewish students in the country’s outlying areas: lower funding and a lack of good teachers. Compounding this is the discrimination in the job market, which does not encourage Arab students to take mathematics from the outset, and also the skills of the teachers who are already in the system. In an oped piece by former MK Issawi Freij published recently in Haaretz (in Hebrew), he noted that the education system in Arab society has in many cases served as a mechanism by which to reward cronies, with teachers hired mainly on the basis of family and political connections.
The program to encourage five-unit math studies is important and significant, but it is also heightening inequality between the communities in the geographical periphery and the center, and between Arab society and Jewish society. It must be accompanied by extra support for these weaker populations, who represent a large pool of students who are definitely capable of coping with the challenge of an exam at the highest level. Care must also be taken not to overemphasize mathematics studies. As a result of the wide interest generated by the program, many students feel obligated to take math at the highest level. Not everyone is capable of this, and there is no point in pressuring them.
In the same measure that mathematics studies are important for life, it should be recalled that it’s also important to teach students how to express themselves clearly verbally and in writing, and how to present ideas in an orderly fashion. In the final analysis, some of life’s biggest questions don’t have a mathematical answer.
Dr. Ehoud Pazy is a physicist.