Teaching mathematics has been my profession in New York City public schools since 1969, first at I.S. 201 in District 5, then at J.H.S. 17 in District 2, and since 1983, at Stuyvesant High School. I’m also the father of a 10-year-old daughter who attends District 2 schools and a member of an organization, Nychold (nychold.com), dedicated to bringing sanity to math education.

I’m a firm believer in public education, the great equalizer. Sadly, over the past 10 years, I’ve witnessed how badly things can go wrong. I am referring specifically to the constructivist math curricula that abound in our city public schools in general and more specifically in District 2, where I live, teach, and raise my daughter.

Constructivist curricula, such as TERC and CMP, forsake algorithms, postulates, and theorems (the foundation of math) as well as teacher-centered learning. Instead, they have students working among themselves in groups, loosely guided by the teacher in a drawn out attempt to “discover” math truths.

When these types of curricula were introduced in District 2 in the 1990s, they were already controversial. They had been in use in both California and Texas, where parents and educators protested their use in great numbers and with varying effect. In numerous cases, the curricula were replaced by more traditional ones. Never had there been such a controversial attempt at math reform. I recall the “new math” of the 1970s and how disastrous a reform attempt that was. Even that failed effort generated significantly less negative publicity than this.

With an eye toward bigger and better things, people in District 2 embraced these curricula. A lot of positive publicity was generated. People in line with the district leadership’s initiatives were regularly promoted within the system. The curricula became entrenched. The district leadership spoke in one voice regardless of the well-known failures of these curricula. “Proving” their effectiveness was more important than honestly assessing them.

We who either teach or parent District 2 students know of the failures of these curricula. We send our children to math tutors in record numbers. Intelligent, hard working children have trouble doing simple math. We who have grown up with an understanding of elementary math find that we can’t help our children; that many of the games they play and homework they do are so convoluted we either can’t figure them out or don’t see their significance. We’re forced to sit by and watch our children’s frustration. When we speak to school officials, we’re condescendingly told that we just need to understand what they’re doing. The truth is that many of us do understand what they’re doing. They’re doing irreparable harm to thousands of children.

In my Upper East Side neighborhood, an incredible number of intelligent young students from the fourth grade and up are seeing private math tutors. Many of these are not the type of children who would normally struggle in arithmetic or elementary algebra. As a result of the way they’re taught elementary math, they find themselves unable to do real math. When they’re taught math in a more traditional way by their tutors, they invariably find themselves relieved and highly critical of the way they’ve been taught mathematics.

At Stuyvesant, we have a disproportionate number of freshmen from District 2 taking our introductory algebra course. Most Stuyvesant students have already completed that course before they enter our school. The ratio of District 2 students to non-District 2 students in those classes is close to twice that same ratio in the freshman class as a whole.

Would you invest all of your money in a speculative and controversial venture and then turn a blind eye to major problems that develop in that venture? That is what District 2 has done with our most precious assets when it concerns their math education.

Math is a science that has been developed over thousands of years. It’s not just about adding, subtracting, multiplying, dividing, and solving the type of everyday problems associated with going to the supermarket. If it were, perhaps these curricula wouldn’t be so bad. Beginning at the middle-school level and continuing to the high school and college levels, it evolves into Euclidean and non-Euclidean geometries, algebra, trigonometry, calculus, and various types of discrete mathematics. Today’s high school student is expected to master a significant amount of the aforementioned.

Constructivist math curricula attempt to teach math by having the students “discover” their own methods for solving problems. A great deal of time and energy is spent having students “discover” things such as if you’re multiplying 98 by 28, you could multiply the “friendly number 100” by 28 and from that subtract that extra 2 x 28. And 2 x 28 can be found by multiplying 2 by 30 and subtracting 2 x 2.

This is fine for this problem and, in fact, is how many good mathematicians would perform this computation in their heads. However, it takes too long and it won’t work for calculations such as 34 x 67 or most others one would need to perform.

The purpose of standard algorithms is to easily and quickly solve a whole class of problems. Once mastered, students no longer struggle with simple calculations. Unfortunately, the constructivist curricula fail to recognize their importance and value. When taught properly, students are asked to do more than just commit them to memory (as constructivists often charge): They learn important principles, such as place value and the distributive property. Students who remain unskilled in their use often crash and burn when faced with the real problems of mathematics.

Math has certain rules. Students must understand these rules in order to succeed in the field. Fundamental principles must be taught. A foundation must be set. Then one can build upon that foundation using the established rules of mathematics. When students are left on their own, or led by a well-meaning teacher who is trained to teach these convoluted and inadequate curricula, not only don’t they learn to do simple arithmetic adequately, but they are also unable to take the natural step of learning to work with variables, which is where algebra begins. In fact, it’s totally unnatural for them.

One must understand both the rules of the game, the fundamentals, and the standard algorithms of arithmetic in order to understand how algebra and higher math work. Without these understandings, constructivist math students have a very difficult time understanding, appreciating, and doing math at higher levels. So we’re stuck with children who have trouble with basic arithmetic and find it difficult, if not impossible, to advance much further.

In middle school and high school, these students rarely complete the curricula because it takes far too long to “discover” truths that can easily be taught much better and faster by a skilled teacher. Even in the rare cases in which students do finish the material, they don’t have a sufficient background to succeed at higher mathematics.

I wonder why District 2 hasn’t required the Regents exam for its students. Could it be that its curricula haven’t adequately prepared students for this minimum competency exam that is so simple that it requires little algebra to succeed? There is a simple solution to this problem. Courageous parents and educators must unite and demand that mathematical sanity be returned to our district and our city. Politics seems to be the only thing that has an effect on our leadership. Let’s let them know that the status quo is no longer acceptable.

Mr. Winokur is a mathematics instructor at Stuyvesant High School.