Problems with American Math Education

Is American math education weak? For sure! There is the anecdotal evidence of every observation of our children and students, the incompetence in the math arena of students who CAN master reading, writing, foreign language, and other subjects.

There is the objective evidence of international standardized testing, in which the American math education system performs far below not only comparably developed countries in Europe and east Asia, but even below what we would generally consider more primitive countries.

And there is the unmistakable evidence of the curriculum itself, the math materials, and the problems the students are doing.

If you can get your hands on American math education books from the Sixties or earlier, I think you’ll see what I mean at a glance:

• I have an Algebra 1 book from 1960 that is harder than the Algebra II book the Honors students at my school use.
• I have a Trigonometry book from the 1950’s that would intimidate almost any A.P. Calculus student I have taught.
• I have an Arithmetic book from the early 1900’s that has an expectation of resourcefulness in every day math far beyond what is expected of the most able students I encounter.

The three basic problems we have with our American math education today are incompetent teachers, bad math materials, and inappropriate topic sequence and student tracking.

1. First, the Math Teachers.
   It is painful and embarrassing to say this, but many math teachers don’t understand what they are teaching very well. I have observed math classes at every level in which the teacher’s explanations were plain wrong. Muddled. Confused.

It is very hard for any student except the natural math star, or one who is getting supported at home by a parent who has the time and ability to teach the material, to be successful.

More common, is the Math teacher who is just a step ahead. The Fifth grade teacher who just knows the curriculum up to there, sort of. The Algebra 1 teacher who can just teach up to Algebra 1. As a teacher, it’s hard to teach a student to be better than yourself when you’re less than confident with the subject. You can bet the students will weak in that subject, too.

When I was working on my Masters degree in math, one of my professors mentioned in one of the classes that he also taught a class in the department of Education across campus.

He described the course. In the certification process, prospective teachers picked a specialty, and they had to pass a test in this special area. The professor was teaching a course for the college students who had chosen math as their special area. The course was designed to help them pass the state exam for certification.

And what was he teaching? Mostly, fraction and decimal operations! Fifth grade math! These college students needed a course on elementary school math to pass their certification test. But the scariest part was, these were the education majors who had self-selected math as their area of special expertise! Even with our low level American Math Education expectations, they were not up to snuff.

What can you do? Don’t be surprised if your child’s math teachers, at any grade level, seems shaky in math, and be prepared to teach the topics yourself. That’s just how it is.


2. Second, the Math Materials.
   In our educational system, various state boards specify topics that are to be taught at each grade level. A publisher would want to meet these requirements, in order to sell the textbooks in the different states.

   The result of the American math education system endeavoring to meet so many topic requirements, and sometimes also a multitude of stylistic or presentation requirements (writing in math, math in different cultures, math across the curriculum) is that almost every elementary and junior high level book tries to achieve more than is possible and thereby fails in its core mission. (This particular problem is not so relevant at the high school level where textbooks are topic specific, e.g., Geometry, or Algebra II.)

   For example, take Third Grade. The primary goal of third grade math is to master multiplication and its applications, and to be introduced to division and its applications.

   It takes a full year of daily practice to master multiplication.

   A third grade book’s content should be roughly half multiplication, a quarter division, and a quarter secondary topics. What I am referring to as secondary topics for third grade are areas such as measurement, geometry, place value, fractions, and also some review and practice with prior material, which would be adding and subtracting with regrouping. But open your child’s Third Grade book, and you may well see that the fourteen or fifteen chapters are almost evenly divided between Addition and Subtraction, Data Analysis and Representation, Geometry, Multiplication and Division, Fractions, Measurement, and perhaps even other topics such as probability, or algebra concepts.

   The huge mass of topics in American Math Education, many of which really do not need to be encountered at this point at all, have forced our main topics to be compressed into too little time for any student to learn them well. The result: we move on, year after year, grade after grade, without mastering the core topics.

   Math is a sequential, cumulative subject. You need to be able to count to add. You need to be able to add to subtract, which is the inverse of addition. You need to be able to add to multiply, which is repeated addition, and which required addition if there are multiple digits. You need multiplication and subtraction to divide. And so on.

   Beyond the skill itself, the mastery of each skill involves mental development that is the foundation for success in the more advanced skill. (That’s why a student who never learned arithmetic can’t do algebra even when equipped with a calculator: he or she missed out on the years of mental development involved in learning arithmetic that would have enabled him or her to learn algebra.)

   The solution is for you to know the core topics at each point, to know what your child should be doing in third grade, and to provide the appropriate amount and level of practice at home. In most cases, it’s not happening at school!

   It is quite possible the math teacher doesn’t even know what the children should be mastering at the given grade level, and so isn’t aware of the gross deficiencies in the materials. It is also possible that if she is aware, she doesn’t have the time or resources to supplement the books appropriately. It is also possible that the school or district mandates certain chapters of the book and the teacher doesn’t have the authority to adjust the curriculum. So expect to supplement your children's education yourself.

3. Third, Developmental Appropriateness.
   The third issue is developmental appropriateness of math materials. Bizarrely, from both ends of the American math education abilities spectrum, we are erring terribly. At the lower end, due to some misguided psychological theories about the Impossiblity of Abstract Thinking at certain ages, arithmetic is held off to some extent in the early grades. (Read here to learn how one really learns and masters math concepts.)

   Addition, subtraction and multiplication used to be taught in first grade. There are plenty of people around with gray hair who can testify to this. There are very few concepts, which are indeed accessible to the six year old mind, and a bunch of memorization, which can be done very well at age 6.

   Often now we let those first years of elementary education slip by with games and projects, and by fourth grade we’re still learning multiplication, and by then we’re almost hopelessly behind. We simply need to start mastering arithmetic younger. You can do this fairly easily at home if it’s not happening at school.

   At the higher end, we have the opposite problem. Students at almost every level are absurdly over-accelerated. Just a generation ago it was normal in American math education for a good college bound student to take algebra in the 9th grade. Now, almost every college bound student, talented or not in math, takes algebra in 8th grade, and the good ones take it in 7th.
   Wow!!! Did we as a nation become more capable of the abstraction of algebra at an earlier age?

   No. We’ve been gripped by an American Math Education mania that encountering the material at a chronologically younger age is good in itself (looks good for college? I’m not sure why it’s so good, but it is!). Most schools in the American math education system have structured their curricula and tracking in this way, with average students accelerated one year above grade level, and above average students accelerated by two years.

Two negative consequences:

1. The students aren’t ready for the math materials and have to work far too hard to achieve only partial success.
2. The schools have to wildly “dumb down” the curriculum because since the bulk of the class isn’t ready for it, most of them would be failing out if they didn’t. And we can’t have that.

What can you do?

This is tough. In today's American math education system, if you resist your child being overaccelerated, you will end up with your child in the “slower track” which isn’t very nice. If you are in a position to pick schools, then finding one that has a solid regular track with 9th grade Algebra 1, or a strong honors track that culminates in senior year calculus would be advantageous.

But if you can’t, you are in a situation of “damage limitation.” You will need to help your child follow what is going on in the classroom, and at the same time make sure that the primary elements of curriculum that should be mastered, are in fact being mastered.

Share a math education memory from your school days?

Are you shocked at how different your child's math education is from how you learned math?

• Were you allowed to use calculators in the classroom?


• Did your teacher expect everyone to memorize the times tables?


• Do you have fond memories of doing your math homework with a sibling or parent


• Was math your favorite subject... or did you dread it?

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