California Math is Broken

California Mathematics is Broken

Math is not going to be successfully taught in California anytime soon.

Political forces ensure that "traditional" texts are the only "state approved" texts. This is despite the fact that traditional texts do not work for most kids and give a shallow education at best. Every 7-10 years a state committee is put to together to approve kindergarten through middle school math texts, using input from math education experts. The last time, the committee threw out the recommendations made by the educators and chose instead only very traditional texts. The state will stop funding for a school which doesn't use a recommended text.

The California State Standards put a priority on learning a lot of topics every year, so there's no time for kids to learn any topics in depth. The TIMS (Third International Mathematics and Science Study) found that math education was better in many other countries. Those countries teach fewer topics a year, but in depth. The kids learn to be puzzled and figure things out. In America, kids are taught many more topics each year, but their learning is shallow. And most California students believe they need to know how to produce answers quickly by memorizing "facts." Instead of working on problems that might take a few days to figure out, most US students are given pages of computations to do each night.

Real math doesn't come in pages of computations. It comes in problems that take hours or days or years to solve. Real math is about understanding relationships and being able to prove to others that a solution is sound. It's about finding clues and composing a solution and then discovering more about it, generalizing it and expanding it, finding ways to use it efficiently and incorporate it into practical systems and then apply what is learned into new areas. All this can be practiced beginning with arithmetic in elementary schools, if we dare to follow the recommendations of our own research.

In contrast, the California Standards assure that there is neither the time nor the flexibility for real teaching, or real learning.

The California annual testing exasperates this. The press reports that scores of 50 abound and that this is abysmal. These are "standardized normalized tests" which means that the test is set up so that the average kid will get a 50. "50" means the fiftieth percentile. This should not be seen as failure.

To discern kids at the 90th percentile from kids at the 95th percentile, there are items on each test that are above grade-level. Schools that perform well are under pressure to get kids to answer more questions correctly, so the school district can get a better score. So the teachers teach even more topics per year, including above grade-level topics. The extra topics pay off a bit, but at the expense of real learning.

Math begins to fall apart in middle school. In elementary school, the kids learn lots of simple procedures to do well on the tests without developing the solid number sense and problem solving skills on which they can build real math ability. In middle school, algebra and geometry are hard, and require a good foundation to build upon, but the foundation isn't there. Failure begins.

There's more. In America, we teach a few standard "American" ways of adding, subtracting, multiplying and dividing. Kids come here from foreign countries and are told that there methods are "wrong." Typically, American elementary school teachers are not math teachers. Many of them are math phobic and can only teach the traditional procedures they were taught. It takes retraining to teach them how to teach kids to play with numbers so they can understand them inside and out and explore relationships and patterns. Districts don't have the funds to retrain teachers, or to hire an extra math teacher to help with curriculum, even before the current budget-cutting.

California has pushed algebra down to 6th, 7th, and 8th grades. But studies have shown that these kids mostly don't have the abstract abilities necessary to understand it. The result is that many kids learn that math is beyond them, and miss the opportunity to spend these years exploring numbers and number relationships, and using math to explore their world.

In foreign countries, kids have courses like Math1, Math2. Here we split math up into algebra, geometry, trigonometry and calculus. Actually, the best way to learn algebra is with geometry problems, and vice versa. And when learning geometry, much of trigonometry is a natural extension. Our rigidity in teaching "subjects" robs math classes of the possibility of being interesting, or building much foundation.

California's traditional math curriculum was built by people who understand little of mathematics, and nothing about learning math. California's curriculum is all about what there is to know, the myriad different topics, and how to perform math operations, rather than understanding math. If the reverse approach was taken, teaching a course so that kids understood mathematical relationships, students would be much more able to apply that understanding to various topics. But understanding math must come first.

When kids learn with a problem-solving approach, they learn to patiently explore problems and discover relationships. They learn to persist and figure out, not the answer, but many answers, many ways of looking at the problem that reveal its structure. And problem solving can be interesting and rewarding, but it means students are allowed to discover and learn, rather than perform memorized procedures on timed tests. Pursuing interesting problems will lead students to all sorts of areas of math.

California's current system of teaching math is broken. It is held together by tradition and politics, rather than good mathemathematics, or good teaching. We are teaching kids to fill out sheets of math problems which they won't find in the world. We're not teaching them how to solve problems, or even to interpret well the myriad statistics that appear in the news.

For a good set of standards, California should follow the NCTM (National Council of Teachers of Mathematics) standards. To know whether we're teaching math effectively, we should get an achievement test that tests deep understanding and problem solving, a more expensive test to administer, but one that reflects the kinds of skills our citizens need. To develop students who can do the kind of math that industry needs, we should use reform" and "integrated" programs that teach children to be problem solvers and discoverers.

The next generation has a host of difficult problems to solve far beyond those that previous generations have traditionally solved. The traditional methods are not sufficient. Either we must change the way we teach math, or we must continue to import math-savvy engineers and scientists from other countries, and increasingly open research centers overseas.

-Randy Strauss

Written February 12, 2003, updated March 10, 2004