There’s wide agreement that American students can achieve more than they do now and that they should be held to higher standards. For states that are trying to develop academic standards for their public schools, the big questions are what to include in these guidelines and how tough to make them. As California, for one, is finding out, serious mistakes can be made in setting such standards—mistakes that threaten our children’s potential for achievement.

California’s Academic Standards Commission in September issued guidelines for reading and math, which will become official once the State Board of Education has revised them to its satisfaction. Whereas I voted to endorse the reading standards, I opposed those for math because the commission issued standards that were too low, basing them on faddish teaching techniques and an unproven organization of the curriculum.

Good academic standards demand a high level of achievement. Yet they also allow educators the freedom to decide how to teach. California’s standards, for example, specify that students be able to do certain calculations in their heads—a clear and reasonable recommendation. The problem is that the standards also tell the teachers how to meet that goal, directing them to stage situations in which students will discover their own "effective strategies" for figuring in their heads.

Student self-discovery is a current fad in math instruction—every student his or her own Archimedes. This "whole-math" approach rejects direct instruction of the student by the teacher. The California standards are rife with such self-discovery prescriptions: "A sense of number and quantity should be fostered naturally as students interact with objects and events in their environment."

Teaching in a way that meets new, higher standards is a difficult task in itself, and those who prepare such guidelines should think long and hard before combining them with some other grand project. In California, those who wrote the standards also decided to take on large-scale planning of curriculum. Instead of working with the regular course sequence of Algebra I, Geometry, Algebra II, for example, they decided to "integrate," or intermingle, the content of those subjects in a new way.

But California’s proposed approach has never been tried anywhere. Some supporters say this is the way top-performing countries such as Japan teach math. But math programs in other countries, including Japan, are very different from American-style "integrated math." California should not push an unproven curriculum on millions of children. As parents and educators know, California’s experiments often spread to the rest of the nation.

For our children to fulfill their potential, they need to be challenged with high standards. Yet those who write standards are under intense pressure to water them down. Some argue that, if standards are too rigorous, many children might fail and be stigmatized. Some say teachers and students might not even try to meet the standards if they are too high. In California, teacher after teacher testified before the commission that various standards were too difficult, even though children in other countries routinely meet similar ones.

If standards don’t seem too high, they’re too low. The designers of the California standards maintain that the guidelines are not intended to be a "ceiling for any child." Yet in practice, standards act as a ceiling, not a floor. Districts and schools will be judged primarily on whether they meet these guidelines. Make standards minimal and learning will be minimal, too.