PROVO — The numbers of mathematical concepts American children are expected to learn each year results in shallow understanding of the subject, says a Stanford University mathematics professor emeritus.

"Our various state standards can be characterized as an inch deep and a mile wide," Jim Milgram said Tuesday during a presentation at Brigham Young University

Milgram helped shape the math curriculum used in California public schools and has critiqued math problems on standardized tests for The Brookings Institution.

Some states require students to learn 100 math concepts in a 180-day school year, Milgram said.

Utah kindergartners are supposed to master 11 objectives, with 37 "sub-standards."

"That's a lot," Milgram said.

By grade six, students in Utah are supposed to be exposed to 15 objectives with 67 sub-standards.

"There are serious mathematical errors in Utah standards," said Milgram, who declined to elaborate, saying "I'm supposed to be upbeat."

Milgram and University of California at Berkeley math professor Hung-Hsi Wu studied math curricula in foreign countries where students score high on math tests, such as Russia and Singapore. They found that students only learn about six concepts before high school but are drilled until they master them.

The professors recommended the California math curriculum focus on six concepts such as place value and basic number skills, fractions and decimals, functions and equations, and measurement.

A year later, on Sept. 12, the National Council of Teachers of Mathematics announced that it, too, recommended cutting the number of concepts to improve mastery. The council said teachers should introduce three new major concepts a year, with about 60-80 percent of instruction being devoted to the topics.

Milgram said that in general, 20 percent of the math questions on state standardized tests are poorly written, especially story problems and "patterns" in which students are expected to identify numbers in a series. The questions do not give students enough information or the possible answers are incorrect.

Milgram said he found fewer problems with sample questions on standardized tests given to Utah schoolchildren.

"That's encouraging," he said.