Religious schools inspire math reasoning.

In Israel, as in other technological societies, public elementary and high schools expose students to a range of mathematics and science classes. Yet ironically, ultraorthodox Jewish schools-which focus on learning to interpret holy texts, along with a smattering of basic arithmetic-provide a better training ground for solving tricky geometry problems than the mainstream facilities do, according to a new study.

Orthodox education's emphasis on examining texts from different perspectives, achieving insights through independent learning, and using strict problem-solving procedures may nurture reasoning skills that apply to novel realms of knowledge, such as geometry, propose Yoram Dembo and Iris Levin, both of Tel Aviv University, and Robert S. Siegler of Carnegie Mellon Univer- sity in Pittsburgh.

The early years of mainstream education in Israel may actually harm students' geometric reasoning skills, the psychologists argue. Classes typically stress solving geometry problems quickly and accurately without delving into the underlying logic of those operations, a pattern also found in many U.S. schools. Geometric understanding in mainstream students blooms only for those who take advanced math instruction in high school, the scientists say. "These findings will displease Israel's mainstream education system, which sees itself as enlightened compared to the ultraorthodox approach," remarks psychologist Nathan A. Fox of the University of Maryland at College Park.

Levin's husband used his ultraorthodox education to prepare for and pass Israel's medical school entrance tests, thus inspiring the study.

The researchers examined geometric reasoning in 240 students: 60 12-to 14- year-olds and 60 16- to 18-year-olds in mainstream schools and equal num-bers of students in the same age groups in ultraorthodox schools.

Only boys took part, since ultraorthodox girls receive less intensive instruction. Volunteers first viewed demonstrations in which a flexible, three-dimensional shape was changed from one form to another-say, from a circle to an ellipse.

Students judged whether a shape's total volume increased, decreased, or stayed the same after each transformation.

A majority of students in each group then received training to clarify how shapes with the same circumference can have different volumes. They either observed whether beads that filled an initial shape also filled its trans- formed shape, or they imagined what would happen to a shape's volume if the actions that transformed it were taken to their extreme-approaching a straight line.

Finally, students attempted to solve new questions about the relation between the volume and the circumference of shapes.

Most strikingly, 12- to 14-year-old ultraorthodox students performed better on all geometric reasoning tasks than their mainstream peers, the researchers report in the January Developmental Psychology. Among 16- to 18-year-olds, only mainstream students taking advanced math courses scored higher than ultraorthodox students. Moreover, ultraorthodox and mainstream students benefited equally from training sessions.

Ultraorthodox youngsters pondered geometry problems much longer than their mainstream peers did, signifying a more reflective and analytical style of thought, Siegler asserts.

Japanese math teachers go into great depth on only a few problems in each class meeting, notes psychologist Nora Newcombe of Temple University in Philadelphia. That approach may spur general reasoning skills like those observed in ultraorthodox students and help to explain Japanese students' overall math superiority, she says.

Adds Siegler, "Mainstream educators have much to learn from ultraorthodox schools."