Brown Bag Teaching Seminar
Thursday, September 7, 12:00-1:00 in LAEB 1254
Dan Gottlieb
What should students be learning?
From SCIENCE NEWS, Vol. 151, January 25, 1997
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 University 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
numbers 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
increase, 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 transformed 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."
-- B. Bower
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