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

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 

-- B. Bower

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