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The Third International Mathematics and Science Study
(TIMSS) has become one of the most referenced studies when
international comparisons are made of pupils' performances. The
1995 study was one of the largest and most comprehensive ever
undertaken, revealing comparative mathematics and science
achievement levels for four age grades in over 40 countries. The
finding that we have become most familiar with is that Asian
countries repeatedly outperform Western nations at all age levels,
with Singapore rating highest overall in mathematical achievement.
But there are lessons to be learned by mathematics educators beyond
simply knowing how individual countries rank on the world-wide
league table. There are significant differences in the content and
breadth of the curriculum, as well as when specific concepts are
introduced and the depth of investigation those children engage in.
The craft and culture of teaching also differs widely across
nations. The challenge is how to use the information to close the
performance gap that exists between nations.
Knowing the critical content and pedagogical factors of the
successful programs that enable so many Asian students to flourish,
should help us begin to improve our own practice and our students'
achievement. These twin aspects of curriculum content and
curriculum delivery have been extensively described in professional
journals and the popular press. The most comprehensive analyses are
in the books, The Learning Gap and The Teaching Gap. The
seminal work of Harold Stevens and James Stigler in 1986, which
measured and examined differences between one state in the U.S. and
three Asian countries, not only spawned the TIMSS report, but has
led to a new generation of studies. These studies continue to
investigate how teaching is performed and received and why so wide
a gap continues between Asian and Eastern and Western nations. The
importance placed on the endeavour is indicated by the amount of
funding the project has been awarded - more than 12 million US
The funding has allowed Stigler and his associates to take up
residence in a former furniture store in Los Angeles that has been
transformed into a state of the art facility. The 42 person team is
composed of researchers, translators, transcribers, visiting
scholars, and professors of psychology and education. Using over a
thousand video tapes of mathematics and science lessons from Japan,
Hong Kong, Germany, the Czech Republic and Australia, as well as
the United States, the multi-national team is developing CD Roms
for use in teacher professional development projects. Each disc
contains nine lessons from various participating nations, showing
how teachers transmit knowledge and assist students' concept
development around specific mathematics topics. Alongside the
digitised video runs a full transcript of the lesson. Viewers are
able to freeze frames, to review, to examine practice - exemplary
or otherwise - to watch students from around the world as they
interact and engage in learning. For a profession known for its
solitary confinement, this is a rare opportunity to open classroom
doors and look inside.
A new project being developed focuses specifically on
cross-national teaching of Algebra - the strand of mathematics that
is regarded in the U.S. as "the gatekeeper" to higher education.
The State of California is collaborating on a teacher development
initiative to raise the standard of algebra instruction and
attainment at the middle school sector.
But before looking too far into
the future, Professor Stigler was interviewed for NRICH readers.
Here, he reflects on the gap between Japanese gifted and talented
mathematics' students and their peers. It is a universal gap that
teachers everywhere have to negotiate within their
Do teachers in Asia differentiate
instruction to meet the needs of pupils?
In the U.S., and in Europe, we ask, "What about the gifted kids?"
In Japan - this generally applies to all Asian countries, but I'll
just refer to Japan - the question is, "What can we do for the slow
learner?" They are not withdrawn from class, the teacher attends to
their needs outside of regular class time and they receive extra
help after school. But, there are no special considerations for
gifted and talented students. It's just not even considered - it's
almost, "How dare they want or expect special treatment." Teachers
simply don't accommodate them. There are no special 'extension'
activities; they are expected to be part of the class.
What is very interesting though, having said this, is that recently
a group has started to ask what should be done for gifted students,
how can their talents be enhanced. The feeling is the exceptional
skills of gifted students need to be developed. It will be
interesting to see if changes begin to emerge.
How is the gap between the gifted
and talented maths students bridged?
The more mathematically capable children are catered for within the
context of the lesson. Rich problems by their nature have something
for all; they are designed to accommodate a variety of levels.
Solutions can be reached by counting strategies or algebraic
reasoning. Students are asked to find other ways of solving the
complex problems, to extend they're thinking, to develop multiple
ways to reach solutions. The attitude of teachers (in Japan) is
that the gifted child needs to persuade others, to explain and
describe ideas and solutions and convince the rest of the students
of his or her point of view.
Is there any setting, tracking,
within or across classes so those children with similar skills have
the opportunity to work together?
We (the U.S.), and Europe seems to be the same, we aim to meet
children's needs by tracking them early on. It is done across age
levels and within classrooms. This is not the case in Japan.
Children's needs are met by engaging their thinking. Otherwise, low
achieving students miss the opportunity of having students, other
than ones with similar learning difficulties, model for them
alternate ways to solve problems. High achieving students in mixed
ability groupings have to find ways of interacting, and
communicating ideas, and this really benefits them.
This is not to say there is no tracking or setting of students.
Asian countries delay tracking. In Japan, up until 10th grade,
classes are heterogeneous. This allows for different rates of the
developmental trajectory. It's what we all know and talk about but
don't do much about! We see it all the time, children who don't get
it one day and then suddenly they take off. We over emphasise
academic intelligence, we have a one dimensional view of gifted and
talented. The Japanese system allows for individual differences,
different types of achievement - leadership, communication skills
Is there a significant difference
in classroom structure, management and teaching style as students
move into the secondary phase of schooling?
There is remarkable continuity in practice right up to the
eighth grade. There is no gap between the levels. The curriculum
flows, the classrooms look the same just more crowded (with bigger
bodies, dressed in uniforms). Look at this lesson on this C.
The lesson shown on the disc is very similar in structure to
those video taped in fourth grade classrooms (Year 5) for an
earlier study. It opens with the teacher posing a problem to the
class. There is an opportunity to collaborate with classmates. The
room is noisy. Students are out of their seats, huddled in small
groups discussing possible ways to solve the given problem. The
teacher circulates, carefully selecting the groups who share their
solutions. A representative of each chosen group uses manipulatives
or displays visuals that the group has made to demonstrate their
thinking. The strategies represented on the board range from least
to most sophisticated in a very organised way. All methods are left
on the board and at the end of the presentations students evaluate
and comment on the various strategies and solutions. They comment
on effectiveness, on efficiency, they look for discrepancies and
lack of logic, and applaud when to acknowledge success and/or
effort. The teacher uses mistakes as teaching opportunities, if
students have not referred to an error then the teacher will guide
their attention. The lesson does not just 'end' with the command,
"Put your books away." The pupils summarise the day's lesson, often
generating a mathematical 'rule'. The teacher records the
definition on the board and students copy it into their notebooks
for reference. Learners have ownership over a rule that is
expressed in their own words and it is more meaningful to them.
Is your goal to identify best
practice and define a formula to close the teaching gap?
No. A really important point that I can't emphasise enough is that
different teaching methods are appropriate to different student
groups. This depends on whether (the groups) are homogeneous or
heterogeneous, and on different contexts, then different methods
are more or less effective. Teaching is a cultural activity. Any
suggestion of trying to transplant a system outside its cultural
context has to be treated cautiously. Teaching is also a private
activity; there is a lack of shared language to describe it.
Teaching is a complex system; no dimension of it is universal.
(Teaching) is hard to see - it is hard to change. Teachers
themselves think they are doing one thing, such as changing their
practice, but their actions are very different from their mental
There are three ways to improve teaching:
- to improve teachers (quality control of the profession)
- to improve teachers' competency (knowledge base)
- to improve teaching methods.
By examining the practice of others, teachers reflect upon their
own practice and also have alternatives to consider. Teaching can
only be improved from inside the classroom. To do this, teachers
need time for quality reflection and planning, only then can they
produce quality programs.
 Third International
Mathematics and Science Study
(TIMSS), (1995). National
 Stevenson, H. & Stigler, J. (1992). The Learning Gap
. New York: Summit
 Stigler, J. & Heibert J. (1999) The Teaching Gap
. New York: Simon
 Steve Olson, Candid Camera:
Can videotaping classrooms uncover essential truths about
, Teacher Magazine, May /June 1999