Transcript TIMSS ANSWERS THESE QUESTIONS:

Third International Mathematics
and Science Study
• What does the study show?
• What does analysis of the data show later
(NCES study 2003)?
• Watch video clips of classrooms - what
types of teaching and learning are in effect?
Stephen Hegedus, Department of Mathematics
MTH310 - Spring 2006
TIMSS ANSWERS THESE
QUESTIONS:
• Are U.S. curricula and expectations as demanding
as those of other nations?
• How does U.S. classroom instruction compare
with that of other countries?
• Do U.S. teachers receive as much support in their
efforts to teach students as their colleagues in
other nations?
• Are U.S. students as focused on their studies as
their international counterparts?
From Attaining Exellence: A TIMSS
Resource Kit, US DoE
How do our BEST 8th graders stack up?
• % in world’s top 10%
50
45
45
40
35
31
32
30
Mathemtics
25
Science
20
18
15
13
10
5
5
0
United States
Singapore
From Attaining Exellence: A TIMSS
Resource Kit, US DoE
Japan
EIGHTH-GRADE CURRICULA
• The eighth-grade mathematics curricula in Japan
and Germany focus on algebra and geometry,
while U.S. curricula still include considerable
arithmetic.
• Topic coverage in U.S. eighth-grade mathematics
classes is not as focused as in Germany and Japan
(although in science, topic coverage may be
similar to other countries in degree of focus).
• U.S. curricula are defined locally, whereas the
curricula of most other nations are established
nationally.
From Attaining Exellence: A TIMSS
Resource Kit, US DoE
EIGHTH-GRADE
MATHEMATICS TEACHING
• What we teach in eighth-grade mathematics, most
other countries teach in the seventh.
• The content of U.S. Eighth-grade mathematics
lessons require less high-level thought than classes
in Germany and Japan.
• The typical goal of a U.S. eighth-grade
mathematics teacher is to teach students how to do
something. The typical goal of a Japanese teacher
is to help students understand mathematical
concepts.
From Attaining Exellence: A TIMSS
Resource Kit, US DoE
Teachers’ Lives
• Unlike U.S. teachers, new Japanese and German
teachers receive long-term structured
apprenticeships in their profession.
• Japanese teachers have more opportunities to
discuss teaching-related issues than so U.S.
teachers.
• U.S. teachers have more college education than
those in all but few TIMSS countries.
• Students diversity and poor discipline are
challenges not only for U.S. teachers, but for their
German colleagues
as well.
From Attaining
Exellence: A TIMSS
Resource Kit, US DoE
Students’ Lives
• Eighth-grade students of different abilities are
typically divided into different classrooms in the
United States and different schools in Germany. In
Japan, no ability grouping is practiced.
• In the United States, students in higher level
mathematics classes study different material than
do students in lower level classes. In Germany
and Japan, all students study the same material,
although in Germany, lower level classes study it
with less depth and rigor.
• Japanese eighthFrom
graders
are preparing for a highAttaining Exellence: A TIMSS
Kit, US DoE
stakes examinationResource
to enter
high school.
Rethinking Common BeliefsWe Know the Problem Is NOT:
• TIME -- U.S. eighth-graders have more
hours of instruction in mathematics and
science that students in Japan or Germany,
• HOMEWORK -- U.S. students do as
much or more.
• TV -- Japanese students watch as much TV,
yet do better in school.
From Attaining Exellence: A TIMSS
Resource Kit, US DoE
Investment In TIMSS
• Provides objective assessment of where we
stand in comparison to other countries.
• Shows aspects of U.S. education that
deserve attention.
• Helps states and localities reflect on :worldclass” education.
From Attaining Exellence: A TIMSS
Resource Kit, US DoE
Procedural Complexity
•
In NCES 2003 report on Seven countries in TIMSS1999:
•
The complexity of the mathematics presented in the lessons is an
important feature of the mathematics but it is difficult to define and code
reliably. The complexity of a problem depends on a number of factors,
including the experience and capability of the student. One kind of
complexity that can be defined independent of the student is procedural
complexity—the number of steps it takes to solve a problem using a
common solution method.
The mathematics problem analysis group developed a scheme for
coding procedural complexity and analyzed every problem worked on
or assigned during each eighth-grade mathematics lesson
(independent and concurrent problems). Problems were sorted into low,
moderate, or high complexity according to the following definitions:
•
•
•
•
•
•
•
Low complexity: Solving the problem, using conventional
procedures, requires four or fewer decisions by the students
(decisions could be considered small steps)
The problem contains no sub-problems, or tasks embedded in
larger problems that could themselves be coded as problems.
° Example: Solve the equation: 2x + 7 = 2.
Moderate complexity: Solving the problem, using conventional
procedures, requires more than four decisions by the students
and can contain one sub-problem
° Example: Solve the set of equations for x and y: 2y = 3x - 4; 2x
+ y = 5.
High complexity: Solving the problem, using conventional
procedures, requires more than four decisions by the students
and contains two or more sub-problems
Role of Mathematical Reasoning
How is Mathematical Reasoning
developed?
•
•
•
Focus on many or similarly related problems
Broader problem-solving situations
Unrelated problems lead to fragmented lessons
Broader Pedagogical Traits
•
•
•
All countries introduced topics through problem solving.
Japan and the Netherlands provided two comparatively distinct
learning environments for students as defined by a few basic
organizational features:
Japanese eighth-grade mathematics lessons focused on presenting
new content through solving a few problems, mostly as a whole class,
with each problem requiring a considerable length of time
In Dutch lessons, private work played a more central role, with eighthgrade students spending a larger percentage of time working on a set
of problems, either reviewing old homework or starting on newly
assigned homework. In these different structures, the teacher, the
written curriculum materials, and the students would seem to play quite
different roles.
Conclusion
• So if TIMSS is assessing complex problemprocedures which are procedurally defined
then we have excellent benchmarks,
• If we are after the development of deep,
conceptual problem-solving then we need to
look further as the studies do show very
different classroom cultures and pedagogies
that have a direct impact on student
performance.