"In view of . . . . [the TIMSS results(1)] . . . . isn't this the
wrong question? . . . . [it's unclear to me what question Jack is
referring to but it may be Arons's question "Whence do we get the
teachers with the background, understanding, and security to
implement such . . .(Benezet-type) . . . instruction?"] . . . . . I
would think that the appropriate investigation would be: How do the
countries that do well teach their students, and should we be
adopting their methods?"
Unfortunately the problem is much deeper than indicated by just the
TIMSS results on math and science, as is indicated by Jerry Epstein's
research.(2) The Benezet/Berman Experiment(4-6) suggests ways to
counter the "Epstein Effect," as well as to drastically improve
GENERAL K-12 instruction.(7a)
Nevertheless, as Jack suggests, it IS worthwhile to examine the
teaching methods of countries whose students did well on TIMSS, and
consider adopting (or adapting) those methods.
In my opinion, physics teachers and physics-education researchers
might consider taking a careful look at the National Research
Council's latest appraisal(1) of TIMSS. As indicated below, the NRC
interprets the results of TIMSS as supporting the NRC's National
Science Education Standards(8) with their emphasis on "inquiry
learning."
Quoting from ref.1b, "Executive Summary" (my CAPS):
"One broad measure of curricular emphasis in mathematics and science
is the amount of time given to these subjects in schools. The results
from TIMSS demonstrate, somewhat surprisingly, that the time spent on
these subjects is higher in U.S. fourth- and eighth-grade classrooms
than it is in many other TIMSS countries. ONLY AT THE SECONDARY LEVEL
DO STUDENTS IN OTHER COUNTRIES APPEAR TO EXPERIENCE MORE MATHEMATICS
AND SCIENCE INSTRUCTION ON AVERAGE THAN DO STUDENTS IN THE UNITED
STATES.
Even when more time is spent on mathematics and science, however,
EXPECTATIONS FOR STUDENT LEARNING IN THE UNITED STATES MAY BE LOWER
THAN ELSEWHERE. In the videotaped eighth-grade mathematics classes in
the United States, Germany, and Japan, the content of each lesson was
compared to the average grade level across all TIMSS countries in
which particular topics received the most attention. By this measure,
the MATHEMATICS CONTENT OF U.S. LESSONS WAS, ON AVERAGE, AT A
MID-SEVENTH-GRADE LEVEL, WHEREAS GERMAN AND JAPANESE LESSONS WERE AT
THE HIGH EIGHTH-GRADE AND BEGINNING NINTH-GRADE LEVELS, RESPECTIVELY.
Attention also has focused on the structure of the curriculum,
particularly on measures of curricular focus and coherence. Focus
refers to the depth with which topics are treated within and across
classes. SEVERAL LINES OF EVIDENCE POINT TOWARD A LACK OF FOCUS IN
U.S. MATHEMATICS AND SCIENCE INSTRUCTION. According to the TIMSS
curriculum analysis, the number of topics in a broad sample of U.S.
textbooks was substantially larger than for textbooks in most other
countries, and U.S. textbooks include more review exercises and
repeat more topics covered in previous grades. Teachers do not
necessarily cover everything included in a textbook, but U.S.
teachers reported in questionnaires that they teach many more topics
over the course of a year than do teachers in Japan or Germany. This
rapid movement from one topic to another suggests that U.S.
INSTRUCTION MAY BE MORE SUPERFICIAL THAN IN OTHER COUNTRIES, WITH
STUDENTS OFTEN FAILING TO ACQUIRE DEEPER UNDERSTANDING OF ANY
PARTICULAR TOPIC.
Coherence, in contrast, refers to the connectedness of the
mathematics and science ideas and skills presented to students over
an extended period of time. In a coherent curriculum, new or more
complex ideas and skills build on previous learning and applications
are used to reinforce prior learning.
AGAIN, SEVERAL FACTORS SUGGEST A LACK OF COHERENCE IN U.S. CURRICULA,
ALTHOUGH THE EVIDENCE IS NOT CONCLUSIVE. According to the TIMSS
curriculum analysis, U.S. TEXTBOOKS TEND TO SWITCH FROM TOPIC TO
TOPIC MUCH MORE FREQUENTLY THAN DO TEXTBOOKS USED IN OTHER COUNTRIES.
The videotapes of eighth-grade mathematics classes showed that
teachers in the United States switch topics more times than do
teachers in Japan and Germany and make fewer references to other
parts of a lesson. ALSO, INTERRUPTIONS OF LESSONS (FOR EXAMPLE, BY
PUBLIC ADDRESS ANNOUNCEMENTS OR OUTSIDERS COMING INTO THE CLASSROOM)
ARE MUCH MORE COMMON IN THE UNITED STATES THAN IN GERMANY OR JAPAN.
When summaries of videotaped lessons from the United States, Germany,
and Japan were analyzed by mathematics teaching experts who did not
know the country where each lesson was taped, the group found that
about 45 percent of U.S. lessons, 76 percent of German lessons, and
92 percent of Japanese lessons achieve a predefined standard of
coherence. USING SEVERAL MEASURES OF QUALITY IN ADDITION TO
COHERENCE, THESE MATHEMATICS TEACHING EXPERTS ALSO JUDGED THE CONTENT
OF U.S. LESSONS TO BE OF LOWER QUALITY THAN THE CONTENT OF LESSONS
FROM JAPAN AND GERMANY.
U.S. national standards and benchmarks in both science and
mathematics cite focus and coherence as critical qualities of
curricula in those subjects. UNLESS A CLEAR SET OF GOALS IS
RECOGNIZED THAT CAN ESTABLISH CONNECTIONS AMONG TOPICS--GOALS SUCH AS
THOSE PROVIDED BY NATIONAL, STATE, AND LOCAL STANDARDS IN MATHEMATICS
AND SCIENCE--IT CAN BE DIFFICULT TO CONSTRUCT COHERENT MATHEMATICAL
AND SCIENTIFIC STORIES IN CLASSES THAT COVER LARGE NUMBERS OF TOPICS."
"Beneath the observable activities that occur in mathematics and
science classes are the external forces and internal motivations that
cause teachers to instruct in particular ways. AMONG THE MOST
POWERFUL OF THESE FORCES ARE TEACHERS' BELIEFS AND GOALS, SOME OF
WHICH CAN BE INFERRED FROM THE VIDEOTAPE STUDIES OF EIGHTH-GRADE
MATHEMATICS IN JAPAN, GERMANY, AND THE UNITED STATES. The videotapes
demonstrate that in German mathematics classes there is a concern for
technique, where technique includes both the rationale that underlies
the procedures and the precision with which the procedure is
executed. A GOOD GENERAL DESCRIPTION OF GERMAN MATHEMATICS TEACHING
AT THIS LEVEL WOULD BE 'DEVELOPING ADVANCED PROCEDURES.'
In Japan the teacher carefully designs and orchestrates the
mathematics lesson so that students use procedures recently developed
in class to solve problems. AN APPROPRIATE DESCRIPTION OF JAPANESE
TEACHING IN MATHEMATICS WOULD BE 'STRUCTURED PROBLEM SOLVING.'
IN THE UNITED STATES THE CONTENT IS LESS ADVANCED AND REQUIRES LESS
MATHEMATICAL REASONING THAN IN THE OTHER TWO COUNTRIES. THE TEACHER
TENDS TO PRESENT DEFINITIONS OF TERMS AND DEMONSTRATES PROCEDURES FOR
SOLVING SPECIFIC PROBLEMS, AND STUDENTS ARE ASKED TO MEMORIZE THE
DEFINITIONS AND PRACTICE THE PROCEDURES. U.S. MATHEMATICS TEACHING IN
THE EIGHTH GRADE COULD BE DESCRIBED AS 'LEARNING TERMS AND PRACTICING
PROCEDURES.'
In the United States, skills tend to be learned by mastering the
material incrementally, with high levels of success at each step.
Confusion and frustration are signs that the earlier material was not
mastered. IN THE STYLE OF TEACHING DOMINANT IN THE UNITED STATES, THE
TEACHER'S ROLE IS TO SHAPE THE TASK INTO PIECES THAT ARE MANAGEABLE,
PROVIDING ALL THE INFORMATION NEEDED TO COMPLETE THE TASK AND PLENTY
OF PRACTICE.
IN JAPAN, TEACHERS TEND TO HAVE STUDENTS STRUGGLE WITH A PROBLEM AND
THEN PARTICIPATE IN A DISCUSSION ABOUT HOW TO SOLVE IT. CONFUSION AND
FRUSTRATION ARE SEEN AS A NATURAL PART OF THE PROCESS AND ARE USEFUL
TO PREPARE THE STUDENTS FOR THE INFORMATION RECEIVED DURING THE
DISCUSSION. THE TEACHER'S ROLE IS TO ENGAGE THE STUDENT, REVEAL THE
MATHEMATICS OF INTEREST, AND HELP THE STUDENTS UNDERSTAND THE PROBLEM
SO THEY CAN ATTEMPT TO SOLVE IT.
A useful way to view these instructional differences among countries
is to see them as unified "scripts" for teaching. THESE SCRIPTS ARE
DEEPLY EMBEDDED IN THE CULTURE OF EACH COUNTRY AND CAN BE RESISTANT
TO CHANGE. However, by appreciating one's individual script and the
scripts common in other countries, teachers can use TIMSS to begin to
examine the assumptions they hold toward teaching and the ingrained
ways in which they approach their responsibilities.
THE U.S. NATIONAL STANDARDS IN MATHEMATICS AND SCIENCE CALL FOR AN
APPROACH TO TEACHING IN WHICH STUDENTS ACTIVELY EXPLORE MATHEMATICAL
AND SCIENTIFIC IDEAS, ASK QUESTIONS, CONSTRUCT EXPLANATIONS, TEST
THOSE EXPLANATIONS, AND COMMUNICATE THEIR FINDINGS TO OTHERS.
ACHIEVING THIS KIND OF INSTRUCTION IN U.S. MATHEMATICS AND SCIENCE
CLASSES WILL REQUIRE REEXAMINING DEEP-SEATED BELIEFS ABOUT TEACHING
AND LEARNING."
3333333333333333333333333333333333333333333333333
3. SCHOOL SUPPORT SYSTEMS
"One of the most significant distinctions between Japanese and U.S.
teachers' days is how much time they have to collaborate with
colleagues. COMPARED WITH JAPANESE TEACHERS, U.S. TEACHERS SPEND MORE
OF THEIR ASSIGNED TIME IN DIRECT INSTRUCTION AND LESS IN SETTINGS
THAT ALLOW FOR PROFESSIONAL DEVELOPMENT AND COLLABORATION. In Japan,
teachers' time is structured in ways that foster collaboration. For
example, they usually share office space with colleagues, and the
blocks of time available for Japanese teachers to prepare for classes
are typically longer than in most U.S. schools.
Preservice teacher education and later professional development are
also important factors influencing the learning environment of
students. IN THE UNITED STATES, TEACHER PREPARATION TENDS TO BE
RELATIVELY EXTENDED COMPARED WITH THE INTERNATIONAL AVERAGE. It is
even longer in Germany, where the typical pattern is four to five
years of university preparation followed by two years of paid student
teaching. IN JAPAN, IN CONTRAST, FIELD EXPERIENCES FOR PRESERVICE
TEACHERS TYPICALLY LAST A MERE TWO TO FOUR WEEKS, BUT THE JAPANESE
APPROACH VIEWS PRESERVICE PREPARATION AS ONLY A SMALL BEGINNING IN A
CAREER MARKED BY MENTORING RELATIONSHIPS.
In-service development also differs markedly from country to country.
JAPAN IN THE PAST DECADE HAS MANDATED AN INTENSIVE MENTORING AND
TRAINING PROGRAM FOR ALL TEACHERS IN THEIR FIRST YEAR ON THE JOB,
REFLECTING THE CULTURE'S WIDESPREAD ASSUMPTION THAT ELDERS SHOULD
GUIDE NOVICES. Japanese teachers also rotate among schools every six
years, creating career cycles unlike those common in other countries.
Professional development opportunities are varied, ranging from
formal training at local resource centers to peer observation and
informal study groups.
IN THE UNITED STATES, PROFESSIONAL DEVELOPMENT IS LESS FORMAL AND
COHERENT. SCHOOLS AND DISTRICTS OFFER A RANGE OF STAFF DEVELOPMENT
PROGRAMS, BUT THESE TEND TO BE SHORT TERM, VARY WIDELY IN FOCUS, AND
OFTEN APPEAR TO TEACHERS AS A MENU OF UNRELATED OPPORTUNITIES.
Although some districts engage in more systematic efforts at
sustained professional development, including sustained mentoring
programs, SHORT-TERM WORKSHOPS REMAIN THE DOMINANT FORMAT.
Educational systems vary in the degree to which they treat teachers
either as professionals or as skilled workers. These differences in
treatment surface in such forms as hiring practices, the organization
of teacher time, the degree to which teachers control aspects of
their work and time, opportunities for continued learning, and the
fostering of collegial relationships among educators.
THE MATERIAL AND SYMBOLIC BENEFITS ACCORDED TEACHERS REFLECT THE
EXTENT TO WHICH THEY ARE TREATED AS EITHER PROFESSIONALS OR SKILLED
WORKERS. FOR EXAMPLE, TEACHERS IN JAPAN ARE PAID MORE IN COMPARISON
TO OTHER WORKERS WITH SIMILAR BACKGROUNDS THAN ARE TEACHERS IN THE
UNITED STATES. EMPLOYMENT BENEFITS ALSO TEND TO BE BETTER IN JAPAN
AND GERMANY. On the other hand, Japanese teachers report that their
profession is respected but not as much as it was in the past.
Finally, student attitudes toward mathematics and science, another
powerful influence on the culture of mathematics and science
education, tend to be positive across countries. Most U.S. fourth and
eighth graders report that they like both mathematics and science,
although fourth graders are more positive than eighth graders.
HOWEVER, STUDENTS IN SOME OF THE HIGHEST-PERFORMING COUNTRIES
RECORDED MARKEDLY LOWER PERCEPTIONS OF THEIR OWN PERFORMANCE COMPARED
WITH STUDENTS ELSEWHERE, SUGGESTING THAT STUDENTS IN HIGH-PERFORMING
COUNTRIES MAY WORK ESPECIALLY HARD TO MEET PERCEIVED SHORTCOMINGS.
The national mathematics and science standards call attention to the
critical importance of the broader culture in shaping teaching and
learning in the United States. TEACHERS NEED THE SUPPORT OF
ADMINISTRATORS, POLICYMAKERS, PARENTS, AND THE BROADER SOCIETY TO
MAKE LASTING IMPROVEMENTS IN MATHEMATICS AND SCIENCE INSTRUCTION."
For other appraisals of the TIMSS results see, e.g., ref. 9-11.
For discussions of educational practices in other countries see,
e.g., refs. 12-15.
Richard Hake, Emeritus Professor of Physics, Indiana University
24245 Hatteras Street, Woodland Hills, CA 91367
<rrhake@earthlink.net>
<http://www.physics.indiana.edu/~hake>
REFERENCES & FOOTNOTES
1. National Research Council (NRC), "Global Perspectives for Local
Action: Using TIMSS to Improve U.S. Mathematics and Science
Education" (National Academy Press, 1999); on the web at (a)
<http://www.nap.edu/catalog/9605.html>; (b) a convenient HTML version
of the "Executive Summary is at
<http://books.nap.edu/html/using_timss/#Summary>; (c) A "Professional
Development Guide" is at <http://books.nap.edu/catalog/9723.html>:
"U.S. students' worst showing was in population 3. . . . (final year
of secondary School . . . . . corresponding to U.S. high school
seniors). . . . In the assessment of general mathematics and science
knowledge, U.S. high school seniors scored near the bottom of the
participating nations. In the assessments of advanced mathematics and
physics given to a subset of students who had studied those topics,
no nations had significantly lower mean scores than the United
States. The TIMSS results indicate that a considerably smaller
percentage of U.S. students meet high performance standards than do
students in other countries."
2. J. Epstein, "Cognitive Development in an Integrated Mathematics
and Science Program," J. of College Science Teaching, 12/97 & 1/98,
pp. 194-201: "While it is now well known that large numbers of
students arrive at college with large educational and cognitive
deficits, many faculty and administrative colleagues are not aware
that many students lost all sense of meaning or understanding in
elementary school. . . . In large numbers our students. . . .[at
Bloomfield College (NJ) and Lehman (CUNY)]. . . . .cannot order a set
of fractions and decimals and cannot place them on a number line.
Many do not comprehend division by a fraction and have no concrete
comprehension of the process of division itself. Reading rulers where
there are other than 10 subdivisions, basic operational meaning of
area and volume, are pervasive difficulties. Most cannot deal with
proportional reasoning nor any sort of problem that has to be
translated from English. Our diagnostic test, which has been given
now at more than a dozen institutions shows that there are such
students everywhere . . . . . (even Wellesley! - see J. Epstein,
"What is the Real Level of Our Students," 1999, unpublished).
4. L. P. Benezet, "The Teaching of Arithmetic I, II, III: The Story of
an Experiment, "Humanistic Mathematics Newsletter #6, May 1991,
pp. 2-14 (reprinted from The Journal of the National Education
Association, Nov. 1935, Dec. 1935, Jan. 1936); on the web at ref. 6.
5. Etta Berman, "The result of deferring systematic teaching of
arithmetic to grade six as disclosed by the deferred formal
arithmetic plan at Manchester, New Hampshire, " Masters Thesis,
Boston University, 1935.
"Three percent of the nation's students reached the Advanced level at
all three grade levels. Twenty-six percent of fourth- and
eighth-grade students and 18 percent of the twelfth-grade students
performed within the Proficient level, while 38 percent, 32 percent,
and 36 percent performed within the Basic level for grades 4, 8, and
12, respectively."
8. (a) National Science Education Standards (Natl. Acad. Press,
1996), on the web at <http://www.nap.edu/readingroom/books/nses/>.
See also
(b) "Designing Mathematics or Science Curriculum Programs: A Guide for
Using Mathematics and Science Education Standards" (Natl. Acad.
Press, 1999), on the web at <http://books.nap.edu/catalog/9658.html>;
(c) "Science Teaching Reconsidered: A Handbook" (Nat. Acad. Press,
1997), on the web at
<http://books.nap.edu/catalog/5287.html>,
9. M. Neuschatz, "What can the TIMSS teach us?" The Science Teacher
66(1), 23-26 (1999). "In the study . . . .(the 12th grade portion) .
. . . U.S. students tied for last place in Physics and scored almost
as low in advanced mathematics. . . . . The explanation . . . . may
not be that our students are getting so little of the physics they
take, but rather that they are taking so little in the first place. .
. .the TIMMS study pitted U.S. students against those with twice as
much physics study under their belts. . . . The U.S. still stands out
among its industrial partners as exposing a smaller proportion of
students to physics in secondary school and encouraging even fewer to
attempt a more intensive study of the subject. The notion put forth
by the TIMSS researchers that the syllabi for our courses tend to be
'a mile wide and an inch deep' seem to have a good deal of merit."
10. R.B. Schwartz, "Lessons from TIMSS," Hands On [TERC - Technical
Education Research Center <http://www.terc.edu>] 21(1), 4 (1999):
"The first study focusing on textbooks, strongly suggests that, in
the absence of clear agreements about what students are supposed to
know and be able to do at each grade or cluster of grades, our
textbooks err on the side of inclusiveness, treating a large number
of topics superficially rather than a handful of topics in depth . .
. . .
The second study examines videotaped classrooms in Germany, Japan,
and the U.S., and this is enormously instructive in what it reveals
about the focus on pedagogy in the three countries. Simply put, the
American lessons, especially when contrasted with Japanese
classrooms, focus much more on procedures and skills, and much less
on concepts, deductive reasoning, and understanding.
Finally, there are detailed case studies of the same three countries
. . .. . (showing, for one thing). . . . that we track much earlier
than either Germany or Japan. . . . ."
11. R.R. Hake, "The Need For Improved Physics Education of Teachers:
FCI Pretest Scores for Graduates of High-School Physics Courses - Is
it Finally Time To Implement Curriculum S?" Physics Education
Research Conference 2000: Teacher Education, Univ. of Guelph, August
2-3, 2000;" on the as web at
<http://www.physics.indiana.edu/~hake/> as
[PERC2000-HSTeach-5.pdf, 8/10/00, 929K]. (16 References).
12. J.W. Stigler & J. Hiebert, "The Teaching Gap: Best Ideas from
the World's Teachers for Improving Education in the Classroom" (Free
Press, 1999): "To really improve teaching we must invest far more
than we do now in in generating and sharing knowledge about teaching
. . . . . . Compared with other countries, the United States clearly
lacks a system for developing professional knowledge and for giving
teachers the opportunity to learn about teaching." This, of course
brings us back to Arons's question "Whence do we get the teachers
with the background, understanding, and security to implement such .
..(Benezet-type) . . . instruction?)"
13. H.W. Stevenson and J.W. Stigler, "The learning gap: Why our
schools are failing and what we can learn from Japanese and Chinese
education" (Summit Books, 1992):