What Are the Roles of Homework and Assessment?
The amount of time students spend on homework assignments is an important
consideration in examining their opportunity to learn mathematics.
Exhibit
6.16 presents the index of teachers’ emphasis on mathematics
homework (emh). Students in the high category had teachers who reported
giving relatively long homework assignments (more than 30 minutes)
on a relatively frequent basis (at least once or twice a week). Those
in the low category had teachers who gave short assignments (less
than 30 minutes) relatively infrequently (less than once a week or
never). The medium level includes all other combinations of responses.
Details from teachers’ reports about the length and frequency
of their homework assignments are found in the reference section in
Exhibit
R3.11.
The results show substantial variation across countries and Benchmarking
entities in the emphasis placed on homework. Together with Italy,
Singapore, and the Russian Federation among the comparison countries,
the Academy School District had more than half its students in the
high category. For the remaining Benchmarking participants, the majority
of students were in the medium category. Very few students were in
the low category. One notable exception is Japan
(34 percent in the low category), where students were more likely
to spend extra time in tutoring and special schools than doing homework.(4)
There was little relationship between the amount of homework assigned
and students’ performance. Again, lower-performing students may
need more homework assignments for remedial reasons.
Since problem-solving activities will potentially be more bene�cial
if they can be extended to out-of-class-situations and stretched over
a longer time, 魅影直播 asked teachers how often they assigned homework
based on projects and investigations. The data in Exhibit
R3.12 in the reference section show that most students (82 percent
on average internationally) had teachers that never or rarely gave
such homework. Even though teachers in some of the Benchmarking entities
reported giving project-based homework more frequently than did teachers
internationally, such assignments did not appear to be made very often.
The Benchmarking entities where approximately one-third or more of
the students were given projects to do as homework at least sometimes
were Connecticut, Massachusetts, Oregon, South Carolina, the Jersey
City Public Schools, the Miami-Dade County Public Schools, Montgomery
County, and the Project SMART Consortium.
One theme in recommendations for educational reform is to make assessment
a continuous process that relies on a variety of methods and sources
of data, rather than on a few high-stakes tests. Exhibit
6.17 shows teachers’ reports about the weight given to various
types of assessment. Teachers in the United States as a whole and
in most of the Benchmarking jurisdictions reported placing less weight
on informal assessment approaches than did teachers internationally.
On average internationally, the most emphasis was placed on students’
responses in class, which were given quite a lot or a great deal of
weight for 77 percent of the students. The next heaviest weight internationally
was given to teacher-made tests requiring explanations (67 percent
of students on average) and to observations of students (64 percent).
While the use of teacher-made tests requiring explanations was similar
to the international average in many Benchmarking jurisdictions, students’
responses in class and observations of students were given less weight
in the United States as a whole and in most Benchmarking entities
(generally for about half the students or less). Exceptions included
Jersey City and Miami-Dade, as well as Chicago to some extent.
Internationally, the least weight reportedly was given to external
standardized tests, teacher-made objective tests, and projects or
practical exercises. On average across countries, about two-�fths
of the students (from 37 to 42 percent) had mathematics teachers who
reported giving quite a lot or a great deal of weight to such assessments.
Across the Benchmarking entities, generally even less weight than
internationally was given to external standardized tests. The jurisdictions
more similar to the international average were Michigan, North Carolina,
Texas, the Academy School District, and Jersey City.
As shown in Exhibit
R3.13 in the reference section, eighth-grade students reported
substantial variation in the frequency of testing in mathematics class.
On average internationally, students were split about in half, with
57 percent reporting having a quiz or test in class almost always
or pretty often and 43 percent reporting such testing only once in
a while or never. At least three-fourths of the students reported
frequent testing in Belgium (Flemish), Canada, the Russian Federation,
and the United States. Across the Benchmarking jurisdictions about
80 to 90 percent of the students reported frequent testing. In contrast,
about half or more reported infrequent testing in the Czech Republic,
Hong Kong, Italy, Japan, and Korea. Within participating entities,
there was a tendency for the most frequent testing to be associated
with lower-achieving students. One could argue that these students
can least afford time diverted from their instructional program. However,
teachers may provide shorter lessons and follow-up quizzes for lower-achieving
students to monitor their grasp of the subject matter more closely.
