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Research findings
Considerable
research evidence within mathematics education indicates
that using small
groups of various
types for different classroom tasks has positive effects
on student learning. Davidson, for example, reviewed
almost eighty studies in mathematics that compared
student achievement in small-group settings with traditional
whole-class instruction. In more than 40% of these
studies, students in the classes using small-group
approaches significantly outscored control students
on measures of student performance. In only two of
the seventy-nine studies did control-group students
perform better than the small-group students, and in
these studies there were some design irregularities.
From a review of ninety-nine studies of co-operative
group-learning methods at the elementary and secondary
school levels, Slavin concluded that co-operative methods
were effective in improving student achievement. The
most effective methods emphasized both group goals
and individual accountability. From a review by Webb
of studies examining peer interaction and achievement
in small groups (seventeen studies, grades 2—11),
several consistent findings emerged. First, giving
an explanation of an idea, method or solution to a
team mate in a group situation was positively related
to achievement. Second, receiving ‘non-responsive’ feedback
(no feedback or feedback that is not pertinent to what
one has said or done) from team mates was negatively
related to achievement. Webb’s review also showed
that group work was most effective when students were
taught how to work in groups and how to give and receive
help. Received help was most effective when it was
in the form of elaborated explanations (not just the
answer) and then applied by the student either to the
current problem or to a new problem. Using small groups
of students to work on activities, problems and assignments
can increase student mathematics achievement. 22 Qualitative
investigations have shown that other important and
often unmeasured outcomes beyond improved general achievement
can result from small-group work. In one such investigation,
Yackel, Cobb and Wood studied a second-grade classroom
in which small-group problem solving followed by whole-class
discussion was the primary instructional strategy for
the entire school year. They found that this approach
created many learning opportunities that do not typically
occur in traditional classrooms, including opportunities
for collaborative dialogue and resolution of conflicting
points of view. Slavin’s research showed positive
effects of small-group work on cross-ethnic relations
and student attitudes towards school.
In the classroom Research
findings clearly support the use of small groups
as part of
mathematics
instruction. This approach can result in increased
student learning as measured by traditional achievement
measures, as well as in other important outcomes. When
using small groups for mathematics instruction, teachers
should: • choose tasks that deal with important
mathematical concepts and ideas; • select tasks
that are appropriate for group work; • consider
having students initially work individually on a task
and then follow this with group work where students
share and build on their individual ideas and work; • give
clear instructions to the groups and set clear expectations
for each; • emphasize both group goals and individual
accountability; • choose tasks that students find
interesting; • ensure that there is closure to
the group work, where key ideas and methods are brought
to the surface either by the teacher or the students,
or both. Finally, as several research studies have
shown, teachers should not think of small groups as
something that must always be used or never be used.
Rather, small-group instruction should be thought of
as an instructional practice that is appropriate for
certain learning objectives, and as a practice that
can work well with other organizational arrangements,
including whole-class instruction.
References:
Cohen, E.G. 1994. Restructuring the classroom: conditions
for productive small groups. Review of educational
research (Washington, DC), vol. 64, p. 1—35.
Davidson, N. 1985. Small group cooperative learning
in mathematics: a selective view of the research. In: Slavin,
R., ed. Learning to cooperate, cooperating to learn,
p. 211—30. New York, Plenum Press.
Laborde, C. 1994.Working in small groups: a learning
situation? In: Biehler, R., et al., eds. Didactics
of mathematics as a scientific discipline, p. 147—58.
Dordrecht, Netherlands, Kluwer Academic Publishers.
Slavin, R.E. 1990. Student team learning in mathematics. In: Davidson,
N., ed. Cooperative learning in math: a handbook
for teachers, p. 69—102. Reading, MA, Addison-Wesley. –.
1995.Cooperative learning: theory, research, and
practice. 2nd edition. Boston, Allyn & Bacon.
Slavit, D. 1996.Graphing calculators in a ‘hybrid’ algebra
II classroom. For the learning of mathematics: an
international journal of mathematics education (Montreal,
Canada) vol. 16, p. 9—14.
Webb,N.M. 1991.Task-related verbal interaction and
mathematics learning in small groups. Journal for
research in mathematics education (Reston,VA),
vol. 22, p. 366—89.
Webb, N.M.;Troper, J.D.; Fall, R. 1995. Constructive
activity and learning in collaborative small groups. Journal
of educational psychology (Washington, DC), vol.
87, p. 406—423.
Yackel, E.; Cobb, P.;Wood,T. 1991. Small-group interactions
as a source of learning opportunities in second-grade
mathematics. Journal for research in mathematics
education (Reston,VA), vol. 22, p. 390—408.
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