1. Cooperative Group Size & Mathematics Achievement
in Middle School Research
Catherine Straka | University of West Georgia | Summer 2014
Research Question
Do cooperative groups of three students result in
greater achievement than a group of two in a
middle school mathematics classroom?
Introduction
Cooperative learning is frequently cited as an essential instructional strategy in middle
school. Generally, it involves small heterogeneous groups of students working together to
achieve a learning task. In addition to a higher level of achievement, one of the primary
benefits for middle school students is the opportunity to develop and enhance interpersonal
communication and teamwork skills. In a review of the research on cooperative learning,
most studies agree that cooperative learning results in improved academic achievement
compared to traditional direct instruction. However, research to determine which group size
yields the most academic achievement has not been studied extensively. Social
interdependence theory hypothesizes that groups will result in greater achievement than
students working alone but that the size of the group is not important (Bertucci, Conte, D.
Johnson, & R. Johnson, 2010). However, the larger the group, the greater the potential for
issues related to interpersonal communication and “social loafing” (Bertucci et al., 2010).
Researchers seem to be divided over whether group results and group size are positively or
negatively correlated (Bertucci et al., 2010). The purpose of the proposed research study is
to provide additional data to answer the question about whether cooperative groups of two
vs. three result in greater academic achievement in a middle school mathematics classroom.
Research Design
Controlled Variables
• Instructional
strategies the same
for control and
experimental groups.
• Teacher the same for
control and
experimental groups.
Independent Variable
• Cooperative group of
two (control) vs.
cooperative group of
three (experimental)
students.
• Random assignment
to either the control or
experimental group by
class.
Dependent Variable
• Academic
achievement as
measured using a
pre- and post-test for
each unit of study.
Proposed Methods of Data Collection
Proposed Timeline
Participants/Setting
• The participants will be on-level mathematics students
from the same grade and the same teacher.
• For this study, co-taught classes would not be used to
ensure that there are no conflicts with students’ IEPs.
• The setting would be a middle school, which includes
grades 6 through 8.
• A middle school can be chosen at random or based on
accessibility to the researcher.
Data Analysis Plan
• Once individual pre- and post-test scores are entered into an Excel
spreadsheet, the software’s statistical features will be used to calculate gains
by individual, group, and class.
• Mean scores will be calculated by individual, group, and class.
• Deviations between the individual and group means and group and class
means will be further analyzed, as well as a comparison between the means
of the 2 control groups and 2 experimental groups.
• Ultimately, the data needs to be formatted in tables and charts for further
analysis, readability, and understanding. An example of a chart that could be
constructed is included below.
References
Bertucci, A., Conte, S., Johnson, D. W., & Johnson, R. T. (2010). The impact size of cooperative group on achievement,
social support, and self-esteem. The Journal of General Psychology, 137(3), p. 256-272. Retrieved from
http://eds.b.ebscohost.com/eds/pdfviewer/pdfviewer?sid=378603dc-8aeb-4423-90d9-
0a682a758f1e%40sessionmgr115&vid=3&hid=115
Coca, D. M. (2013). The influence of teaching methodologies in the learning of thermodynamics in secondary education.
Journal of Baltic Science Education, 12(1), 59-72. Retrieved from
http://eds.b.ebscohost.com/eds/pdfviewer/pdfviewer?sid=0f4f2534-8cbd-4dcd-a64f-
34eae54df69f%40sessionmgr198&vid=7&hid=116
Hampton, D. R., & Grudnitski, G. (1996). Does cooperative learning mean equal learning? Journal of Education for
Business, 72(1), p. 5-7. Retrieved from
http://eds.a.ebscohost.com/eds/detail?sid=f67e72df-0ce7-47f6-87754d7c66901a1b%40sessionmgr4002&vid=8
&hid=4103&bdata=JnNpdGU9ZWRzLWxpdmUmc2NvcGU9c2l0ZQ%3d%3d#db=bth&A=9612132721
Hsiung, C. (2012). The effectiveness of cooperative learning. Journal of Engineering Education, 101(1), pages 119-137.
Retrieved from
http://eds.a.ebscohost.com/eds/pdfviewer/pdfviewer?sid=818b87c9-e960-42b5-9d36
a60ff32245e2%40sessionmgr4004&vid=6&hid=4103
Kose, S., Sahin, A., Ergun, A., & Gezer, K. (2010). The effects of cooperative learning experience on eighth grade students’
achievement and attitude toward science. Education 131(1), p. 169-180. Retrieved from
http://eds.b.ebscohost.com/eds/pdfviewer/pdfviewer?sid=ef1dd1b1-6ee6-4c7d
8d857986351352c3%40sessionmgr112&vid=7&hid=115
Yamarik, S. (2007). Does cooperative learning improve student learning outcomes? Journal of Economic Education, 38(3),
p. 259-277. Retrieved from
http://eds.b.ebscohost.com/eds/pdfviewer/pdfviewer?vid=3&sid=ef1dd1b1-6ee6-4c7d-8d85-
7986351352c3%40sessionmgr112&hid=115
• Pre- and post-test data will be collected for students individually for each
course unit during the length of the study.
• An independent evaluator will be used to grade the student tests to eliminate
potential bias from the teacher, as the status of each class as a control or
experimental group will be known to the teacher. The teacher will create a
grading rubric or matrix for use by the evaluator for consistent grading.
• Individual student data will be entered into an Excel spreadsheet for analysis,
including calculating individual, group, and class means and deviations from
the means.
• Additionally, significant deviations from the class mean will be followed up
with interviews with students and the teacher to collect supplemental
qualitative data regarding possible causes for the variance.
The research design is quasi experimental. One teacher’s on-level mathematics classes
will be used for the study to eliminate differing teachers and instructional strategies as
factors. Two classes will be randomly assigned to the control group, which means the
students will be assigned to work in groups of two. Two classes will be randomly assigned
to the experimental group, which means the students will be assigned to work in groups of
three. The data from any groups within each class that do not conform to the class’s
experimental designation will be excluded from the study. These factors will assure the
internal validity of the study.
Student data will be collected from the Cognitive Abilities Test (CogAT) and the Iowa Test
of Basic Skills (ITBS), which are both standardized, nationally norm-referenced tests, to
assess baseline student abilities and determine any significant gaps between students.
Combining the scores for both tests, a list of the students in each class would be generated
in descending order to use in assigning students to groups to ensure all groups have similar
abilities.
Students will individually take a pre- and post-test for each course unit to collect
quantitative data regarding the students’ academic achievement. The length of the study is
four six-week grading periods or 24 weeks.
The research study would start at the beginning of the school year so that no
change in classroom routine is perceived by the students. The proposed
timeline for the study is four six-week grading periods or 24 weeks.
30
32
34
36
38
40
42
44
46
48
Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7
CorrectAnswers
Post-Tests
Achievement by Group Size
Group of 2 Group of 3
