The Effects of Cooperative-Summative Assessments on Major Exam
Performance
Elizabeth Giebler
This paper was completed and submitted in partial fulfillment of the Master Teacher Program, a 2-year faculty
professional development program conducted by the Center for Teaching Excellence, United States Military
Academy, West Point, NY, 2015.
Abstract
Extensive research has been conducted in the area of cooperative learning and its effects
on student performance within the classroom. Most cooperative learning in the classroom is
done through class activities and used formatively. This study looks at the effects of cooperative
learning within summative assessments and its effects on student performance on major exams.
The study contained a control group with students who took all quizzes in an individual format
and an experimental group who took quizzes under three models, individual, cooperative, and
mixed. Each model was administered for one quarter of the academic year. The results showed
that the experimental group individual model showed no statistical significant difference over the
control group, the cooperative model showed a decline in the experimental group’s performance
for the final exam, and the mixed model showed a statistically significant increase in the
experimental group’s performance on both the midterm and final exams.
Introduction
High student performance on major exams is necessary for success in a higher education
mathematics course. In higher education the majority of a course's points, if not all, come from
student performance on major summative assessments. At the United States Military Academy
Preparatory School (USMAPS) class time is devoted to a reverse learning model called the
Thayer Method. The Thayer Method is a type of reverse learning model where students read the
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assignment ahead of time and spend class time applying the material learned through application
activities, board work, and recitation (Shell, 2002). It is the researcher’s experience that the
Thayer Method of instruction is effective in encouraging mathematical discussion, understanding
of the material, and providing information to the instructor through formative assessment.
One area of improvement that all instructors struggle with is having all of the students in
a classroom engage in the material and mathematical concepts. Cooperative learning is one
strategy to improve student engagement and has been shown to improve understanding of the
mathematical concepts and performance (Johnson, Johnson, & Smith, 2014). Performance and
conceptual understanding are goals of any instructor for students in a course. Even the best
cooperative learning models may only engage 75 to 80 percent of a class. It is during summative
exams that an instructor has the highest level of focus and engagement from the students in a
class. However, summative exams are traditionally individual in nature and therein lies the
problem. Instructors want to ensure increased scores through deeper understanding of the
concepts and not through rote memorization of procedures. However, individual summative
exams in the researcher’s experience have resulted in cramming and rote memorization of facts
for the sake of the grade and class standing, which is counter to the goals of higher education.
The push in academics is for students to achieve deeper understanding through increased
rigor, application based problem solving, cooperative learning, and mathematical discussions
(Smith & Stein, 2011). Cooperative learning is typically applied during class activities and
projects and there exists a plethora of studies on the benefits of cooperative learning and its link
to higher performance and understanding of the material (Johnson et al., 2014). While a wealth
of information is available on in-class cooperative activities and strategies, as they apply to the
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classroom and formative assessments, there is no research or studies that the researcher could
find on the results of implementing cooperative learning strategies within summative
assessments. Can the implementation of cooperative learning strategies within summative
assessments increase student understanding due to the cooperative nature of the activity and the
inherent on-task engagement seen during exams?
Background
Cooperative-learning is known through hundreds of studies to increase student
performance, engagement, retention, and understanding (Johnson et al., 2014). Why then is
cooperative learning not used at the college-level more vigorously? Ewell (2001) answers this
question with his belief that while instructors apply scientific rigor to their research they fail to
apply the same to their teaching. This failure to apply research supported methods to classroom
instruction is due to a belief that faculty know how to teach and the responsibility is on the
student not the teacher (Ewell, 2001). Studies show that the learning structure that has the most
impact and should be used a majority of the time in classrooms is cooperation (Johnson,
Johnson, & Smith, 2006).
Cooperation
When a group of two or more students work together toward a common goal in
cooperation, they maximize individual and group learning. Competitive learning may be
mistaken for group learning because students work together. However, competitive learning is
fundamentally different in that students are not working toward a common goal but against each
other for an academic goal such as a good grade (Johnson, et al., 2014).
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Cooperation has its roots in social interdependence theory. Work by Kurt Lewin in the
1920s and 1930s showed that it is goal achievement that motivates cooperation and competition.
Morton Deutsch, a student of Lewin's, formulated a theory of cooperation and competition with
three types of social interdependence: Positive interdependence (cooperation), Negative
interdependence (competition), and No interdependence (Deutsch, 1962). Positive
interdependence is a direct relationship where the success of one is perceived only in terms of the
success of the others in the group so as one benefits so do the others, conversely negative
interdependence is an inverse relationship where the success of one is perceived as being at the
cost of another's success, in other words one can only succeed if another fails (Johnson et al.,
2014).
Deutsch's work posits that cooperation is a high-impact structure for the classroom
environment. However just putting students together for an assignment or task is not cooperative
learning. The conditions by which cooperative learning occurs is set forth in social
interdependence theory through "positive interdependence, individual accountability, promotive
interaction, social skills, and group processing" (Johnson et al., 2014, p. 93). Cooperation
requires that members of a group are linked positively with one member’s achievements
benefitting the others as stated previously. For positive interdependence to develop, group
members must know who needs help and be sure that no member can benefit from the work of
the others without working. To promote positivity, group members must "promote each other's
success by helping, assisting, supporting, encouraging, and praising each other's efforts to learn"
(Johnson et al., 2014, p.94). When cooperative learning is implemented correctly, studies have
shown that it promotes metacognitive thought, persistence, goal accomplishment, intrinsic
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motivation, increased time on task, and transfer of learning (Johnson et al., 2014). All of the
previously mentioned outcomes of cooperation are goals of any institution and instructor for
their students.
Approach and Methodology
This study was conducted with a single section of Precalculus students from eight
sections of the Precalculus Mathematics course at USMAPS. Students are placed into a
Precalculus section randomly from the population of students who place in Precalculus as
determined by a placement exam. The section chosen from the 2014-2015 academic year as the
experimental group had 17 students in the first semester and 13 students in the second semester.
The 2013-2014 academic year data for a section from the same instructor was used as the control
group since the same lessons, activities, quizzes, midterm, and final were used in the 2014-2015
academic year. The section chosen for the control group had a similar population of students
with 16 students in the first semester and 15 students in the second semester.
The study was designed to test if cooperative (group) assessments have an impact on
student performance on major assessments as measured by the midterm and final exam scores.
All quizzes in the 2014 academic year were individual, allowing for a baseline control group. In
the 2015 academic year, the first half of the first semester (first quarter) students took all quizzes
as individual exams, and during the second half of the semester (second quarter) all quizzes were
administered as a whole-class group. During the first half of the second semester (third quarter)
quizzes alternated with three quizzes in group format and three as individual quizzes.
Each group quiz contained six problems that addressed all the standards and concepts
covered in the previous year's corresponding individual quiz (see Appendix A). To cover all
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concepts in a small amount of problems, each problem contained multiple concepts within the
problem to be solved.
Each question on the group quiz required critical thinking to solve in an effort to promote
mathematical discussions during the solution. The first half of the class the students worked as a
group to come to a consensus on the solutions, methods, and concepts needed to solve the six
problems. The students in the class were allowed to choose how they went about the process of
solving and verifying the problems; no guidance on the method of solution was given by the
instructor. Solutions for each of the problems would be presented and defended by a chosen
student to demonstrate understanding of the concepts. To ensure participation and engagement
by all members of the class, the instructor randomly chose the student who would solve and
defend the problem.
At the end of the solution time the instructor drew from a basket six student names, one
student for each of the six problems. The chosen students were given a blank copy of the
problem and came to the board to work the problem without the use of notes or assistance from
others. When the solutions were finished six more names were drawn to brief the solution and
defend. If the original solution written on the board was incorrect then it was during the solution
brief that the student could state the error and/or misconception that occurred. The group quizzes
were scored on accuracy of the solution and conceptual understanding. Conceptual
understanding was achieved through the student’s answer to conceptual questions asked by the
instructor during the question defense. Everyone in the class received the same group grade.
A student could opt out of the group quizzes and take an individual quiz; however, once a
student opted out, he or she could not return to group quizzes. Individual quizzes were given in a
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class setting and each student completed the quiz individually and received individual scores
based solely on his or her performance on the quiz. Any student opting out of the group quiz
was removed from the study.
Students’ midterm and final exams were individual exams and were team graded by the
faculty to ensure consistency in grading. The mathematics department administers the midterm
and final exams at the same time of day each year. Since identical midterm and final exams
were administered in 2015 as 2014, the researcher used the midterms and final exams to measure
any possible benefits of the group quizzes.
Variables
The independent variable in this study was quiz administration procedures (individual,
group, or mixed) and the dependent variable was the midterm and final exam scores. As with
any study, there are extraneous variables that may have some impact on the results of the study.
The two basic types of variables in this study are situational and participant.
Situational. Situational variables include the time of day the exam was administered,
temperature of the classroom, and instructor. All mathematics midterms are the first exam on
test days and finals are the second exam on test days. This means that both the control and
experimental group took their corresponding exams during the same time of day. All classrooms
in the USMAPS building are climate controlled. The control and experimental group may not
have taken their quizzes and exams in the same room however the climate on an individual level
of the building is similar and both the experimental and control group tested on the same floor.
The same instructor administered the quizzes and exams for both the control and experimental
group. Some instructors will answer questions during an exam at varying levels. Since the same
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instructor administered the exams it can be infered the same level of assistance was given for
both groups.
Participant. Participant variables include ability level, pre-knowledge, sleep, and class
composition. The mathematics department gives a pre-test at the start of each year to the
students that determines their placement in algebra/trigonometry, precalculus, or calculus.
Students who place in precalculus are randomly assigned to a section of precalculus. The
placement exam and random assignment to a section does not eliminate ability level and preknowledge differences in students but implies the spread of the differences is equitable in each
course. Differences in the amount of sleep a student has can effect scores and performance. All
students have a designated lights out time which ensures a certain minimum level of sleep in the
students. However, all variablility in sleep patterns can not be eliminated or predicted. The
composition of a classroom to include gender and prior service can have a possible impact on the
performance of the students in one classroom over another. Demographic information on gender
and prior service was not considered in this study, since the section population was chosen
randomly from the overall population the same variability would be present in both the control
and experimental groups.
Findings
Since the instructor gave individual quizzes to both groups in the first quarter of each
year, the researcher used the results to assess prior knowledge and ability level to establish a
baseline for comparison. The 2014 control group had a midterm exam mean of 83 percent,
standard deviation of 11.56, and final exam mean of 81.9 percent, standard deviation of 10.3
with 16 students. The 2015 experimental group had a midterm exam mean of 85.8 percent,
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standard deviation 7.05 and final exam mean of 80.4, standard deviation 8.9 with 17 students
(see Figure 1).
Figure 1. Descriptive statistics for the control (2014) and experimental (2015) group midterm and final exams in quarter 1.
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Examining the results and the box-plot in figure 2 it is evident the two groups are academically
comparable.
Figure 2. Box-plots for the control (2014) and experimental (2015) group midterm and final exams in quarter 1.
While figure 2 shows a much larger spread in the first quartile of the data for the 2014 midterm
and final exams this spread is due to a student with very low scores as compared to the rest of the
class. The low score of 57.5 percent is within three standard deviations of the mean and was
therefore not excluded as an outlier but it does skew the visual for the spread of the data (see
Appendix C for actual student scores). The control and experimental group means were within
three percent of each other which is not a statistically significant difference. Therefore the
researcher could assume that if the experimental group were to continue with individual quizzes,
the results in quarter 2 and 3 would be comprable to the 2014 control group. This assumption
allowed the researcher to observe any change in performance attributed to the implementation of
the group quizzes (see Appendix B for alternate visual displays of the data as histograms for
comparison).
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In quarter 2 the instructor administered all quizzes to the experimental group using the
group method previously outlined in this paper. The midterm exam results show a decline in the
experimental groups performance. Figure 3 shows the quarter 2 descriptive statistics for each
group’s exam.
Figure 3. Descriptive statistics for the control (2014) and experimental (2015) group midterm and final exams in quarter 2.
The decline in the mean on the experimental group final exam of 2.5 percentage points is not
statistically significant while the 5.6 percent decline on the midterm is. There are too many
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variables involved to attribute this decline to any one reason however it can be speculated that
the decline may be due to the learning curve involved in the change in structure with the
cooperative group methods. The second quarter results indicate that group quizzes may not help
students achieve higher performance on major exams. The box-plots in figure 4 also show the
decline during the midterm and the return to comparable results on the final.
Figure 4. Box-plots for the control (2014) and experimental (2015) group midterm and final exams in quarter 2.
The quarter 3 results with the mixed-model are more promising. Both the midterm and
final exam results for the experimental group were higher than the control group with less spread
over the data. The experimental group’s midterm range was half a percent higher than the
control group with a 5.2 percentage point increase in the mean. The experimental group’s final
exam demonstrated less spread with a range 13.5 percentage points lower and a mean that was
11.8 percentage points higher. The median for the final exam also shifted from 67.5 to 85.5
which is a significant shift in the data considering the decreased spread and higher mean. The
results indicate that the mixed model for quizzes may have a positive effect on students’
performance on the midterm and final exams. Figure 5 shows the descriptive statistics for both
EFFECTS OF COOPERATIVE ASSESSMENTS
groups on each exam and Figure 6 shows the spread of the data and shift in the median for the
midterm and final.
Figure 5. Descriptive statistics for the control (2014) and experimental (2015) group midterm and final exams in quarter 3.
Figure 6. Box-plots for the control (2014) and experimental (2015) group midterm and final exams in quarter 3.
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Since the third quarter was conducted with a mixed model (both group and individual
quizzes) a comparison of the individual quizzes can be made. Figure 7 shows the averages for
each group on the three individual quizzes during the third quarter.
Figure 7. Table comparing the individual quizzes for the control group (2014) and experimental group (2015) in quarter 3.
The results show that the two group means were within one percent of each other on every
individual quiz (see Appendix C for all individual scores). The consistency in quiz results and
increase in performance on major exams implies a correlation between the mixed model and
student performance on major exams. There are too many variables that are unaccounted for in
the study for any definite conclusion to be drawn. However, the results do indicate that the
mixed model warrants further study.
Recommendations
Based on the third quarter results the researcher recommends to continue with a mixed
model for quiz format. However, this study was conducted with a small population—only one
section—and would need to be applied to a larger group to determine any external validity. Due
to the number of extraneous variables and the size of the study, further research is recommended
for the application of a mixed model for quizzes. The results of the test study in this paper show
that there appears to be a correlation between cooperative-group quizzes and student
performance on major exams. Further research may want to look at student perception and
behavior outcomes as a result of the group quizzes. No prior research in the area of cooperation
within formative assessments could be found by the researcher.
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Conclusion
Cooperative learning has been shown to increase student performance. After conducting
the test research and analyzing the results no statistically significant difference was found
between the control group and the experimental group with all individual exams in the first
quarter. This result was expected since the cadet candidates' population from 2014 and 2015 are
similar. Also, the instructor used the same syllabus, textbook, lessons, and quizzes in both years.
The second quarter exam results showed a small decrease in student performance to start and
leveled off by finals. Students in the second quarter took all group quizzes so this result is
surprising as the research on cooperative learning would lead one to believe that the cooperative
and rigorous nature of the quizzes would increase student understanding and be reflected in the
midterm and final exam scores. The mixed model in the third quarter showed a significant
increase in midterm and final exam scores over the control group. The mixed model's results
indicate that the researcher should continue with a mixed model for classroom quizzes and that
further study needs to be conducted to verify the results. The number of extraneous variables
and the size of the experiment leave areas for further research and study before the results can be
applied to a larger population.
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References
Deutsch, M. (1962). Cooperation and trust: Some theoretical notes. In M. R. Jones (Ed.),
Nebraska symposium on motivation (pp. 275-319). Lincoln, NE: University of Nebraska
Press.
Ewell, P. (2001). Questioning our assumptions. Change, 33(6), 4-5.
Johnson, D. W., Johnson, R. T., & Smith, K. A. (2006). Active learning: Cooperation in the
university classroom (3rd ed.). Edina, MN: Interaction book company.
Johnson, D. W., Johnson, R. T., & Smith, K. A. (2014). Cooperative learning: Improving
university instruction by basing practice on validated theory. Journal on Excellence in
college Teaching, 25(3&4), 85-118.
Shell, A. E. (2002). The Thayer method of instruction at the United States Military Academy: a
modest history and a modern personal account. PRIMUS XII, 1 (September 2002), 2738.
Smith, M. S., & Stein, M. K. (2011). 5 Practices for orchestrating productive mathematics
discussions. Reston, VA: The National Council of Teachers of Mathematics, Inc.
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Appendix A
Sample group quiz
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Appendix B
Histograms of the control and experimental data for the midterm and finals during all three quarters.
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Appendix C
Data for student midterm and final exam scores
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