Since the impact of positive and negative
reinforcement on students has not yet been established,
this study attempted to determine how reinforcement
type affected the mental math performances of sixth
grade students at a Midwest suburban STEM (science,
technology, engineering, and mathematics) school. The
students were each given a twenty-question fraction test
(Table 1A). During the test, the students held a heart
rate monitor with their hands and answered the math
questions orally. Prior to the test, the thirty students were
divided into three groups: control (no reinforcement),
positive (positive reinforcement), and negative (negative
reinforcement). Prior to test administration, students in
the positive-reinforcement group were told that if they
earned an “A” on the test, they would receive candy;
students in the negative-reinforcement group were told
that if they did not meet their teacher’s expectations,
they would come in at recess and after school to study
fractions; students in the control group were told that
their results were anonymous and would not affect
their academic career. Each group represented a mix
of ethnicities, genders, backgrounds, and academic
performances (Table 1B). To ensure similar ability
levels between groups, each group had a similar (within
0.36%) average on their current math class grade
(Figure 1). We hypothesized that students given positive
reinforcement would have the highest average score,
followed by negatively-reinforced students and then the
control group.
The average score of the control group on the oral math
exam was 56.5% correct (Figure 1). For the negativereinforcement
group, the average score was 61.5%
correct (Figure 1); the average score of the positivereinforcement
group was 71.5% correct (Figure 1). The
positive-reinforcement group had the highest average
score, followed by the negative-reinforcement group.
Both reinforcement groups had a higher score than the
control group, which received no type of reinforcement.
These findings are consistent with our hypothesis that
students given positive reinforcement would have the
highest average score, followed by negatively reinforced students, and then the control group.
While a trend consistent with the hypothesis was found in the data, there was no significant difference
between the performance of the groups (ANOVA, F =
0.89, p = 0.422), perhaps due to the small sample size
(n = 30) and high variability in the groups, as shown
by the large range of the oral exam scores (Figure 1).
The control group’s scores ranged from 100% correct
to 5% correct; the negative-reinforcement group’s
scores ranged from 80% to 25% correct; the positivereinforcement
group’s scores ranged from 100% to
40% correct. The high variability in each of the groups,
combined with the small number of test subjects, could
have resulted in the statistical insignificance, despite the
trend being consistent with the hypothesis.
Looking at individual student performance, only four
students of the thirty performed at the same level or
better on the oral math exam as in their current math
class (Table 1B). Two students who performed at the
same level both had a class grade of 100% and received
100% on their oral exam (Table 1B, students 1, 2). Two
students had oral exam scores that were higher than
their class grade (current class grades of 88.71% and
90.32%; their oral math exam scores were 90% and
95%, respectively) (Table 1B, students 21, 20). All four of
these students were in either the positive-reinforcement
group or the control group (one same, one better in each
group). All other students, including all the students in
the negative reinforcement group, had oral exam scores
that were lower than their current math class grade
(Table 1B).
Students’ heart rates during the oral exam were
also recorded. The average heart rate of the control
group while taking the oral exam was 98.28 BPM (beats
per minute); the average heart rate of the negativereinforcement
group was 96.72 BPM; the average heart
rate of the positive-reinforcement group was 87.17 BPM
(Figure 2). The positive reinforcement group had the
lowest average heart rate, followed by the negative
reinforcement group. Both groups had a lower average
heart rate than did the control group (Figure 2). Average
heart rates for the groups were found to be statistically
significantly different (ANOVA, F = 4.05, p = 0.029).
The positive reinforcement group had a significantly
lower average heart rate than did the control (t-test, p
= 0.005) and the negative-reinforcement groups (t-test,
p = 0.042). Due to students completing the oral exam at
different speeds, heart rates for specific questions could
not be compared across the groups.