SAMPLE ANCOVA TABLES AND DISCUSSION
Testing the Difference in Students’ Achievement
The null hypothesis stating that there is no significant difference in the students’
achievement using the flipped classroom approach (experimental) and conventional method
(control) in teaching General Mathematics as revealed in the posttest during the first and second
trial runs was tested using ANCOVA at 0.05 level of significance.
First Trial Run. Using One-Way Analysis of Covariance (ANCOVA) to test, analyze, and
interpret the difference on the posttest while controlling pre-test as covariate in the experimental
and control groups, the main effects of Table 3 (f-ratio = 90.766 and p-value < 0.05) reveals that
there is a significant difference between students’ achievement in the posttest results of the control
and experimental groups during the first trial run in favor of the treatment using Flipped Classroom
Approach. The adjusted R squared shows that 59.20% of the variation of students’ achievement is
accounted for by the variations in the use of the Flipped Classroom Approach and Conventional
Method.
Table 3.
One-way ANCOVA to test the difference in students’ achievement using the
Flipped Classroom Approach (experimental group) and conventional method
(control group):1st trial run
Type III
Sum of
Squares
527.814a
Source of
Variation
Corrected Model
Mean
Square
Df
F-ratio
p-value
2
263.907
58.237
.000
Intercept
602.260
1
602.260
132.901
.000
Covariates
Main Effects
Error
140.614
411.317
348.936
1
1
77
140.614
411.317
4.532
31.029
90.766
.547
.000
37428.000
80
876.750
79
Total
Corrected Total
a. R Squared = .602 (Adjusted R Squared = .592)
*Significant at the 0.05 level
Tests of Between-Subjects Effects
Dependent Variable: Posttest
Type III Sum of
Source
Squares
df
Mean Square
F
Sig.
2.346a
2
1.173
.372
.692
168.676
1
168.676
53.512
.000
Pretest
1.121
1
1.121
.356
.555
Group
1.272
1
1.272
.403
.529
Error
116.629
37
3.152
Total
6097.000
40
118.975
39
Corrected Model
Intercept
Corrected Total
a. R Squared = .020 (Adjusted R Squared = -.033)
Allowing students to observe videos outside of the classroom or before class time provides
more class-time to be utilized for active learning. Active learning can involve activities, discussion,
independent problem solving, student-created content, project-based learning, and inquiry-based
learning (Bergmann, Overmyer, & Wilie, 2012). Additionally, having more class-time can create
a classroom environment which uses collaborative and constructivist learning (Tucker, 2012).
Constructivist learning occurs when students acquired knowledge through direct personal
involvements such as activities, projects, and discussions (Ultanir, 2012). The flipped classroom
increases the regularity of these personal experiences using activities, making students who are
active learners (learning through analyzing, evaluating, and synthesizing), rather than passive
learners (learning by acquiring of information from hearing, seeing, and reading) (Minhas, Ghosh,
& Swanzy, 2012; Sams, 2013).
Second Trial Run. By employing One-Way Analysis of Covariance, Table 4 indicates the
test of significant difference in students’ achievement in the posttest results of the control group
and experimental group during the second trial run. Consistently, the main effects (f-ratio=54.575
and p-value < 0.05) reveal that there is a significant difference in students’ achievement when they
are taught using Flipped Classroom Approach and using Conventional Method in teaching
Mathematics in the second trial run. Thus, the experimental treatment using a Flipped Classroom
Approach proves to be better than the Conventional Method. The adjusted R squared shows that
53.60% of the variation of students’ achievement is accounted for by the variations in the use of a
Flipped Classroom Approach and Conventional Method.
Table 4.
One-way ANCOVA to test the difference in students' achievement using the
Flipped Classroom Approach (experimental group) and conventional method
(control group): 2nd trial run
Type III
Source of
Mean
Sum of
Df
F-ratio
p-value
Variation
Square
Squares
Corrected Model
473.613a
2
236.807
46.714
.000
Intercept
919.845
1
919.845
181.454
.000
Covariates
Main Effects
Error
Total
112.363
276.660
390.337
1
1
77
112.363
276.660
5.069
22.165
54.575
.000
.000
35226.000
80
Corrected Total
863.950
a. R Squared = .548 (Adjusted R Squared = .536)
79
*Significant at the 0.05 level
Tests of Between-Subjects Effects
Dependent Variable: POSTTEST2
Type III Sum of
Source
Squares
df
Mean Square
F
Sig.
341.603a
2
170.801
21.223
.000
Intercept
723.546
1
723.546
89.905
.000
Covariate
33.578
1
33.578
4.172
.048
Main Effects
263.077
1
263.077
32.689
.000
Error
297.772
37
8.048
Total
20665.000
40
639.375
39
Corrected Model
Corrected Total
a. R Squared = .534 (Adjusted R Squared = .509)
Aligned to the findings in the first trial run that there is a significant difference in students’
achievement when they are taught using Flipped Classroom Approach (experimental) and
Conventional Teaching Method (control) in favor of the treatment variable warrants the claim that
Flipped Classroom Approach could increase students’ mathematics achievement. This observation
is similar to the study of Strayer (2008), The effects of the Classroom Flip on the Learning
Environment, presented that students in a flipped classroom environment preferred the method and
exhibited a high level of innovation and cooperation as compared to students in a traditional
classroom setting. His outcomes also specify that students in a flipped classroom experience a
lesser level of task orientation than students in a traditional classroom. Additionally, another study
that was accomplished by Finkel (2012) on a high school in Michigan, found out that the failure
rate of ninth grade math students downed significantly from 44% to 13% after using flipped
classroom (Goodwin & Miller, 2013). Another study also conducted by Rotellar & Cain (2016)
on the achievement of pharmacy students who used the flipped classroom model as well; they
found a “steady improvement in students’ academic scores.
SAMPLE REGRESSION ANALYSIS TABLES AND
DISCUSSION
Regression Analysis
Table 7 shows the regression analysis of Computation Skills, Metacognitive Skills, and
Mathematics Performance. Using the stepwise method, Table 7 presents which model best
predicted students’ performance in Mathematics.
Table 7
Model
1
2
Regression Analysis for Determining Predictors of Students’ Mathematics
Performance
R
R2
Adjusted
SE
F-value
p-value
2
R
a
.593
.352
.344
3.37086
47.735
.000a
.670b
.449
.436
3.12645
35.393
.000b
a. Predictors: (Constant), Computation_Skills
b. Predictors: (Constant), Computation_Skills, Metacognitive_Skills
c. Dependent Variable: Performance
The data show that there is a significant overall relationship of the model wherein
Computational Skills is the independent variable and Students’ Mathematics Performance is the
dependent variable (R = .593, p < .05). Likewise, there is also a significant overall relationship of
the model comprising two independent variables specifically Computational Skills and
Metacognitive Skills (R = .670, p < .05).
Considering the R2 statistic, “Model 2” the better model in predicting students’
performance in Mathematics with two predictors because it posted a higher value of 0.449 known
as the coefficient of determination which indicates the proportion of variance of the dependent
variable (Mathematics Performance) that can be explained by the variation that also occurs in both
independent variables (Computation and Metacognitive Skills). In this case, approximately 45%
of the variation in Mathematics Performance can be explained based on the amount of variation
that occurs between the students’ Computation and Metacognitive Skills. The “Std. Error of the
Estimate” indicates the amount of dispersion for the prediction equation.
More importantly, a p-value less than 0.05 indicates a significant result. In this case, the
statistical value confirms that Computation and Metacognitive skills are statistically valid
predictors of Mathematics performance.
Statistics Associated with the Predictors of Students’ Mathematics Performance in the
Multiple Regression Analysis
Model
Unstandardized Standardized
t
p-value
Coefficients
Coefficients
B
SE
Beta
(Constant)
76.330
1.819
41.964
.000
Computation_Skills
1.179
.171
.593
6.909
.000
(Constant)
73.255
1.861
39.357
.000
Computation_Skills
.897
.174
.451
5.157
.000
Metacognitive_Skills
.656
.168
.342
3.911
.000
Table 8
1
2
a. Dependent Variable: Performance
*Model: Mathematics Performance = 73.255 + 0.897 Computation Skills + 0.656 Metacognitive Skills
The unstandardized beta coefficients contain a value that indicates whether the relationship
is direct or inverse. In this case, the “Unstandardized Coefficient” for Model 2 of the Computation
Skills = 0.897 and Metacognitive Skills = 0.656, both indicating a direct relationship.
The coefficient values can be plugged into the regression equation used to plot the line of
regression. This equation is Y1=a + b1X1 + b2X2. To determine the value of Y 1 ( Mathematics
performance), take sum of the constant, the product of the coefficient of computation skills and its
actual value and the product of the coefficient of metacognitive skills and its actual value based on
the test scores.
In this case, by following the equation, Mathematics Performance = 73.255 + 0.897
Computation Skills + 0.656 Metacognitive Skills. For a Computation Score of 10 and
Metacognitive Score of 15, Mathematics Performance = 73.255 + 0.897(10) + 0.656(15), predicts
a Mathematics performance (GPA) of 92.065. Thus, both Computation skills and Metacognitive
skills of students significantly predict their performance in Mathematics.
In a particular study done by Mohamad & Mahamod (2014), it was found out that
awareness in metacognitive skills can boost students’ interest in a particular subject thus improving
their performance. In addition, the said skills also are important in improving and training the
students to maximize their ability to solve problems. In the study done by Jacobs & Harkamp
(2012), the student’s ability in solving mathematical problems can be improved. Furthermore, the
findings from the study of Bayat & Tarmizi (2010) showed that there is a positive and moderate
significant relationship between a metacognitive overall strategy and performance in the Algebra
problem-solving. On the other hand, Lunsford & Poplin (2011), found out that computation skills
are an important factor of student success in elementary statistics regardless of the level of
mathematics presented, or the virtual emphasis on computation versus interpretation by the
instructor.
With the findings revealed, students must acquire skills in Metacognitive and Computation
since these are essential for them to maximize their performance in any Mathematics course.
Teachers, with the use of sufficient resources, play a great role in it.