Journal of Education and Training Studies Vol. 5, No. 6; June 2017
56
Table 18. Wilks lambda equality of groups test
Scores
Wilks’ Lambda
F
Sd1
Sd2
P
Writing mathematical sentence
.615
173.596
1
277
.000
Looking for a pattern
.829
57.126
1
277
.000
Systematic listing strategy
.755
90.127
1
277
.000
Estimation and control
.654
146.439
1
277
.000
Backward studying
.970
8.574
1
277
.004
Drawing figures
and diagrams
.849
49.228
1
277
.000
According to Table 18, when significance level of each independent variable separating individuals with high and low
problem solving success depending on the strategies they used is analysed, it is seen that writing mathematical sentence
[F
(1-277)
=173.596, p<.01], looking for a pattern [F
(1-277)
=57.126, p<.01], systematic listing [F
(1-277)
=90.127, p<.01],
estimation and control [F
(1-277)
=146.439, p<.01], backward studying [F
(1-277)
=8.574, p<.01], drawing figures and
diagrams [F
(1-277)
=49.228, p<.01] are significant. According to Çokluk (2012), as Wilks’ Lambda values converges to 1,
the effect of the strategies in separating the groups decreases.
In this context, in terms of Wilks’ Lambda values, the
strategy with the least contribution to separation is seen to be backward studying while the one with the most
contribution to separation is seen to be “writing mathematical sentence” strategy. In the next stage, in order to determine
the strategies with the most
contribution to separation, standardized discriminant coefficients and structure matrix
coefficients were analysed and Table 19 shows the findings.
Table 19. Standardized coefficients for discriminant function and structure matrix coefficients
Scores
Standardized coefficients
Structure matrix coefficients
Writing mathematical sentence
-.153
-.624
Looking for a pattern
.328
.358
Systematic listing strategy
.672
.449
Estimation and control
.756
.573
Backward studying
-.024
.139
Drawing figures and diagrams
.168
.332
According to Table 19, it was determined that the strategy with the most contribution to separating students with high
and low problem solving success was “estimation and control” strategy (.756), followed by systematic listing (.672),
looking for a pattern (.328) and drawing figures and diagrams (.168) strategies respectively and that “backward
studying” and “writing mathematical sentence” strategies had a counter effect in separation.In terms of structure matrix,
it was seen that in separation, the variable with the most correlation with discriminant function was “writing
mathematical sentence” strategy but the correlation was negative (-.624). This finding enables us to see that as “writing
mathematical sentence”
strategy is used more, the likelihood of appearing in the group with high problem solving
success decreases. The strategies increasing the likelihood of appearing in the group with high problem solving success
are seen to be estimation and control (.573), systematic listing (.449), looking for a pattern (.358), drawing figures and
diagrams (.332) and backward studying (.139).
In the next stage, the case of problem solving strategies’ classifying
students with high and low problem solving success and Table 20 shows the findings.
Table 20. Classification results obtained as a result
of discriminant analysis
Low success
High success
Total
Group
f
%
F
%
f
%
Low success
136
90.66
14
9.34
150
100.00
High success 19
14.73
110
85.27
129
100.00
Total accurate classifying percentage=88.17%
According to Table 20, it is seen that 136 out of 150 students with low success according to the problem solving
strategies they used were classified accurately and accurate classification rate for low success group was 90.66%. In
terms of the same case for students with
high problem solving success, 110 out of 129 students were classified
accurately and accurate classification rate is seen to be 85.27%. Accurate classification rate
of discriminant function
according to strategies is seen to be 88.17%. According to Kalaycı (2005), accuracy of classification depends on relative
chance and maximum chance criteria. In this study, the sampling consists of 279 students and 53.76% (150) of them
showed low success while 46.24% (150) of them showed high success in problem solving. Therefore, these values are
also chance values for both groups.
As a result of analysis, the fact that accurate classifying percentage (88.17%) is
much higher than these two values enabled us to see that the obtained discriminant function achieved accurate
classification beyond classifying upon chance.
Chia sẻ với bạn bè của bạn: