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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.

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