Journal of Education and Training Studies Vol. 5, No. 6; June 2017
50
obtained. In order to determine reliability of this scoring, the relation between the scores given by three experts to students
was analyzed using Weighted Kappa test and the value thus obtained (r=.81) showed that there was a good agreement
among scorers. Later, having the average of the scores given by the experts, literal comprehension score was obtained
for each student. With a reference to the mean scores, in order to determine validity of the scale, confirmatory
factor
analysis (DFA) was conducted and it was seen that the fit indices of the model set up with the one-factor structure of the
scale (χ²/sd=1.638, RMSEA=0,040, TLI=0,91, IFI=0,95, GFI=0.99) were sufficient.
In order to evaluate inferential comprehension skill, a text- which was developed by Başaran (2013), consisted of 226
words and was called “
Mantarlar”- and a scale- which was prepared with a reference to the text, whose reliability and
validity were assured upon expert opinion and which consisted of 5 questions- were used. The questions in the scale
consisted of such implicit questions as finding the main idea, finding a title, lessoning,
developing empathy, forming
cause and effect relation. Because it was seen during pilot scheme that 15 minutes was enough to answer the test, the
implementation process were structured with a reference to this duration. The answers of the students were scored as 3, 2,
1, 0 from precise answers to inaccurate answers. While loading the data statistically, replies to each question were coded
and no scoring operation was done at this stage. Later, the codes were analyzed by experts who had completed PhD on
reading comprehension in elementary school teaching; domain experts scored each code by reading the text. The codes
on which statistical means were loaded were turned into scores with a reference to expert opinions and so inferential
comprehension score given by each expert to each student was obtained. In order to determine reliability of this scoring,
the relation between the scores given by three experts to students was analyzed using Weighted Kappa test and the value
thus obtained (r=.64) showed that there was a good agreement among scorers. Later, having the average of the scores
given by the experts, inferential comprehension score was obtained for each student. With
a reference to the mean
scores, in order to determine validity of the scale, confirmatory factor analysis (DFA) was conducted and it was seen
that the fit indices of the model set up with the one-factor structure of the scale (χ²/sd=1.467, RMSEA=0,052, TLI=0,95,
IFI=0,96, GFI=0.98) were sufficient.
Problem solving scale: First of all, a problem-solving achievement test was developed to classify the errors made by the
students in the research. The problem-solving achievement test is composed of 10 word problems used in the studies
performed by Ulu (2011), Altun (2007), Yazgan and Bintaş (2005), Griffin and Jitendra (2008). While developing the
test, expert opinion of three experts having completed their PhD in mathematics education in elementary teaching. The
experts decided that the test had better be comprised of questions that were appropriate for using problem solving
strategies suggested by MEB (2005). Table 2 shows the strategies that could be used in solving the questions in this test.
Table 2.
Strategies that could be used in solving the questions in problem solving test
Questions
Writing
a
mathematical
sentence
Drawing
a
diagram
Work
backwards
Guess and
Checking
Logical
reasoning
Eliminating
Systematic
listing
1
x
x
2
x
x
x
3
x
x
x
4
x
x
x
x
5
x
x
x
6
x
x
7
x
x
x
8
x
x
x
9
x
x
x
10
x
x
x
x
The study to assess the validity and reliability of the scale was performed on 124 fourth-grade
students at the school
with the closest score to the Kütahya average based on the 2014/2015 YEP (Placement Scores). Firstly, the item
difficulty and item distinctiveness of each question and secondly, the reliability coefficient (KR-20) of the scale was
calculated in order to determine its validity and reliability. According Tekin (1997), items with an item difficulty index
between 0 and 1 and difficulty indices between 0.30 and 0.70 are of a moderate difficulty level. The item difficulty
indices of items in the scale vary between 0.32 and 0.48, which indicates that all of the problems
in the test are of a
moderate difficulty. The distinctiveness index varies between -1 and +1, with a value of 0.40 or higher demonstrating
the distinctiveness of the items (Tekin, 1997). The distinctiveness indices of items in the test vary between 0.43 and
0.64, which indicates that all of the items are distinctive. The KR-20 value for the internal consistency of the scale was
calculated as 0.84. If the KR-20 value is 0.70 or higher, it shows that the test has a high level of internal consistency and,
therefore, reliability (Büyüköztürk, 2006).
According to Şekercioğlu, Bayat, and Bakır (2014), factor analysis of the scales scored as 0-1 should be conducted on
tetrachoric correlation matrice. Because problem solving scale is scored as 0-1, construct validity (factor analysis) of the
scale was done on tetrachoric correlation matrice. According to the analysis result, the fact that KMO value was .898
Journal of Education and Training Studies Vol. 5, No. 6; June 2017
51
shows that the scale has sufficient sampling size for factor analysis and Barlett test results (X2(45) =881.338; p<.01)
show that the variables have equal variance (Büyüköztürk, 2006). As a result of analysis, factor loads of the scale items
varied between .898 and .496 and since factor loads were sufficient, it was decided to keep all the items in the scale
(Büyüköztürk, 2006). It was also seen that with its one-dimension structure, the scale explains 66.32%
of problem
solving variance. Also confirmatory factor analysis (CFA) was performed to determine the validity of the scale based on
the average scores, and it was seen that fit indices of the model established with the scale's one-factor structure
(χ²/sd=1.144, RMSEA=0.023, TLI=0.99, IFI=0.99, GFI=0.97) are sufficient.
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