Psychometric properties of an inventory to determine the factors that affect students’ attitudes toward mathematics

Abstract

This study explored the reliability and validity of the inventory
that measures attitudes toward mathematics among middle school students. The
original version of Attitudes toward Mathematics Inventory (ATMI) was adapted
and translated into Arabic language and administered to middle school students
in the United Arab Emirates (UAE). The data were analysed to establish the
reliability and construct validity as well as the factor structure of the instrument.
Our results showed that four factor model was the best fit using confirmatory
factor analysis. The findings from this study indicated that the translated version
of the inventory can be effectively used in Arabic speaking countries.
Keywords: math attitudes, reliability, validity, factor analysis.

Full text

www.psye.org © Psychology, Society, & Education 2014, Vol.6, Nº 1, pp.
ISSN 2171-2085 (print) / ISSN 1989-709X (online)
*Correspondencce: Myint Swe Khine, Science and Mathematics Education Centre, Curtin Universi-
ty, Perth, Australia.Email: m.khine@curtin.edu.au
Psychometric properties of an inventory to determine the
factors that affect students’ attitudes toward mathematics
Myint Swe Khine1* and Ernest Afari2
1Curtin University, Perth, Australia
2Petroleum Institute, Abu Dhabi, United Arab Emirates
(Received November 12, 2013; Accepted April 6, 2014)
ABSTRACT: This study explored the reliability and validity of the inventory
that measures attitudes toward mathematics among middle school students. The
original version of Attitudes toward Mathematics Inventory (ATMI) was adapted
and translated into Arabic language and administered to middle school students
in the United Arab Emirates (UAE). The data were analysed to establish the
reliability and construct validity as well as the factor structure of the instrument.
Our results showed that four factor model was the best t using conrmatory
factor analysis. The ndings from this study indicated that the translated version
of the inventory can be effectively used in Arabic speaking countries.
Keywords: math attitudes, reliability, validity, factor analysis.
Propiedades psicométricas de un inventario para determinar los factores
que afectan a las actitudes de los estudiantes hacia las matemáticas
Resumen: El presente artículo analiza la abilidad y validez del inventario que
mide las actitudes hacia las matemáticas entre los estudiantes de secundaria. La
versión original de las actitudes hacia la Matemática Inventory (ATMI) fue adap-
tado y traducido al árabe y se administró a los estudiantes de secundaria en los
Emiratos Árabes Unidos. Los datos se analizaron para establecer la abilidad y
validez de constructo, así como el factor de estructura del instrumento. Nuestros
resultados muestran que el modelo de cuatro factores fue el mejor ajuste en el
análisis factorial conrmatorio. Los resultados de este estudio indican que la
versión traducida del inventario puede ser utilizado con ecacia en países de
habla árabe.
Palabras clave: actitudes hacia las matemáticas, abilidad, validez, análisis fac-
torial.
INTRODUCTION
The effects of attitudes towards science and mathematics have been of inter-
est to educators around the world. Numerous research studies to explore how the
attitudes affect academic achievement and outcome variables have been conduc-
ted in various contexts over the past 40 years. However the progress in this area
has been stagnated by the limited understanding of the conception about attitude,
constituents, and inability to determine the multitude of variables that made up
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such a concept (Khine & Saleh, 2011).
Ruffell, Mason and Allen (1998) studied attitude to mathematics and noted
that attitude is a complex notion, and it is not a quality of an individual. The li-
terature is lled with many attempts in dening and searching for the constructs
that make attitudes. Some are controversial and some provides conicting re-
sults. Past research on mathematics anxiety or attitudes toward mathematics has
identied differences between countries (Zan et al, 2006; Hannula, 2012).
Singh et al. (2002) reiterate the fact that although cognitive abilities of stu-
dents and their home backgrounds are important factors for achievement, other
affective variables such as attitudes and motivation plays an important role. In
addition students’ interaction with their peers also is a factor that can affect their
attitudes toward a subject (Fishbein & Ajzen, 1975).
McLeod (1994) proposed that an attitude towards Mathematics is a positive
or negative emotional disposition towards Mathematics. According to Hart
(1989), attitude towards Mathematics comprises three components: an emotional
response to Mathematics (positive or negative), a conception about Mathematics,
and a behavioural tendency with regard to Mathematics. Ma and Kishor (1997, p.
27) dened attitudes towards Mathematics as “an aggregated measure of a liking
or disliking of mathematics, a tendency to engage in or avoid mathematical
activities, a belief that one is good or bad at Mathematics, and a belief that
Mathematics is useful or useless”. It is with this in mind that the denition for
attitude towards mathematics, used for our study, is the feelings that a person has
about Mathematics, based on their beliefs about Mathematics.
To examine the effect of attitudes, achievement and gender on mathematics
education, Arslan et al (2012) conducted a study with 197 middle school stu-
dents using Attitude Survey toward Mathematics. The ndings of this research
indicated that attitude of students’ towards mathematics and achievement scores
in Mathematics have a signicant difference in terms of their gender and grade
levels. Female students revealed more positive attitudes towards Mathematics
than male students and also had higher grades than male students.
Chamberlin (2010) reviewed instruments that accessed the inuence of affec-
tive variables in mathematics and elaborated on different instruments that measu-
re mathematics anxiety, attitude, value, enjoyment, self-efcacy and motivational
factors. In his opinion in the elds of educational psychology and mathematics
education there have been many studies on affective measurements, but practical
application and true value are yet to be materialised. The importance of affec-
tive variables in mathematics learning has also been highlighted by Ledens et
al (2010). They stated that mathematical achievement is not only a function of
cognitive factors but also the affective factors such as motivation, self-efcacy
beliefs and attitudes. In the same vein, Popham (2005) asserted that students’
affective dispositions such as attitude, value, and interest are powerful predictors
of students’ subsequent behaviour. He described that students should develop
positive concepts of themselves as learners and they should become more inter-
ested in the subject they study (p.84.) He concluded that by collecting evidence

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KHINE ET AL. Psychometric properties of the Arabic version of ATMI
of important affective changes in students’ behaviour overtime, teachers can gain
important information about the students. These will in turn be useful for desig-
ning relevant instructional strategies.
Historically the work by Aiken (1970) focused on the relationship between
attitude and achievement in mathematics and noted that these two variables have
reciprocal inuence, in that attitudes affect achievement and achievement in
turns affect attitudes. In the last decade non-cognitive affective variables that can
affect mathematics learning have been examined by various researchers. Since
then, there has been myriad of instruments developed and tested in various con-
texts.
In essence, most of the instruments used Likert-type response where students
answer to the extent of agreement to the questions. Whitin (2007) reported a
new way of measuring attitudes toward mathematics among young children. The
instrument requires to complete an open-ended statement rather than responding
to the scale. One of the questions include “Math is easy when ….”. She conclu-
ded that information gained from the survey will be helpful for teachers to make
better instructional plans.
Akin and Kurbanoglu (2011) examined the relationships between mathe-
matics anxiety, attitudes and self-efcacy among university students in Turkey.
When correlation analysis was used, mathematics anxiety was found to be nega-
tively related to positive attitudes and self-efcacy, positively to negative attitu-
des. In Champion et al (2011) study, students’ attitudes towards mathematics was
examined in relation to the careers perspectives. The results showed that while
students held mostly positive attitudes about the value of mathematics in their
career, business students expressed more positive attitudes than those reported
by non-business students.
Using secondary data set from Trends in International Mathematics and
Science Study (TIMSS), Mullis et al. (2008) and Helal (2009) examined and
interpreted the results on how 4th and 8th grades students in Dubai schools perfor-
med in international comparative studies in 2007. About students’ affect towards
mathematics, they found that among 4th grade students, 81% gave a highly po-
sitive response to statements related to their affection for mathematics. This -
gure dropped to 54% at the 8th grade level. More primary school students in the
UAE appeared to be enjoying the study of mathematics than secondary students.
Nearly 25% of all 8th grade students indicated that they dislike mathematics or
nd it boring. The study also indicated that 8th grade students in the UAE hold
learning mathematics in lower grade than majority of the Arab countries. This
may be due to the existence of poor-quality instruction and learning in some
schools within the UAE educational system, and the fact that, on the whole, tea-
ching methods are based on rote memorization (Gaad, Arif & Scott, 2006; Shaw,
Badri, & Hukul, 1995).
The study also indicated that 8th grade students in the UAE showed less con-
dence in their mathematical abilities than students in 4th grade. Almost 68% of
4th grade students maintained a high condence in learning mathematics. At the

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8th grade level, there was a decline in condence, as only 51% of the students
feel condent in their mathematics learning. Students in 8th grade in other Arab
countries, including Bahrain, Egypt, Jordan, Kuwait and Qatar, displayed higher
feelings of condence in mathematics than the UAE.
According to Helal (2009), results showed that 10-year-old boys in the Uni-
ted Arab Emirates showed higher condence in mathematics learning than boys
in other Arab countries. Nearly 70% of 4th grade boys were highly condent
in their mathematics learning, compared to 51% in Kuwait, 60% in Qatar and
34% in Yemen. The result was similar for 10-year-old girls in the UAE, where
65% expressed high condence in mathematics learning ability. This compares
to 60% in Kuwait, 63% in Qatar and 36% in Yemen. Among 14-year-old girls,
high condence in mathematics learning ability was registered by 47% in the
UAE. This was signicantly lower than that of girls in Bahrain (58%), Egypt
(52%), Jordan (56%), Kuwait (55%), Qatar (57%) and Saudi Arabia (50%). In
comparison, 54% of 14-year-old boys in the UAE registered high condence in
learning mathematics. This was less than the condence of students in Egypt
(57%) and Jordan (59%), but higher than that of students in Bahrain (47%) and
Saudi Arabia (44%).
As mentioned above much of the research on students’ attitude to mathema-
tics were carried out in Western countries and most of the instruments used in
those studies were in English. There is a need to extend this research to other
countries using questionnaires in their native languages to collect primary data
for empirical analysis. The present study explored the validation and factor
analysis of the attitudes toward mathematics inventory when translated into Ara-
bic language and administered to middle school students in the UAE. The details
of the methods and results are described in the following sections.
METHOD
Participants
Our adaptation was part of a larger study among Arab speaking middle
school students in the UAE. Thirty-nine grade 6 and 7 students (21 males and
18 females) took part in the adaptation process. The sample for the larger study
involved Grade 6, 7, 8 and 9 students (N = 269) attending three middle schools in
the UAE. Of these, 166 (61.7%) were males and 103 (38.3%) are females. Their
mean age was 12.03 years.
Procedure
Considering practices recommended in the literature on adaptation guidelines
(e.g., Hambleton, 2001, 2005; Hambleton & Patsula, 1998), we employed an
iterative procedure of translating, piloting and modifying instructions, examples
and items if needed. The adaptation process took four months.

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KHINE ET AL. Psychometric properties of the Arabic version of ATMI
The ATMI was originally developed in English and so we rst determined
the cross-cultural validity of the existing English version of the ATMI. This cul-
tural assessment was undertaken jointly by the researchers and bilingual experts
from the UAE. We considered the equivalence of the content (item relevance);
Semantics (that the questions held the same meaning across languages); Concept
(similarity of theoretical construct); and Technical features (the appropriateness
and method by which each question was asked for the existing English version
of the ATMI) (Streiner, 1993).
Because all of the participants involved in our study spoke English as a sec-
ond language, an Arabic translation was created to ensure that they were able to
understand the items. The ATMI was translated into the Arabic language using a
standard research methodology of translation, back-translation, verication and
modication as recommended by Ercikan (1998) and Warwick and Osherson
(1973). Each item was translated into Arabic by a professional translator from
the UAE. The next step involved an independent back-translation of the Arabic
version into English by a different professional translator, who was not involved
in the original translation. Items of the original English version and the back-
translated version were then compared by the authors to ensure that the Arabic
version maintained the meanings and concepts in the original version. The trans-
lated version was ne-tuned during the pilot test through iterations of modify-
ing translations, administering these modications to other students of the pilot
sample, and implementing further modications, if needed.
The survey was administered to the students during one class period in the
last quarter of the academic year, by the mathematics teachers with guidance
from the researchers. The researchers made arrangements with the schools and
the class teachers took the responsibility of administering the printed question-
naire to their students. The inventory took approximately 20 minutes to complete.
Instrument
The Attitudes toward Mathematics Inventory (ATMI) was originally develo-
ped by Tapia and Marsh (2004) in English. The inventory comprises of 49 items
and constructed to cover six domains related to attitudes towards mathematics.
These are condence, anxiety, value, enjoyment, motivation and parent/teacher
expectations. The items were constructed using Likert-scale format and the stu-
dents respond to the statement in ve-point scale ranging from strongly agree (5),
agree (4), neutral (3), disagree (2) and strongly disagree (1). Out of 49 questions,
12 items have negative wordings. According to the developers, these domains
were considered due to the previous studies that reported as important factors.
The nal version of the ATMI comprises 40 items with four subscales, na-
mely, self-condence (15 items), value (10 items), Enjoyment (10 items) and
Motivation (5 items). An example of an item from the self-condence scale is
“I believe I am good at solving math problems”, an example of an item from the
value of mathematics scale is “A strong math background could help me in my

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professional life”. An example from the Enjoyment scale is “I am happier in a
math class than in any other class. Also an example of the motivation scale is “I
am willing to take more than the required amount of mathematics.’
DATA ANALYSIS
Descriptive Statistics
The descriptive statistics of the ATMI items are shown in Appendix 1. The
mean scores ranged from 2.60 to 4.40. All the standard deviations (SD) were
above 1.00 (1.749 to 1.996), indicating a large spread of item scores around the
mean. As recommended by Tabachnick and Fidell (2007), the data was examined
for multivariate normality, multicollinearity and outliers before assessing the fac-
tor structure of the responses. The bivariate correlations, tolerance, and variance
ination values indicated that neither bivariate nor multivariate multicollinearity
was present. Because maximum likelihood estimation assumes multivariate nor-
mality of the observed variables, the data were examined with respect to univa-
riate and multivariate normality (Teo & Lee, 2012).
All the items of the ATMI showed a skew or kurtosis value less than the
cut-offs of │3│or │8│respectively, as recommended by Kline (2010), and this
supported the univariate normality in the items. The value of the Mardia’s coef-
cient (a standard measure of multivariate normality) obtained in this study, using
AMOS 22, was 235.785. This value, as required, was less than [p (p + 2)] where
p = the number of observed variables in the model; 40(42) = 1680 (Raykov &
Marcoulides, 2008). Therefore the requirement of multivariate normality was
satised and the data was considered adequate for conrmatory factor analysis.
Exploratory approach
To examine the validity of the ATMI when translated into Arabic and used at
the middle school level in the UAE, principal axis factoring with oblique rotation
was used. We examined the suitability of the data for exploratory factor analysis
(EFA) with the Kaiser-Myer-Olkin (KMO) measure of sampling adequacy and
the Bartlett test of sphericity. As suggested by Tabachnick and Fidell (2007), cri-
teria for suitability are KMO > .8 and a p-value for Bartlett’s χ2 of less than .01.
A scree plot was also inspected, and an item was considered to load on a
factor if it had a factor loading in the pattern matrix greater than .3, and did not
load on any other component.
Conrmatory approach
Factor structure of the ATMI was examined by conrmatory factor analysis
(CFA) using AMOS 22. The t of models were evaluated by Chi-square statistics
and t indices including the Comparative Fit Index (CFI: Bentler, 1990), Tuker-

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KHINE ET AL. Psychometric properties of the Arabic version of ATMI
Lewis Index (TLI: Bentler & Bonett, 1980). The CFI and TLI are both t indices,
ranging from 0 (indicating poor t) to 1 (indicating a perfect t). For these two
indices, a value greater than .90 indicates a psychometrically accepted t to the
data. A value greater than or equal to .95 indicate a good t (Hu & Bentler, 1999).
Root mean square error of approximation (RMSEA) is one of absolute t indices
and a measure of discrepancy between the observed and model implied covarian-
ce matrices adjusted for degree of freedom. The values of RMSEA of .05 or less
indicate close t, less than .08 indicate a reasonable t, less than .10 indicate a
mediocre t, and greater than .10 indicate an unacceptable t (Brown & Cudeck,
1993). Another t index commonly referred to is the Standardized root mean
square residual (SRMR). A value of SRMR less than .05 indicate a well-tting
model (Byrne, 2010). One of the most common t index is Chi-squared statistics
(χ2). As suggested by Hu and Bentler, 1999, χ2 is strongly dependent on sample
size, χ2/df ratios instead of probability values are presented for each model. As
recommended by Byrne (2010) and Tanaka, 1993, χ2/df ratios ranging from 2 to
5 are considered to be adequate model t. We also used the chi-squared change
(∆χ2) statistics (Hu & Bentler, 1999) to test for differences in t between the
3-factor and 4-factor models.
RESULTS
The inter-item correlations between the ATMI items were adequate for fac-
tor analysis (KMO = .912; Bartlett’s χ2 = 5171.98, p < .000). Item and factor
analyses were conducted to identify those items whose removal would improve
the internal consistency reliability and factorial validity of the ATMI scales.
Principal axis factoring with oblique rotation was used because one can assume
that the scales of the ATMI are somewhat related (Coakes & Ong, 2010). Prior
to conducting the factor analysis, the assumptions which underlie the application
of the principal axis factor analysis, including the proportion of sampling
units to variables and the sample being selected on the basis of representation,
were considered. Factor analysis (Table 1) reports the structure for the ATMI
comprising 40 items in the 4 factors. The two criteria used for retaining any item
were that it must have a factor loading of at least 0.40 on its own scale and less
than 0.40 on each of the other three ATMI factors.
Item analysis indicated that, all the 40 items had sizeable item-remainder
correlations (i.e. correlations between a certain item and the rest of the scale
excluding that item). Table 1 reports the factor loadings for the sample of 269
students for the Arabic version of the ATMI.
All the 40 items of the ATMI had a loading of at least 0.40 on their a priori
scale and no other scale. The percentage of variance and the eigenvalue associ-
ated with each factor are recorded at the bottom of Table 1. The percentage of
variance for different factors ranged between 3.89% and 28.27%, with the total
percentage of variance accounted for by the 40 items being 49.17%. The largest
contribution to variance was for the Factor 1 scale (28.27%). The eigenvalues

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21
Table 1. Factor loadings, percentage of variance and eigenvalues for the ATMI
Items Factor 1 Factor 2 Factor 3 Factor 4
ATMI37 .85 .02 -.04 -.28
ATMI39 .84 .02 -.08 -.21
ATMI38 .81 -.02 -.02 .01
ATMI32 .81 -.08 -.09 -.04
ATMI30 .78 -.12 -.08 .07
ATMI31 .76 .04 .02 -.03
ATMI27 .72 -.11 -.01 .21
ATMI23 .65 .06 -.08 .16
ATMI36 .64 .03 .24 .10
ATMI34 .63 .06 .17 .00
ATMI14 .62 -.06 .26 .09
ATMI24 .60 .03 -.15 .19
ATMI33 .60 .11 -.01 .31
ATMI25 .56 -.04 -.25 .23
ATMI6 .02 .83 .07 -.02
ATMI4 -.11 .81 -.06 .06
ATMI2 -.06 .80 .09 .06
ATMI5 -.05 .79 .01 -.04
ATMI3 .00 .78 -.03 -.11
ATMI7 .11 .75 .03 -.05
ATMI8 -02 .72 -.08 -.13
ATMI9 .11 .70 -.04 .02
ATMI35 -.09 .65 .09 .21
ATMI1 -.07 .62 -.15 -.08
ATMI40 .07 .57 .11 .12
ATMI20 -.03 -.06 .88 -.07
ATMI19 .00 .01 .85 -.04
ATMI18 .11 .04 .82 -.06
ATMI17 .09 -.08 .79 -.00
ATMI21 -.04 .06 .78 .06
ATMI16 .03 .03 .73 .10
ATMI26 .09 .02 .68 .06
ATMI22 .07 .01 .67 .03
ATMI10 .10 -.09 .57 .24
ATMI28 .13 -.06 -2.0 .81
ATMI29 .03 .03 -.25 .80
ATMI15 .28 .00 -.13 .75
ATMI13 .09 -.05 -.30 .70
ATMI12 .12 .03 -.26 .65
ATMI11 .19 .08 -.22 .59
Eigenvalue 11.31 4.56 2.25 1.55
% variance 28.27 11.39 5.62 3.89
Table 1. Factor Loadings, Percentage of Variance and Eigenvalues for the
ATMI
for different ATMI scales ranged from 1.55 to 11.31. The results for the factor
analysis with oblique rotation, reported in Table 1, strongly support the factorial
validity of the 40-item, 4-scale, Arabic version of the ATMI when used in Mid-
dle school classes in the UAE. These ndings are consistent with the four-factor
solution obtained by Tapia and Marsh (2004), the developers of ATMI. Table 1
reports the results of the principal axes analysis with oblique rotation.

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KHINE ET AL. Psychometric properties of the Arabic version of ATMI
Convergent validity
We examined the convergent validity of the 40 items of the ATMI. The con-
vergent validity was estimated by composite reliability and average variance
extracted. The interpretation of the composite reliability is similar to that of
Cronbach’s alpha, except that it also takes into account the actual factor loadings
rather than assuming that each item is equally weighted in the composite load
determination (Wang, Wu & Wang, 2009).
The results (Table 1) indicate that all the factor loadings of the 40-item ATMI
met the minimum requirement of .5 suggested by Hair, Black, Babin and Ander-
son (2010), ranging from .56 to .88. This indicated that convergent validity is
demonstrated at the item level.
The results (Table 2) of the composite reliability of each construct indicated
that all of the four factors exceeded the minimum reliability value of .7 as sugges-
ted by Fornell and Larcker (1981), ranging from .87 to .93. The nal criterion
for the convergent validity was a measure of average variance extracted (AVE)
for each factor. The AVE were all above the recommended .5 level (Fornell &
Larcker, 1981; Hair, Anderson, Tatham & Black, 1992; Nunnally & Bernstein,
1994), which means that more than one-half of the variance observed in the items
was accounted for by their hypothesised factors (Wang et al., 2009). Therefore
all factors in the measurement model had adequate convergent validity.
22
Table 2. Composite reliability and average variance extracted and inter-correlations of the
variables and descriptive statistics.
Construct CR AVE Factor 1 Factor 2 Factor 3 Factor 4
Factor 1 .93 .51 (.71 )
Factor 2 .93 .56 .15 (.75 )
Factor 3 .92 .57 .63** -.07 (.75 )
Factor 4 .87 .52 .68** -.02 .62** (.72 )
Mean 51.1 33.59 37.15 24.00
SD 17.53 13.00 12.17 7.44
**p< 0.01
Average variance extracted (AVE) is computed by ∑λ2 / ∑λ2 + ∑ (1 – λ2);
Composite reliability (CR) is computed by (∑λ)2 / (∑λ)2 + ∑ (1 – λ2), where λ = standardized
loadings. The bold elements in the main diagonal are the square roots of AVE and the off-
diagonal elements are the shared variance.
Table 2. Composite Reliability and Average Variance Extracted and Inter-Co-
rrelations of the Variables and Descriptive Statistics
Discriminant validity
Discriminant validity assesses the degree to which the constructs differ from
each other. We assessed the discriminant validity by comparing the square root of
the average variance extracted for a given construct and all the other constructs.
As suggested by Barclay, Higgins and Thompson (1995), the square root of the
average variance extracted (AVE) should be greater than the inter-construct co-
rrelation. The results in Table 2 conrm that discriminant validity was achieved.

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Conrmatory Factor Analysis
We also used conrmatory factor analysis (CFA) to examine two 40-item
ATMI models using AMOS 22, with maximum likelihood procedure as the tech-
nique for parameter estimation. The rst model tested a three-factor for which,
Tapia and Marsh (2000) found in their studies. The second model tested a four-
factor model found in a study by Tapia and Marsh (2004). The t indices for the
four–factor model and the three factor model are given in Table 3.
From Table 3, it can be seen that the 4-factor model had an acceptable t to
the data (χ2 = 1013.89, CFI = .934, TLI = .927, RMSEA = .040, SRMR = .054).
The 3–factor model are also given in Table 3, from which it can be seen that this
model did not obtain an acceptable t to the data (χ2 = 1171.20, CFI = .897, TLI
= .893, RMSEA = .055, SRMR = .057). As mentioned earlier, the chi-squared
change (∆χ2) statistics was used to test for differences in t between the 3-factor
and 4-factor models. The ∆χ2 test revealed that the 4-factor model provided a
statistically better t than the 3-factor model (∆χ2 = 157.31, df = 10, p < .001).
We therefore concluded that the four-factor model appears to be a relatively good
approximation to the data.
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Table 3. Fit indices of the 3-factor and 4-factor models
Fit index Level of acceptable fit 3-factor model 4-factor model
χ2n.s at p < .05 1171.20, p =.000 1013.89, p =.000
χ2/df < 5 1.67 1.44
CFI > .9 .90 .93
TLI > .9 .89 .93
RMSEA <.06 .06 .04
SRMR <.05 .06 .05
Table 3. Fit Indices of the 3-Factor and 4-Factor Models
DISCUSSION
The purpose of this study was to assess the reliability and validity of the ATMI,
a questionnaire that measures attitudes in mathematics learning. Convergent and
discriminant validity was determined through exploratory factor analysis and
internal consistency reliability. Results of a screeplot clearly showed the ATMI
can be extracted into four factors Also, the correlation matrix obtained through
oblique rotation indicated that each measures a different dimension. The square
root of the average variance extracted (AVE) was greater than the inter-construct
correlation. The convergent and discriminant validity of the items in the ATMI
was therefore established. Results of CFA conducted in this study supported a
four-factor solution as established by Tapia and Marsh (2004).
This study is signicant because it is one of the few studies that has assessed
ATMI on an Arab elementary school sample and a carefully translated version of
a questionnaire for measuring mathematics attitudes has been made available for
researchers and educators in the Arabic-speaking countries. The generalisation

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KHINE ET AL. Psychometric properties of the Arabic version of ATMI
of the results to other populations should be made with caution as this study in-
volved a relatively small number of students and classes. The UAE is a country
with seven emirates (states) and no sample was drawn from any of the other six
emirates. So the representativeness of the sample could be limiting factor in that,
compared to the general elementary school population in the UAE, our sample
could not be representative of the full range of elementary schools and students.
It is therefore unclear whether our ndings would apply to other elementary
schools in the UAE.
The study has shown that the ATMI can be used to determine the mathematics
attitudes of younger sample with high reliability and validity. This study contri-
butes to the existing literature on the attitude measurements and the use of self-
report questionnaires to determine the attitudes of students towards mathematics.
ACKNOWLEDGEMENT
Grateful acknowledgement is made to Martha Tapia and George Marsh II for
permission to use the inventory in this study.
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3
Appendix 1. Descriptive Statistics of the Items in the ATMI
Item Mean SD Skewness Kurtosis
1 Mathematics is a very worthwhile and necessary
subject. 4.09 1.944 .20 -1.40
2 I want to develop my mathematics skills.
4.28 1.841 .51 -1.28
3 I get a great deal of satisfaction out of
mathematics experiments. 4.09 1.837 .20 -1.38
4 Mathematics helps develop the mind and teaches a
person to think. 4.37 1.778 .33 -1.33
5 Mathematics is important in everyday life.
4.42 1.876 .48 -1.28
6 Mathematics is one of the most important subjects
for people to study. 4.31 1.914 .36 -1.28
7 High school mathematics courses would be very
helpful no matter what I decide to study. 3.87 1.854 .71 -1.00
8 I can think of many ways that I use mathematics
outside of school. 3.75 1.905 .17 -1.42
9 Mathematics is one of my most dreaded subjects.
3.20 1.890 .49 -1.15
10 My mind goes blank and I am unable to think
clearly when studying mathematics. 3.20 1.867 -.32 -1.49
11 Studying mathematics makes me feel nervous.
3.06 1.867 -.08 -1.24
12 Mathematics makes me feel uncomfortable.
2.95 1.891 -.22 -1.18
13 I am always under a terrible strain in a
mathematics class. 2.97 1.829 -.22 -1.36
14 When I hear the word mathematics, I have a
feeling of dislike. 2.94 1.951 -.11 -1.37
15 It makes me nervous to even think about having to
do a mathematics experiment. 2.60 1.843 -.51 -1.11
16 Mathematics does not scare me at all.
3.96 1.996 -.50 -1.30
17 I have a lot of self-confidence when it comes to
mathematics 3.58 1.753 -.65 -1.01
18 I am able to do mathematics experiments without
too much difficulty. 3.80 1.749 -.71 -.84
19 I expect to do fairly well in any mathematics class
I take. 3.84 1.848 -.81 -.87
20 I am always confused in my mathematics class.
3.28 1.873 -.71 -1.05
21 I feel a sense of insecurity when attempting
mathematics.
2.90 1.844 -.27 -1.35
22
I learn mathematics easily.
3.63
1.815
-.15
-1.44
23
I am confident that I could learn advanced
mathematics.
3.64
1.757
-.30
-1.27
24
I have usually enjoyed studying mathematics in
school.
3.63
1.819
-.10
-1.32
25
Mathematics is dull and boring.
3.20
1.908
-.59
-1.01
26
I like to do new experiments in mathematics.
4.40
1.829
-.49
-1.15
27
I would prefer to do an experiment in mathematics
than to write an essay.
4.25
1.822
-.13
-1.40
28
I would like to avoid using mathematics in college.
3.28
1.934
-.70
-.96
29
I really like mathematics.
3.65
1.848
-.61
-1.00
30
I am happier in a mathematics class than in any
other class.
3.06
1.743
-.12
-1.40
31
Mathematics is a very interesting subject.
3.65
1.840
.26
-1.23
32
I am willing to take more than the required amount
of mathematics.
3.37
1.765
-.11
-1.35
33
I plan to take as much mathematics as I can during
my education.
3.45
1.821
-.36
-1.05
34
The challenge of mathematics appeals to me.
3.53
1.767
-.28
-1.31
35
I think studying advanced mathematics is useful.
3.89
1.816
.23
-1.43
36
I believe studying mathematics helps me with
problem solving in other areas.
3.74
1.751
-.08
-1.25
37
I am comfortable expressing my own ideas on how to look for
solutions to a difficult mathematics experim ent.
3.84
1.727
.04
-1.33
38
I am comfortable answering questions in
mathematics class.
3.87
1.829
-.03
-1.26
39
A strong mathematics background could help me in
my professional life.
4.13
1.804
.14
-1.23
40
I believe I am good at mathematics experiments.
4.14
1.812
.15
-1.50
Appendix 1. Descriptive Statistics of the Items in the ATMI

15
© Psy, Soc, & Educ, 2014, Vol.6, Nº1
KHINE ET AL. Psychometric properties of the Arabic version of ATMI
3
Appendix 1. Descriptive Statistics of the Items in the ATMI
Item
Mean
SD
Skewness
Kurtosis
1
Mathematics is a very worthwhile and necessary
subject.
4.09
1.944
.20
-1.40
2
I want to develop my mathematics skills.
4.28
1.841
.51
-1.28
3
I get a great deal of satisfaction out of
mathematics experiments.
4.09
1.837
.20
-1.38
4
Mathematics helps develop the mind and teaches a
person to think.
4.37
1.778
.33
-1.33
5
Mathematics is important in everyday life.
4.42
1.876
.48
-1.28
6
Mathematics is one of the most important subjects
for people to study.
4.31
1.914
.36
-1.28
7
High school mathematics courses would be very
helpful no matter what I decide to study.
3.87
1.854
.71
-1.00
8
I can think of many ways that I use mathematics
outside of school.
3.75
1.905
.17
-1.42
9
Mathematics is one of my most dreaded subjects.
3.20
1.890
.49
-1.15
10
My mind goes blank and I am unable to think
clearly when studying mathematics.
3.20
1.867
-.32
-1.49
11
Studying mathematics makes me feel nervous.
3.06
1.867
-.08
-1.24
12
Mathematics makes me feel uncomfortable.
2.95
1.891
-.22
-1.18
13
I am always under a terrible strain in a
mathematics class.
2.97
1.829
-.22
-1.36
14
When I hear the word mathematics, I have a
feeling of dislike.
2.94
1.951
-.11
-1.37
15
It makes me nervous to even think about having to
do a mathematics experiment.
2.60
1.843
-.51
-1.11
16
Mathematics does not scare me at all.
3.96
1.996
-.50
-1.30
17
I have a lot of self-confidence when it comes to
mathematics
3.58
1.753
-.65
-1.01
18
I am able to do mathematics experiments without
too much difficulty.
3.80
1.749
-.71
-.84
19
I expect to do fairly well in any mathematics class
I take.
3.84
1.848
-.81
-.87
20
I am always confused in my mathematics class.
3.28
1.873
-.71
-1.05
21
I feel a sense of insecurity when attempting
mathematics.
2.90
1.844
-.27
-1.35
22
I learn mathematics easily.
3.63
1.815
-.15
-1.44
23 I am confident that I could learn advanced
mathematics.
3.64 1.757 -.30 -1.27
24 I have usually enjoyed studying mathematics in
school.
3.63 1.819 -.10 -1.32
25 Mathematics is dull and boring.
3.20 1.908 -.59 -1.01
26 I like to do new experiments in mathematics.
4.40 1.829 -.49 -1.15
27 I would prefer to do an experiment in mathematics
than to write an essay.
4.25 1.822 -.13 -1.40
28 I would like to avoid using mathematics in college.
3.28 1.934 -.70 -.96
29 I really like mathematics.
3.65 1.848 -.61 -1.00
30 I am happier in a mathematics class than in any
other class.
3.06 1.743 -.12 -1.40
31 Mathematics is a very interesting subject.
3.65 1.840 .26 -1.23
32 I am willing to take more than the required amount
of mathematics.
3.37 1.765 -.11 -1.35
33 I plan to take as much mathematics as I can during
my education.
3.45 1.821 -.36 -1.05
34 The challenge of mathematics appeals to me.
3.53 1.767 -.28 -1.31
35 I think studying advanced mathematics is useful.
3.89 1.816 .23 -1.43
36 I believe studying mathematics helps me with
problem solving in other areas.
3.74 1.751 -.08 -1.25
37 I am comfortable expressing my own ideas on how to look for
solutions to a difficult mathematics experim ent.
3.84 1.727 .04 -1.33
38 I am comfortable answering questions in
mathematics class.
3.87 1.829 -.03 -1.26
39 A strong mathematics background could help me in
my professional life.
4.13 1.804 .14 -1.23
40 I believe I am good at mathematics experiments.
4.14 1.812 .15 -1.50