Geometry anxiety scale for secondary school students
Aysun UmayProcedia - Social and Behavioral Sciences
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Geometry is taught as a subject-matter in mathematics courses at elementary school level, and as an independent course at secondary school level in Turkish education system. When the success levels of students regarding these two subjects are examined, it can be seen that there are differences. Anxiety is an important variant on success in mathematics. But whereas geometry is considered as a different field from mathematics by the students, mathematics anxiety cannot cover geometry anxiety completely and that geometry anxiety can be observed separately from mathematics anxiety. Thus the aim of this study is to develop a scale for secondary school level students in order to determine their anxiety towards geometry.
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was one of the most productive systematists of his time. His probably best-known work, the Handbuch der systematischen Weichtierkunde (1929)(1930)(1931)(1932)(1933)(1934)(1935), completed only months before his death, has become an indispensable source of information for any worker in the field. Few other works have subsequently reached the breadth and depth of information that Thiele had accumulated on the phylum Mollusca. The Handbuch was originally issued in four parts by Gustav Fischer Verlag in Jena. It was subsequently combined in two cloth-bound volumes and sold as a hard-cover edition. With each subsequent part after 1929, Thiele supplied extensive additions and corrections to the earlier text. As these additions and corrections have different dates of publication, they are included in this translation as footnote on appropriate pages rather than merged into the main body of the text. The third and final part of the English edition comprises 'Theile' 3 and 4 (the second volume of the original). The first three parts provide an indispensable resource for taxonomic and anatomical research. The fourth part is the highlight of Thiele's work completed only a few months before his death. ). Although a considerable number of his works dealt with sponges and crustaceans, he is best known for his extensive contributions to malacology. These contributions range from smaller review articles to major monographs (e.g., as part of the VALDIVIA German Deep-Sea Expedition series) to handbooks that have become standards in the field of malacology. His probably best-known work, the Handbuch der systematischen Weichtierkunde (1929-1935) has become an indispensable source of information for any worker in the field. Few other works have subsequently reached the breadth and depth of information that Thiele had accumulated on the phylum Mollusca. His now 'traditional' systematic arrangement of taxa in the Handbuch has been followed by thousands of workers and has become the basis for the arrangement of scientific collections throughout the world. Although many parts are now outdated due to subsequent work, the Handbuch is still an important source of information and of great taxonomic significance as it comprises more anatomical data than the other major handbooks in use, i.e., Wenz's work as part of the Handbuch der Paldozoologie, or the Treatise on Invertebrate Paleontology, and because it contains a large number of new taxa described by Thiele. To meet the demand, the Handbuch was reprinted in its original form in 1963 (by A. Asher & Co., Amsterdam). Workers less familiar with the German language have had to resort to translation services, and there is likely hardly a page in the Handbuch that has not been translated at least once. Dr. Joseph Rosewater, Curator of Mollusks at the National Museum of Natural History in Washington, VI D.C., initiated a request for a full English translation of Thiele's Handbuch, shortly before his untimely death in 1985.
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Procedia Social and Behavioral Sciences 15 (2011) 966–970
WCES-2011
Geometry anxiety scale for secondary school students
Yasemin Sa÷lam a *, Belma Türker b, Aysun Umay b
a
b
Hacettepe University, Department of Secondary Mathematics Education Beytepe, Ankara, 06800, Turkey
Hacettepe University, Department of Elementary Mathematics Education Beytepe, Ankara, 06800, Turkey
Abstract
Geometry is taught as a subject-matter in mathematics courses at elementary school level, and as an independent course at
secondary school level in Turkish education system. When the success levels of students regarding these two subjects are
examined, it can be seen that there are differences. Anxiety is an important variant on success in mathematics. But whereas
geometry is considered as a different field from mathematics by the students, mathematics anxiety cannot cover geometry anxiety
completely and that geometry anxiety can be observed separately from mathematics anxiety. Thus the aim of this study is to
develop a scale for secondary school level students in order to determine their anxiety towards geometry.
© 2011 Published by Elsevier Ltd.
Keywords: Mathematics anxiety, geometry anxiety, secondary school level;
1. Introduction
In the Turkish education system, geometry, an important field within mathematics, is taught as a topic within
mathematics in primary school, and in secondary school as a subject independent from it. Encountering mathematics
and geometry as two different subjects in the rest of their learning process leads said subjects to be regarded as
separate entities by students. When students' success levels concerning these two subjects are examined, the results
encountered are dissimilar; it can be observed that in mathematics, success levels are higher compared to geometry.
Students' success levels in mathematics have been the subject of various studies and have been examined
considering different variables (Fenemma & Sherman, 1977; Singh, Granville, & Dika, 2002 et al). Taking into
consideration that there are more than a handful of variables affecting success levels, the idea that mathematics
anxiety concept, which affects students' mathematics success levels considerably cannot completely cover the
subject of geometry anxiety and that geometry anxiety can be observed separately from mathematics anxiety, has
emerged.
1.1. Anxiety and Mathematics Anxiety
There is no consensus on the nature of anxiety; nonetheless it is considered to be composed of two distinct
components and is classified accordingly: Trait anxiety and state anxiety (Balo÷lu, 1999). While trait anxiety refers
* Yasemin Sa÷lam. Tel.: +90-312-2978601; fax: +90-312-2978600.
E-mail address: ysaglam@hacettepe.edu.tr.
1877–0428 © 2011 Published by Elsevier Ltd.
doi:10.1016/j.sbspro.2011.03.222
Yasemin Sağlam. / Procedia Social and Behavioral Sciences 15 (2011) 966–970
967
to ‘relatively stable individual differences in anxiety proneness’, state anxiety consists of a ‘transitory emotional
condition’.
On the other hand, mathematics anxiety refers to combination of concepts such as test stress, low self-confidence,
anxiety of failure and negative attitude towards learning (Bessant, 1995). Furthermore, certain pedagogic practices,
negative behavior on the teacher's part and difficulties students have with mathematics at an early age (Cornell,
1999; Jackson & Leffingwell, 1999 as cited in Brady & Bowd, 2005) contribute to the emergence of mathematics
anxiety. As a matter of fact, mathematics anxiety is not a concept created solely by the school and school
environment. The development of concepts such as "not being good at maths" and the transfer of such concepts
from parents to the children, contribute to the creation of an anxiety of this kind (Haylock, 2003; Furner& Duffy,
2002 as cited in Jackson, 2008). Moreover, the almost direct association of success or intellect levels with
mathematics; mathematics taught after primary school taking on abstract quality that is detached from everyday life;
curriculums that are intensive and severely consecutive, are amongst the causes of the emergence of mathematics
anxiety. Such factors also lead to the development of fear, anxiety and negative attitude, which contribute hugely to
students' failure (U÷urel & MoralÕ, 2006). Mathematics anxiety is also an important phenomenon in the
development of educated individuals (Yenilmez & ÖzabacÕ, 2003). This brand of fear is a significant factor that
hinders the discovery and development of people's mathematics skills (Civelek, Meder, Tüzen, & Aycan, 2000). The
relation between mathematics success and mathematics anxiety was demonstrated in various studies (Ma & Xu,
2003). This anxiety has an adverse affect on students' success levels and obstructs their attendance to courses on
mathematics (Hembree, 1990).
The aim of this study is to develop a geometry anxiety scale concerned with determining students' anxiety with
regard to geometry.
2. Methodology
The scale developed during this study, has been devised by the reevaluation for secondary school students, of a
geometry anxiety scale previously evolved by researchers for elementary school students.
2.1. Sampling
The samples of this study consist of 250 high school students from the city of Ankara attending various grades
(9th, 10th, 11th, 12th grades) in different types of secondary schools (high schools, Anatolian high schools, private
high schools, and vocational high schools). The distribution of said students according to gender and the type of
schools they attend were presented in Table 1.
Table 1. The distribution of students according to gender and type of school
Gender
High School
Female
Male
Total
82
43
125
Vocational
School
14
8
22
Private School
6
6
12
Anatolian High
School
51
40
91
2.2. The Adaptation Process of the Elementary School Anxiety Scale
In the beginning of the adaptation process, the items on the geometry anxiety scale developed for elementary
school students were reexamined by the researchers. Seeing as geometry is a part of mathematics on elementary
school level, items describing geometry as a topic within mathematics were rearranged for secondary school level,
in which it is an independent subject. An expert was consulted for the new items on the geometry anxiety scale,
prepared in the five-point likert-type with an item pool of 25 items and the grammatical structure of the items were
checked by a linguist. The study was carried with 250 students.
968
Yasemin Sağlam. / Procedia Social and Behavioral Sciences 15 (2011) 966–970
2.3. The Analysis of Data
The analysis utilized in this study was carried out using SPSS 15.0 program with meaningfulness level set at .05.
While the positive items included in the scale have been coded as 5 (I absolutely agree), 4 (I agree), 3 (neutral), 2 (I
do not agree), 1 (I absolutely do not agree), the negative ones have been coded as 1, 2, 3, 4, 5.
The item analysis of the Geometry Anxiety Scale developed for secondary school students has been examined by
using item-total correlation. Principal Component Analysis was employed in order to examine the structural validity
of this scale. Factor analysis is one of the widely used multivariate statistics methods that turn multiple interrelated
variants into a limited number of meaningful independent factors (Kleinbaum, Kupper, & Miller, 1998 as cited in
KalaycÕ, 2006).
Before commencing with factor analysis, Kayser Meyer Olkin (KMO) scale of sampling adequacy and the
Bartlett test were employed for their appropriateness for the factor analysis of the data set. In these tests the KMO
result is supposed to be higher than .60 and the Bartlett test result, significant (Büyüköztürk, 2007). In this study,
the KMO sampling suitability coefficient was found to be .93 and the Bartlett Sphericity text Ȥ2 value, found to be
2404.666 (p< .001). After the data set was found suitable for factor analysis, principal components analysis with a
varimax rotation, a factorization method was used. In the aftermath of the rotation process, three factors with an
eigenvalue higher than 1.00 emerged. Then, items in which the difference of loading in more than one factor is less
than 0.20 were removed from the scale and thus the scale was finalized with two factors.
3. Features of Geometry Anxiety Scale
The scale developed during this study, has been devised by the re-evaluation for secondary school students, of a
geometry anxiety scale previously evolved by researchers for elementary school students. After the analysis of reexamined data it can be said that a valid and reliable scale that determines the level of anxiety concerning geometry
in secondary school students was brought into literature. The final form of the scale was presented in Appendix-1.
3.1. Reliability and Validity of the Scale
According to Nunally (1967), if the reliability of a scale in relation to the alpha (Į) coefficient is higher than .80,
the scale is reliable. The reliability of the Geometry Anxiety scale developed for secondary school students was
found to be 0.939. According to this result, this scale devised for secondary school students is reliable. During the
preparations of items, expert views and total point correlation coefficients of items which are higher than .40
regarded as the validity dimension of the scale.
3.2. The Structure of the Scale
It was observed that 15 of the analyzed items were gathered under two factors with eigenvalues higher than 1
(Table 2). The first factor was named as the “Anxiety according to geometry perception” and the second factor
“Geometry anxiety related to social environment”. The variance accounted by these two factors regarding the scale
is 63%. The communalities concerning the common variance of the two factors defined in connection with the items
were detected to range between 0.405 and 0.753. Accordingly, it was discovered that together, the two factors
appearing to be important factors represent the total variance of the items and the generality of the variance
concerning the scale. According to the final scale, the distribution of items into factors and factor loadings are as
follows.
Table 2. Factor Loading of the Geometry Anxiety Scale
Item
12.
5.
1.
4.
Factor 1
,798
,777
,772
,764
Factor 2
Yasemin Sağlam. / Procedia Social and Behavioral Sciences 15 (2011) 966–970
10.
14.
16.
2.
9.
3.
17.
7.
8.
6
969
,756
,720
,720
,701
,697
,688
,634
,854
,759
,690
While the first factor, consisting of 11 items, explains 42% of the total variance related to the scale, the second
factor, consisting of 4 items, explains 21% of them.
References
Baloglu, M. (1999). A comparison of mathematics anxiety and statistics anxiety in relation to general anxiety, Retrieved from the ERIC database
(Record Details - ED436703).
Bessant, K. C. (1995) Factors associated with types of mathematics anxiety in college students. Journal for Research in Mathematics Education,
26(4), 327–325.
Brady, P., & Bowd, A. (2005). Mathematics anxiety, prior experience and confidence to teach mathematics among pre-service education
students. Teachers and Teaching: Theory and Practice, 11(1), 37–46.
Büyüköztürk, ù. (2007). Sosyal bilimler için veri analizi el kitabÕ [Data Analysis Handbook for Social Sciences]. Ankara: Pegem A Publication.
Civelek, ù., Meder, M., Tüzen, H., & Aycan, C. (2000, May 24-26). Matematik Ö÷retiminde KarúÕlaúÕlan AksaklÕklar [Troubles Encountered in
Mathematics Teaching]. Matematik Sempozyumu Bildiriler KitabÕ, 140-151, Ankara: Milli E÷itim BasÕm Evi.
Fenemma, E., & Sherman, J. (1977). Sex-Related Differences in Mathematics Achievement, Spatial Visualization and Affective Factors.
American Educational Research Journal, 14, 51-71.
Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research inMathematics Education, 21(1), 33–46.
Jackson, E. (2008). Mathematics anxiety in student teachers. Practitioner Research in Higher Education, 2 (1). 36-42.
KalaycÕ, ù. (2006). SPSS UygulamalÕ Çok De÷Lúkenli østatistik Teknikleri [Multivariate and Applied Statistics Techniques using SPSS], Ankara:
Asil YayÕn.
Ma, X., & Qu, J. (2004). The Causal Ordering of Mathematics Anxiety and Mathematics Achievement: A Longitudinal Panel Analysis. Journal
of Adolescence, 27 (2), 165í179.
Nunnally, J. C. (1967). Psychometric theory. New York: McGraw Hill.
Singh, K., Granville, M., & Dika, S. (2002). Mathematics and science achievement: Effects of motivation, interest, and academics. Journal of
Educational Research, 95, 323–332.
8÷urel, I., & Morali, S. (2006). Karikatürler ve Matematik E÷itiminde KullanÕPÕ [Cartoons and their use in mathematics teaching]. Milli E÷itim
Üç AylÕk E÷itim ve Sosyal Bilimler Dergisi, 35(170).
Yenilmez, K., & ÖzabacÕ, N. ù. (2003). YatÕOÕ O÷retmen Okulu O÷rencilerinin Matematik øle ølgili TutumlarÕ Ve Matematik KaygÕ Duzeyleri
ArasÕndaki øliúki Uzerine Bir AraúWÕrma [A research about the relationship between the mathematics anxiety and the attitudes of boarding
teacher school students towards mathematics]. Pamukkale University Journal of Education, 2(14), 132-146.
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Yasemin Sağlam. / Procedia Social and Behavioral Sciences 15 (2011) 966–970
Appendix-1
1.
2.
3.
4.
5.
6.
7.
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9.
10.
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15.
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Geometri dersleri beni tedirgin eder.
Geometri konularÕ derste anlatÕOÕrken anlamama ra÷men tek baúÕma
kaldÕ÷Õm zaman yapamÕyorum.
Geometri derslerine nasÕl çalÕúaca÷ÕPÕ bir türlü bilemiyorum.
Geometri en çok korktu÷um derstir.
Geometride bir konuyu anlasam bile sonraki konularda yine zorluk
yaúayaca÷ÕPÕ düúünürüm.
Geometri derslerinin iúlenece÷i günlerde okula gelmek istemem.
Geometri derslerinde, sÕQÕfta göz önünde bir yere oturmak istemem.
Geometri derslerinde herkesin içinde soru sormaktan çekinirim.
Geometri ile ilgili sorularÕn daha çok oldu÷u sÕnavlardan yüksek not
alamayaca÷Õma inanÕyorum.
Matematik dersinde baúarÕOÕ olsam bile geometride baúarÕOÕ olamam.
Testlerde geometri ile ilgili bölüme geldi÷imde tedirgin olurum.
Geometri derslerinde tahtaya kalkmaktan hoúlanmam.
Geometri en sevdi÷im dersler arasÕndadÕr.
Geometri sorularÕQÕ çözmek zorunda olmak beni kaygÕlandÕUÕr.
Geometri çalÕúÕrken kendimi rahat hissederim.
Kesinlikle
KatÕlmÕyorum
KatÕlmÕyorum
KararsÕ]Õm
KatÕOÕyorum
Kesinlikle
KatÕOÕyorum
Geometry Anxiety Scale for Secondary School Students
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