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Mathematics Attitude Scale: Construction, Validity and Reliability
S.Singaravelu
Assistant Professor, Vivekananda College of Education, Puducherry – 605 008, India
The present study is a report of the development of a new instrument to measure students’ attitude towards mathematics, and to determine the underlying dimensions of the instrument by examining the responses of 200 students. The data is collected from VIII standard students of Pondicherry region. The reliability coefficient obtained is high.
Factor analysis with a varimax rotation yielded four factors: Self-confidence, Fear of learning Mathematics, Usefulness and applicability of Mathematics, Enjoyment in learning Mathematics, Motivation in learning mathematics and Experience with Mathematics Teacher. Psychometric properties were sound and the instrument, Mathematics Attitude Scale (MAS), can be recommended for use in the investigation of students’ Mathematics Attitude.
KEYWORDS: Mathematics Attitude Scale, Construction, Validity & Reliability.
INTRODUCTION:
Many students of today consider mathematics as a tougher subject compared to other subject. As the concept in mathematics is abstract in nature, they find it very difficult to learn. There are many factors that affect Mathematics Achievement but one of the important causes among them is Mathematics Attitude. It is said “Sooner or later those who won are those who believe they can”. So Attitude towards mathematics plays a significant role in developing Mathematics Achievement which in turn develops positive mathematics Attitude.
Students’ attitudes toward mathematics as a school subject, including both the subject itself and the learning of the subject, and their implications for mathematics instructions have long received considerable attention from the mathematics education community. In particular, the relationship between attitudes toward mathematics and achievement in mathematics had traditionally been a major concern in mathematics education research (Ma & Kishor, 1997).
Mathematics Attitude is defined is just a positive or negative emotional disposition toward mathematics (McLeod, 1992; Haladyna, Shaughnessy J. & Shaughnessy M., 1983)
Mathematics Attitude is defined by the emotions that he/she associates with mathematics (which, however, have a positive or negative value), by the individual’s beliefs towards mathematics, and by how he/she behaves related to Mathematics (Hart, 1989)
Mathematics Attitude is defined as the pattern of beliefs and emotions associated with mathematics. (Daskalogianni & Simpson, 2000)
The following are the results of students who has negative attitude towards Mathematics 1. Fear to perform tasks that are mathematically related to real life incidents, such as
dividing a restaurant bill amongst diners or developing a household budget 2. Bunking the mathematics classes
3. Developing a dislike towards Mathematics problem and Mathematics teacher
Abstract
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problems
5. An inability to perform in a test or test-like situations, and
6. Utilization of tuition classes that provide little success (McCulloch Vinson, Haynes, Sloan & Gresham 1997).
PURPOSE OF THE STUDY:
Purpose of this study is to design a tool to assess Mathematics Attitude of the VIII standard students. Dimensions of Mathematics Attitude are found out using Factor analysis. Face or Content validity and construct validity is established for the tool. Tool reliability is established using spilt half method and Sample reliability is established by test-retest method.
SAMPLE:
Sample consists of 200 VIII class students selected at random from Puducherry region. Sample consists of 102 boys and 98 girls.
DEVELOPMENT OF MATHEMATICS ANXIETY SCALE ITEM
DEVELOPMENT:
Mathematics Attitude Scale (MAS) is designed by the researcher to investigate the underlying dimensions of Attitude towards Mathematics. The 43 items of the MAS are designed in the domains of Mathematics Attitude to address factors considered important in research. It is four point scales ranging from strongly agree to strongly disagree. Items are designed to measure: Self-confidence, Fear of learning Mathematics, Usefulness and applicability of Mathematics, Enjoyment in learning Mathematics, Motivation in learning mathematics and Experience with Mathematics Teacher. This is done after carefully reviewing the related literature.
Component Related Studies Meaning
Self-confidence Doepken.D et al(1970) Linn & Hyde (1989) Randhana, Beamer &
Lundberg,(1993)
Academic Exchange (2004)
Designed to measure students’ self- confidence in Mathematical performance
Fear of learning Mathematics
Hauge (1991)
Terwlliger & titus(1995) Academic Exchange (2004)
Designed to measure feeling of fear, anxiety and its consequences when encountering
Mathematics/mathematical problem.
Usefulness and applicability of Mathematics
Longitudinal study of American youth (1990), Doepken, D et al (1970) Academic Exchange (2004)
Designed to measure students beliefs on usefulness, worth, relevance or applicability of Mathematics in day to day life and in country development Enjoyment in
learning Mathematics
Ma (1997) Thorndike – Chirst (1991) Academic Exchange (2004)
Designed to measure the degree to which students enjoy working mathematics and mathematics class Mathematics as
Motivation
Singh, Granville & Dika (2002) Thorndike – Chirst (1991) Academic
Designed to measure students motivation in learning Mathematics and go for higher studies
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Experience with Mathematics
Teacher
Kenscheft (1991) Dossey (1992) Doepken.O (1980) et al
Designed to measure the experience of students with their Mathematics teacher
FACTOR ANALYSIS:
The data are analyzed by means of a principal components analysis with varimax rotation.
Table 3.3
Communalities of 43 items of MAS
Item No Initial Extraction Item No Initial Extraction
1 1.000 .385 23 1.000 .927
2 1.000 .946 24 1.000 .875
3 1.000 .875 25 1.000 .796
4 1.000 .863 26 1.000 .737
5 1.000 .882 27 1.000 .832
6 1.000 .873 28 1.000 .768
7 1.000 .754 29 1.000 .779
8 1.000 .922 30 1.000 .801
9 1.000 .803 31 1.000 .710
10 1.000 .630 32 1.000 .936
11 1.000 .848 33 1.000 .858
12 1.000 .803 34 1.000 .953
13 1.000 .698 35 1.000 .860
14 1.000 .677 36 1.000 .726
15 1.000 .975 37 1.000 .982
16 1.000 .834 38 1.000 .887
17 1.000 .975 39 1.000 .830
18 1.000 .602 40 1.000 .704
19 1.000 .947 41 1.000 .938
20 1.000 .994 42 1.000 .925
21 1.000 .838 43 1.000 .970
22 1.000 .934
The communalities on table 3.2 indicates how much variance in each item is explained by the analysis. In item 1, only 38.5% of variance is explained by the extracted factors, remaining all items have explained high percentage of variance. Hence item 1 is dropped.
Table 3.4
Total Variance explained by the components of MAS Comp
onent
Initial Eigenvalues Extraction Sums of Squared Loadings
Rotation Sums of Squared Loadings
Total Total Cumulat ive %
% of Varianc
Cumulat ive %
% of Varia
Cumulat ive %
% of Vari
Cumulati ve %
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e nce ance
1 10.763 25.031 25.031 10.763 25.031 25.031 6.973 16.215 16.215 2 7.495 17.430 42.460 7.495 17.430 42.460 6.776 15.758 31.973 3 5.923 13.774 56.234 5.923 13.774 56.234 6.311 14.677 46.651 4 4.399 10.231 66.465 4.399 10.231 66.465 6.204 14.429 61.079
5 4.025 9.362 75.826 4.025 9.362 75.826 4.965 11.547 72.627
6 3.243 7.542 83.368 3.243 7.542 83.368 4.619 10.742 83.368
Table no 3.3 summaries the total variance explained by the solution to the analysis .Table 3.5 showing rotated component matrix of MAS
Component
1 2 3 4 5 6
Item 2 .476 -.107 -.062 .622 .538 .166
Item 3 -.161 .012 -.198 .045 .864 .248
Item 4 .735 -.250 .461 .076 -.187 .081
Item 5 .190 .081 .896 .004 .187 .041
Item 6 .713 -.290 .504 .086 .120 -.063
Item 8 .258 .151 .841 -.272 .183 .132
Item 9 -.004 -.011 .284 .281 -.312 .739
Item 10 .639 -.006 .292 -.034 -.363 -.057
Item 11 -.030 -.225 -.038 .793 .373 -.167
Item 12 .135 -.158 .758 .425 .055 .028
Item 13 .222 .207 .395 -.072 .602 .286
Item 14 .789 -.071 .066 -.109 -.096 .155
Item 15 .181 .146 .118 -.228 .247 .891
Item 17 .183 .144 .116 -.226 .245 .890
Item 18 .104 -.143 .194 .039 .659 -.311
Item 19 .813 -.148 .353 -.320 -.140 .135
Item 21 -.265 .434 -.378 .489 .432 -.102
Item 22 .070 .316 .866 -.075 -.203 .182
Item 23 .149 .239 .598 -.452 -.051 .250
Item 24 -.317 -.165 -.040 .103 .850 .114
Item 25 .303 .041 .270 .758 .055 -.228
Item 27 .690 .438 .077 .225 .326 .004
Item 29 -.576 -.338 -.029 .022 .532 -.222
Item 30 .568 .360 .475 .217 -.220 .164
Item 31 .363 -.437 .271 .144 -.107 .531
Item 32 .498 .332 .537 .335 .377 .147
Item 34 .178 -.061 .296 .888 -.088 .183
Item 35 .414 .139 .493 -.168 -.137 .615
Item 36 .493 -.116 -.429 .095 -.003 .509
Item 37 -.182 .455 .273 .085 .763 -.279
Item 38 -.122 .643 .027 .084 -.233 .629
Item 39 -.037 .754 -.141 -.440 .217 .002
Item 40 -.385 .636 -.190 -.256 .214 .057
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Item 41 .119 .859 -.130 -.204 .020 .357
Item 42 .248 .851 .267 -.117 .190 .135
Item 43 -.034 .856 .248 .065 -.329 -.249
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.
a. Rotation converged in 11 iterations.
Table no 3.4 summaries the Factor loading after the rotation is carried out. For each items, its strong loading is highlighted. Thus the highlights indicate which items load most strongly on which factor as specified.
The various indicators of factorability are good, and the residuals indicate that the solution is a good one. Six components with higher Eigen values are confirmed; the scree plot also indicates six components.
The components and the variables that load on them are shown in table 3.6 Table 3.6
The components found by the principal component analysis and the variables that load on them
C1 C2 C3 C4 C5 C6
Item4 Item6 Item10 Item14 Item19 Item27 Item30
Item38 Item39 Item40 Item41 Item42 Item43
Item5 Item8 Item12 Item22 Item23 Item32
Item2 Item11 Item21 Item25 Item34
Item3 Item13 Item18 Item24 Item29 Item 37
Item9 Item15 Item17 Item31 Item35 Item36 The final tool consists of 36 items.
Fig 3.1
Validity:
i) Content or Face Validity
w w w . o i i r j . o r g I m p a c t F a c t o r 1 . 9 5 8 Page 155 Content or Face validity of MAS is established by giving the scale to two experts (Professors) each in the field of Education and Mathematics and thereby incorporating necessary modifications.
ii) Construct Validity
Construct validity of MAS is established by correlation with Mathematics Attitude Scale designed by R.Vasuki & Dr. V. Rajeswari (2008) and Attitude towards Mathematics Scale designed by Praveena. P (2007). The correlation coefficients between the two tests with MAS are found to be 0.82 and 0.86 respectively.
Reliability:
Reliability of MAS is established by test-retest method and spilt half method. MAS is administered to 200 VIII standard students at an interval of 3 months duration. The correlation coefficient between the two tests is found to be 0.82. Thus sample reliability is established. Also the odd number items and even number items are scored separately and the correlation coefficient between the two half tests is found to be 0.86. The reliability of full test is calculated using the Spearman-Brown prophecy formula is found to be 0.92. Thus tool reliability is established by the investigator.
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