Development and Validation of an Instrument to Measure Attitudes towards the Use of Computer in Learning Mathematics

The aim of the study was to develop and validate an instrument suitable to measure attitudes towards the use of computer in learning mathematics (ATCLM). A total of 214 (132 = males: 82 = females) teacher trainees participated in the study. Factor Analysis (FA) was performed on 47 items relating to the use of computer in learning mathematics using Principal Component Analysis with Varimax (orthogonal) rotation. With Eigen values greater than 1, FA retained 13 factors with the first accounting for 15.56% of the variability and a total of 62.39% of the variance for the entire set of variables. To examine the strength of relationship among the items, the Kaiser Meyer Olkin (KMO) and Bartlett’s test were used. The KMO measure of sampling adequacy was 0.78 whiles the Bartlett’s test of sphericity was significant with x 2 = 3510.253 (p< 0.0001). A factor loading cut-off point of 0.40 was used as the inclusion criterion for factor interpretation. Based on these, seven factors namely: Confidence in Mathematics (CM), Confidence with Computer (CC), Mathematics Anxiety (MA), Computer Anxiety (CA), Value of using Computer for Learning Mathematics (VCLM), Interest in using Computer for Learning Mathematics (ICLM), and Anxiety in using Computer for Learning Mathematics (ACLM). Cronbach’s alpha values for the 7 scales ranged from .735 to .880.


Introduction
Information and Communication Technology (ICT) have become one of the fundamental building blocks of modern society. Many countries, including Ghana now regard the mastering of the basic skills and concepts of ICT as an important part of our educational system. With the introduction of ICT into the school curriculum, students are now expected to use ICT effectively within their lessons, regardless of the subject they are learning [1]. ICT plays a critical role in the educational systems [2]. To this end, various new models of education are evolving in response to the new opportunities that are becoming available by integrating ICT into the teaching and learning environment. The effective integration depends to a large extent on teacher's familiarity and ability in the information technology learning environment. Teachers' roles in the integration process are to create an effective, efficient atmosphere and a multimedia environment with the help of technologies. These environments are important for teacher-student interaction and communication [3].
Mathematics teachers need to know exactly how ICT is used as a teaching and learning tool, for their own purposes and to help students to use them. It has therefore become necessary to monitor how teacher trainees perceive ICT and how it can be used in the learning of mathematics in the classroom. This study is therefore aimed at developing and validating an instrument suitable to measure students' attitudes towards the use of computer in learning Mathematics.

Literature Review
Researches on the development of instrument to measure attitudes towards mathematics and computer have been done by many in the field of mathematics education. Table 1 outlines researchers and the instruments developed.
From Table 1, it is evident that little research has been conducted in terms of developing instruments for attitudes towards the use of computer in learning mathematics as in the case of [5,6,9]. The rest are either measuring attitudes towards mathematics or computer as in the case of [4,8,9,13,14]. Hence the development of this instrument will be a useful tool in determining students' attitude towards using computer in learning mathematics.

Participants
The participants for the study were level 200 teacher trainees from three colleges of education in the northern region of Ghana. A total of 214 (132 = males: 82 = females) teacher trainees responded to the questionnaire. Of this number, 124, 21, 56 and 13 were offering General programme, Mathematics, Science, and French respectively. The researchers personally administered the questionnaire to the participants in their various colleges.

Instrument Development Process
The instrument (ATCLM) was designed as a tool for measuring attitudes towards the use of computer in learning mathematics. The ATCLM consisted of 47 items, some of which were generated by the authors with some selected and modified from [1,9,16]. Each item was presented as a statement with 7 statements each for the Confidence in Mathematics (CM), Confidence with Computer (CC), Mathematics Anxiety (MA), and Computer Anxiety (CA) scales. The other scales such as the Value of using computer for learning mathematics (VCLM), Interest in using computer for learning mathematics (ICLM) and Anxiety in using computer for learning mathematics (ACLM) had 5, 8 and 6 items respectively. A mixture of both positive and negative worded items were used to reduce response bias. A five -point Likert scale was used to rate each item in terms of, 1 = Strongly Disagree (SD), 2 = Disagree (D), 3 = Undecided (U), 4 = Agree (A) and 5 = Strongly Agree (SA). In responding to each of the items under a particular scale, respondents were asked to indicate the extent to which they agree or disagree to the items on the five-point Likert scale. A higher score indicated a more positive attitude towards using computer in learning mathematics. The negatively worded items were reverse coded before the computation of the Cronbach's alpha coefficient.

Factor Analysis Process
Exploratory Factor Analysis (EFA) was performed on 47 items relating to the use of computer in learning mathematics using Principal Component Analysis with Varimax (orthogonal) rotation. Using Eigen values greater than 1, the EFA retained 13 factors with the first accounting for 15.56% of the variability and a total of 62.39% of the variance for the entire set of variables. Initially, to examine the strength of relationship among the items, the Kaiser Meyer Olkin (KMO) and Bartlett's test were used. The KMO measure of sampling adequacy was 0.78, above the commonly recommended value of 0.5 by [17]. The Bartlett's test of sphericity was also significant with x 2 = 3510.253 (p< 0.0001). The communalities of the 47 items ranged between 0.56 and 0.72, confirming that each item shared some common variance with other items. The Test gave the indication that factor analysis was suitable for the data. As recommended by [18,19], a factor loading cut-off point of 0.40 was used as the inclusion criterion for factor interpretation. Based on these, the seven scales were further retained, namely: i. Confidence in Mathematics (CM) ii. Value of using computer for learning mathematics (VCLM) iii. Confidence with Computer (CC) iv. Interest in using computer for learning mathematics (ICLM) v. Mathematics Anxiety (MA) vi. Anxiety in using computer for learning mathematics (ACLM) vii. Computer Anxiety (CA). NOTE: The item codes in the first column of Table 2 represent the item numbers and the corresponding scales they are measuring. For example, CM2 is item number 2 which is measuring Confidence in Mathematics; CC13 is the 13 th item which is measuring Confidence in Computer, etc.
From Table 2, it is seen that out of the initial 47 items, 35 are loaded onto the seven scales based on the strength of the loads. 6 items (CM2, CM4, CM3, CM1, CM5 and CM6) are loaded onto the Confidence in Mathematics scale. This scale measures the confidence level of teacher trainees towards mathematics. The second scale, Confidence with Computer had 5 items (CC10, CC13, CC8, CC9 and CC11) loading onto it. It measures teacher trainees' confidence level in working with computer. The third scale, Mathematics Anxiety had 6 items (MA19, MA15, MA16, MA21, MA20 and MA17). These items measure the anxiety level of teacher trainees. The Computer Anxiety, Value of using computer for learning mathematics, Interest in using computer for learning mathematics, and Anxiety in using computer for learning mathematics scales each had 5 (CA27, CA24, CA25, CA22 and CA23), 4 (VCLM32, VCLM33, VCLM31 and VCLM29), 5 (ICLM40, ICLM39, ICLM41, ICLM34 and ICLM38), and 4 (ACLM43, ACLM47, ACLM44 and ACLM46) items loads respectively.

Reliability Analysis of the Instrument
According to [20], the term reliability generally refers to the consistency of a measure. Reliability analysis on the seven scales was performed and their corresponding Chronbach's coefficient alpha recorded. Chronbach's coefficient alpha estimates the consistency of items included in a questionnaire. Values range from 0 to 1, with higher values (> .7) indicating greater reliability [19]. From Table 3, the Cronbach's alpha for the seven scales ranged from .735 to .880 with a total of 0.933, which indicates a high level of internal consistency for our scales.

Summary and Conclusions
The aim of the study was to develop and validate an instrument suitable to measure attitudes towards the use of computer in learning mathematics (ATCLM). Review of literature reveal that most instruments developed are mostly centered on attitudes towards mathematics or computer with very little work on the use of computers in learning mathematics. A total of 214 (132 = males: 82 = females) teacher trainees participated in the study. Factor Analysis (FA) performed on an initial 47 items relating to the use of computer in learning mathematics retained 13 factors with the first accounting for 15.56% of the variability and a total of 62.39% of the variance for the entire set of variables. A factor loading cut-off point of 0.40 was used as the inclusion criterion for factor interpretation and the initial 47 items were reduced to 35. These 35 items loaded on to 7 factors (scales) namely: Confidence in Mathematics (CM), Confidence with Computer (CC), Mathematics Anxiety (MA), Computer Anxiety (CA), Value of using Computer for Learning Mathematics (VCLM), Interest in using Computer for Learning Mathematics (ICLM), and Anxiety in using Computer for Learning Mathematics (ACLM). Cronbach's alpha values for the 7 scales ranged from .735 to .880 with a total of 0.933, which indicates a high level of internal consistency for the scales.
Based on the above results, the instrument (ATCLM) was developed (See appendix) and will be a good tool to be used by researchers in determining the attitudes of students towards the use of computers in learning mathematics.