4.6 Telefonía Móvil
4.6.12 Servicios de Red inteligente, Tarificación adicional y Números cortos
Factor analysis is a method for investigating whether a number of variables of interest are linearly related to a smaller number of unobservable factors. In this section, factor analysis is carried out prior to hypothesis testing to reduce the number of variables into a smaller number of factors. The validity of a scale is determined to ensure that the measurement scale measures what it is intended to measure (Wilson and MacLean, 2011:73). In order to ensure the reliability and validity of the research instrument, this section will report on the outcome of the Cronbach alphas and average inter-item correlations of the scale in Section A to Section F of the research
139 instrument utilised for this study. Thus the results of factor analysis of this study are presented in Tables 4.9 to 4.13 below.
Table 4.9: Factors of learning attitude/experience in mathematics in early school years
Total variance explained: 71.4%
Factor
1 2 3
Mathematics is my least favourite subject back in my school days
A1 0,865 0,097 0,055
Anything Numerical is a struggle for me
A2 0,806 0,072 0,034
My early school year’s performance in mathematics is below average
A3
0,789 0,063 -0,073
Mathematics lessons are not inspiring to me
A4 0,068 0,865 -0,187
Mathematics literacy was easier than mathematics for me in high school
A5
0,147 0,608 0,474
Lecturers negative attitudes lead to my disinterest in mathematics
140 Tables 4.9 to 4.10 indicate the factors of learning attitude in mathematics in early school years and the anxiety affecting students’ mathematics performance. There are three factors in learning attitude, brought down to two factors, as we cannot have a factor with one variable. The numbers in the columns of the factor analysis tables represent the loadings (correlations) of variables with factors. For example, in Table 4.9, struggling with anything involving numeracy (0.806) is highly related to factor 1 (poor mathematics performance since early school affects interest in mathematics, Table 4.15) while mathematics not being interesting due to teacher’s negative attitude to teaching the subject is highly related (0.865) to factor 2 (negative attitude towards mathematics, Table 4.15).
As shown in Table 4.9, the scale for Section A, pertaining to factors of learning attitude/experience in early school years returned a total explained variance value of 0.714 for the entire scale. This was a high total variance explained about 71% indicating that the test is 71% more valid and reliable. The variable of ‘mathematics lessons not inspiring’ and ‘mathematics literacy was easier than mathematics in high school’ is highly related to factor 2 (negative attitude towards mathematics in table 4.15). As all of these values exceeded the acceptable level of 0.6 (Malhotra, 2010:319), this scale is deemed reliable and can be accepted.
The newly created factors formed by averaging the variables loaded in factors are presented in Table 4.14.
Table 4.10 Factors of anxiety affecting students’ mathematics performance
Total variance explained: 60.9%
Factor
1 2 3
I find bridging mathematics challenging
B1 0,767 0,228 -0,246
Bridging mathematics generally makes me feel nervous
B2 0,709 0,338 -0,111
Bridging mathematics makes me feel uneasy
B3 0,649 0,375 -0,361
141 B4
I get uptight during bridging mathematics tests
B5 0,599 0,280 -0,080
My mind goes blank whenever I write my bridging mathematics tests
B6
0,102 0,877 -0,085
From the above table 4.10, the scale for Section B relating to factors of anxiety affecting mathematics performance returned a total explained variance of 0.609 for the entire scale. This shows that about 61% of the total variance was explained and the test is 61% more valid and reliable. The variable, “I find bridging mathematics challenging” -B1 (0.767); “Bridging mathematics generally makes me feel nervous” - B2 (0.709) up to B5 (0.599) shows that they are all highly related to factor 1(bridging mathematics is challenging).
I am unable to think clearly whenever I write my bridging mathematics test
B7
0,190 0,838 0,022
Bridging mathematics makes me feel confused
B8 0,373 0,647 -0,277
I get a sinking feeling when I try to do bridging mathematics problems
B9
0,443 0,590 -0,193
I worry about my ability to solve mathematics problems
B10 0,413 0,581 -0,047
I find bridging mathematics interesting
B11 -0,218 -0,106 0,779
I think that I will use mathematics in the future
B12 0,058 0,056 0,703
Bridging mathematics is one of my favourite subjects
B13 -0,436 -0,259 0,673
I generally enjoy learning mathematics n
B14 -0,320 -0,141 0,668
Bridging mathematics relates to my day to day life
142 In table 4.10 we also observe that the variables from construct B6 (My mind goes blank whenever I write my bridging mathematics tests) to construct B10 (I worry about my ability to solve mathematics problems) are all highly related to factor 2 (Anxiety causes inability to think clearly). For constructs B11 (I find bridging mathematics interesting) to B15 (Bridging mathematics relates to my day to day life) all these are highly related to factor 3 (Interest in bridging mathematics).
From the analysis above, this suggests that anxiety is a strong factor influencing success in bridging mathematics and with a Cronbach alpha coefficient of 0.68.
Table 4.11: Factors of mathematics motivation (Intrinsic Goal Orientation)
Total variance explained: 52.5%
Factor 1
Learning mathematics as a student can improve my logical thinking
C1 0,865
In a bridging mathematics class, I would like to have more projects and questions' for homework, which will help me learn more, even though this would not improve my scores
C2
0,773
I will work harder to get better scores in mathematics
C3 0,761
My greatest wish as a student is to understand the content of the learning material in a mathematics class
C4
0,643
In the bridging mathematics class I would like to have some challenging materials that would encourage me to learn more
C5
0,536
In the above table 4.11, the scale for Section C relating to factors of mathematics motivation (Intrinsic Goal Orientation) returned a total explained variance of 0.525 for the entire scale. This means about 53% of the total variance was explained and the test is 53% more valid and reliable. The variables C1, “Learning mathematics as a student can improve my logical thinking.” (0.865) up to C5 “In the bridging
143 mathematics class I would like to have some challenging materials that would encourage me to learn more” (0.536) are highly related to factor 1 (Mathematics motivation Intrinsic Orientation). From this we can conclude that lack of Motivation (Intrinsic Goal Orientation) can have a strong influence on the success rate in bridging mathematics with a Cronbach alpha coefficient of 0.76.
Table 4.12: Factors of mathematics motivation (extrinsic Goal Orientation)
In table 4.12 above the scale for Section D relating to factors of mathematics motivation (extrinsic Goal Orientation) returned a total explained variance of 0.671 for the entire scale. This means about 67% of the total variance was explained and the test is 67% more valid and reliable. The variables D1 “I’d like to have higher grades in bridging mathematics in order to get other peoples' recognition” (0.844) up to D3 “My wish is to choose a mathematics related course (for example Engineering, Accounting, etc.) in my degree programme here at MGI” (0.644) are highly related to factor 1 (Extrinsic motivation in doing mathematics). From D4 (0.874) to D5 (0.836),
Total variance explained: 67.1 Factor
1 2
I’d like to have higher grades in bridging mathematics in order to get other peoples' recognition
D1
0,844 0,056
I want to get higher scores in bridging mathematics class because I want
to demonstrate my capability to my other classmates D2
0,743 0,322
My wish is to choose a mathematics related course (for example
Engineering, Accounting, etc.) in my degree programme here at MGI D3
0,644 0,218
My desire is to get better grades in my bridging mathematics class
D4 0,086 0,874
I believe I can get higher grades than my classmates in bridging mathematics
D5
144 these variables are more closely related to factor 2 (Aspiration of higher grade in mathematics).
All these point to the fact that lack of motivation (extrinsic Goal) can have a strong impact on success in bridging mathematics with a Cronbach alpha coefficient of 0.68.
Table 4.13: Factors of mathematics motivation (Task value)
Total variance explained: 59.2%
Factor
1 2
I feel the learning materials or topics in bridging mathematics are useful
E1
0,788 -0,059
What I learn in the bridging mathematics class can be useful in daily life
E2
0,699 -0,091
I am always interested in the learning material in bridging mathematics
E3
0,661 0,493
The skills I learn from bridging mathematics can be applied in other classes
E4
0,658 0,218
I like every topic and content in the bridging mathematics class
E5 0,525 0,471
My poor performance in the bridging mathematics test negatively affects my morale to study harder
E6
0,104 -0,870
In table 4.13 above the scale for Section E relating to Factors of mathematics motivation (task value) returned a total explained variance of 0.592 for the whole scale, which explains about 59% of the variance. This means 59% of the test is more valid and reliable. The variables E1 “I feel the learning materials or topics in bridging mathematics are useful” (0.788) up to E5 “I like every topic and content in bridging
145 mathematics class” (0.525) are all highly related to factor 1, mathematics motivation (tasks and skills related). This implies that mathematics motivation (task value) has a strong relation to the success rate in bridging mathematics with a Cronbach alpha coefficient of 0. 57).
Table 4.14: Factors of teaching strategies in mathematics
Total variance explained: 64.4%
Factor
1 2 3
My poor performance in bridging mathematics is as a result
of my lecturer's ineffective teaching strategy F1
0,797 -0,036 -0,069
My bridging mathematics lecturer cannot explain
mathematics concepts easily enough for me to understand F2
0,741 -0,248 -0,032
Lecturers’ lack of patience to encourage struggling students in mathematics classes makes them feel uncomfortable, enough to dislike the subject
F3
0,609 0,014 0,345
The bridging mathematics materials (for example study guides, textbooks) for learning are self-explanatory enough for success F4
0,252 0,771 0,088
My lecturer’s method of teaching bridging mathematics is
good enough and needs no improvement F5
-0,362 0,755 -0,149
My bridging mathematics lecturer is always well prepared for his/her lessons as can be noticed in his/her execution of the topic in the classroom
F6
146 Lecturers should at least use more than one approach to
teaching topics in bridging mathematics, especially when students are struggling to understand
F7
0,061 0,121 0,849
Lecturers should always adopt the “show-and-tell” approach to solving mathematics problems
F8
-0,004 -0,031 0,793
Finally, as indicated in table 4.14 above, the scale for Section F relating to Factors of teaching strategies in mathematics retuned a total explained variance of 0.644, which is strong and explains about 64% of the variance. The test validity and reliability is 64% .The variables F1 “My poor performance in bridging mathematics is as a result of my lecturer’s ineffective teaching strategy,” (0.797) up to F3 “Lecturers’ lack of patience to encourage struggling students in mathematics classes makes them feel uncomfortable, enough to dislike the subject,” (0.609) are all highly related to factor 1, “Ineffective teaching strategies affect poor performance in mathematics”.
In contrast, variables from F4 to F6 are all highly related to factor 2, “Appropriate teaching and learning materials”. The variables from F7 to F8 are also highly related to factor 3, “Flexibility and variability in teaching approaches to bridging mathematics”. This shows no relatedness in the variables used in this scale, as different factors can be attributable to the various items, with almost the same Cronbach alpha. Thus, we can say that teaching strategies in bridging mathematics is not a strong factor affecting the success rates of the participants in bridging mathematics as depicted by its low Cronbach alpha coefficient (0.40).
In this study the various factors affecting achievement in mathematics such as, learning attitude, anxiety, and motivation and teaching strategies have been labeled with new variables that were observed in the process of research. These labels ranges from 1 to 3, under each of these labels are various numbers of variables loaded i.e. coded titles given to observe behavioural patterns from the questionnaires administered.
147 Table 4. 15: Creation and labels of new variables (Factors)
Section Factor Labels
Number of variables loaded Learning attitude/experience in mathematics in early school years
1
Poor mathematics performance since early school affects interest in
mathematics
3
2 Negative attitude towards
mathematics 3
Anxiety affecting students’ mathematics performance
1 Bridging mathematics is challenging 5 2 Anxiety causes inability to think
clearly 5
3 Interest in bridging mathematics 5 Mathematics
motivation (Intrinsic Goal )
1 Mathematics motivation (Intrinsic
Goal Orientation) 5
Mathematics motivation (Extrinsic Goal
Orientation)
1 Extrinsic motivation in doing
mathematics 3
2 Aspiration of higher grade in
mathematics 2
Mathematics motivation (Task
value)
1 Mathematics motivation (tasks and
skills related) 6
Teaching strategies in mathematics
1 Ineffective teaching strategies affect
poor performance in mathematics 3
2
Appropriate teaching and learning materials improve interest in
mathematics
3
3 Flexibility and variability in teaching
148