3.3 Instrument
3.3.2 Teacher Support
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3.3.2 Teacher Support.
In the present study, student sense of teacher supportiveness was assessed by
Teacher as Social Context Questionnaire (TASC; Belmont, Skinner, Wellborn &
Connell, 1992). This scale was designed for investigating teenagers according to the perception of teacher’s providing autonomy support, structure, and involvement. In TASC, teacher provision of autonomy support (8 items) includes four sub-categories:
choice, control, respect, and relevance. (e.g., My teacher give me a lot of choices about how I do my schoolwork). Providing structure (8 items) comprises four sub-categories: contingency, expectations, support, and adjustment/monitoring (e.g., Every time I do something wrong, my teachers acts differently). Teacher provision of involvement (8 items) includes four sub-categories: affection, attunement, dedication of resources, and dependability. (e.g., My teachers spends time with me).
Appendix C contains the originally instrument. Previous studies have provided evidence for the reliability and internal consistency of this scale (Zimmer-Gembeck, et al., 2006 ; Sierens, et al., 2009).
3.3.2.1 Exploratory factor analysis of Teacher Support scale
“Teacher Support” scale was translated from “Teacher as Social Context Questionnaire.” Based on the theoretical dimensions of the original scale, the
“Teacher Support” scale contained three subscales; therefore, three factors were predetermined as the numbers of factors in the process of factor analysis rather than choosing a factor based on the criterion of eigenvalue greater than one. Table 3.6 shows the exploratory factor analysis of the “Teacher Support” scale. Appendix D showed the instrument used in the present study.
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The first subscale was “Involvement”. The preliminary factor analysis showed
that item 13, item 21, item 14, item 11, item 12, and item 22 did not belong to this factor, so they were deleted. Therefore, this factor contained six items, the eigenvalue of this factor was 6.58, and this factor could explain 27.42 % of the variance. They were item 2 ”My teachers really cares about me” (這位老師關心我)
(factor loading = .89), item 3 “My teacher knows me well” (這位老師相當瞭解我) (factor loading = .75), item 1 “My teachers likes me” (這位老師喜歡我) (factor loading = .75), item 4 “My teachers just doesn’t understand me” (這位老師不是很懂我) (factor loading = .65), item 6“ My teachers talks to me “ (這位老師會和我談 話) (factor loading = .61), and item 5 “My teachers spends time with me “ (這位老 師會花時間在我身上) (factor loading = .55).
The second subscale was “Autonomy Support” which contained six items,
eigenvalue of this factor was 1.53, and this factor could explain 6.37 percentages of
the variance. They were item 15 “My teacher makes sure I understand before he/she
goes on.” (這位老師在課程繼續之前會確定我已經了解前部分的內容) (factor loading = .68), item 18 “My teacher doesn’t give me much choice about how I do my schoolwork.” (關於怎麼學習或做作業他（她）並沒有給我不同的選擇或方法) (factor loading = .67), item 17 ” My teacher gives me a lot of choices about how I do my schoolwork.” (關於怎麼學習或做作業，這位老師會給我不同的選擇) (factor loading = .67), item 16 “My teacher checks to see if I’m ready before he/she starts a new topic.” (在開始新的單元之前，這位老師會詢問我是否已經準備好) (factor loading = .61), item 23 “My teacher talks about how I can use the things we learn in school.” (這位老師會談論到如何應用學校所學的知識) (factor loading = .35), anditem 24 “My teacher doesn’t explain why what I do in school is important to me.” (這
位老師沒有解釋為什麼學校所學的知識，對我是很重要的) (factor loading = .37).‧ 國
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The third subscale was “ Structure ” which comprised six items, the eigenvalue of
this factor was 1.02, and this factor could explain 4.24 % of the variance. They were
item 10 “My teacher keeps changing how he/she acts towards me.” (這位老師對待我 的方式時常在改變) (factor loading = .60), item 9 “Everytime I do something wrong, my teacher acts differently.” (每次當我做錯事時，這位老師的反應都不一樣) (factor loading = .59), item 20 “ It seems like my teacher is always telling me what to do” (這位老師似乎一直不斷告訴我應該怎麼做) (factor loading = .43), item 19“My teacher is always getting on my case about schoolwork.” (對於學校的課業，這 位老師干預得很多) (factor loading = .42), and item 7 “ I can’t depend on my teacher for important things.” (學習上的事情，我不能依賴他) (factor loading = .39), item 8 “I can’t count on my teacher when I need him/her.” (生活上的事情我不能依 賴他) (factor loading = .34).
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Table 3.6 Factor loadings of Teacher Support scale
Observed variables Involvement Autonomy
Support Structure
Percentage of variance explained 27.42 6.37 4.24
Note. * indicates items were deleted
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3.3.2.2 Confirmatory Factor Analysis of Teacher Support scale
Confirmatory Factor Analysis was used to test whether three latent variables of this scale fit with the observed variables. Three sets of the fit indices of scale displayed the quality of the whole model (RMSEA= .055 ; GFI= .94 ; AGFI = .92, NFI = .96, NNFI = .97, PNFI = .79, PGFI = .69 , See Table 3.7).Table 3.7 CFA indices of Teacher Support scale
Absolute fit dices Relative fit indices Parsimonious indices X2 df RMSEA GFI AGFI NFI NNFI PNFI PGFI 359.79 125 .055 .94 .92 .96 .97 .79 .69
First, absolute fit indices show how covariance matrix matches among theoretical model and observed data, which include three indices AGFI (adjusted goodness of fit index), GFI (goodness of fit Index), and RMSEA (the root mean square error of approximation). The value of AGFI and GFI above .90 represented the good fit of the model. AGFI (.92) and GFI (.94) of “Teacher Support” scale were all above .90, showing a good fit of the scale. Another absolute fit index is RMSEA.
The criterion of RMSEA is that the value below .06 is considered good model fit, between .06 and .08 is reasonable fit, as well as between .08 and .10 is mediocre fit.
RMSEA of “ Teacher Support “scale was .055, indicating a reasonable fit of the scale. The second set of indices is relative fit indices, which include NFI (normed fit index) and NNFI (non-normed fit index). They compare the increase of fitness between theoretical model and independent model. The higher value means the better fitness of the data. The value of NFI and NNFI that above .90 represents good fit of the model. NFI and NNFI of the scale were all above .90, showing good quality of the scale. The third set of index is parsimonious fit indices, which measure
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how the model can be estimated by the least parameters under the criteria of the model fit. The value of PNFI (parsimony normed fit index) and PGFI (parsimony goodness of fit index) higher than .50 represents an acceptable result. PNFI (.79) and PGFI (.69) of the scale were all above .50.
Second, item reliability, composite reliability, and average variance extracte show the reliability between observed items and variables in the scale (See Table 3.8). Individual item reliability means the variance that can be explained by each item. Usually, the value of individual item reliability above .45 represents a good reliability. However, items in the subscale “Teacher Support of Structure” were all under the criterion of .45. The next index is composite reliability, which measures the reliability between several observed items and one latent valuable. Often, the criterion of composite reliability is .70, indicting good composite reliability of each factor. The composite reliability of the three factors were “Teacher Support of Involvement” (.85), “Teacher Support of Autonomy Support” (.77), and “Teacher Support of Structure” (.52). Average variance extracte shows the total variance of latent variable that can be explained by the observed variables. Usually .40 is the criteria of average variance extracte. Average variance extracte of the three subscales were .49 for “ Involvement”, .36 for “Autonomy Support”, and .27 for “Structure”.
However, the indices of two subscales “ Involvement” and “Autonomy Support ” failed to reach this criterion.
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Table 3.8 Reliability indexes and Average variance extracte of Teacher Support scale
Observed variables Item reliability Composite reliability
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Third, lambda (λ) and error variance (δ) are two indices that can also present the quality of the scale. Lambda is factor loading between each observed variable and the latent variable. Often, the value of lambda is between 0.5 and 0.8, and should reach a significant level. The values of some items are lower than 0.5, but most lambdas were between 0.5 and 0.8 (λ11 to λ203). Another index is error variance.
This value should be all positive and in a significant level. All error variances of this scale were all positive and significant (δ1 toδ20), which reached the basic criterion of the measurement.
In addition, modification indices (MI) in this confirmatory factor analysis (MI
> 10) suggested that the correlation between error variance should be set to increase the fitness of the model. Therefore, the correlations of error variance were set between δ1 and δ2,δ3 andδ4, δ15 andδ16, δ17 and δ18, as well as δ9 and δ10. Table 3.9 and Figure 3.3 depict the parameters of “Teacher Support” scale.
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Table 3.9 The parameters of CFA in Teacher Support scale
Parameter Estimates S.E t-value S.D
Estimates Parameter Estimates S.E. t-value S.D.
Estimates λ11 0.79 0.04 22.09 0.79 φ21 0.75 0.03 25.83 0.75 λ21 0.85 0.03 25.26 0.85 φ13 0.77 0.05 15.14 0.77 λ31 0.73 0.04 20.70 0.73 φ23 0.73 0.06 12.95 0.73 λ41 0.52 0.04 13.32 0.52 δ1 0.38 0.03 12.30 0.38 λ51 0.67 0.04 18.41 0.67 δ2 0.27 0.03 10.05 0.27 λ61 0.61 0.04 16.23 0.61 δ3 0.46 0.03 14.79 0.46 λ152 0.57 0.04 14.04 0.57 δ4 0.73 0.04 17.00 0.73 λ162 0.55 0.04 13.44 0.55 δ5 0.55 0.03 15.88 0.55 λ172 0.72 0.04 18.87 0.72 δ6 0.63 0.04 16.56 0.63 λ182 0.59 0.04 14.53 0.59 δ15 0.68 0.04 15.82 0.68 λ232 0.65 0.04 16.51 0.65 δ16 0.70 0.04 16.02 0.70 λ242 0.49 0.04 11.92 0.49 δ17 0.48 0.04 12.61 0.48 λ73 0.56 0.06 11.21 0.56 δ18 0.65 0.04 14.96 0.65 λ83 0.53 0.06 10.59 0.53 δ23 0.58 0.04 14.71 0.58 λ93 0.20 0.05 4.29 0.20 δ24 0.76 0.05 16.65 0.76 λ103 0.43 0.05 9.28 0.43 δ7 0.69 0.05 12.76 0.69 λ193 0.29 0.05 6.23 0.29 δ8 0.72 0.05 13.48 0.72 λ203 0.06 0.05 1.21 0.06 δ9 0.96 0.05 17.72 0.96 δ10 0.81 0.05 15.97 0.81 δ19 0.92 0.05 17.32 0.92 δ20 1.00 0.06 18.10 1.00
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Figure 3.3 CFA diagram of Teacher Support scale
Involvement
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3.3.3 Learning Engagement
This study applied “Engagement vs Disaffection with learning scale” which was developed by Wellborn (1991) and it included four subscales: Behavioral Engagement, Behavioral Disaffection, Emotional Engagement, and Emotional Disaffection. Previous studies have provided evidence for the reliability and internal consistency of this scale (Skinner & Belmont, 1993 ; Marchland & Skinner, 2007 ; Skinner, et al., 2008). Appendix E contains the full list of the original instrument.
3.3.3.1 Exploratory factor analysis of Learning Engagement scale
Behavioral engagement and emotional engagement were adopted from“Engagement vs Disaffection with learning scale.” The exploratory factor analysis of “Behavioral Engagement” and “Emotional engagement” are shown in Table 3.10.
Appendix F displays this “Learning Engagement” scale used in the present study.
The first learning engagement measurement is “Emotional Engagement”, which contained five items (item 11, item 12, item 13, item 14. and item 15),
eigenvalue of this factor was 6.17, and this factor could explain 61.70 % of the variance.
The second learning engagement measurement was “Behavioral Engagement”
which comprised five items (item 1, item 2, item 3, item 4, and item 5), eigenvalue
of this factor was 1.02, and this factor could explain 10.22 % of the variance.
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Table 3.10 Factor loadings of Learning Engagement scale
Observed variables Emotional Engagement Behavioral Engagement 01.在他（她）的課堂上，我會努力地把功課
做好 .11 .70
02.在他（她）的課堂上，我很盡力 .20 .71
03.在他（她）的課堂上，我會參與課堂討論 .28 .49
04.在他（她）的課堂上，我上課時是專心的 -.08 .97
05.在他（她）的課堂上，我認真聽講 -.09 .95
11.在他（她）的課堂上，我的感覺不錯 .76 .06
12.在他（她）的課堂上進行課程活動時，我
是有興趣的 .86 -.00
13.在他（她）的課堂上，我覺得有趣 .91 -.00
14.在他（她）的課堂上學習新東西時，我覺
得愉快 .83 .06
15.在他（她）的課堂上進行課程活動時，我
會被吸引的 .88 -.01
Eigenvalues 6.17 1.02
Percentage of variance explained 61.70 10.22
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3.3.3.2 Confirmatory Factor Analysis of Learning Engagement measurement
Confirmatory factor analysis was applied to examine the fit of the subscales and observed items. Quality of whole scale and internal quality of the scale were examined. First, quality of whole model can be screened by three sets of the fit indices including absolute fit indices, relative fit indices, and parsimonious fit indices. Second, internal quality of the scale can also be screened by item reliability, composite reliability, and average variance extracte. Third, lambda (λ) and error variance (ε) reveal the basic requirement of the scale.
First, to examine the quality of the scale, three set of the fit indices: absolute fit indices, relative fit indices, and parsimonious fit indices were proposed. The result showed that the whole model had a fair fitness (RMSEA= .099 ; GFI= .93 ; AGFI
= .89, NFI = .98, NNFI = .98, PNFI = .74, PGFI = .57 , See Table 3.11). Absolute fit indices show how covariance matrix matches among theoretical model and observed data, which include three indices AGFI (adjusted goodness of fit index), GFI (goodness of fit Index), and RMSEA (the root mean square error of approximation).
The value of AGFI and GFI above .90 represents the good fit of the model. AGFI (.89) and GFI (.93) of “Learning Engagement” scale were a little under .90, showing a fair fit of the scale. Another absolute fit index is RMSEA. The criterion of RMSEA is that the value between .08 and .10 is mediocre fit. RMSEA of this scale was .099, indicating a mediocre fit of the scale. The next indices are relative fit indices, which include NFI (normed fit index) and NNFI (non-normed fit index). They compare the increase of fitness between theoretical model and independence model. The higher value means the better fitness of the data. The value of NFI and NNFI that above .90 represents good fit of the model. NFI and NNFI of the scale were all above .90,
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showing good quality of the scale. The next indices is parsimonious fit indices, which include PNFI (parsimony normed fit index) and PGFI (parsimony goodness of fit index). They measure how the model can be estimated by the least parameters under the criteria of the model fit. The value of PNFI and PGFI higher than .50 represents an acceptable result. PNFI (.74) and PGFI (.57) of “ Learning Engagement ” were all above .50.
Table 3.11 CFA indices of Learning Engagement scale
Absolute fit dices Relative fit indices Parsimonious indices X2 df RMSEA GFI AGFI NFI NNFI PNFI PGFI 246.32 34 .099 .93 .89 .98 .98 .74 .57
Second, the indicators examining internal quality of the instruments were:
individual reliability of each observed variables, composite reliability, and average variance extracte (See Table 3.12). Individual reliability of each item displayed that most items range from .50 to .85, showing a good reliability of this scale. Second, composite reliability is calculated by factor loadings and errors variances of observed items. The composite reliability of the two factors: “Behavioral Engagement” (.91) and “Emotional Engagement” (.94) were all above .70, indicting good composing reliability of each factor. The next index is average variance extracte, which expresses the variance of latent variables that can be explained by the observed items. The average variance extracte of three latent variables were all above .60: “Behavioral Engagement” (.68) and “Emotional Engagement” (.76), showing a good reliability of the subscales.
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Table 3.12 Reliability indices and Average variance extracte of Learning Engag-ement scale
Observed variables Item reliability Composite reliability
Average variance extracte Behavioral Engagement
(η4)
Y41 0.66
Y42 0.76
Y43 0.51
Y44 0.74
Y45 0.70 0.91 0.68
Emotional Engagement (η5)
Y511 0.61
Y512 0.80
Y513 0.85
Y514 0.79
Y515 0.77 0.94 0.76
Third, lambda displays the factor loading of observed variables, all of which were all between .05 and 0.8 (λ41 to λ515). Moreover, all error variances of observed variables were all positive and significant (ε41 to ε515). Table 3.12 and Figure 3.4 depict the parameters of “Learning Engagement” scale among all items.
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Table 3.13 The parameters of CFA in Learning Engagement scale
Parameter Estimates S.E. t-value Standardized Estimates
λ414 0.81 0.03 24.80 0.81
λ424 0.87 0.03 27.61 0.87
λ434 0.72 0.03 20.68 0.72
λ444 0.86 0.03 26.98 0.86
λ454 0.84 0.03 25.94 0.84
λ5115 0.78 0.03 23.62 0.78
λ5125 0.89 0.03 29.18 0.89
λ5135 0.92 0.03 30.79 0.92
λ5145 0.89 0.03 29.02 0.89
λ5155 0.88 0.03 28.35 0.88
ε
41 0.34 0.02 15.24 0.34ε
42 0.24 0.02 13.91 0.24ε
43 0.49 0.03 16.58 0.49ε
44 0.26 0.02 13.97 0.26ε
45 0.30 0.02 14.65 0.30ε
511 0.39 0.02 16.66 0.39ε
512 0.20 0.01 14.34 0.20ε
513 0.15 0.01 12.72 0.15ε
514 0.21 0.01 14.46 0.21ε
515 0.23 0.02 14.91 0.23φ45 0.77 0.02 40.08 0.77
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Figure 3.4 CFA diagram of Learning Engagement scale
Behavioral
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Chapter Four Results
This study examined the proposed model, which included the relationship among teacher support, basic needs, and learning engagement in Taiwanese high school context. This study surveyed high school students across Taiwan.
Confirmatory factor analysis and exploratory factor analysis were conducted to examine the instruments used in this study. This chapter presented the statistical outcomes of structural equation modeling.