Descripción y Explicación de los Resultados

In the previous chapter, data was explored using existing models either directly from the literature or shaped by regression analysis and my own interpretation of narrative sense in variables. Principal component analysis (PCA) offers the opportunity to turn this around, starting with a numerical analysis which lets the data emerge in patterns which can then be explored to see if they suggest a narrative. I therefore call these ‘components’ as distinct from the ‘variables’ in the analysis described in chapter 5 or ‘themes’ described in the narrative analysis chapters.

There are some slight differences in how phrasing is used in the literature, so here I simply use the terminology adopted by the SPSS software. PCA is a type of factor analysis, which looks for groups of items which combine to explain variance. A researcher then makes an interpretation of what these groups of items might mean (i.e. assigns a descriptive label). Rotated principal component analysis is used in SPSS to refer to particular types of factor analysis, where rotation simply refers to a set of mathematical assumptions which help interpretation by avoiding too much clustering of items. This is essentially the difference between exploratory and confirmatory PCA (or factor analysis), with rotation only really used where it gives a clear improvement over the standard solution. The results of analysis will simply be a list of components with different items weighted according to the strength of influence. Ignoring low scores (i.e. from -0.5 to 0.5) helps to uncover a coherent group, which ideally suggests a real-world explanation for the group.

The first step was to use a scree plot to determine how many useful components would be found in an exploratory PCA. This indicated four important components, although as is typical

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of exploratory PCA the first component contained too many variables to be particularly meaningful so it is usually easier to start with the other components and work backwards. For example, component 3 drew together items 4 to 8 (using feedback to plan subsequent lessons, using feedback to plan for observations, being seen to act on feedback, saving something special for observations, and using a mentor’s ideas during an observation). This suggested a narrative of using feedback for improving lessons, and perhaps also a strategic use of feedback or a sensitivity to assessment needs.

Rotated PCA helps make these kinds of interpretations by avoiding overlapping items. Following the descriptions of different types of rotation in Field (2009), oblimin rotation was chosen, the output being simplified in the table below. The rotated solution looks broadly similar to the unrotated version, but the first component now has fewer items, many of which have moved into the second component. There are now also five components which seem important compared to the four components in the unrotated analysis.

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Component

Contributing items

1 20 The main purpose of the feedback seemed to be...(i)...to improve faults in my teaching

21 The main purpose of the feedback seemed to be...(ii)...to guide me to improve generally

22 The main purpose of the feedback seemed to be...(iii)...to help me meet my own goals

23 The main purpose of the feedback seemed to be...(iv)...to make sure the pupils got good lessons

24 The main purpose of the feedback seemed to be...(v)...to make me work harder

25 The main purpose of the feedback seemed to be...(vi)...to make sure I had evidence for each QTS standard

26 The main purpose of the feedback seemed to be...(vii)...to prove that the school had met their responsibilities to the university

28 I pushed myself to make a good job of every task, whether or not I thought it was important

29 I paid careful attention to any advice or feedback I was given 30 Feedback came in time to be useful

31 Feedback matched up with observation focus criteria

32 I used the advice and feedback to...(i)...improve my practice generally 33 I used the advice and feedback to...(ii)...figure out how to get the best grade

34 I used the advice and feedback to...(iii)...figure out what they really wanted me to do

2 -1 In feedback sessions, my contributions were welcomed -2 The feedback was tailored for me as an individual learner -3 Feedback gave me clear priorities for my next observation

12 The feedback from different observations on the same placement was inconsistent

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Component

Contributing items

person who gave me feedback

16 It would not have been appropriate to question the decisions of the main person who gave me feedback

19 The main purpose of the feedback sessions seemed to be to reinforce the status of the main person who gave me feedback

-21 The main purpose of the feedback seemed to be...(ii)...to guide me to improve generally

-22 The main purpose of the feedback seemed to be...(iii)...to help me meet my own goals

-27 The grade I received was not influenced, positively or negatively, by any personal factors between me and the person who gave me the grade -30 Feedback came in time to be useful

-31 Feedback matched up with observation focus criteria

-32 I used the advice and feedback to...(i)...improve my practice generally 35 The expectations on me were far too high

3 7 I made sure that my observed lesson had something special in it

8 I make sure that my observed lesson used an idea from the main person who gave me feedback

10 I had some special activities which I saved for observed lessons

11 I tried out my observed lessons beforehand to make sure they worked 4 4 I carefully looked at my previous feedback when planning for my next

lessons

5 I carefully looked at my previous feedback when planning for my next observation

6 It was important to be seen to act on feedback

28 I pushed myself to make a good job of every task, whether or not I thought it was important

29 I paid careful attention to any advice or feedback I was given

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Component

Contributing items

5 9 My observed lessons were the same as my normal practice

13 I would have behaved the same in feedback sessions even if placements were not assessed

14 I was confident about assessing the quality of my own work

15 I trusted my own judgement more than the judgement of the main person who gave me feedback

17 I didn’t just focus on what the main person who gave me feedback wanted, I did what I felt was important

Numbers indicate item number in the survey, negative numbers indicate disagreement with that item. For example, component 2 includes a pattern of response which agrees with item 12 and disagrees with item 1.

Table 7 Contributing items to rotated PCA

Since the first two components still use over half of the available items, it is easier to look for narrative sense in the smaller components and then work backwards. As an explanation is found for each of the smaller components, those meanings can be left out of the larger components, which should help indicate the main overall sense of these two larger components.

Component 5 suggests students feeling confident in their own judgement and acting upon those judgements. When including items with loadings between 0.4 and 0.5, it also suggests a lack of concern about assessment, either because students were confident in their abilities or that they focused on something they felt was more important (e.g. their pupils’ learning). Component 4 suggests an industrious approach which has something to do with a very focussed use of feedback. It may also indicate a more professional approach, that the student sees themselves more as a teacher than as a learner. Component 3 gives a strong sense of one-off performance rather than the more general strategic approach in component 4,

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beginning to separate ideas such as performing for assessment (e.g. saving special activities, mirroring a tutor’s techniques) or performing to the general expectations of life as a teacher (e.g. consistent hard work, visibly taking on advice).

With these more defined narratives considered, component 2 can now be seen to add to the idea of managing relationships with a description of negative experiences of feedback and feedback which did not serve the student’s own interests. The rotation seems to have found a commonality between negative relationships with mentors and negative experiences of feedback, particularly feedback which has poor opportunities for dialogue.

This relationship in component 2 in turn allows a clearer narrative to come through from component 1, which can be seen to express a wide range of positive uses of feedback. Component 1 is also interesting since it suggests that positive features and uses of feedback relate, that good feedback is useful, and used, for a range of purposes rather than a particular type of feedback being more important for assessment needs or for learning needs.

6.1.1

Appropriateness of the model

It is standard practice to explain the appropriateness of any rotated solution to support the case for keeping the components. The first measure is the Kaiser-Meyer-Olkin Measure of Sampling Adequacy. This ranges from 0 to 1 with a generally accepted threshold of 0.6 to establish acceptability of a model. My rotated solution scored .888. Next, it is essential to be able to reject the null hypothesis of Bartlett's Test of Sphericity. My model had chi- sq(595)=6929, p<0.000, comfortably rejecting the null hypothesis. Communalities were all greater than 0.3, giving reassurance that all items were at least partly related to each other. Finally, the reproduced correlation matrix showed the vast majority of residuals were below

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0.5, with only 29% above this threshold. Squaring and then taking a square root of each value gave a mean of 0.0375, indicating the overall small size of the residuals. Each of these measures gives reassurance for the appropriateness of the overall model. The appropriateness of each factor is judged separately by the amount of variance it explains, as well as the visual interpretation of a scree plot as already described. Factor one explained 22.87%, factor two 10.12%, factor three 5.55%, factor four 5.1% and factor five 3.97%. This makes a stronger case for the first two factors and a reasonable case for factors three and four. Factor five has a less convincing score, suggesting that it might be worth incorporating into one of the other factors or ignoring completely. In a mixed methods design, this is not a decision to be taken purely on the percentages: each factor should also be considered in terms of the narrative sense it makes.