Additional Data Analysis using Chi-s quare

This section illustrates sub-group comparisons; these are mainly built around chi-square data, sets of tables plus comments. The chi-square test is one of the most widely used non- parametric tests (Reid, 2006). The Chi-Square (χ2), as a contingency test, was used to compare the opinions of the groups where there is no control group. The c hi-square test is a “goodness of fit” test is used to compare a set of frequencies with those generated by a control group or, occasionally, and tells us how well a set of observations fits the outcome predicted by the hypothesis being tested.

In using chi-square, he number of categories may vary widely. The sue of the concept of degrees of freedom allows for this. The number of degrees of freedom is the number of

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values in the final calculation of statistics that are free to vary (e.g. Reid, 2006; Brace et al., 2000). In this case, this related to the number of categories of frequencies. It is important to state the number of degrees of freedom for any calculated chi-square value. More detail on the use of chi-square is in appendix M.

There are some limitations of chi-square test. For example, the chi-square test does not give us much information about the strength of the relationship or its substantive significance in the population (Reid, 2006). Secondly, the chi-square test is sensitive to sample size. The size of the calculated chi-square is very strongly related to the size of the sample, independent of the strength of the relationship between the variables. The sensitivity of chi-square to sample size may make a weak relationship statistically significant if the sample is large enough. Thirdly, the chi-square test is sensitive to small frequencies in one or more of the cells in the table. Frankfort-Nachmias and Leon-Guerrero (2011:350) pointed out that: "most researchers limit the use of chi-square to tables that

either (1) have no frequency values below 5 in value or (2) have no more than 20 percent of the frequency values below 5 in value”:

For example, in this study, the frequencies of responses to items were compared by gender using chi-square as a contingency test. There can be no control group in such gender comparisons. What chi-square indicates is whether men and women differ, in statistical, terms. This is express, for example: χ2= 7.56, df= 3, p= < 0.05.

Similar tests were carried out for other items in the teacher-educator and student-teacher questionnaires. In this section, I present only those chi-square results which show statistically significant chi-square values to differentiate the opinions within groups for the sake of simplicity and clarity. Each statement shows the questio n number in the same way that these were numbered in the questionnaires (Note: the questionnaires themselves are attached in Appendix A and B)

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6.4.1.1 Gende r Comparisons by Chi-s quare in Teacher-educator Data

The following table shows only those chi-square values within groups of males and females.

No Views Group SD D A S A χ2 df p

Q11(d)

I think inquiry -based pedagogy in science will benefit student-teachers who are only seeking the right answers

Male 0 3 11 1

10.6 2 p<.01 Female 0 12 9 14

Q11(e)

I think that an inquiry -based pedagogy in science should be used in initial teacher education

Male 6 5 4 0

7.8 2 p<.05

Female 3 23 9 0

Table 6.15: The frequencies of distribution by Gender

The differences between males and females are dubious in that the category numbers are so low. Overall, there is slight trend that females are less positive.

No Views Easily solved A minor Problem Serious Barrier Cannot be O vercome χ 2 df p Q14(i)

I have not been taught using an inquiry-based approach very much Male 8 3 4 0 7.1 2 p<.05 Female 6 16 10 3

Table 6.16: The frequency of distribution by Gender

Table 6.16 shows that females were more likely than males to agree with ‘I have not been taught using an inquiry-based approach very much’. All other chi-square values for males and females in relation to the remaining part of the questionnaire showed that the differences between both of the groups were non-significant. Additionally, chi-squares by gender were found in the student-teachers’ groups to be as follows:

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6.4.1.2 Comparisons on Gender in Student-teachers Data

No Views Group SD D A S A χ2 _{df p}

Q12(j)

Inquiry-based approaches will work well only with the most able student-teachers

Male 11 30 48 62

14.2 3 p<.01 Female 44 115 161 108

Q12(i)

I could never have access to enough resources to teach using an inquiry-based method

Male 7 26 64 53

17.6 3 p<.01 Female 21 119 206 83

Q12(h)

It is not possible to assess student-teachers for their abilities in inquiry-based skills

Male 9 26 77 39

22.9 3 p<.01 Female 28 159 175 67

Q10(c)

Enhances my understanding of the procedure of scientific investigation

Male 5 24 64 57

8.8 3 p<.05 Female 10 47 242 130

Q9(b)

Enables me to only seek the right solutions to science problems

Male 2 26 74 49

10.9 3 p<.05 Female 8 93 244 83

Q9(a)

Enables me to learn how to identify and ask appropriate questions Male 2 11 64 73 11.0 3 p<.05 Female 4 24 248 151 Q7(d) Welcomes my scientifically oriented questions Male 9 15 61 66 8.4 3 p<.05 Female 17 47 225 139

Table 6.17: The frequency of distribution on Gender

Table 6.17 shows that females and males generally responded with positive views. Looking at all the items in the table above, it was found that; overall, females were more likely to agree than males with the views offered to them. Table 6.15, Table 6.16 and 6.17 above shows that female group (in both teachers and students) are more likely to agree with the views than males.

6.4.1.3 Comparisons by Age groups of teacher-educators

No Views Group Not

important Of some importance Very Important Essential χ 2 df p Q12(d) Science literacy Younger 0 2 11 22 n.s 3 p<.05 Older 1 0 5 9

Table 6.18: The frequency of distribution by age groups

Table 6.18 shows that both groups, i.e. younger and older, responded with the positive views. It is appeared from their responses that overall, the junior group was more likely to take the view that inquiry is important or essential in developing science literacy.

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6.4.1.4 Comparisons of the courses taught by teacher-educators

No Views Group SD D A S A χ2 _{df p}

Q11(k)

I think that an inquiry-based pedagogy in science will encourage critical thinking

S T 1 8 17 2

13.3 3 p<.001

BT 1 2 7 11

Table 6.19: the frequency of distribution by courses taught

No Views Group Of some

importance Important Ve ry Important Essential χ 2 df p Q12(b) Abilities to carry out experiments properly S T 2 0 12 14 6.1 2 p<.05 BT 1 0 17 4 Q12(e) Understanding of the key ideas of science S T 1 0 8 19 6.6 2 p<.05 BT 1 0 14 7 BT 0 0 16 6

Table 6.20: The frequency of distribution by courses taught

Tables 6.19 and 6.20 show that BT were generally more likely to take the view that inquiry-based pedagogy is very important in building ‘abilities to carry out experiments properly’; ‘understanding of the key ideas of science’ and ‘the ability to think critically and challenge ideas’. However, the majority of teacher-educators belong to ST essentially think that inquiry is essential in achieving these outcomes offered to them.

6.4.1.5 Comparisons by Courses Studied by Student-teache rs

It appears from Tables 6.21 and 6.22 (see Appendix M) that, overall, the BT and ST groups in students hold positive views regarding inquiry-based approaches in science. Thus, BT was more likely to hold the views in each item.

6.4.1.6 Comparison by Years of Study of Student-teache rs

Table 6.22 (see Appendix M) shows that, overall, student-teachers in each year of study are positive towards inquiry-based pedagogy. It is noted that student-teachers in their 3rd year are more likely to be positive about inquiry-based pedagogy. This is because 3rd _year student-teachers have studied most of the science course and science teaching method course and tend to have more positive view about inquiry-based pedagogy.

Table 6.23 (see Appendix M) shows that 3rd year student-teachers were more likely to hold the view that insufficient time could be serious barrier or that it cannot be overcome

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in implementing inquiry than that of the 1st and 2nd year student-teachers. Second-year student-teachers are however of the view that insufficient time is a serious barrier.

6.4.2 Relationship between Inquiry and Othe r Measures Within the teacher-