Values on the learning and conceptions of statistics

4.1.1 Overview

As stated in Section 1.4.1, Study One was intended to investigate pre-service EFL teachers’ views on statistics which involved values on learning and conceptions of statistics, as well as the relationships between the two factors. The first phase of the study aimed at answering the first three research questions stated in Section 1.4.1.

For the convenience, the three research questions were re-stated below. The findings from this phase of study were reported by referring to these research questions.

1. What are categories of Indonesian pre-service EFL teachers’ value on the learning of statistics?

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2. What are categories of Indonesian pre-service EFL teachers’ conceptions of statistics?

3. Is there any relationship between their values on the learning statistics and conceptions of statistics?

4.1.2 Indonesian pre-service EFL teachers’ values on learning and conceptions of statistics

The theory of task value (Eccles et al. 1983; Eccles and Wigfield, 2002) which is defined as the reasons or incentives students believe they would receive from engaging in the activity was taken as the basis in analyzing data in this study. Detailed elaboration of task value theory was discussed in the Chapter Two (Section 2.2.1.3).

The theory was considered better able to describe the ways in which students’ value on learning of statistics in this study when the task was specifically related to learning statistics.

4.1.2.1 Three components of values on learning statistics

The 38 written responses and 23 interview transcripts which were analyzed for this study shows that there are three rather than four components of values on learning statistics: intrinsic, attainment, and utility values. The cost component was not identified in my data, which might be due to the limitation of methodology used, particularly related to the proper questions proposed in interviews to probe student thinking of this component. Nonetheless, I may argue that empirically, cost was not the component that would be thought naturally by our students in expressing their value on learning statistics. Moreover, the quantitative empirical research reported in literature (e.g., Eccles & Wigfield 1995; Parsons, Adler, and Meece 1984) have also suggested that task value could be represented by the three components. Despite the different methodology used, our study could echo the findings of these studies.

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Table 4.1.1 presents the keywords used in categorizing responses into the corresponding components, and the number of responses for each component, which is also shown as a percentage of 38 students, to indicate the proportion of respondents. Brief sample quotes retrieved from interview transcripts or written responses are also provided as the illustrative features of the corresponding groups.

Table 4.1.1 Components of values on learning of statistics

Components Keywords

I feel satisfied every time I can get the correct solutions

The important thing is I can get A+

(-) Pass the course, pass the exam

9 (23.7%)

I study statistics to pass the exam

It’ll be helpful in doing my thesis research

(-) Useless, no benefit

2 (5.3%)

I haven’t seen any benefit from what I’ve learned

no evidence 2

(5.3%)

A colleague researcher and I initiated the analysis by attempting to classify each student into either positive or negative values for each component based on his/her responses for the open-ended questions and/or interview. Yet, it was found that some written responses had insufficient information about the attainment and utility components. Those students were classified into “no evidence” in the two components.

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Intrinsic values, which correspond to the enjoyment students get from learning statistics, could be identified from all students’ responses. 22 students expressed positive intrinsic value, while 10 students expressed negative intrinsic value on learning statistics. On the other hand, six students expressing both positive and negative responses, which could not be interpreted precisely as positive or negative value. For example, S5 stated his deep satisfaction in learning statistics:

“The feeling when getting correct solutions of difficult problems… it’s like the feeling when achieving a big success…”

However, in another part of the transcript, he gave another statement about his unfavorable feeling about statistics:

“…because I have to memorize those confusing formulas that mix-up of alphabetical letters and numbers.”

Similar cases also emerged from five other students, who had common characteristics of having low interest in statistics but sometimes feeling challenged and satisfied. Hence, these students were categorized as having both positive and negative values of intrinsic component.

As for attainment values, a positive value was defined as one representing students who express an ambition and set a target for obtaining a high grade or outperforming other students in learning statistics. The negative value, in contrast, represented a group of students with avoidance components of need-achievement motivation (Atkinson 1964) who set the lowest target in learning such as to pass the exam or the course. There were nine insufficient responses from this component which were classified as no evidence. In addition, two students expressed distinctive response related to attainment value were found, whom could neither be classified as positive nor negative attainment value in learning statistics. These students conveyed their view that they put more concern on understanding the materials rather than scores or competitive ambition. One of these statements was quoted below:

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“…scores will follow when we can understand (the materials), the important thing is to understand. After understanding, the chance of making mistakes will certainly be lessen… I do not target the scores.”

This expression might exhibit the views on attainment to be beyond scores, to gain mastery. Hence, the two students’ responses were assigned into the beyond attainment values component.

Utility values, on the other hand, could be determined for 36 students, two of whom could be classified easily into negative values. These two students were unaware about the usefulness of learning statistics and claimed that the course was meaningless for them and they could not see any benefit in learning it. It was also observed that most of students’ responses within the positive utility values mentioned that one of the usefulness of statistics was for doing their undergraduate research.

4.1.2.2 Relationships among components of values on learning statistics

There was another finding that emerged from the analysis of values on learning statistics—a student having a positive value in one component was not an indicator that he/she was also positive in other components. Table 4.1.2, 4.1.3 and 4.1.4 show respectively the number of students for the relationships between intrinsic and attainment, intrinsic and utility, and attainment and utility components.

As for students who had beyond positive and negative attainment value, it was noticed that they expressed positive values in both intrinsic and utility components (see Tables 4.1.2 and 4.1.3), which means that they could feel enjoyment in learning statistics and believed about the usefulness of learning the course for their future.

Table 4.1.2 shows that, approximately, 32% (12 out of 38) of the students had positive values in both intrinsic and attainment values on learning statistics. There were about 10% (4 out of 38) of the students who expressed positive intrinsic and negative attainment values on learning statistics. One of them mentioned her low confidence

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or negative ability beliefs (Eccles et al. 1983) in statistics that made her set a low target in learning statistics.

“No, I don’t target high score because I know my own ability, it seems that I’m not competent enough to get high scores in statistics, even though I like this course…”

On the contrary, about 8% (3 out of 38) of students expressed negative intrinsic and positive attainment values. This may simply explain that the students’

motive in learning was an achieving motive (Biggs 1985), with which they have high ambition for outperforming others in class whether or not they like the course. For example, one of these students stated her dislike of the statistics course in her written response.

“I don’t really like it. The materials are confusing and there are too many formulas.”

Yet, later she stated that to get the high score is her target in learning statistics.

“My target in learning this course is to obtain high scores.”

Table 4.1.2 Relationship between intrinsic and attainment components Intrinsic

Table 4.1.3 Relationship between utility and attainment components Utility

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Table 4.1.4 Relationship between intrinsic and utility components Intrinsic

Total

(+) Both (-)

Utility

(+) 21 6 7 34

(-) - - 2 2

No evidence 1 - 1 2

Total 22 6 10 38

From Table 4.1.3 it can be seen that almost half of students (17 out of 38) showed positive values in both attainment and utility components. There were 8 students expressed positive utility together with negative attainment values, which means that those students were aware about the usefulness of learning statistics, yet they did not think that it would be important to perform well on learning statistics.

It was also found that, from Table 4.1.4, out of the 34 students within the positive utility value, 7 of them were grouped into the negative intrinsic value. A sample quote from one of students within this group is as below.

“Statistics will be helpful for doing my thesis research, but I don’t really like it. It’s very difficult and confusing.”

This student admitted the benefit of learning statistics for her thesis, yet she was not fond of the course because it was difficult for her to understand the materials.

4.1.3 Indonesian pre-service EFL teachers’ conceptions of statistics

A phenomenographic method was applied in this study to qualitatively explore different conceptions of statistics among 44 (33 females and 11 males) pre-service English as foreign language (EFL) teachers. The data collection for this study is conducted in the same time to that for the value on leaning statistics (Section 4.1). A two-stage data collection was conducted via an open-ended questionnaire and a semi-structured interview. The open-ended questionnaire focused in this study included three questions:

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Q1. Did you study hard in the statistics course?

Q2. Please give your reasons.

Q3. What targets do you set to achieve when learning statistics?

Q4. If someone asks you what statistics is about, how will you explain it?

The analysis was mainly focused on students’ responses to Q4, which was intended to elicit their conceptions of statistics, while responses to Q1, Q2 and Q3, which were about attitudes toward learning statistics, were used to clarify their responses to Q4 as attitude is related to conceptions (Gal, Ginsburg, & Schau, 1997).

The data analysis conducted in this stage resulted in the initial categories of conceptions of statistics. Each student was assigned to his/her broadest conception category so that each student belonged to only one category of conception as presented in Table 4.1.5 The initial categories found in this stage are insufficient to judge the whole range of students’ conceptions of statistics as well as their distributions within each category due to the weak source of data used. Nonetheless, these categories were beneficial to get a rough idea about the variation of students’

conceptions of statistics and contributed to the second stage of data collection in the way in which the main questions for the semi-structure interview and analysed interview data were designed.

Table 4.1.5 Students’ distributions for the initial category based on written responses Category Number of students Number of Interviewees

Calculating 3 1

Calculating and graphing 5 2

Data for representing phenomena 8 5

Analyzing and interpreting data 17 10

Process of investigation 3 3

Critical thinking in investigation 8 2

Total 44 23

Based on their distribution in each category of conception in their written responses, 23 (19 females and 4 males) students were invited to take part in semi-structured interviews. Each student was interviewed individually by one of the authors

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in Bahasa Indonesia. The interviewer began each session, which lasted 30–60 minutes, by asking students to read and interpret their statements from the open-ended questions. Several questions were posed to clarify their conceptions. The interviews were audio-taped and transcribed for further analysis.

Both interview transcript and written response of each student were subsequently utilized for more comprehensive analysis. After this analysis, more comprehensive meanings of students’ conceptions of statistics were revealed which altered some initial categories. For instances, there was a student initially assigned into data for representing phenomena category as she mentioned brief sentence about statistics as a set of data and values to show phenomena. Yet, interview session later revealed her broader understanding of statistics to involve investigation processes and evaluating research results which exhibited her conception of statistics to be in process of investigation category (the final categories and their meanings are discussed in Section 4.1.2.1). Hence, it may be inferred that students’ tendency to address specific parts of their ideas in the open-ended questionnaire would not necessarily imply their unawareness of other parts. This fact echoed the different coverage of the open-ended questionnaire and interview methods in revealing students’ ideas or understandings (Harris & Brown, 2010).

4.1.3.1 Six categories of conceptions of statistics

From the analysis of students’ written responses and interview transcripts, six categories of conceptions of statistics emerged from this phase: calculating, graphing, representing, analyzing, investigating, and thinking. The categories, ranging from fragmented to more extended conceptions, might be partly hierarchical and inclusive, i.e., students in the fragmented conceptions tended to focus only on specific parts of statistics, while some students who held more extended conceptions acknowledged the conceptions in the lower categories. Further study is required to specify the

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structure of these conceptions. Table 4.1.6 summarizes the key words and descriptions of these six conceptions.

Calculating data. This conception focuses on the technical aspects of statistics.

Statistics is conceived as a method for using formulas to calculate particular values such as percentages, means, and medians. For example, students stated that:

In statistics we learn about numbers, like mean, median, modes, quartiles.

We need basic math to learn statistics. We can find solutions depending on what values are asked from the given data…like median or modes.

(S11)

Statistics is about values of data, right? The data we get about particular issues … to calculate something correctly, the certain correct values. (S12)

Calculating and graphing data. The emphasis in this conception is on calculating as well as on graphing data. Although the focus on technical aspects of statistics made this conception similar to the previous one, it was considered that this category is a broader conception because graphical representation is pervasive in data analysis.

The following two examples of conceptions describe this characteristic.

It is about a set of numbers which contain values, there are frequencies…

or mean, modes, median… how to find middle values, lower bound. There are also diagrams to display the data. (S13)

Statistics is about numbers, arrangements of numbers, to display in charts… it’s about how we display the data. (S17)

Data for representing phenomena. This conception concerns the meanings and functions of statistical data. It exhibits the qualitative shift of conceptions from the previous category to an awareness of the role of contexts in statistics. Statistics is deemed as both a technical tool to find particular values or construct graphs and a tool that can help convey information about some phenomena. Hence, data are

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understood as numbers with contexts which can be transformed to be used as a means for communicating phenomena. Yet, the transformations have been limited to using tabular and graphical representations and simple summaries of statistics, as shown in the two responses below.

Statistics is about a set of numbers on some issues, to provide a description or explanation about the issues which we want to inform people.

(S15)

It is about organizing data into graph, to show problems … to make them more visible for people. (S22)

Analyzing and interpreting data. Here statistics is conceived as an investigative process involving collecting, organizing, and analyzing data, interpreting the results, and drawing conclusions. This category may seem similar to the first two categories since they focus on applying techniques. However, an awareness of the need to connect the analysis results to data contexts makes this category different, since the awareness of this connection distinguishes statistical data analysis from merely dealing with instrumental applications. Moreover, students in this category were aware about using statistics to convey information as well as about processes used in solving statistical problems. Thus, the category of data for representing phenomena is inclusive in the category of analyzing and interpreting data. In this way, statistical data is understood as numbers with contexts that can be used not only to communicate problems but also as means of solving problems.

Statistics is about how to collect numbers about particular issues being questioned, like height of students…and we have to draw some conclusions about this height… we learn about how to analyze and organize the data …like arranging them in table…and something like that.

(S14)

… when working with problems given in statistics, sometimes we need to start by collecting data, then arranging them in diagrams or tables, finding some values to describe the problem within the data, such as mean… and we can say something to answer the problem based on the analysis results.

(S8)

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Process of investigation. This category is similar to the previous category in that it focuses on solving problems. However, there are two differences between the two categories. First, the statistical problems in this category are conceived to be beyond institutional context, including the wider world and society. Second, this category emphasizes more on the complete processes involved in investigation (Franklin &

Garfield, 2006) including finding problems and formulating research questions in addition to collecting, analyzing and interpreting data. Accordingly, statistical data is regarded as the provision of numbers with contexts and results of statistical analysis, which can be used as scientific guides in making decisions about the issues being investigated. The following statements illustrate this conception.

Statistics is about research method, a scientific way to find an issue, to collect data about it, organize and analyze them in the proper way, to be able to draw conclusions and come up with reasonable decisions based on the analysis results. (S18)

It’s a science to help us do research, to solve some issues or problems, to know what questions need to answer and then what data to collect. The results we get from here can be used to say something about the problems.

(S10)

Critical thinking in investigation. In this final category, statistics is viewed as a way of thinking, looking and interpreting phenomena in life. It is essential to base claims and decisions on valid statistical evidence and be aware of falsifying statistical results.

Thus, research results are also considered as data that can be criticized and evaluated. The following statements show the details of this conception.

Any claim or argument without data would be a lie. We can show which one is true by using statistics. So, statistics is about how to do research, to collect data, and to make someone aware that he cannot just claim anything arbitrarily. (S20)

When we get quantitative information from some sources, by using statistics, we’ll be aware that there may be something wrong… or something missing with the information, could be the improper method used or else. We can argue or criticize them. (S2)

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Table 4.1.6 Categories of Conception of Statistics from the Phenomenographic Study

Category Keywords Description

Calculating data (calculating)

Counting; using formulas Statistics is about procedures for finding particular values when given a

Counting; using formulas Statistics is about procedures for finding particular values when given a