Study two: Textbook Analysis - CHAPTER THREE METHODOLOGY

CHAPTER THREE METHODOLOGY

3.2 Study two: Textbook Analysis

The purpose of Study Two, as has been stated in Section 1.4.2 was to develop an analytical framework for analyzing the accessibility of statistics texts and to apply the framework for analyzing college statistics textbooks written in English and Indonesian

languages. Therefore, this study composed of two parts: development of an analytical framework and textbook analysis. The analytical framework developed in the first part was intended to assess the accessibility of statistics texts. The framework would be utilized in analyzing and comparing the accessibility attributes between two versions of statistics textbooks in the second part of the study. In doing so, a coding scheme was developed by determining operational classifications for each component under accessibility attributes for practical use. The findings from this analysis would be beneficial in designing statistics texts for Study three.

3.2.1 Development of the analytical framework

The first part of Study Two was intended to develop an analytical framework for analyzing statistics text from the perspective reading to learn. In the light of this purpose, the accessibility components of statistics text were identified by mapping to the five attributes of accessibility of science text (McTigue & Slough, 2010). The discussions about these attributes were provided in Section 2.5.1. Accordingly, the first main research question of Study Two stated in Section 1.4.2 was divided into five sub research questions as follows.

a. With respect to the attribute of text concreteness, what are the components of statistics texts which may relate to student learning through reading?

b. With respect to the attribute of voice of author, what are the components of statistics texts which may relate to student learning through reading?

c. With respect to the attribute of text coherence, what are the components of statistics texts which may relate to student learning through reading?

d. With respect to the attribute of selective use of visual, what are the components of statistics texts which may relate to student learning through reading?

e. With respect to the attribute of integrated visual and verbal, what are the components of statistics texts which may relate to student learning through reading?

3.2.1.1 Conceptualizing components for accessibility attributes

It took three phases in conceptualizing the framework: (1) adopting the accessibility attributes of science text; (2) reviewing literature in statistics education related to features of statistics texts, readability of mathematics texts, and other related texts aligned with graphs or visual information; and (3) elaborating the accessibility attributes and their key components by referring to the critical components of readability of mathematics text and the related features of statistics text found in the second phase.

Based on literature review, several components were assigned for each attribute. In the processes of selecting proper components for each attribute, discussions between researchers and experts were conducted as the validating process. After several stages of discussions and revisions, only the first two most prominent components were kept for each attribute. For example, there were three components initially assigned for the attribute of text concreteness: type of statistical terms, meaning extensions, and sample contexts. While Shuard and Rothery (1984) suggested that context can provide clue for comprehending difficult mathematics words, context in statistics has more crucial role, particularly to provide meanings in analysing and interpreting data (Rossman, Chance, & Medina, 2006). Several literatures suggested that when a concept is elaborated using meaningful and familiar sample contexts, it will be more accessible for readers to grasp the idea (Abdelbasit, 2010; Franklin & Garfield, 2006). In contrast, there were other literature suggested that familiar sample context can be a distraction for students’ understanding specific concepts, such as for correlations, in which students life experiences contribute to the formation of their beliefs which would be maintained when judging associations between variables (e.g., Alloy & Tabachnik, 1984; Wright & Murphy, 1984).

Considering the conflicting effects of sample context on learning statistics, we omitted this component from the attribute of text concreteness.

3.2.2 Textbook analysis

The intentions of conducting textbook analysis in this study was not only to provide a feasibility of the accessibility framework developed in the previous part of Study Two (see Section 3.2.1), but also to explore the characteristics of the different versions of textbooks which might contribute to the opportunity for pre-service EFL teachers learning statistics through reading. The purpose of this textbook analysis is, therefore, to investigate the different characteristics of the different versions of statistics textbooks with regard to the accessibility attributes of statistics text. The statistics topic focused for the analysis is data distribution, which is one topic included in the introductory statistics course in Indonesia. In more particular, the second main research question of Study Two stated in Section 1.4.2 was further elaborated into five sub-questions as follows.

a. With respect to the attribute of text concreteness, what are the different characteristics between the English and Indonesian textbooks?

b. With respect to the attribute of voice of author, the what are the different characteristics between the English and Indonesian textbooks?

c. With respect to the attribute of text coherence, what are the different characteristics between the English and Indonesian textbooks?

d. With respect to the attribute of selective use of visual, what are the different characteristics between the English and Indonesian textbooks?

e. With respect to the attribute of integrated visual and verbal, what are the different characteristics between the English and Indonesian textbooks?

3.2.2.1 Selecting textbooks to be analyzed

Two introductory statistics textbooks for college students were selected for the analysis, one is written in English language and the other is in Indonesian language.

The English textbook version was Introduction to the Practice of Statistics (Moore,

McCabe, & Craig, 2009), which is among the best seller textbooks in the popular bookstore websites, e.g., www.amazon.com. The Indonesian version was Metoda Statistika (Sudjana, 2002), which is also the popular textbooks in local bookstores in Indonesia and widely used by statistics lecturers in Indonesian universities. The intentions of selecting the two versions of textbooks for analysis in this study were to find the possible strengths and weakness of each version for pre-service EFL teachers learning through reading. The assumptions were that the language can be the main barrier for pre-service EFL teachers learning from the English version, but it presents statistical aspects more comprehensively. On the other hand, the Indonesian version might present the limited aspects of statistics, but the problem contexts presented can help students grasp the ideas. Therefore, finding the strength and weakness of the two versions of the textbooks can provide useful insights into the more effective ways of designing learning materials for these students to learn statistics through English language.

3.2.2.2 Determining units of analysis

The first step in using the analytical framework to analyze textbook is to determine the unit of analysis within the text. Since the focus of analysis in this study was on how the sub-topics under data distribution are addressed in the corpus part of textbooks, the types of text would be initially categorized based on text goals usually used in statistics textbooks.

In general, the texts in a textbook can be separated into three parts: (1) corpus, which is the main body of texts; (2) summary, which contains the brief review of a section or chapter; and (3) exercises, which contains the pool of exercises related to the statistical ideas within the section or chapter. Most studies on textbook analysis in statistics discussed in literature review (e.g., Cobb, 1987; Harwell, Herrick, Curtis, Mundfrom, & Gold, 1996) were grounded on analyzing all these parts of textbooks. In

this study I aimed at exploring how the sub-topics under data distributions are elaborated in the textbooks. Since such introduction is usually arranged in the corpus part, only the corpus parts related to the sub-topics were used in the analysis.

The texts within the corpus parts might be categorized into different types.

Specific to mathematics textbook, Shuard and Rothery (1984) classified five types of text usually used by authors. First, exposition of concept and methods, including explanation of vocabulary, notions and rules and also summary. Second, instructions to the reader to write, draw or do. Third, example and exercises for reader to work on, which often involve routine or non-routine problems and investigations. Fourth, peripheral writing such as introductory remarks, meta-exposition (writing about the exposition), ‘jollying the reader along’, giving clues, etc. Last, signal which includes headings, letters, numbers, boxes or logos. The classification of mathematics text based on text goal has also been proposed by Yang (2016). Seven types of text goals include: (1) to introduce something related to the object; (2) to explore the object; (3) to describe the object; (4) to explain or elaborate the object; (5) to show worked examples related to the object; (6) to provide questions for practice; and (7) to talk about the object.

Accordingly, we may notice some of these types of text goals usually used in presenting statistical ideas within the corpus part of college statistics textbooks. For instances, introducing, describing, showing examples, etc. Text types such as instructions or exploration might be considered uncommon in college statistics textbooks. Hence, by considering the types of mathematics text proposed in previous studies, I specified the types of text to suit the context of this study and the selected textbooks used. The types of texts used in this study and their operational definitions are discussed in the following.

Operational definitions. The operational definitions of the five types of texts are provided in Table 3.2.1. The five types of text goals are defined according to the goals of texts in elaborating the focused concepts.

Table 3.2.1 Operational definitions of four types of text goals Type of text goal Operational definition

Introductory Text [I]

Introductory text is intended to introduce something related to the focused statistical concept and is usually presented before elaborating the concept.

For example, describing problem contexts that would require to apply the concept, talking about the importance of the concept.

Explanatory Text [E]

Explanatory text is intended to explain, elaborate, or illustrate the focused statistical concepts.

For example, elaborating the definition of a concept of spread,

elaborating the steps to construct a graph, explaining the properties of a concept, etc.

Worked Example [W]

Worked example is used to provide the problem related to the focused concept along with its solution steps and a final solution.

For example, an example used to illustrate how calculate mean value of a data set.

Practice [P]

The practice is intended to provide problems which serves as practice after introducing new concepts.

3.2.2.3 Topics focused in the analysis

The analysis of textbooks conducted in this study aimed at showing how the topics under data distribution are presented in the text. Referring to literatures on data distribution (in section 2.2.2) and the selected college statistics textbooks mentioned in the previous section (3.2.1.2), the topics under data distributions to be analyzed in this study are presented in Table 3.2.2.

Generally, the topic of data distribution in college statistics can be divided into graphical displays and numerical summary. In more specific, graphical displays include graphs for qualitative and quantitative data, while numerical summary includes measures of center and spread. Since the purpose of graphs and summaries are two look at the distribution of data, the textbooks also include the discussions on shape of distributions. Therefore, the sub-topics under data distribution in this study

are: (1) graphs of qualitative data; (2) graphs of quantitative data; (3) measures of center; (4) measures of spread; and (5) shape of distribution.

Table 3.2.2 The topics and sub-topics for the concept of data distribution

Topic Sub-topic

Data display - Graphs for quantitative data - Graphs for qualitative data Statistical Measurement - Measures of center

- Measures of spread Shape of distribution

- Examining shape of distributions from data display - Examining data distributions from statistical

measurements 3.2.2.4 Development of a coding scheme

A coding scheme was developed by exploring related literature and referring to the statistics textbooks both in English and Indonesian versions. Operational definitions of the components and their operational classifications for each accessibility attribute were formulated for a practical analysis of statistics text accessibility.

The attribute of text concreteness

Multiple meanings of statistical terms. Statistical terms are the terms used specific to statistics. The terms can be abstract for some readers as they have been used in different meanings in daily life. There are, at least, three types of statistical terms listed in literature with regard to their meanings in natural language, i.e., (1) terms which are found only in statistics contexts; (2) terms which are shared with natural language and have comparable meanings, but the statistical meanings are more precise; (3) terms which are shared with natural language but have distinct meanings (e.g., Kaplan et al., 2009, 2010; Kaplan, Rogness, & Fisher, 2012; Lesser, Wagler, Esquinca, &

Valenzuela, 2013; Rangecroft, 2002; Thompson & Rubenstein, 2000). There are also statistical terms which are made up from more than one words, such as boxplot and standard deviation. The words can share with natural language and can have

comparable or distinct meanings. For instance, the word box in boxplot can be connected to the appearance of the boxplot. Thus, I further extend the second type of statistical terms as the terms which are made up from more than one words which are shared with natural language and have comparable meanings.

Meaning extensions of statistical terms. Berenson (1997) has suggested that it is helpful to make connections between students’ prior understandings of the terms and the specialized meaning in the text. The connections can be addressed for the terms having multiple meanings, which may relate to students’ prior understandings. Some statistical terms may have been used by students in their daily life which may have comparable or distinct meanings, such as average and mean. Sometimes, different statistical terms can be used by different textbooks to address a similar statistics concept, such as stemplot and stem and leaf plot. Some college students who read a statistics textbook may have learned a concept in a different term from another learning sources or during their high schools. Therefore, for each statistical term elaborated in the textbooks, the meaning extensions can be categorized as no meaning extension is addressed, connecting to the different term used in presenting the similar statistics concept, or connecting to the similar term used in natural language.

The attribute of voice of author

Approach to statistical terms. Referring to Garfield and Franklin (2011), three components of statistical cognitions should be addressed in elaborating statistical terms are statistical basic knowledge, statistical reasoning, and statistical thinking.

Statistical basic knowledge for presenting statistical terms may include knowledge about meanings of terms and symbols, about reading data displays, and about procedures for calculating and graphing. Statistical reasoning may include elaborating of the properties of statistical terms in specific conditions, the connections between

one statistical term to another, and interpretation of data distributions. Statistical thinking may include elaborating or encouraging thinking about producing data or thinking about evaluating and criticizing data. For instance, how the limitations of specific statistical methods can influence the analysis results for specific contexts. A textbook that uses the combinations of the three statistical cognitions would be more accessible for students to learn the statistics contents they should learn, rather than that emphasizes only on one type of statistical cognitions, such as on basic knowledge only (Cobb, 1987; Franklin & Garfield, 2006; Garfield & Franklin, 2011). The approach to statistical terms is, therefore, categorized into the three components of statistical cognitions: basic knowledge, reasoning, and thinking.

Meanings of data. Idris & Yang (2017) identified three perspectives of statistical data:

data as numerical numbers, data as numbers in problem contexts, and data as number for investigation. These categories can be also assigned as the meanings of statistical data addressed in a statistics textbook in elaborating statistical terms. For instance, a statistics textbook might address data as numerical number in a worked example for elaborating the term mean by focusing on procedures for calculations.

Data as numbers in problem contexts might be addressed by elaborating and connecting the results of calculations into the contexts of data. Lastly, data as numbers in investigation might be addressed by encouraging thinking about the rationale of using the mean value in describing data for such contexts. Hence, another way to make statistics contents more accessible for students when reading to learn statistics texts, the meanings of data addressed should not be limited to data as numerical numbers. When analyzing the analysis units, an additional category of meaning of data is added: data as numerical numbers with contexts. This category is different from the data as numerical numbers in that the contexts of data are provided.

However, it is also different from the meaning of data as numbers in problem contexts

in that the contexts of data are not connected to the interpretation of analysis results.

Therefore, four categories of meaning of data are assigned.

The attribute of text coherence

Coherence of approach to statistical cognitions. The structures used to arrange statistical cognitions in presenting focused statistical terms can include surface coherence and deep coherence. The surface coherence is related to the similar or different ways in which statistical cognitions are arranged in presenting the focused statistical terms. For example, a textbook frequently uses a specific type of statistical cognitions in the beginning or at the end of the discussions of each focused statistical term. The deep coherence, on the other hand, is related to which statistical cognitions are used in presenting concept connections. The concept connections are concerned since it is important to point out the interrelated concepts and big ideas when introducing a statistical concept (Chan, Ismail, & Sumintono, 2015; Franklin & Garfield, 2006; Garfield & Ben-Zvi, 2004). For examples, by connecting center and spread (Garfield & Ben-Zvi, 2004), considering issues about data production when using data as supporting examples, revisiting fundamental ideas (e.g., variability) whenever appropriate as well as emphasizing common elements in data analysis arising in different situations (Rossman & Chance, 2014). I consider the deep coherence to be more related to the accessibility of statistics texts than the surface coherence.

Therefore, in this study, the coherence of approach to statistical cognitions concerns only on the ways in which statistical cognitions are used in presenting concept connections. There are four possible types of statistical cognitions which can be used in providing the concept connections in an analysis unit: the combinations of two or more statistical cognitions, statistical thinking, statistical reasoning, or statistical basic knowledge. While the concept connections are categorized into connecting the focused statistical terms to big ideas in statistics, connecting to other terms in the

different sub-topics, and connecting to the different terms within the same sub-topics, or none when there is no concept connection is provided in the analysis units with the corresponding statistical cognition.

Coherence of meanings of data. Similar to that in coherence of statistical cognitions, the structure of meanings of data addressed in presenting focused statistical terms can include surface and deep coherence. Surface coherence of meanings of data is related to the ways in which meanings of data are addressed in the discussions of

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