Study two was designed to analyze statistics text with regard to the opportunity for reading to learn statistics by developing an analytical framework and utilizing the framework to analyze and compare to versions of statistics textbooks. Consequently, this chapter is presented in two main sections: (1) framework development; (2) Textbook analysis. In the framework development, the processes and results of developing an analytical framework with regard to accessibility attributes were described, while in the textbook analysis, the processes and results of analyzing textbooks were described.
5.1 Framework development 5.1.1 Overview
As has been pointed out in Chapter Three that this study aimed to conceptualize a framework for analyzing statistics text from the perspective of reading to learn. The accessibility attributes of science texts were adapted and the features of statistics texts and readability of mathematics texts were used to conceptualize components of accessibility attributes for statistics texts. Accordingly, the research questions for this study were 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?
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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?
5.1.2 Accessibility attributes of statistics texts
In this section, I elaborate each accessibility attribute of statistics texts, together with its components, based on the five accessibility attributes of science texts by McTigue and Slough (2010). The resulted components, operational definitions and their significance are presented in Table 5.1.1.
5.1.2.1 Concreteness of text
The specialized terminologies or vocabularies used in mathematics may be abstract for some readers. Accordingly, since statistics uses so much of mathematics terminology, the categories suggested by Shuard and Rothery (1984) are considered relevant for statistics, yet there is an additional category specific for statistics content proposed by Rangecroft (2002): terms which occur in both Statistical English (SE) and Mathematical English (ME), but have a different meaning in SE from their meaning in ME. Each of these categories of terms has specific problems for readers (e.g., Kaplan, Rogness, & Fisher, 2012), even for statistical terms having comparable meanings to natural language, their meanings in mathematics or statistics are more precise (Thompson & Rubenstein, 2000). For example, while in statistics the term average is usually used to describe the process of finding the mean of a data set, in daily language it may be referred to describe what is typical and what is normal (Kaplan, Fisher, & Rogness, 2009). When facing such kind of terms, students may incorrectly associate the terms with those they have already used in daily life (Kaplan et al., 2009; Kaplan, Fisher, & Rogness, 2010; Rangecroft, 2002). Hence, the multiple
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meanings of statistical terms with relate to students’ prior understandings can be considered as a component for the attribute of concreteness of statistics text for students.
In addition, 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. Therefore, we assign the meaning extensions addressed by the authors to identify the issue of multiple meaning of statistical terms as another component under this attribute.
5.1.2.2 Voice of author
Mathematics texts often contain of the variety of purposes, such as introducing concepts, principles, or procedures, giving examples or practices, etc., which also occur in statistics texts. How these purposes are arranged in the texts when introducing a concept might affect student reading (Shuard & Rothery, 1984). Specific for statistics texts, these different purposes in the statistics text may be related to types of statistical cognitions (Garfield & Franklin, 2011) being exposed by the authors in the texts. For instance, basic knowledge is presented when introducing the term mean by providing a formula followed by showing worked example, whereas the statistical reasoning is presented when the author gives arguments why mean is more proper to be used for certain kind of problem context compared to median.
Franklin and Garfield (2006) suggested that the outcome of learning statistics should not be limited to understanding the procedural concepts without grasping the underlying ideas. The arrangements of statistical cognitions in the text is important not only for its effect on reading difficulty but also for identifying the extent to which statistics contents are provided. Therefore, we assign the approaches used by the authors in arranging the statistical cognitions when introducing a statistical term as one of the component under the attribute of voice of author.
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On the other hand, data serves as a key element in statistics, which is somewhat different from that in mathematics (Rossman et al., 2006). Most statistical terms cannot be elaborated without connecting to data. Statistics textbooks may be used a diverse perspective in presenting data in elaborating the terms. For instance, when providing a worked example for the term mean, a statistics textbook might present data as numerical numbers without contexts while focusing on the calculating technique, as numbers with meaningful contexts by elaborating and connecting the results of calculation into the context of data, and then as the numbers for evaluation by encouraging students’ thinking about the rationality/sensibility of using the mean value in such context situations. In this way, the arrangements of different perspectives of statistical data used in elaborating a statistical term may be assigned to the attribute of voice of author. It can reveal how and in what extent statistical concepts are provided in the texts. This component is essential since perspective of data associates with the reasoning (Bakker & Gravemeijer, 2004; Konold, Higgins, Russell, & Khalil, 2015) and conception of statistics (Idris & Yang, 2017).
5.1.2.3 Text coherence
The structure of concepts presented in the textbook is an essential factor for text to be coherent and, thus, more accessible (McTigue & Slough, 2010). By referring to Meyer (2003) and Shuard and Rothery (1984), we suggest that presenting the ideas related to statistical terms by organizing them in a logical structure can facilitate students’ comprehensions. The coherent of statistics texts can be analysed by identifying the similar or different ways used by the author in arranging statistical cognitions and perspectives on data across the different statistical terms elaborated in the textbooks. These two components are, therefore, assigned under the attribute of text coherent.
147 5.1.2.4 Selective use of visual
This attribute can be viewed as specific to the visual information provided in statistics text, which includes table and graphs. There are various types of visual information used in statistics textbooks, which may have different purposes. Specific for graphs used in statistics, Graham (1987) categorized four purposes of using statistical visual information: (a) describing data; (b) summarizing data; (c) comparing and contrasting;
and (d) generalizing and contrasting. All types of graphs can be assigned into those purposes. For instances, table, bar graphs, line graphs, histograms and stemplots are usually used for the first, third and fourth purposes. Boxplots are commonly used for summarizing data in addition to the third and the fourth purposes. Table, on the other hand, can be also used for organizing information before constructing graphs (Friel, Curcio, & Bright, 2001). Another purpose of using visual information in a statistics textbook is for learning graph, such as, illustrating the procedures on how to organize data. Identifying the types and purposes of visual information can reveal the match between the visual information and the intention of the text as suggested by McTigue and Slough (2010) for science text. In addition, similar to the statistical cognitions for the attribute of voice of author, identifying types and purposes of visual information used by the author in elaborating statistical terms can indicate how and to what extent the ideas related to the terms are provided in the texts. The various types of visual information used in statistics texts together with their purposes, therefore, are assigned as the two components under the attribute of selective use of visual information.
5.1.2.5 Integration of visual and verbal information
There are several topics in statistics which rely heavily on visual information. When reading statistics textbooks, a student might need to jump around and across the pages to associate text with graphs. Placing the visual and related verbal information
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close to each other within the same visual field has been recommended as a technique for reducing cognitive load for comprehending the text (Hegarty & Just, 1993; Mayer & Moreno, 2003; Shuard & Rothery, 1984). Furthermore, students may use different referencing strategies when reading texts containing visual information which influence their comprehension (Jian & Wu, 2015). Since the different sequences of verbal and visual information used in the text to presenting statistical terms might associate with different referencing strategies (Jian & Wu, 2015; Mason, Pluchino, Tornatora, & Ariasi, 2013), we consider these sequences as a component under the attribute of integrated visual and verbal.
On the other hand, referring to the multimedia learning theory (Mayer &
Moreno, 2003), integrated presentation, in which the text is placed within the graphic next to the elements it is describing, allows a reader to devote more cognitive capacity to essential processing. Specific for statistical graphs, the visual characteristics of statistical graphs, Friel et al. (2001) suggested that labels or units of measure may contribute to graph comprehension. Thus, we consider the information provided in visual information in forms of captions, labels, and data scales may also contribute reading comprehension, since it provides additional clue for the readers when looking at the visual information.
Table 5.1.1 Components underlying the accessibility attributes of statistics texts and their significance
Attribute and the
related components Operational definition Significance Text concreteness:
The unfrequently used words or the words that have been used in different meaning affect reading difficulty (Kaplan et al., 2009, 2010;
Shuard & Rothery, 1984) - Meaning extension
of statistical terms
The connections of meanings of statistical terms related to
It is helpful to make connections between students’ prior
understandings of the words and
149 Attribute and the
related components Operational definition Significance students’ prior understanding
which are addressed in the text
the specialized meaning in the text (Berenson, 1997). 2004; Idris & Yang, 2017; Konold, Higgins, Russell, & Khalil, 2015) and conception of statistics (Idris &
Yang, 2017)
The same way used to arrange concept structures throughout the books might be easier for reader to follow (Meyer, 2003); The
arrangement of variety of purposes in a mathematics text may influence reading (Shuard & Rothery, 1984)
Purpose of using graph is among the critical factors influencing graph comprehension (Friel et al., 2001);
The purpose of using graph can indicate type of knowledge presented (Garfield & Ben-Zvi, 2004)
- Purpose of visual information
The purpose of referring to the visual information in elaborating statistical terms
Integration of verbal information and visual display:
- Sequence of verbal strategies used by a reader in comprehending texts (Jian & Wu, about text (Friel et al., 2001)
150 5.1.3 Discussions
An analytical framework has been conceptualized by assigning components for the five accessibility attributes of statistics texts, which are adapted from the accessibility attributes of science text proposed by McTigue and Slough (2010). Since analyzing text accessibility requires taking the contents and the intended readers into consideration, the features of statistics were referred when assigning the components of each accessibility attribute and the intended readers should be specified prior to doing the analysis.
Using this analytical framework for analyzing statistics textbooks can reveal not only the strengths and weakness of the textbooks for particular readers to comprehend, but also to what extent the content knowledge of statistics is presented in the textbooks. This issue is addressed under the attributes of voice of author and selective use of visual information. The content knowledge of statistics involved statistical cognitions (Garfield & Franklin, 2011), perspectives of data (Bakker &
Gravemeijer, 2004; Idris & Yang, 2017; Konold, Higgins, Russell, & Khalil, 2015), and purposes of using visual information (Friel et al., 2001; Graham, 1987). Therefore, the analytical framework proposed in this study can be utilized by teachers or researchers in statistics education to compare different versions of statistics textbooks with regard to the student opportunity to learn through reading. Besides, it can contribute on statistics teaching since it can identify the features should be possessed by learning materials or textbooks for learning statistics through reading to particular students.
Although the framework in this study is specifically assigned for statistics texts, it is not restricted for further expansion in other mathematics topics. For instance, when geometry is taken as the content to be analyzed, the components for each accessibility attribute can be modified and elaborated by referring to the levels of
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geometric thinking (Van Hiele, 1986) and cognitive processes and reasoning in learning geometry (Duval, 1995, 1998).
5.2 Textbook analysis 5.2.1 Overview
This section presents the findings from analyzing textbooks conducted by applying the analytical framework of statistics text accessibility which has been developed as described in the previous section. The purpose of analyzing textbook in this study is to explore how the English and Indonesian versions of college statistics textbooks address specific topics under data distribution with regard to the components of accessibility attributes of statistics text. In particular, three main topics related to data distributions are included in this analysis: data display, numerical measurement, and shape of distribution. Before delving into the results of analysis, I will initially present the distributions of these topics in the two version of textbooks.
5.2.2 The sequence of concepts under data distribution
There are several differences between the two selected statistics textbooks with regard to the numbers and the sequences of concepts of data distribution presented.
The English textbook presents the topics under data distribution in one chapter, divided into three sub-chapters: data displays, numerical summaries, and normal distributions. In the Indonesian textbook, the topics related to distribution are separated in four different chapters. Data displays is discussed in one chapter, followed by table of frequency distribution and histograms, in which shape of distributions is also included, then measures of center, and measures of spread.
5.2.3 Presentations of text goals
Aside from the four types of text goals defined in Chapter Three (see Table 3.2.1), three additional types of text goals were found while doing the analysis. These
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additional types of text goals arose due to the different characteristics of the writing styles between college textbooks and school textbooks. By differentiating these types of text goals, it is expected that the different characteristics of textbooks could be revealed more vividly. For example, formal definitions and formulas in school textbooks might need to be presented together with their elaborations, hence they can be assigned as the explanatory text. In college textbooks, however, the definition and formula may be presented separately from the explanations. This type of text goal would not be appropriate to be assigned as explanatory text, thus, an additional type was added and named as definition and formula.
On the other hand, the college textbooks may not commonly use the exploration text before defining a concept like that in school mathematics textbooks.
This was the reason of not including the Exploratory text in the previous type of texts defined in Chapter Three. However, there was a type of text found during the analysis of textbooks in this study, that is used to clarify misconceptions of students. This type of text is presented after elaborating the concepts, which makes it different from the Exploratory text defined by Yang (2016). This type of text was then defined as Clarification text in this study.
One of the different characteristics between mathematics and statistics is types of examples. In addition to the worked examples like those in mathematics, statistics may require to show examples of problem contexts to elaborate concepts.
Although the textbooks assign this text as example, it cannot be assigned to worked examples because it is not intended to show the solution for solving problems. For this type of example, I assigned the exemplary text as another type of text goal in statistics textbooks. Table 5.2.2 shows the definitions and distribution of the six types of text (introduction text, explanatory text, illustration text, worked example, practice) in the topics under data distributions in each version of textbooks.
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Table 5.2.2 Types of text and their distributions in the two versions of textbooks
No Type of text goal English
(101)
Indonesian (148)
1
Introductory text [I] is intended to introduce something related to the focused statistical concept and is usually presented before elaborating the concept.
7.92% 12.16%
2
Definition and formula [DF] is intended to show the formal definition or formula related to the focused statistical concept.
7.92% 17.57%
3 Explanatory text [E] is intended to explain or elaborate
the focused statistical concepts. 37.62% 40.54%
4
Clarification text [C] is intended to explain and clarify the underlying ideas related to the focused concept which may lead to misconceptions.
12.87% 2.03%
5
Exemplary Text [EP] is the examples intended to illustrate or elaborate the meaning of focused concepts in contexts of problem.
7.92% 2.03%
6
Worked example [W] is the examples intended to provide the problem related to the focused concept along with its solution.
11.88% 25.68%
7 Practice [P] is intended to provide problems which
serves as practice after introducing new concepts. 13.86% 0.00%
Table 5.2.2 shows that the English version textbook provides all the seven types of text goals, while the Indonesian version textbook does not provide text intended for practice [P] within its corpus part of texts. Explanatory text [E] takes the highest percentages in both versions of textbooks, which is higher in the Indonesian version (40.54%) than in the English version (37.62%). Worked example [W] and definition and formula [D] respectively take the second and third highest analysis units in Indonesian textbook, while the Practice [P] and Clarification [C] are the second and third highest analysis units in English textbook. This data shows that, when elaborating new concepts in the topic of data distribution, Indonesian version more likely provides works examples and formal definition or formulas related to the concepts, while English version emphasizes on providing practice for students to work on after introducing new concepts and clarifying the underlying ideas of the concepts.
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To give a better description on the distribution of types of text goals, Figure 5.2.1 illustrates how these seven types of text goals are distributed within the three main topics under data distributions.
All the three topics in English version provides more analysis units in expository texts [E], in which the topic of measure takes the highest percentages (16%). This topic also has the highest percentages of analysis units for worked example [W] (6%) and definition and formula [DF] (4%). Indonesian version also provides more analysis units for expository texts [E], except for the topic of measure, in which worked example is more dominant (23%). Similar to that in English, [W] and [DF] are also the highest in the topic of measure. When analyzing the analysis units, we found that this topic in Indonesian version emphasizes on presenting procedures for counting measurements values with a very small clarification of misconceptions.
5.2.4 Presentation of accessibility attributes of statistics text 5.2.4.1 Text concreteness
The attribute of text concreteness has two focused components: the multiple meanings of statistical terms and the meaning extensions of statistical terms
The attribute of text concreteness has two focused components: the multiple meanings of statistical terms and the meaning extensions of statistical terms