New National Framework Mathematics 8+ Pdf

Textbooks are widely accepted as a common feature of classrooms worldwide and are important vehicles for the promotion of curricula. Consequently their content and structure are very important for the promotion of a specific vision of curriculum. There are many features of textbooks, some which go unknown to the authors, which have a significant impact on their target audience. Such features can have positive or negative impacts on learning. Textbook analysis is a means by which these features can be identified and hence the effectiveness of textbooks be established. The author in her research on mathematics textbooks has established a framework for textbook analysis based on the work of Halliday (1973), Morgan (2004), the TIMSS study (Valverde et al., (2002)) and Rivers (1990) which comprises four key elements; Content, Structure, Expectation and Language. The author is hence using her own research on mathematics textbooks to develop and highlight aspects of textbook analysis. Textbook analysis is particularly important to support educational reform and hence this chapter sets out to establish the significance of conducting textbook research and highlighting best practice in the area.

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Int. Rev. Cont. Lear. Res. 2, No. 1, 1-13 (2013) 1

E-mail: lisa.okeeffe@ul.ie

A Framework for Textbook Analysis

Lisa Okeeffe

Mathematics Learning Centre, University of Limerick, Ireland Email Address: lisa.okeeffe@ul.ie

Received: 2 Jun. 2012, Revised 6 Aug. 2012; Accepted 1 Nov. 2012

Abstract: Textbooks are widely accepted as a common feature of classrooms worldwide and are important vehicles for the

promotion of curricula. Consequently their content and structure are very important for the promotion of a specific vision of

curriculum. There are many features of textbooks, some which go unknown to the authors, which have a significant impact on their

target audience. Such features can have positive or negative impacts on learning. Textbook analysis is a means by which these

features can be identified and hence the effectiveness of textbooks be established. The author in her research on mathematics

textbooks has established a framework for textbook analysis based on the work of Halliday (1973), Morgan (2004), the TIMSS

study (Valverde et al., (2002)) and Rivers (1990) which comprises four key elements; Content, Structure, Expectation and

Language. The author is hence using her own research on mathematics textbooks to develop and highlight aspects of textbook

analysis.

Textbook analysis is particularly important to support educational reform and hence this chapter sets out to establish the

significance of conducting textbook research and highlighting best practice in the area.

Keywords: Textbook analysis, Theoretical frameworks, Textbook Language Analysis

1.1 Introduction

It is accepted worldwide that mathematics and science textbooks have a major influence on classroom

practice (Valverde et al., 2002). Textbooks are important tools for the promotion of specific types of

curricula. They are organised in a purposeful way, and consequently their content and structure are very

important for the promotion of a specific vision of a curriculum.

Over the past twenty years changes in practice and teaching methodologies have led to concerns regarding

the quality of mathematics and science textbooks. Robitaille and Travers (1992) express the view that

textbook content and how such textbooks are used impact directly on students' learning. While it is widely

accepted that the curriculum is central to influencing the choice and treatment of subject matter in

mathematics classrooms, one of the key factors in implementing this content is the textbook (Schmidt,

McKnight, Valverde, Houang, and Wiley, 1997). Many researchers (Skemp, 1982; Van Dormolen, 1986;

Pimm, 1997; Hiebert and Carpenter, 1992; Dowling, 1996; Orton, 2004) have looked specifically at some

of the key concerns with mathematics textbooks; however, few researchers have examined the textbook as

a whole with the exception of the Third International Mathematics and Science Study (TIMSS) (Valverde

et al., 2002).

The author's main focus and research to date is primarily concerned with the analysis of mathematics

textbooks. The Irish Mathematics Education system is currently in the midst of rolling out a new

mathematics curriculum entitled Project Maths. Project Maths differs greatly from the old curriculum in

terms of intention, the aim of Project Maths is to move away from didactical teaching styles and teaching

to the exam and instead focus on teaching and learning for understanding. Hence, the introduction of this

new curriculum has placed a spotlight of many features of Irish mathematics classrooms, one such feature

being the mathematics textbook. Hence the author's work on mathematics textbooks to date can inform

educators and policy makers alike on the quality of the mathematics textbooks.

International Review of Contemporary Learning Research

An International Journal

@ 2013 UOB SPC, University of Bahrain

2 Lisa Okeeffe: A F ramework for Textbook Analysis

1.2 The Role of Textbooks in Education

Textbooks are artefacts. They are a part of schooling that many stakeholders have the chance to

examine and understand (or misunderstand). In most classrooms they are the physical tools most

intimately connected to teaching and learning. Textbooks are designed to translate the abstractions of

curriculum policy into operations that teachers and students can carry out. They are intended as

mediators between the intentions of the designers of curriculum policy and the teachers that provide

instruction in classrooms. Their precise mediating role may vary according to the specifics of

different nations, educational systems and classrooms. Their great importance is constant.

(Valverde et al., 2002: 2)

According to both Ravitch (2003) and Valverde et al., (2002) textbooks are vitally important, they play a

significant role in shaping teachers', students' and families' views of school subjects. Textbooks can be

defined simply as books which are written for the purpose of teaching and/or learning. However, as noted

by Venezky (1992: 437) "from a single set of curriculum guidelines an infinite number of textbooks could

be built, each with its own interpretation of the intent of the guidelines". Textbooks are the closest thing

students have to working from the curriculum and the purpose of these textbooks is to assist with student

learning. Despite such an obvious relationship between the textbook and the student there is limited

evidence which outlines how students actually use their textbooks. In the context of education in general

and mathematics education in particular research which highlights textbook use is limited to how teachers

use their textbooks. Textbooks are a vital ingredient of successful learning. The importance of their role

can never be exaggerated. Mathematics teachers have been found to rely on textbooks for at least 90% of

their teaching time (Mikk, 2000). Such a statistic can only highlight the need for good textbooks.

The role of the textbook varies greatly from classroom to classroom and teacher to teacher, however

Gelfman, Podstrigich, and Losinskaya (2004) provide a basic outline for the intermediary role of the

textbook:

 To teach and encourage students to construct new knowledge,

 To balance detail and precision of information,

 To provide logical and consistent mathematical systems,

 To bring about new questions,

 To provide students with active, creative, many sided information.

While Sewall (1992) goes so far as to say that it is almost impossible to achieve a high level of education

without the use of textbooks. According to Valverde and Schmidt (1998) the major failing of textbooks

occurs when teachers try to cover every aspect of it, hindering or ignoring the application of suitable

methodologies for teaching and learning where necessary. Horsley and Laws (1992) claim that notion of

teachers not using textbooks effectively cannot be correct if there are good textbooks in place. The purpose

of the textbook is to help and motivate students to learn. Mikk (2000: 17) highlights the need for exciting,

imaginative textbooks; "students have many sources of information available, if their textbooks are dull,

they are unwilling to study them. Interesting and enthusiastic textbooks develop curiosity and interest in

the subject".

In conjunction with is central role in the classroom the textbook also carries the burden of the role of link

between intended and implemented curriculum. Curriculum is a central variable in TIMSS and is used to

compare national systems of education. The conceptual framework for TIMSS is based on the now well-

known tripartite model of curriculum (Robitaille et al., 1997):

 intended curriculum

 implemented curriculum

 attained curriculum.

Lisa Okeeffe: A framework for Textbook Analysis 3

Valverde et al., (2002) regard the textbook as the potentially implemented curriculum (Figure 1) forging a

direct link between intended and implemented curricula.

Figure 1: Textbooks and the Tripartite Model (Valverde et al. 2002: 13)

In Figure 1, the intended curriculum is formed by the educational system and national policy, comprising

"content standards, curriculum guides, frameworks or other such documents" (Valverde et al., 2002: 9).

The implemented curriculum is created by a combination of classroom practice and the teacher. Valverde

et al., (2002) create a powerful link between the intended and the implemented curricula in their creation of

the potentially implemented curriculum, affected primarily by the textbook. Hence, TIMSS posits and

develops a powerful link between curriculum and textbooks, which they strengthen by describing the

textbook as a 'surrogate curriculum'. This point is expanded by Venezky (cited in Robitaille et al., 1997:

50) when he points out that a single set of curriculum guidelines can spawn a myriad of textbook

representations. In this context the bi-directional link between the textbook and curriculum is a powerful

insight.

1.3 The Importance of Textbook Analysis

The practice of using textbooks is, according to Robinson (1981), as old as the practice of writing. The

word textbook appeared in the 1830's long after 'collocation' textbook (Love and Pimm, 1996). According

to Walbesser (1973) the first arithmetic textbook was written by Isaac Greenwood in 1729; `Arithmetick,

Vulgar and Decimal'. The sequencing of this textbook was as follows:

 Present a rule,

 Provide example which uses the rule,

 Exercises for students to apply the rule,

 Formal proof of the rule.

4 Lisa Okeeffe: A F ramework for Textbook Analysis

While Walbesser was referring to the situation present in the seventeen hundreds, the reality is that little

has changed. This process of "rule - example – practice is still with us today" (Walbesser, 1973: 63).

Lockhart (2002: 16) quotes Bertrand Russell when he speaks of how little change is evident in

mathematics,

"I was made learn by heart: `The square of the sum of two numbers is equal to the sum of their

squares increased by twice their product' - I had not the vaguest idea what this meant and when I

could not remember the words, my tutor threw the book at my head, which did not stimulate my

intellect in any way".

Walbesser also informs of the indifference of publishers with regard to visual appeal of the textbooks, it

was 1834 before drawings appeared in American mathematics textbooks. Walbesser noted an emphasis on

the practice of rule-example-practice in his research more than thirty years ago and despite his research

being dated little has changed with regard the process of rule-example-practice or in the development of

textbook appeal.

The educational value of a textbook is crucially important. According the Mikk, (2000: 77) "Textbook

analysis dates back to 900 AD when Talmudists counted words and ideas in texts". A textbook is

something which students will be reading on a daily basis and any messages, no matter how small or

innocent, are open for interpretation by a young impressionable mind. The process of developing, editing

and publishing of a textbook should incorporate a number of people. Mikk (2000) suggests that this

`working team' should comprise a subject specialist, a teacher, an education psychologist, an illustrator and

a text specialist in order for all considerations to be embraced. Good textbooks need to consider content,

value forming aspects, motivational elements, accessibility, illustrations, study guides etc.; they must

encourage a thirst for knowledge. Vygotsky (1956, cited in Mikk, 2000: 69) talks about the `zone of

proximal development'. He identifies the need for textbooks to direct students to such a zone, one where

there is optimal learning. Difficult tasks cause frustration and tasks which are considered too easy have

little influence on students' progress. There is a need for textbooks to encourage students to work in this

zone. Research can help ensure textbooks are focused on reaching such a goal.

In the Cockroft Report (Cockroft, 1982), there is reference to the increase in popularity of a `Problem

Solving' approach in the early 1980's, however, Cockroft notes that despite the change in curriculum focus

and the obvious acceptance of this approach, textbooks never followed suit and as such the textbooks were

one of the main factors contributing to its failure in that they failed to adapt accordingly. Since the

Cockroft Report many curriculum initiatives have applied a problem solving approach or an adapted

problem solving approach. One such initiative is currently underway in Ireland at present. Project Maths, a

new mathematics curriculum which was implemented nationwide in September 2010, incorporates many

of the ideals of the problem solving approach such as focusing on problem solving strategies more so than

emphasising the memorisation of rules and procedures. In a recent report conducted by O'Keeffe and

O'Donoghue (2011b) they noted that historically, mathematics teaching and classrooms in Ireland have

been strongly influenced by commercially produced school textbooks that have promoted a view of

mathematics concerned mainly with skills and instrumental learning (NCCA, 2005). This view of

mathematics curriculum is not compatible with the new curriculum initiative Project Maths. Hence,

mathematics textbook analysis is essential to ascertain the view of mathematics that is portrayed by the

newly designed mathematics textbooks. If such didactical emphases dominate through the new generation

of mathematics textbooks then the success of Project Maths is likely to be severely compromised. Hence

textbook analysis can support the development and success of evolving curricula and new teaching and

learning initiatives.

1.4 The TIMSS Study – Mathematics and Science Textbook Analysis

The Third International Mathematics and Science Study (1995) (TIMSS) provides the foundation for much

research on mathematics and science textbook analysis. TIMSS devised a common framework to compare

Lisa Okeeffe: A framework for Textbook Analysis 5

systems of education through analyses of curricula, related documents and artefacts. They are known as

curriculum frameworks. Each framework is characterised by the same three elements that are further sub-

divided (Robitaille et al., 1997):

 subject matter content

 performance expectations

 perspectives or context.

These frameworks are applied to the curriculum or any piece of the curriculum that is seen as promoting

the intended, implemented or attained curriculum and includes artefacts such as textbooks, curriculum

guides, standards documents etc. TIMSS employs two separate frameworks viz. the curriculum framework

for mathematics, and curriculum framework for science. The TIMSS model was formulated to deal with

evolving curricula.

1.5 Initial development of a framework for Mathematics Textbook Analysis

In much of her own work on mathematics textbook analysis the author looks to the Third International

Mathematics and Science Study (1995) (TIMSS) for its theoretical underpinnings. The mathematics

framework is a tool for studying curriculum or any piece of curriculum or artefact. Indeed the view

supported by TIMSS is that 'A textbook is a surrogate curriculum…' (Robitaille et al., 1997: 50). Hence,

in her study the author adapted the TIMSS framework for mathematics curriculum analysis for use as a

tool for mathematics textbook analysis (O'Keeffe, 2011a).

Thus we start with the TIMSS framework for mathematics curriculum analysis as a tool for textbook

analysis. It has three dimensions:

 Structure

 Performance expectations

 Perspectives.

Subsequently, the mathematics framework was adapted and refined for use in TIMSS as an instrument for

mathematics textbook analysis per se.

Hence, the TIMSS mathematics curriculum framework as it evolved is adapted and further refined as

outlined below for the author's own research. The 'perspectives' dimension captures student data and is

not used in the author's textbook analysis study. In any case it was not envisaged that all three dimensions

would be applied to every piece of curriculum. The structure dimension encompasses issues concerning

content and the structure of knowledge and information in the textbook and the make-up of the textbook.

This line of reasoning led to an analytical tool with two dimensions and three elements as follows:

 Structure

 Structure

 Content

 Expectation.

Further refinements were added to this TIMSS instrument by O'Keeffe (2011a) in order to allow for a

finer-grained analysis. Refinements based on the work of River's (1990) and Mikk (2000) that reinforce

and add to the TIMSS model around content and expectation and structure analysis respectively, are

included here. The initial evolved model comprises three key elements (Figure 2).

Figure 2: Initial Development of the framework for Mathematics Textbook Analysis (O'Keeffe, 2011b)

6 Lisa Okeeffe: A F ramework for Textbook Analysis

1.5.1 Structure Analysis

Textbook structure adds to or takes from textbook comprehension suggesting that succession and

connections between text elements need to be analysed carefully. Halliday and Hasan (1993 cited in Mikk,

2000: 94) broke text cohesion/structure down into 5 parts; reference (pronominal, comparatives, articles),

substitution (nominal, clausal, etc.), ellipsis (nominal, verbal, etc.), conjunction (additive, temporal etc.),

lexical (same item, general item, etc.). Mikk (2000: 99) illustrates by way of a matrix table how one can

easily analyse the structure of a text and record diagrammatically how frequent ideas/topics appear and

therefore connections are visualised. In order for a structure to impact positively there are a number of key

issues which need to be incorporated. These were analysed in the TIMSS report as `Physical Scale'. While

the structure of the knowledge within a textbook is vital the physical structure will determine whether the

intended audience will even consider the text. It includes many aspects such as those outlined by Valverde

et al. (2002); Area and framing, Elements (pictorial, verbal, design), Colour and Non colour, Information

levels, Unification and Separation.

1.5.2 Content Analysis

Textbook content influences the selections and emphases applied by teachers and students, consequently

impacting on learning outcomes (Mulryan, 1984). Rivers (1990) discusses four aspects of content analysis

which are similar to those outlined by Gerbner (1969). She created four subheadings in the area of content

analysis:

 Motivational factors - which includes historical notes, scientist and mathematician biographies,

career information, applications and photographs,

 Comprehension cues - focuses on colour and graphics,

 Technical Aids - includes all material related to calculators and computers,

 Philosophical Position - emphasis and predominant philosophy.

These subheadings are easily identified for analysis and their role in effective teaching is transparent.

Wittlin (1978), whose work on museum exhibits was connected with science textbook analysis by

Robinson (1981), insists that the very first objective of any textbook must be to attract student attention.

Then the focus switches to presenting the message clearly and comprehensibly, and finally maintaining

attention (Robinson, 1981). The following table outlines Wittlin's recommendations, which need to be

considered in content analysis especially with regard to motivational factors. According to Wittlin (1978)

one must first attract attention (Initial Arousal), then present a clear and concise message (Attending

Message reception) and finally maintain attention (Maintenance of Attention).

Table 1: Factors to Consider for Textbook Analysis, Wittlin (1978)

Attending Message Reception

To Avoid the Danger:

Relevance, Interest,

Dissonance, Sensory,

Appeal, Appeal to effect

To Avoid the Danger:

White Space, Signal Noise,

Planned Redundancy,

Integration of multiple channels,

Hierarchal organisation under key

areas

To Avoid the Danger:

Change modality,

Insert questions ,

Vary senses used,

Drama of Issues

Lisa Okeeffe: A framework for Textbook Analysis 7

1.5.3 Expectation Analysis

Expectation is the third element of the TIMSS framework for textbook analysis. Performance expectations

are embedded throughout textbooks and will impact significantly on how students choose to deal with the

topics presented. For example if the focus of a mathematics textbook is on repetition and practice then a

student will subconsciously look to replicate a previous method as soon as he/she encounters a question,

without attempting to use any problem solving skills. The most basic consideration of expectation is that

students and teachers alike will read and understand the material presented (Valverde et al., 2002). The

TIMSS Report (Valverde et al., 2002) identified expectation as crucial to textbook analysis and identified

19 different expectations that can be placed on students throughout textbook chapters. The Rivers Matrix

(Rivers, 1990) also contains an expectation component. It looks to examine the presence of emphases and

philosophies throughout textbooks. Both the emphasis and philosophy put forward by a textbook have a

direct bearing on student expectations.

1.6 A framework for Mathematics Textbook Analysis

The author extends and develops her framework for mathematics textbooks analysis (identified in Figure

2) by applying an analytical tool adapted from the language analysis of written texts (student's own written

texts), functional grammar analysis (Morgan, 2004). The language analysis tool enables the researcher to

develop an overall view of the textbook in terms of student learning while also allowing for a better

understanding of the difficulty of the mathematical language as encountered by students using textbooks.

1.6.1 Language

Students should be able to communicate mathematics, both `verbally and in written form' (NCTM, 1989).

However, it seems that students are expected to acquire this communicative ability by osmosis. That is,

they must acquire it themselves from textbooks or notes. Also, much of the notation and symbols used in

these textbooks may not be conducive to learning. Mulryan (1984) describes primary textbooks as having

an excessive vocabulary load, variability of word meaning, insufficient repetition of mathematical terms

and inadequate vocabulary control. How to use mathematical language is not something that is taught in

Irish mathematics education, yet the significance of the language of mathematics to learning is

acknowledged. When analysing mathematical textbook language Newall (1990) found a number of

features in textbook language such as discourse type (narration, description etc.), coordinators (connectors

between sentences) and semantic structures. These features can provide a basis to inform textbook analysis

of mathematical language. Mulryan (1984) provides three subheadings for language, analysis; word

signifiers, notational signs and graphical signs. These areas can be analysed, with consideration of Newall's

language features, under the following headings:

 Word signifiers:

o General vocabulary: word signs used regularly in daily life e.g. and, from.

o Mathematical terms: term with specific mathematical meaning, there are two types

technical or special.

o Technical vocabulary: word signs peculiar to math e.g. Heptagon, multiple.

o Special vocabulary: word signs used in daily life which have different mathematical

meaning e.g. match, set, group or figure.

o Abbreviations: shortened or abbreviated technical words such as cm, km, HCF etc.

o Letters: alphabetical letters which represent numbers, lines.

 Notational signs:

o Notation signs: Hindu- Arabic number systems or signs such as >.

 Graphical signs:

o Pictorial/diagrams symbols: pictures/graphs which demonstrate mathematical principles.

8 Lisa Okeeffe: A F ramework for Textbook Analysis

The most significant feature of language is of course the words used. In a study carried out by Marks et al.

(1974), they replaced 15% of the words in a text with more commonly used words and presented the text

to 600 6th grade students. They found that comprehension was increased from 47% to 73%. Word length

also has a significant impact on student learning, the longer the word the more information there is

contained in it, making it more difficult to fully understand. Mathematical terms need to be explained, and

their meanings need to be understood by the reader. The development of thinking can be divided into three

stages, active, figurative and abstract. This would suggest that when learning/teaching the focus should be

on being actively involved and engaged in ideas and where possible physical objects. The visual centre in

our brains is approximately thirty times bigger than the audio centre hence it is often easier to understand

something which is visual.

Sentence complexity is known as syntactic complicacy and involves sentences and paragraphs. To

comprehend a sentence one must first remember it, long sentences cannot be remembered easily thus

making them complicated. Luria (1975) analysed sentence complexity and found that the following causes

confusion; inversion (a later event being mentioned before earlier one for example if a textbook mentions

simultaneous equations with three unknowns before simultaneous with two unknowns), multi-meaningful

phrases, subordinate connections, distant constructions, triplet comparisons and double negation. A study

carried out by Glynn and Britton (1986) focused on analysing frequency of words, sentence length, study

aims, emphasising headings, questions for actualising and prior knowledge. They found that all of the

above played a vital role in students' ability to acquire the knowledge, their time spent reading the text and

the mental effort it took for them to do so. Another study carried out by Klare (1963) found that suitable

readability levels proved to increase effectiveness of text in over 68% of cases they investigated.

1.6.2 Readability

The term readability refers to a number of factors which influence the reader, including interest and

motivation, legibility of the print, complexity of the words and sentences in relation to the ability of the

reader. Interest and motivation are especially significant for a textbook. John Holt, quoted by Mann (1981)

defines a textbook as "a book that no-one would read unless they had to". This idea is reinforced by Wiest

(2003) who highlights the significance of reader interest to readability levels of a textbook, the more

interest the book can evoke from the reader the deeper the level of comprehension and understanding

attained. Wiest also talks about including novel or demanding stimuli in favour of simple stimuli since

engaging students in fantasy demands higher comprehension levels. Davy 1987 (cited in Mikk, 2000: 79)

noted that textbooks with familiar words are easier to understand. Mikk (2000: 79) used an electro-

oculograph to fix the eye movements of students while reading a passage and found that they spent more

`time and fixations' on unfamiliar words. Word frequency assessment (Cloze Test) is the most common

method for assessing familiarity of words. This can then create a frequency dictionary, for the students in

the subject area, to create a list of commonly used words. Wiio (1968, cited by Mikk (2000: 81)) devised a

modification ratio which can be used as an indication of text complicacy. Many formulae such as this have

been created and modified over the years, and it is recommended that to ensure an accurate result more

than one formula should be applied to your text.

There are many varieties and adaptations of readability formulae, the most commonly used formulae are

the Flesch Reading Ease and Flesch - Kincaid Grade level (TxReadability, 1998).

Flesch Reading Ease

 The Flesch Reading Ease gives an output from 1 - 100. The higher the output the easier a text is to

read.

 The Flesch Reading Ease Formula = 206.835 - (1.015 _ ASL) - (84.6 _ ASW).

o Where ASL is the average sentence length, i.e. the number of words in the whole text

divided by the number of sentences.

o ASW is the average number of syllables per word, i.e. the syllable count for the whole text

divided by the word count for whole text.

Lisa Okeeffe: A framework for Textbook Analysis 9

Flesch - Kincaid Grade level

 The Flesch -Kincaid Grade level gives a grade readability result. The output value will indicate

which grade level the text is most suitable for.

 The Flesch -Kincaid Grade Formula = (0.39 _ ASL) + (11.8 _ ASW) - 15.59.

o Where ASL is the average sentence length, i.e. the number of words in the whole text

divided by the number of sentences.

o ASW is the average number of syllables per word, i.e. the syllable count for the whole text

divided by the word count for whole text.

However, these readability tests are designed to analyse English-language paragraphs. Much mathematics

research, which involves readability measurement, uses the above tests as a basis of comparison of

readability levels but none of these readability tests can effectively and accurately measure the actual

readability of a mathematical text. Mathematical texts as previously stated combine ordinary English with

mathematical English and symbols (Taylor and Hargreaves, 1999). This varied information embedded in

mathematical text is unlikely, according to Thomas (1997), to ever be fully understood by such English-

language based readability tests. This raises the issue for a need to create a mathematically focused test for

readability. Many studies have indicated the obvious lack of correlation between standard readability

scores, problem solving performance and comprehension (Paul, Nibbelink, and Hiiver, 1986; Hembree,

1992; Wiest, 1967). Despite the direct connection between readability and problem solving (a highly

topical element in many countries including Ireland), "research in reading and mat hematics continues to

attract little attention" (Thomas, 1997: 39).

1.6.3 A framework for Mathematics Textbook Analysis

Researchers have identified that mathematics is a complicated, diverse but unique language. Bullock

(1994) reinforced the significance of this language when highlighting the fact that Newton had to invent

calculus in order to develop and express his ideas and in 1987 Pimm compared the learning of mathematics

to the learning of a foreign language. Language analysis and its significance has been widely researched

for a number of years and has formed a significant part of mathematical research from the early 1990's,

with, for example, the work of Halliday (1973); Skemp (1982); Van Dormolen (1986); Pimm (1987);

Noonan (1990); Chapman (1993); Dowling (1996); Mikk (2000); Morgan (2004); Orton (2004), with

Mikk and Morgan focusing particularly on the role of language in mathematics texts or textbooks. For the

purpose of mathematics textbook analysis the author draws primarily upon the work of Halliday (1973)

and Morgan (2004). Halliday's research provides the basis for much language analysis in many different

subject areas, focusing on the functional aspects of language. He outlines this functional aspect as the way

in which language is used, the purpose that it serves and the way in which a reader can achieve these

purposes. One of the reasons Halliday outlines for following this line of investigation is to \establish

general principles relating to the use of language". For this reason Halliday's functional grammar analysis

is applicable to this study, as the author is seeking to not only analyse the language present in mathematical

text but also to research the overall effectiveness of the language for teaching and learning. Halliday's

functional grammar analysis is based on three elements:

 Ideational Function,

 Interpersonal Function,

 Textual Function.

Halliday developed his functional grammar analysis for language in general and the language of

mathematics never featured as a standalone unit within his work. However, in 2004 Morgan applied this

functional grammar analysis to mathematics texts. Morgan (2004) applied Halliday's functional grammar

analysis framework to students' own written mathematical texts. She describes how the ideational function

can look specifically at the mathematics and the mathematical activities presented while the interpersonal

function highlights sources of concern in the mathematics language such as the use of the word "we"

10 Lisa Okeeffe: A F ramework for Textbook Analysis

(identified by Pimm (1987). as a cause for concern). The textual function identifies the formation of

argument in a mathematical text and any message portrayed via reports, descriptions or narratives.

Morgan's framework (2004) for mathematics language analysis can be applied effectively to any

mathematical text. The framework originated with the work of Halliday (1973) and is not mathematically

specific, however, Morgan herself used this framework for analysing students' own mathematical writings

and now the author has applied it to school mathematics textbooks. Morgan's framework, while applied in

its entirety, differs from the analysis in this study with regards to the interpretation element. The function

of the language analysis tool is to work in conjunction with the other elements of textbook analysis to

provide an overall view of the impact of the mathematics textbook on student learning. Thus providing a

framework for Mathematics Textbook Analysis with four key elements (the theoretical underpinnings of

which are provided in Table 2);

 Structure,

 Content,

 Expectation,

 Language.

Table 2: Theoretical Frameworks Supporting Mathematics Textbook Analysis

TIMSS

(Valverde et al., 2002)

Provides overall structure for

textbook analysis

Significant to three key

elements:

1. Content Analysis

2. Structure Analysis

3. Expectation Analysis

Reinforces the TIMSS

framework and adds new

dimension

Significant to two key

elements:

1. Content Analysis

2. Expectation Analysis

Reinforces the TIMSS

framework and adds new

dimension

Significant to one key

elements:

1. Structure Analysis

Strengthens textbook

analysis by providing a

fourth element for analysis

Significant to one key

elements:

2. Language Analysis

TIMSS (2002)

The most well-known, international textbook study was conducted by TIMSS and reported by Valverde et

al. (2002). TIMSS involved an in-depth analysis of 630 mathematics and science textbooks. The TIMSS

analysis comprised of three key elements; Content, Structure and Expectation. In order to effectively and

systematically complete research on mathematics textbook analysis the TIMSS method of both analysis

and presentation provides many insights.

Rivers (1990)

In 1990 Janelle Rivers undertook a two-part analysis of first year algebra textbooks in South Carolina.

Phase 1 of her study focused on a comparison of five textbooks, and in-depth analysis of the:

 Motivational Factors,

 Comprehension Cues,

 Technical Aids,

 Philosophical Orientation.

Lisa Okeeffe: A framework for Textbook Analysis 11

She also looked at the cost and sales figures for each textbook. Part 2 of her study was based on the

changes made to each textbook based on the NCTM 1 standards. Part 1 of the Rivers study is directly

applicable to this research study with the first three of the Rivers elements (listed above) overlapping and

reinforcing the data analysis and collection of the TIMSS content analysis. The fourth and final element

supports the TIMSS expectation analysis.

Mikk (2000)

Mikk (2000) encompasses many issues and concerns of mathematics textbook analysis related to the use,

evaluation and analysis of textbooks. In his research Mikk illustrates by way of a matrix table how one can

easily analyse the structure of a text and record diagrammatically how frequent ideas/topics appear and

there- fore connections are visualised (Appendix D) (Mikk, 2000: 99). This method of structure analysis is

combined with that of TIMSS to strengthen the data collection for structure analysis.

Morgan (2004)

Having spent a number of years as a mathematics teacher Morgan completed her PhD in 1995 which

focused on the analysis of discourse of written mathematical reports. Following on from here Morgan has

continued her research in the area of language and mathematics. One of the key areas emerging from

Morgan's work is the analysis of written mathematical text; however she focuses on student's own

mathematical writings. Her work is primarily based on Halliday's functional grammar analysis. This

framework, created by Halliday (1973) which was applied to mathematics by Morgan (2004), is utilised in

this research study to analyse the language of the mathematics textbooks.

1.7 Conclusion

It is likely that the central role of textbooks in the classroom will continue despite the emphasis on e-

learning and e-learning objects and curriculum initiates such as that underway in Ireland at present. While

the 'textbook' as we know it may change, the pedagogical considerations of the 'text material' will still

focus on enhancing and supporting teaching and learning and hence the core values of the traditional

textbook will remain important. Studies such as TIMSS have demonstrated the practical importance of

curriculum materials, namely the textbook, in mathematics and science teaching and learning. Mathematics

teaching and learning are both impacted by the quality of the mathematics textbooks that are available.

Therefore research in the area of mathematics textbook analysis is worthy of consideration.

The TIMSS model for curriculum analysis provides much of the theoretical underpinnings required to

effectively analyse mathematics and science textbooks. However, it is important to note that while the

TIMSS framework does provide a robust model for mathematics and science textbook analysis which

allow for evolving curricula ensuring its applicability into the future, it is not without shortcomings. The

author's research (O'Keeffe, 2011a) has identified some areas for inclusion such as analysis of textbook

language. The language of mathematics is an essential part of mathematics and how it is presented and

developed within mathematics textbook can impact on student learning. Hence, it stands to reason that a

framework for textbook analysis should consider the overall impact of the language in the textbook. The

framework for mathematics textbook analysis as presented by the author is built on the TIMSS model but

provides a further adaption which contributes to improving the analysis of the textbook as a 'whole'. The

author's framework for mathematics textbook analysis comprises of four key areas; Content, Structure,

Expectation and Language each of which emerged from the literature as contributing to the overall

effectiveness of a textbook.

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... According to Ivić et al (2013), improving the quality of textbooks is a crucial and meaningful factor to improve the quality of education in general; "particularly in developing countries, there is no single factor in improvement in the quality of education which is comparable with textbooks in terms of its impacts". Okeeffe (2013) pointed out that a good textbook must encourage the thirst for knowledge, consist of valuable contents and creativity-inspired aspects, motivational factors, accessibility, illustrations, learning guides. Textbook analysis is practical and meaningful in assessing the quality of textbooks as well as gaining a more general view of the role, the primary content of the textbook, the meaning and value that textbooks offer. ...

In the context of Educational Revolution 4.0, text mining with digital tools plays an important role. Various techniques and softwares have been employed in text mining, among which the clustering technique using Atlas.ti, a German software, is widely used thanks to its versatility and open access. This article presents the results of clustering Mathematical terms in Algebra textbook in Vietnamese high schools with the support of Atlas.ti. Initial research results can yield the insight into the relationship among Mathematical terms in the curriculum, thereby, aiming for a better teaching process.

Tuan Anh Bui
Ho Thi Diem Chinh
Chi Hong Nguyen
Linh Yen Nguyen

... In comparison to other materials, textbooks are considered as the most important source of knowledge and the most organized tool for achieving the goals of a specific foreign language curriculum. O'Keeffe thinks that textbooks can help in establishing teachers' and students' views on subject (O'Keefe, 2013). In addition, they are the only constant which has been continuously adapted to suit the challenges of learning any subject, especially foreign languages. ...

Nuriah Fadliah Husain
Muhammad Zuhri Dj
Musfirah Musfirah

This research studied an EFL textbook entitled "Be smart in English for grade X of Senior High School Linguistics and Cultural Studies" to find out two things within it. Those are the types of culture and cultural meaning represented through its texts and images within the EFL textbook. To determine the types of culture, the researcher uses categorization proposed by Cortazzi and Jin while to reveal the cultural meaning, the researcher uses Pierce's semiotic principal. The researcher conducts a descriptive qualitative research specifically library research because the researcher got the main data from the document review. In addition, semiotic analysis is used in this research to have a complexity analyzing of the cultural sign. The result of this study shows an imbalance portion of cultural content appearance. The percentage shows in four types of cultures that there are 25 of source culture appearance (21%), 15 times of target culture appearance (13%), 10 times of International culture appearance (8%), and neutral culture appeared as much 69 times (58%). Then, cultural content that has been analyzed using semiotic analysis presented the cultural content appeared majority from image as much 73 times (61%) and texts as much 46 times (39%).

David G. Levasseur
Elizabeth Remland
Martin S. Munz

Speech delivery pedagogy has both changed dramatically over the last several centuries and remained remarkably fixed over the last 100 years. In the early 1900s, this pedagogy underwent a dramatic shift from an "elocutionist approach" to a "natural approach" to speech delivery. Since that time, speech delivery pedagogy has remained in an essentially petrified state while our understanding of nonverbal behaviors – the very behaviors at the heart of speech delivery – has grown exponentially. In this essay, we draw upon the expansive nonverbal communication literature to argue for a new approach to teaching speech delivery – an approach we refer to as the interconnected approach. This interconnected approach re-emphasizes the importance of speech delivery, structures the topic of speech delivery around coherent nonverbal clusters, and acknowledges the unnatural pathway to developing a natural speech delivery.

Alfonso Segundo Gómez Mulett

En este trabajo se analizó el papel desempeñado en la implementación de la matemática moderna en Colombia por la serie Matemática Moderna Estructurada, la de mayor aceptación por los profesores del nivel de bachillerato colombiano, a partir de la reforma curricular de 1976. El estudio siguió una metodología cualitativa de tipo documental y descriptivo, basada en el análisis de contenido. Se concluyó que los textos de la serie satisficieron los requerimientos curriculares del momento en que fue utilizada, pero su implementación causó problemas en el aprendizaje de la matemática moderna, porque sus conceptos no se acoplaron adecuadamente con la llamada matemática clásica.

Joaquim Guerra

Textbooks are a resource that is widely used in language classes. For this reason, they are also one of the principal topics in research on the field of didactics. Several studies were conducted about Portuguese as mother tongue textbooks, but there is a lack of researches and information concerning the textbooks of Portuguese as a foreign language. In this study, the researcher analyses the discourse of the authors/editors in the 'opening texts' of textbooks for (European) Portuguese as a foreign language, for levels A1 and A2 of the Common European Framework of Reference. The study shows that writing competence is relatively neglected by the authors, and infers that might reflect the way that teaching and learning activities for writing are put into practice. Further research will allow to verify if there are indeed activities for learning to write and how they were thought out and organised. Keywords: Language teaching, writing competencies, Portuguese, foreign language, textbooks, writing competencies.

This study aimed to evaluate the "Active Skills for Reading" through a checklist, and an interview. This book was being used at Chabahar Maritime University as a general coursebook for BA students. For this purpose, 84 students and 4 teachers were selected. After data collecting, the quantitative data were analyzed by SPSS version 26. The findings revealed that the appearance and content of the book was attractive and up-to-date. Generally, it indicated that the textbook had met students' needs, and it could be a good book in the hand of a good teacher.

The textbook is considered to be the main medium of language learning and the main tool for differentiation in classrooms with language and cultural diversity. The number of such heterogeneous classrooms has significantly increased during the last decades in Russian primary schools due to the growth in the population of migrant children in Russia (mostly from the former Central Asian republics of the USSR). Given this fact, it seems important to review and refine requirements for modern textbooks, which are intended to be a relevant tool for developing language proficiency and literacy of migrant children. Therefore, language experts and teachers need a revised model for objective language textbook evaluation that addresses current educational challenges. This paper presents a new framework for evaluation of educational content based on a conception of the 'textbook as a corpus'. With qualitative and quantitative methods, this framework assesses such features as textbook language, cultural aspects of its content and illustrative material contained within a textbook. For this purpose, a Text-Image Russian Textbooks Corpus (TIRTEC) for primary school children with different language proficiency in Russian (first, heritage, additional, non-native, second, foreign) has been created and annotated. All Russian language coursebooks can be divided into three types: for L1 (students with Russian as a first language), FL (students studying Russian as a foreign language out of Russian community) and L2 (students studying Russian as a second, third, etc. language within Russian environment). In this paper, we focus on a detailed analysis of Russian textbooks for migrant children, who learn Russian in Russia. The textbook series selected were evaluated with such parameters as text diversity, vocabulary input, readability, and visual and cultural (including pragmatic) aspects. By analyzing data collected from these books according to the selected criteria assessed by corpus linguistic methods, one can show the level of complexity and comprehensibility of the educational materials, reveal the methodological design of the textbook, and determine the congruence with the educational needs of the multicultural young language learners.

The aim of this paper is to evaluate the quality of environmental visualization of selected regions in Czech geography textbooks for primary and lower secondary schools. The method of quantitative content analysis of visuals was used. The categories of quantitative analysis were defined based on the content of the environmental and geographical curriculum, for example landscape type, emotional charge etc. The results show a relatively similar structure of environmental visualization between textbooks: emotionally positive visuals showing the protection of cultural-historical heritage and protection of nature dominate. The exception is the Moravskoslezský kraj, which is visually presented in a negative way compared to other regions. In textbooks there are a minimum of abstract visuals or visuals showing the tendencies of environmental components.

Maximus Tamur

In global competition, Indonesian learners have not shown the intended achievement. PISA research reveals the lower mathematical literacy level of Indonesian learners. The Learners' difficulty in mathematics is likely due to text-oriented learning and abstract object of mathematical analysis. This article particularly attempts to address the implementation of mathematic software toward the enhancement of learners' ability of mathematical literacy. Based on the discussion, it can be concluded that mathematic software-based learning can be applied to enhance learners' ability of mathematical literacy related to the exploration of a concept, reasoning, systematic-logic and analytical thinking as well as learning interest on mathematics

James Hiebert
Thomas P. Carpenter

the goal of many research and implementation efforts in mathematics education has been to promote learning with understanding / drawing from old and new work in the psychology of learning, we present a framework for examining issues of understanding / the questions of interest are those related to learning with understanding and teaching with understanding / what can be learned from students' efforts to understand that might inform researchers' efforts to understand understanding the framework we propose for reconsidering understanding is based on the assumption that knowledge is represented internally, and that these internal representations are structured / point to some alternative ways of characterizing understanding but argue that the structure of represented knowledge provides an especially coherent framework for analyzing a range of issues related to understanding mathematics (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Carolyn Marks
Marleen Doctorow
M. C. Wittrock

It was hypothesized that by varying the frequency of 15 percent of the words in elementary school reading materials, gains in the comprehension of the meaning of entire passages could be produced. To test this hypothesis, 222 sixth graders were randomly assigned to two reading treatments, presented simultaneously in the same room, differing only in the frequency of 15 percent of the words used in the stories. Reading comprehension was significantly increased (p > .0001) with high frequency story passages. Results indicated that increases in the frequency of a small percentage of words enhanced story comprehension, while a few less familiar words inhibited comprehension of the total passage. The data suggest that, in the design of reading materials for use in elementary schools, sizable increases in reading comprehension can be produced by increased attention to the semantic variable of word frequency.

Eric Love
David John Pimm

Concrete materials have a long history in the mathematics classroom, although they have not always been readily accepted or used appropriately. They disappeared when written computational methods arose and little premium was placed on understanding the algorithms being learned. Comenius and Pestalozzi began the process of reintroduction, with Montessori and many others in the present century providing new materials and new rationales for their use, so that today one finds hundreds of 'manipulatives' available. Arguments have persisted, however, as to whether common tools from daily life might be better than specially constructed educational materials and whether, in fact, all such materials might do more harm than good. Educational materials are not miracle drugs; their productive use requires planning and foresight.

Brent Davis

The question of how to teach mathematics has become increasingly problematic in recent years as critics from diverse perspectives have offered wide-ranging, and often seemingly incommensurate, challenges to conventional conceptions of the teacher's task. This article represents an effort to "bring into dialogue" some of the varied commentaries on mathematics teaching, using an enactivist framework to interpret and to propose an alternative way of framing mathematics teaching. In this report, the manner in which the teacher listens is offered as a metaphoric lens through which to reinterpret practice, as a practical basis for teaching action, and as a means of addressing some of the critics' concerns. The report is developed around an extended collaborative research project with a middle school mathematics teacher.