1. No category

UNIVERSIDAD VERACRUZANA
FACULTAD DE IDIOMAS
T
E
S
I
S
Perceptions of English Teachers about the Inductive and
Deductive Approaches
QUE PARA OBTENER EL TÍTULO DE:
LICENCIADA EN LENGUA INGLESA
PRESENTA:
Rubí Elizabeth Méndez Jacobo
ASESORA DE CONTENIDO:
María Teresa Madrid Carretero
ASESORA DE LENGUA:
Patricia May Reidi Ryan
Xalapa de Enríquez, Veracruz
Abril 2014
1
Acknowledgements
Primeramente, gracias a DIOS, por ser mi principal guía y permitirme lograr
alcanzar esta meta.
Quiero dedicar esta tesis y agradecer de una manera muy
especial a mis padres María de Jesús y Ramón quienes a
lo largo de toda mi vida han apoyado y motivado mi
formación académica. Gracias
por el infinito apoyo,
paciencia y amor que me han brindado a lo largo de mi
vida, de mis estudios y a lo largo de este proyecto.
Gracias por heredarme uno de los más grandes tesoros
que pueda dársele a un hijo; estudios profesionales.
Gracias a mi asesora de contenido Mtra. María Teresa
Madrid Carretero y a mi asesora de lengua la Mtra.
Patricia May Reidi Ryan por su paciencia, apoyo y
confianza en mí como persona y en mi trabajo.
Agradesco a
mi pre jurado: Dra. Carmen Baez, Mtro.
Carlos Palestina, y Mtra. María del Pilar Balbuena por sus
valiosas sugerencias. Gracias por todo su tiempo invertido
en la revisión de esta tesis.
Gracias a Iván Amador que a pesar de la demanda de su
trabajo siempre estuvo ahí, del otro lado de la bocina,
escuchándome y alentándome siempre a seguir adelante.
Gracias por todo su amor y apoyo, por que hasta en mis
momentos más desesperantes hizo todo lo posible por
cambiar mi angustia y desesperación por inspiración y
motivación.
1
2
Table of contents
Acknowledgements
1
Introduction
4
CHAPTER ONE: Theoretical Framework
5
1 Grammar
5
1.1 Swan’s metaphor about the creation of a functional language
5
System
1.1.1 Limitations of Swan’s metaphor about a new language system
1.2 Types of grammar
6
7
1.2.1 Prescriptive grammar
7
1.2.2 Descriptive grammar
8
1.3 Approaches to grammar
8
1.3.1 Syntax
9
1.4 Parts of speech
10
1.5 Related Concepts
12
1.5.1 Form and meaning
12
1.5.2 Function
14
1.6 Teaching grammar
16
1.7 The deductive approach
17
1.7.1 Advantages and disadvantages of
19
the deductive approach
1. 8 The inductive approach
1.8.1 Advantages and disadvantages of
20
21
the inductive approach
1.9 Learning styles
21
CHAPTER TWO: Methodology
22
2.1 Context
22
2.2 Participants
23
2
2.3 Instruments
23
CHAPTER THREE: Results and Discussion
25
3.1 Quantitative Analysis
26
3.1.1 Analysis of the personal information section
26
3.1.2 Analysis of the deductive approach section
27
3.1.3 Advantages and disadvantages
28
3.1.3.1 Advantages
29
3.1.3.2 Disadvantages
30
3.2 Analysis of the inductive approach section
3.2.1 Advantages and disadvantages
32
33
3.2.1.1 Advantages
34
3.2.1.2 Disadvantages
35
3.2.2 Usage of the deductive and inductive
37
3.3 Qualitative Analysis
39
3.4 Discussion
51
Conclusion
55
References
57
Appendices
Appendix 1
59
Appendix 2
63
Appendix 3
65
Appendix 4
67
Appendix 5
69
3
INTRODUCTION
For English teachers it might be relevant to know the different approaches to teach
grammar in order to make their students’ lessons more meaningful. There are two
main approaches which are commonly used in grammar teaching, deductive and
inductive. These approaches have advantages and disadvantages. Nevertheless,
both approaches may be combined in order to use suitable choices depending on
the grammatical point to be presented.
In this paper, I attempt to explore the two main approaches of teaching grammar,
the inductive approach and the deductive approach. The deductive approach is
when the teacher goes straight to grammar explanation followed by practice of the
grammar point. (Harmer, 2007:81). On the other hand, the inductive approach is
when the teacher provides examples of the grammar point to be learnt and allows
students to discover the pattern by themselves. (Thornbury, 1999:49).
The main goal of this research is to know the English teachers’ perspectives of the
use of these approaches when teaching grammar. Furthermore, I attempt to find
out to what extent teachers consider such approaches efficient. Also, I attempt to
explore students’ experiences when having lessons with these approaches, from
the teachers’ point of view. Besides, I want to find out to what extent teachers
consider these approaches efficient for applying them in the classroom.
4
CHAPTER ONE: Theoretical Framework
1 Grammar
The word “grammar” means more than a set of rules to produce a well-formed
sentence. Grammar is the system we use consciously or unconsciously to express
words to succeed in communication (Thornbury, 1999:1-3). Swan (2006a:4)
mentions that the best way to comprehend ‘what grammar is’ is to imagine
language without grammar.
In order to clarify Swan’s statement, the following interpretation is presented. This
information describes Swan’s metaphor about a fictional experiment to create a
functional language system. The following information is intended to help grasp the
concept of grammar.
1.1 Swan’s metaphor about the creation of a functional language system
Swan’s (2006a:4,5) metaphor refers to an intelligent kind of primate who wants to
create an effective language system. The author clarifies that there is a
communication system that already exists; it consists of sounds and body
language. Sounds are chosen because of the vocal variety and the fact that they
work even when eyesight cannot be used.
The next step is deciding different words to name the things in the environment
(each house, each stone in the tribe and so on) but this will not function. First, it is
too much work naming each thing; secondly, it will not allow talking about new
things, like a new plant or mountain. A better idea is to create word families where
words may be divided into classes. Therefore, words like ‘house’ or ‘stone’ can be
about any house, any stone, etc. Then, they decided to create words to refer to the
characteristics of things (‘good’ ‘hot’ or ‘green’). Likewise, they decided to create
5
words that might refer to express different events, situations, and changes in the
environment (‘walk’ ‘born’ ‘jump’).
By now this system allows those primates to do three things. First, it enables them
to call someone’s attention to the existence of something by using only one word,
(‘house!’, ‘river!’, ‘tree!’). Secondly, those primates are capable of combining words
to have a more precise meaning (‘big house’ or ‘small tree). Thirdly, they are able
to combine words to express events or states of affairs (‘cross river’ ‘run child’ or
‘ride horse’).
1.1.1 Limitations of Swan’s metaphor about a new language system
According to Swan (2006a:5-6), this language system is advanced in comparison
to the system of cries and grunts. However, he claims to perceive three limitations:
The first limitation is word order. When expressing something that involves more
than one object, such as, ‘kill brother snake’, it will not be clear if your brother has
killed a snake or if a snake has killed your brother. The second limitation is
vocabulary. It does not allow providing details like time or the reasons why
something happens. The third limitation is communicative status. This system does
not permit questions, negations or suggestions, only requests and affirmative
statements. Context or common sense may help to understand the desired
meaning to communicate in the case of these three limitations. Nevertheless, it will
not always be possible to have context. Therefore, there are three points that the
author considers necessary in order to have a successful language system:
(i)
a way of saying what word goes with what—of indicating how general
concepts need to be grouped in order to represent particular elements in
the world
(ii)
a way of expressing agency and other relationships
(iii)
a way of indicating the communicative status of your utterances—
statement, question, suggestion, negation, or whatever.
(Swan, 2006a:6)
6
For the purpose of this work, further information about this metaphor might not be
appropriate. The only purpose of including it was to have a broader idea of Swan’s
statement that imagining language without grammar might help to understand
more clearly its importance.
1.2 Types of grammar
There are two main ways of looking at grammar depending on the function;
prescriptive and descriptive. In the following paragraphs, the characteristics of
each one will be described:
1.2.1 Prescriptive grammar
In general, people often associate the word grammar with the knowing and
handling of rules, that is to say, something that indicates the dos and don’ts of a
language. A common rendition of a rule is, for example, when someone says ‘In
present simple you should always add ‘s’ or ‘es’ to the verb following a third
person’. (Odlin, 1994:1)
Prescriptive rules were developed by a group of people who had the belief that
they could protect the language from any change. Most of these rules were created
in the eighteenth and nineteenth century. Prescriptive grammar distinguishes
between using the ‘correct’ or the ‘incorrect’ forms of a language. Sometimes
making a decision between what is right or wrong does not affect the idea of what
someone is trying to express. In other words, communication is achieved even if
there are some grammatical mistakes. Nevertheless, it is important to have a
standard of languages to facilitate communication when interacting with other
highly different dialect regions, as in the case of Indian English, British English,
Australian English, and etcetera. It can also facilitate the process of teaching or
learning a new language if the target language is codified. (Davies and Fraenkel,
2003:39-40; Odlin, 1994:1-2; Swan, 2006b:291)
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1.2.2 Descriptive grammar
Descriptive rules describe how a language is actually used instead of how it should
be used. Descriptive grammar provides the picture of a language in a certain form
(standard written Australian English, standard spoken British English, Canadian
English or American English) and not what a group of people consider should be
correct. Descriptive grammar looks at the languages in a more detailed way than
prescriptive grammar because it does not only focus on standard dialects but also
on nonstandard dialects, which make use of slang and jargon to communicate,
such as the language used by young people, military personnel, doctors, people
without or limited academic education, etc. Another characteristic of descriptive
grammar is that sometimes it pays attention to both the contemporary and earlier
usage of a language. (Odlin: 1994:3-4; Swan, 2006b:291)
1.3 Approaches to grammar
For the purposes of this paper I use the term grammar to refer mainly to the body
of language. This type of information is usually used by people in the process of
teaching and learning English as a foreign language.
Grammar can have different meanings for different people. Sometimes it might
even have negative connotations. Some people may describe grammar as a group
of arbitrary rules that complicate the process of learning a foreign language. For
some individuals it might constitute a collection of academic or traditional
terminology such as: ‘past continuous’, ‘future’, ‘simple past’, etc. (Davies and
Fraenkel, 2003:31,32; Swan, 2006a:3)
But not everybody sees grammar in one way. From a more formal perspective,
grammar is partly the study of how language manipulates words in order to create
well-formed sentences. It is a set of rules that people consciously or unconsciously
8
follow to express themselves and succeed in communicating. (Davies and
Fraenkel, 2003:32-34; Ur, 1988: 76)
In dictionaries, grammar is often described as a set of rules to follow but this
definition can be considered an incomplete one. As Swan puts it, it is “as if one
defined ‘a bus as a large vehicle constructed of one or two levels’, without
mentioning that it is used for public transport” (Swan, 2006a:3). So, a complete
definition should not include only a description but the function as well, and its
purpose is to enable success in communicating either in the spoken or the written
language. (Swan, 2006a:3; Ur 1988: 76)
1.3.1 Syntax
Syntax is a component of grammar which studies the order of words and it focuses
on three main aspects. The first aspect is: the way words should be placed in a
sentence. The second aspect is: how words can be placed in a sentence. The third
aspect is: which words are better to replace in conventional sentences. (Davies
and Fraenkel, 2003:41-42; Harmer, 2007:60; Thornbury, 1999:1-4)
A sentence implies using a series of language elements that people use to
successfully communicate ideas, intentions, feelings, etc. For instance:
‘It’s warm in here.’ (Harmer, 2007:60)
In this sentence the author suggests that the speaker needs to arrange the order of
words to convey the message.
Grammar tries to explain why some sentences are accepted and others are not. A
well-formed sentence is considered to be so if its elements are placed in the right
order (according to conventional grammar rules). For instance, in the sentence It’s
warm in here’, there is a subject (It), there is a verb (is), there is a complement
9
(‘warm’- named complement because it provides details of the subject), and there
is an adverbial (‘in here’ named adverbial because it illustrates the verb). As was
mentioned before, to make the sentence work, the elements should be in the
correct order (according to conventional grammar rules). We can have the same
elements but if they are placed in the wrong order, our sentence will not make
sense and because of that we will be not able to transmit the message. (Harmer,
2007:60; Thornbury, 1999:2-3)
It is important to be aware of the kind of words we use in each part of the sentence.
For instance, according to conventional grammar rules we cannot use a verb in the
adverbial slot (‘It’s warm go’). (Harmer, 2007:60)
Other examples are the sentences below which are grammatically acceptable:
We are not at home right now.
Right now we are not at home. (Thornbury,1999:1)
but these are not:
Not we at right home now are.
We is not at home right now. (Thornbury,1999:2)
However, there are some changes that are allowed in the structure of a sentence
and those changes will modify the meaning of the sentence. For instance, when
the position of the subject and the verb (subject-verb → verb-subject) is changed,
the meaning of the sentence is transformed into a question (‘Is it warm in here?’).
(Davies and Fraenkel, 2003:41-42; Harmer, 2007:60-61)
1.4 Parts of speech
In the previous section we found information about syntax. Syntax emphasizes the
importance of the order of words to succeed in communicating ideas, feelings,
intentions, etc. In this section, the information presented is about the parts of
10
speech, their definition and the different categories that exist according to Crystal
(2010), Harmer (2007) and Thornbury (2002).
For a long time, words have been classified into word classes, also called ‘parts of
speech’. Most grammars recognize the existence of eight parts of speech. (Crystal,
2010:95)
Next, I will describe the parts of speech according to Harmer (2007:65). I consider
this classification appropriate because in his work Harmer focuses on teaching
English as a foreign language. The definitions that he uses are clear and each part
of speech’s definition is complemented with examples. In this way learners are
able to understand how to use it.
Part of speech
Examples
1. Noun: word(s) that is the name of a person, a thing, an activity
etc.
-I love New York.
2. Pronoun: a word used in place of a noun or noun phrase.
-Look at him!
3. Adjective: a word that gives more information about a noun or
-She is so impetuous.
pronoun.
4. Verb: word(s) used to describe an action, experience or state.
-I don’t believe you!
5. Adverb: word(s) that describes or adds to the meaning of a
-Please act sensibly this
evening.
verb, adjective, another adverb or a whole sentence.
6. Preposition: word(s) used to show the way which other words
-Put that in the box.
are connected.
7. Determiner: definite article; indefinite article; possessives;
-Few people believe him.
demonstratives; quantifiers.
8. Conjunction: a word that connects sentences, phrases or
clauses.
-Full of energy and ready to
go.
Adapted from Harmer (2007: 65)
There are some grammarians who consider determiners as adjectives. Therefore,
interjections are regarded as the eighth part of speech. Interjections are the noises
11
that people make to express an attitude while speaking and these also can be
written to express some feelings, for instance, Wow!, Ugh!, Oh!. (Crystal, 2010:10)
These parts of speech can be classified into two sets using as reference the
meaning linked to these words. First, we have the group of words that help to build
the grammatical structure of a sentence named grammatical words. Those are
prepositions, conjunctions, determiners and pronouns. Then, we have the group of
words that bring the main information of a sentence called content words. Those
words are nouns, verbs, adjectives and adverbs. (Crystal, 2010:95; Thornbury,
2002:3,4)
The first group of words is a closed group: this means that it is not easy to add a
new grammatical word. The last time a word was added to this group was in the
sixteenth century. On the other hand, the second group is an open group; the
number of words that can be added to this group is literally limitless. Some new
words recently added are – googling, facebook, twitter, cybersex. (Crystal,
2010:95; Thornbury, 2002:3,4)
1.5 Related Concepts
In previous sections I mentioned the characteristics of prescriptive and descriptive
grammar, as well as the parts of speech according to some authors. In the
following pages I am going to try to introduce the concepts of form and meaning,
and function using information from Davies and Fraenkel (2003), Harmer (2007),
Spratt et al. (2005) and Thornbury (1999).
1.5.1 Form and meaning
The purpose of this section is to present information on the three main aspects
required for the understanding of the role of grammar in the teaching of English as
a foreign language. This information has to do with the fact that a well-formed
sentence is equally important as using it in the appropriate context. Thornbury
12
shows the following example about a message used to ask people to leave a voice
mail:
‘This is 2680239. We are at home right now. Please leave a message after the beep’.
(Thornbury, 1999:3)
The structure of the sentence ‘We are at home right now’ is grammatically correct,
but depending on the context, it does not make sense. So, another important point
to take into consideration of grammar is meaning-making potential (Harmer,
2007:63,64; Thornbury, 1999:3). Grammar allows communicating meanings but
vocabulary can do it too, for example:
Tickets! (Thornbury 1999:3)
In this example, the author shows that although it is composed of only one word,
the meaning can be interpreted if the context is the appropriate one; if the context
is ‘passengers expecting an inspector to check their tickets’ the word ‘Tickets’ will
succeed in communicating the message. That is to say, language does not have to
be complex to express a clear meaning. In fact, it is similar to the language in
childhood, by using individual words together, but as they are used in the precise
moment it does not cause difficulties interpreting them. (Harmer, 2007:63,64;
Thornbury, 1999:3,4) For instance:
Milk!
Daddy shoes.
Give balloon.
Using individual words is not exclusive of children who start speaking a language.
Adults also use them in some cases (Thornbury, 1999:4), for example:
- Coffee?
- Please.
- Sugar?
- Never touch the stuff.
(Davies and Fraenkel, 2003:48)
According to Thornbury (1999:4) a rule can be stated here: ‘the more context, the
less grammar’. But in the case in which a third person is involved, only using a
word like Tickets will not be enough. For example if A has to phone B to ask C
13
about some tickets A already booked, instead of using the word Tickets it would be
better:
Can you ask C to send me the tickets that I booked last Friday?
(Adapted from Thornbury, 1999:4)
When there is little or no information of the context, it is really difficult to interpret
what someone wants to communicate. In such situations, grammar comes and
helps to make the spoken or written message clearer. Therefore, the person who
receives the message can understand the intention to be transmitted clearly.
(Harmer, 2007:63-64; Thornbury, 1999:3,4)
The implications of this are related to the students learning that making well-formed
sentences is as important as knowing the diverse meanings they can have
according to the circumstances and when to use them. From this point of view
grammar is an instrument that allows making meanings. Consequently, language
teachers should guide their students to pay attention not only in the form of the
language but also to the meanings that can be expressed with such forms.
(Harmer, 2007:63,64; Thornbury, 1999:3,4)
1.5.2 Function
In the last section, I pointed out that knowing the meaning of a sentence is as
important as knowing the form. In the next paragraphs, I will try to describe the
concept of function according to Davies and Fraenkel (2003), Spratt et al (2005)
and Thornbury (1999).
Spratt et al. (2005:17) define the concept of function as “the reason why we
communicate”. That is to say, to express the spoken or written message’s intention
to the audience clearly. For example, the speaker or writer wants to express an
apology, an agreement, a clarification, an invitation, etc.
14
Thornbury (1999:6) provides an example (from the film Clueless, 1995) to show a
misunderstanding caused by the fact that the young man does not understand the
meaning of a question.
Father:
Young man:
Father:
Do you drink?
No, thanks, I’m cool.
I’m not offering, I’m asking you IF you drink. Do you think I’d offer alcohol to
teenage drivers taking my daughter out?
(Thornbury, 1999:6)
In this example, the young man did not understand the question’s function. The
question ‘Do you drink?’ has more than one meaning; it could be used to offer a
drink or to ask if you drink alcoholic beverages. Processing the language implicates
more than only trying to understand the words and the grammar the speaker or
writer is using; it is also about trying to achieve the intention, that is to say, the
function of the message. (Davies and Fraenkel, 2003:34; Spratt et al 2005:17-19;
Thornbury, 1999:6)
There are some form-functions that are easy to identify (Thornbury, 1999:6). Next,
there are some examples to illustrate form and function:
Form
Would you like…?
Function
Invitation or offer
If only I hadn’t…
Regrets
(Thornbury, 1999:6,7)
One function may have a wide variety of forms and indicate the same function. On
the other hand, it is also possible to have the same form but different functions.
(Davies and Fraenkel, 2003:34; Spratt et al 2005:17,18)
For instance, different ways of expressing warning:
Form
Function
You’d better not do that.
I wouldn’t do that, if I were you.
Warning
Mind you don’t do that.
If you do that, you’ll be in trouble.
(Thornbury, 1999: 7)
15
For example, using the form ‘If…,…will…’, to express different functions:
Form
Function
If you do that, you’ll be in trouble.
Warning
If you lie down, you’ll feel better.
Advice
If it rains, we’ll take a taxi.
If you pass your driving test, I’ll buy
you a car.
Plan
Promise
(Thornbury, 1999: 7)
In spite of the absence of a direct relation between form and function, it is
considered important to classify some grammatical structures with functions, such
as ‘Requesting information, denying, complaining, etc.’ (Davies and Fraenkel,
2003:44; Spratt et al 2005:17-18)
1.6 Teaching grammar
Ur (1996:76) claims that teaching the grammar of a foreign language is considered
a controversial subject. She also mentions that a vast majority of people agree that
knowing a language, apart from other aspects, is to have knowledge about its
grammar, but this grammar may likewise be acquired in an intuitive way as people
learn their first language.
English Language Teaching (ELT) is complex due to the great variety of students
or group of learners’ different characteristics, such as, “age, level of English,
attitude towards English, and exposure to and real need of the language.”(Davies
and Fraenkel, 2003:196). There are suggested ways of teaching for each of these
groups of learners and yet some teachers do not use them. Sometimes it may be
because of the lack of training or experience, for instance, “some teachers try to
explain grammar rules to quite young learners, try to get elementary teenagers to
write long error free compositions” (ibid.189). Some teachers might frequently use
an inappropriate approach because of the imposition of the place they work, the
16
book of the course and the tests. In other cases it might be because of the way
they were trained. (Davies and Fraenkel, 2003:189-194; Ur, 1996:77-78)
There is a low probability for teachers to choose the way in which they want to
teach. This is because institutions often set regulations about certain specific
aspects that ‘control’ the classroom teaching activities. (Davies and Fraenkel,
2003: 191; Ur, 1996:76-78)
For instance:

A course book and perhaps other materials (controlling what is taught and to
some extent how)

A course calendar (controlling how fast the teaching progresses)

Test (controlling what is taught, when, and generally influencing the way teachers
teach and students study – the so-called ‘backwash effect’)
(Davies and Fraenkel, 2003:192)
For teachers, it is important to have different options instead of only one view of
language in learning and teaching. There are varied approaches to grammar which
might be appropriate for teaching different groups of learners. (Davies and
Fraenkel, 2003:189-194; Ur, 1996:76-78)
In the following paragraphs I will make reference to two main approaches to teach
grammar. These approaches are the ones on which my work is based, the
deductive and the inductive approaches.
1.7 The deductive approach
The following paragraphs contain information about what the deductive and the
inductive approaches are. They also include information about how these
approaches are used in teaching a foreign language. The paragraphs also include
information on their advantages and disadvantages according to Thornbury (1999).
17
The deductive approach (rule-driven) is linked to the Grammar-Translation Method
(developed from the practice of teaching Latin and Greek around the 18th and 19th
centuries) which might often have negative connotations since it implies having the
typical grammar-translation lessons which start with a presentation of the grammar
point, regularly in the first language of the class. So, as students have classes in
their mother tongue they will have fewer opportunities to be in touch with the
foreign language. (Anderson and Larsen-Freeman, 2011:13; Thornbury, 1999:29;
Harmer, 2007:81-82)
Here is a possible setting which exemplifies the deductive approach:
…on arriving in a country you have never been to before, you are told that
as a rule people rub noses when greeting one another, and so you do
exactly that. (Thornbury,1999:29)
In a deductive approach the teacher presents, at the very beginning of the class,
the grammar rules. Then, the explanation is followed by examples in which the rule
previously presented is used. (Harmer, 2007:81; Thornbury, 1999:29) In the next
paragraph, there is an example of an activity in which the deductive approach is
described.
In this activity, the teacher starts showing some images of people doing different
activities (having breakfast, going to school, taking a bath, etc.) to students. After
that, he or she writes on the board a sentence about one of the images (for
instance, She’s having breakfast.) and asks students to notice that the example is
in the ‘present continuous’ form. Then, students are asked to repeat the sentence
aloud after the teacher. He or she once again focuses students’ attention on the
structure (present continuous) by isolating some parts of the sentence (‘she’s’,
‘having’) and the teacher repeats the activity with the other sentences. When the
teacher believes that the students have almost memorized those sentences’
structures, she or he continues with the next stage of the activity. Now, the teacher
says a key word aloud, for example ‘have’ and then students have to say the
18
corresponding sentence according to the verb aloud, for example ‘She’s having
breakfast’ or if the teacher says the word ‘go’ aloud, then students say the
sentence ‘He’s going to school’ aloud. Finally, students write their own sentences
using the grammatical structure they learnt in the lesson and the teacher makes
the corresponding corrections if necessary. (Harmer, 2007:81-82)
1.7.1 Advantages and disadvantages of the deductive approach
Some facts that have been recognized about using the deductive approach involve
aspects that might be regarded positively or negatively. That is to say, they contain
advantages and disadvantages. In the following table, a classification of such
aspects may be seen.
Advantages
Disadvantages
It goes straight to the point, and can therefore
It starts the lesson with a grammar presentation
be time-saving.
may be off-putting for some students, especially
younger ones.
It respects the intelligence and maturity of
It encourages a teacher-fronted, transmissions
many students (especially adult).
style classroom with the grammar explanation.
It confirms many students’ expectations about
It is less memorable an explanation than a
classroom learning.
demonstration.
It allows the teacher to deal with language
It encourages the belief that learning a language
points as they come up.
is simply a case of knowing the rules.
(Adapted from: Thornbury, 1999:30)
These pros and cons of the deductive approach may be dealt with appropriately
depending on the skills of the teachers in presenting the rule explanation. This
consequently depends on how helpful or useful the rule is. (T. Madrid, personal
communication)
19
1.8 The inductive approach
Unlike the deductive approach, the inductive approach starts with samples of the
language in use which are intended to help students to discover the grammar rule.
The inductive approach basically consists in allowing students become involved in
the new language through as much exposure as possible of suitable input without
explaining anything to them at the beginning. Thus, students may generate their
own knowledge. (Harmer, 2007:82; Thornbury, 1999:49)
Following a useful example of what inductive learning is:
…on arriving in the same country (as the first example of deductive approach),
you observe several instances of people rubbing noses on meeting so you
conclude that this is the custom, and proceed to do likewise (Thornbury,
1999:29).
An inductive approach is strongly related to methods which are based on the
natural learning process like the Direct Method also called the Natural Approach
(created by Stephen Krashen and Tracy D. Terrel in 1983), which coincide in the
fact that knowledge is better acquired by using the necessary amount of
information. Apart from that, some students are good at discovery activities and
they enjoy those activities. Since learners are deeply involved in the process of
acquiring a new language, they develop a positive attitude because they find the
activities are meaningful. However, there may be learners who may not respond in
the same way, maybe because they are not used to working in this way. (Harmer,
2007:82-83; Thornbury, 1999:49-54)
20
1.8.1 Advantages and disadvantages of the inductive approach
In the table below a series of advantages and disadvantages of the inductive
approach are presented.
Advantages
Disadvantages
Learners discover for themselves the rules.
Learners’ time and energy spent in working out
Therefore, the rules may become meaningful.
rules.
Learners are more actively involved in the
Learners’ time taken to work out a rule may be
learning process.
at the expense of time spent in practicing the
rule.
Learners’ abilities for pattern-recognition and
Learners may hypothesize the wrong rule
problem-solving are favored.
Learners
have
the
opportunity for
extra
language practice.
Learners (engaged in) solving activities within
the inductive approach should have teachers
capable to plan suitable lessons.
Learners engage in a process of preparation
Learners who would prefer simply to be told
for greater self-reliance.
the rule might be frustrated.
(Adapted from: Thornbury, 1999:54,55)
These pros and cons of the inductive approach may be dealt with appropriately
depending on the skills of the teachers in presenting the rule explanation. This
consequently depends on how helpful or useful the rule is. (T. Madrid, personal
communication)
1.9 Learning styles
The way teachers use the deductive and inductive approaches is definitely linked
in a greater or lesser extent to the students’ learning styles. Teachers may have
some notion about their students’ learning styles or preferences and take them into
consideration to some extent when planning a lesson or activity. In order to have a
broader idea, I used information from Reid (1995) and Nunan (1991).
21
A learning style is the persistent pattern of behavior used to learn a subject, that is
to say, the particular preferences each individual has when learning about
something. The learning style of people depends on the personality, the sociocultural background, and the experiences in the education of each person. (Nunan,
1991:167,168; Reid, 1995:5,6,) In the following paragraph I am going to mention
some of those learning styles (visual, tactile, kinesthetic, and auditory).
Visual learners need visual stimulation like pictures, movies, and videos. Tactile
and kinesthetic learners may often be classified in one category. Kinesthetic
learners enjoy Total Physical Response activities; they basically enjoy any activity
which does not require them to be in their chairs for long periods. Tactile learners
enjoy activities where they may touch and handle objects. Auditory students enjoy
activities which involve discussions, conversations and group work. These learners
usually demand oral directions. (Nunan, 1991:170,171; Reid, 1995: 34-36)
CHAPTER TWO: Methodology
2.1 Context
This research Project was developed at the Faculty of Language of the
Universidad Veracruzana which is located in Xalapa, Veracruz. The Faculty of
Language offers two undergraduate courses: one in English and one in French.
This project was focused on the BA degree in English. In the year 2008 the Modelo
Educativo Integral y Flexible (MEIF) started to substitute the previous curriculum,
the Plan 90. The Plan 90 included ten semesters; the first six semesters were
common core and the last four semesters were intended to train students in
different areas: Teaching English as a Foreign Language, Translation, and
Literature. Students were allowed to choose one area from the three offered by the
BA in English.
22
The students of MEIF may graduate after a minimum of seven and a maximum of
ten periods according to the way they organize their courses and the number of
credits they obtain. This model comprises various areas that might be combined so
that the students are able to ‘taste’ a menu of courses offered by the Faculty of
Language as well as by many other faculties. However, the Basic Area subjects
must be passed before students reach 50% of the total number of credits. The
Basic Area comprises English, Computación, Habilidades del Pensamiento and
Lectura y Redacción. Another important aspect of MEIF students is that they have
to obtain a certain number of credits to graduate from the English degree. They
may have a minimum of 35 credits and a maximum of 63 per term. Those credits
depend on the subjects because there are some subjects in which the number of
credits is higher than in others.
2.2 Participants
The participants on whom this piece of research focused were English teachers of
the English degree of the Faculty of Language of the Universidad Veracruzana.
The participants included six male and nine female teachers between 25 and 65
years of age who were selected at random. The participants’ qualifications were
varied; there were participants with qualifications from BA to Ph.D. All of them have
either taught or are still teaching English courses at all levels, from beginner to
advanced.
2.3 Instruments
This paper attempts to offer the findings related to the way teachers deal with the
deductive and the inductive approaches for the teaching of grammar in English
courses. These findings come from the information provided by the participants. In
order to obtain the information I used a questionnaire. I also did documentary
research that enabled me to handle theoretical information. Furthermore, I
employed my own personal experience as a learner and teacher of English as a
23
foreign language for carrying out the analysis. This is a small-scale research paper;
therefore the requirements for gathering and analyzing data have been satisfied.
To design the questionnaire I had to make decisions about the kind of questions I
needed to include. The questions were in English, I considered it appropriate
because the participants were English teachers. The first draft I designed eight
questions. Then, my advisor made some observations about those questions and
asked me to add some others that she considered important. I added four more
questions. The first questionnaire revised, corrected and piloted included twelve
items. The first draft corrections were basically considering that the language used
in the questions was appropriate for the language level of the participants.
Likewise, my advisor and I revised that the questions were not ambiguous. As well,
we checked that questions were clear enough to have the information required.
(Drever and Munn; 1990:22-27)
For the people who work on a questionnaire and are familiarized with it, it is difficult
to believe that someone else could interpret any question in a different way (Drever
and Munn; 1990:33-34). So, when the questionnaire was considered “ready”, I
piloted it for the first time. I only asked three people to answer my questionnaire to
see what results the questionnaire returned. Of these three people only one person
returned the questionnaire answered. I thought I had to ask other people to answer
it but despite having only one questionnaire to revise, it was very useful. This first
piloting helped me to identify some items in the questionnaire that involved the
term deductive and inductive at the same time. Because I made the decision to use
one questionnaire, both terms needed to appear in the same instrument. The fact
that the two terms were used in the search for information and that they had to be
used together might cause some slight confusion that made the information
useless. Therefore, I worked very carefully trying to achieve an efficient tool to
gather the data in spite of the risk of being a little bit “puzzling”.
24
The first step was to divide the questionnaire into two parts, one for each approach
so the participants could have a clear idea about which approach they were
responding. Then, the order of some questions was changed in order to make the
answering process easier (Drever and Munn; 1990:27-28). To make it even
clearer, each part was divided into sections. These sections were called sección
uno, sección dos and sección tres. The Spanish heading was kept because when
designing the questionnaire those headings looked very clear in the organization of
the questionnaire.
This new model was reviewed and revised many times with the help of my advisor
and it was corrected as many times as needed. Maybe because of that, when the
questionnaire was piloted for the second time some of the participants only made
some tiny suggestions which helped me to improve it. These piloted questionnaires
were also taken into consideration for this research as the corrections did not affect
the information gathered.
As I am not from the city where the study took place, I do not know English
teachers who do not belong to the Faculty of Language. So, most of the
participants of this research project were English teachers I met during my BA
studies. Many of these were my teachers, others I met when they were students
like I was and others I met at the Language School and I had the confidence to ask
them to help me.
CHAPTER THREE: Results and Discussion
In this chapter the questionnaire results are presented. They are divided into two
main sections. In the first one, a quantitative analysis is made about the number of
participants and the types of questions. In the second section a qualitative analysis
is presented and the information is processed at a deeper level. The qualitative
analysis is of higher importance for the aims of this paper since it implies looking
into the teachers’ beliefs and finding out how they influence their teaching.
25
3.1 Quantitative Analysis
Here is an overview of the statistical information. The first part of the analysis is
about the closed questions analyzed at a quantitative analysis level. Although there
are some questions that relate to the students’ performance when using the
inductive or deductive approach, the questionnaire was only administered to the
teachers. Teachers responded to these kinds of questions according to their
perception of their students’ performance. (See Appendix 1)
3.1.1 Analysis of the personal information section
This is section one of the first part of the questionnaire. In the first part of the
questionnaire some personal information about the participant was collected. The
personal information collected was about their age, sex, qualifications, years of
teaching experience, and the teachers’ level(s) taught, they teach or had taught.
(See Appendix 2)
 Age: 27% of the participants are at an age between 25 and 34 years old, 33%
of the participants are at an age between 35 and 44 years old, 13% of the
participants are at an age between 45 and 54 years old, and 27% of the
participants are at an age between 55 and 65 years old. (See Graph 1 in
Appendix 2)
 Sex: 40% of the participants are male and 60% female. (See Graph 2 in
Appendix 2)
 Qualifications: 19% of the participants have a BA, 6% of the participants have
a specialization Diploma in ELT, 56% of the participants have an MA, and 19%
of the participants have a Ph.D. (See Graph 3 in Appendix 2)
26
 Years of teaching experience: 14% of the participants have between 1 and 4
years of experience, 14% of the participants have between 5 and 9 years of
experience, 13% of the participants have between 10 and 14 years of
experience, 20% of the participants have between 15 and 19 years of
experience, 13% of the participants have between 20 and 24 years of
experience, 13% of the participants have between 25 and 29 years of
experience and 13% of the participants have 30 or more years of experience.
(See Graph 4 in Appendix 2)
 Level(s) of English taught: 11 out of 15 participants teach beginner level. 10
of the 15 participants teach elementary level. 12 of the 15 participants teach
lower-intermediate level. 9 out of 15 participants teach intermediate level. 4 out
of 15 participants teach upper-intermediate level and 7 of the 15 participants
teach advanced level. (See Graph 5 in Appendix 2)
3.1.2 Analysis of the deductive approach section
This is section two of the first part of the questionnaire. This part of the
questionnaire was designed with the purpose of finding out whether the
participants have used the deductive approach. Also, this section helped to have
an overview about whether they consider it efficient or not. It is also intended for
exploring both the teachers’ and learners’ feelings (from the teachers’ perspective)
about this approach. (See Appendix 3)
Next, each item is presented along with the percentage of responses.
Item 1 “Have you used the deductive approach with your students?”
93% of the participants answered “Yes” and 7% of them answered “No” to the
question. (See Graph 1 in Appendix 3)
27
Item 2 “I consider that teaching grammar using the deductive approach is efficient.”
67% of the participants answered “Yes”, 7% of the participants chose “No”, 13% of
the participants answered “Both” and a 13% of the participants did not answer but
they answered the next stage of the question. (See Graph 2 in Appendix 3)
Item 3 “Choose from A-D to describe how you feel when you use the deductive
approach.”
53% of the participants answered “Confident”; 13% of the participants chose
“Relaxed”, 7% of participants underlined “Confident and Relaxed”; 20% of the
participants did not answer but they answered the next stage of the question and
7% of the English teachers did not answer because of the note below in question
two (*If the answer is NO, go to SECTION III question 5). (See Graph 3 in
Appendix 3)
Item 4 “Choose from A-E to describe your students’ response when grammar is
presented in a deductive way.”
7% of the participants chose “Excellent”; 46% of the participants answered “Very
good”; 33% of the participants reported “Satisfactory”; 7% did not choose any of
the options provided, they wrote “depends” and 7% of the participants did not
answer because of the note below in question two (*If the answer is NO, go to
SECTION III question 5). (See Graph 4 in Appendix 3)
3.1.3 Advantages and disadvantages
This is section three of the first part of the questionnaire. This section is intended to
show what advantages and disadvantages teachers consider from the most
relevant to the least significant when using the deductive approach. This section is
divided into two main parts, advantages and disadvantages.
28
3.1.3.1 Advantages
The first part of this section corresponds to the advantages when using the
deductive approach. First, you might see the statement and the table used on the
questionnaire applied to the participants. Then, you may appreciate the graph that
corresponds to this statement.
a). Number the advantages that you notice using the deductive approach. List
them from 1 (most noticeable) to 4 (least noticeable).
Advantages of the deductive approach
It goes straight to the point, and can
therefore be time-saving.
It respects the intelligence and maturity of
many students (especially adult).
It confirms many students’ expectations
about classroom learning.
It allows the teacher to deal with language
points as they come up.
Other(s):__________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
In Graph 1 you may perceive the answers of the participants in percentages.
Graph 1 is integrated by four graphs (each corresponding to an advantage which is
written below its corresponding graph). Each color of the bars corresponds to the
number the participants gave to the advantage (e.g. the blue bar is number 1; the
red bar is number 2 and so on).
29
Graph 1
3.1.3.2 Disadvantages
The second part of this section is about the disadvantages when using the
deductive approach. First, you may see the statement and the table used on the
questionnaire applied to the participants. Then, you might appreciate the graph that
corresponds to this statement.
30
b). Number the disadvantages that you notice using the deductive approach. List
them from 1 (most noticeable) to 4 (least noticeable).
Disadvantages of the deductive approach
It starts the lesson with a grammar
It
encourages
a
teacher-fronted
presentation; this may be off-putting for
transmissions style classroom with the
some students, especially younger ones.
grammar explanation.
It is less memorable explanation than
It encourages the belief that learning a
demonstration.
language is simply a case of knowing the
rules.
Other(s):__________________________________________________________________
_________________________________________________________________________
______________________________________________________________________
In Graph 2 you may perceive the answers of the participants, in percentages.
Graph 2 is integrated by four graphs (each corresponding to a disadvantage which
is written below its corresponding graph). Each color of the bars corresponds to the
number the participants gave to the disadvantage (e.g. the blue bar is number 1;
the red bar is number 2 and so on).
31
Graph 2
3.2 Analysis of the inductive approach section
This is section one of the second part of the questionnaire. This part of the
questionnaire was designed with the purpose of finding out whether the
participants have used the inductive approach and if they consider it efficient. This
section is also intended for exploring both the teachers’ and learners’ feelings (from
the teachers’ perspective) about this approach. (See Appendix 4)
Item 1 “Have you used the inductive approach with your students?”
100% of the participants answered “Yes” (among those who answered “Yes” there
was a case in which a teacher wrote “Very little” as his/her answer but I decided to
include the information). (See Graph 1 in Appendix 4)
32
Item 2 “I consider that teaching grammar using the inductive approach is efficient.”
87% of the participants agreed that teaching grammar using the inductive
approach is efficient and 13% of the participants did not answer this question but
7% of those answered the next stage of the question. (See Graph 2 in Appendix 4)
Item 3 “Choose from A-D to describe how you feel when you use the inductive
approach”
33% of the participants answered “Confident”; 33% of the participants choose
“Relaxed”; 20% of the participants selected “Confident and Relaxed”; 7% of the
participants underlined “Stressed” and 7% of the English teachers did not answer
but they answered the next stage of the question. (See Graph 3 in Appendix 4)
Item 4 “Choose from A-E to describe your students’ response when grammar is
presented in an inductive way”
13% of the participants answered “Excellent”; 46% of the participants chose “Very
good” (7% of the teachers who chose this option added extra information, see
Qualitative analysis-Item 3); 20% of the participants underlined “Satisfactory” (7%
of the teachers who chose this option added extra information, see Qualitative
analysis-Item 3); 7% of the participants selected “Poor” and 13% of the participants
did not answer but 7% out of this percentage added extra information (See
Qualitative analysis-Item 3). (See Graph 4 in Appendix 4)
3.2.1 Advantages and disadvantages
This is section two of the second part of the questionnaire. This section intends to
show what advantages and disadvantages of the inductive approach teachers
consider the most relevant and the least significant when teaching grammar. This
section is divided into two main parts, advantages and disadvantages of this
approach. The first part corresponds to the advantages when using the inductive
approach.
33
3.2.1.1 Advantages
The first part of this section is about the advantages when using the inductive
approach. First, you may see the statement and the table used on the
questionnaire applied to the participants. Then, you might appreciate the graph that
corresponds to this statement.
a). Number the advantages that you notice using the inductive approach. List them
from 1 (most noticeable) to 5 (least noticeable).
Advantages of the inductive approach
Learners discover for themselves the rules.
Therefore, the rules may become
meaningful.
Learners are more actively involved in the
learning process.
Learners’ abilities for pattern-recognition
and problem-solving are favored.
Learners have the opportunity for extra
language practice.
Learners engage in a process
preparation for greater self-reliance.
Other/s:______________________________
____________________________________
____________________________________
of
In Graph 3 you may visualize the answers of the participants, in percentages.
Graph 3 is integrated by four graphs (each corresponding to an advantage which is
written below its corresponding graph). Each color of the bars corresponds to the
number the participants gave to the disadvantage (e.g. the blue bar is number 1;
the red bar is number 2 and so on).
34
Graph 3
3.2.1.2 Disadvantages
This second part of this section is about the disadvantages when using the
inductive approach. First, you may see the statement and the table used on the
questionnaire applied to the participants. Then, you might appreciate the graph that
corresponds to this statement.
b). Number the disadvantages that you notice using the inductive approach. List
them from 1 (most noticeable) to 5 (least noticeable).
35
Disadvantages of the inductive approach
Learners’ time and energy spent in
working out rules.
Learners’ time taken to work out a rule may
be at the expense on time spent in practicing
the rule.
Learners may hypothesize the wrong rule.
Learners (engaged in) solving activities within
the inductive approach should have teachers
capable to plan suitable lessons.
Learners who would prefer simply to be
told the rule might be frustrated.
Other/s:_____________________________
____________________________________
____________________________________
In graph 4 you may visualize the answers of the participants, in percentages.
Graph 4 is integrated by four graphs (each corresponding to a disadvantage which
is written below its corresponding graph). Each color of the bars corresponds to the
number the participants gave to the disadvantage (e.g. the blue bar is number 1;
the red bar is number 2 and so on).
Graph 4
36
3.2.2 Usage of the deductive and inductive
This is section three of the second part of the questionnaire, and the last part of it.
In this section, participants were asked to indicate their preferences when teaching
(Inductively, deductively or using a combination of both approaches) and to
indicate by means of underlining a figure the percentage of each approach they
use when teaching grammar. In the last case the total of both approaches should
be of 100%. In general, there is a low probability that only one approach is used to
teach grammar; however, I considered it an interesting fact to have the participants
identify the percentage of each approach that they consider they use when
teaching grammar.
Item 1 “How do you prefer teaching grammar? Inductively, deductively or using a
combination?
0% of participants chose “inductively”, 0% of participants chose “deductively” and
100% of the participants chose “a combination” of both approaches. (See Appendix
5)
Item 2.1 Deductive approach: 27% of the participants underlined 21% to 30%; 6%
of the participants use it 31% to 40%; 13% of the participants underlined 41% to
50%; 20% of the participants use it 51% to 60%; 7% of the participants chose 61%
to 70%; 7% of the participants practice it 71% to 80%; 7% of the participants chose
“more than 80%”, and 13% of the participants did not answer this part of the
questionnaire but 7% of them wrote their reasons (See the Qualitative AnalysisItem 10). (See Graph 5)
37
Graph 5
Item 2.2 Inductive approach: 6% of the participants underlined 10% to 20%; 13%
of the participants 21% to 30%; 7% of the participants chose 31% to 40%; 27% of
the participants use it 41% to 50%; 7% of the participants use it 51% to 60%; 27%
of the participants use 61% to 70% and 13% of participants did not answer this part
of the questionnaire but 7% of them wrote their reasons (See the Qualitative
Analysis-Item 10). (See Graph 6)
38
Graph 6
3.3 Qualitative Analysis
In this part of the analysis, the questions or statements analyzed are the ones in
which participants provided reasons for their answers. There are several areas in
the questionnaire in which the participants added their opinions.
In some
questions or statements, teachers were asked to provide reasons for their answers
in order to have a broader idea of why they chose them. In other cases some
teachers added information apart from their answer even when it was not
requested in the questionnaire. Finally there were some questions or statements in
which a space, called “other(s)” was provided in case teachers wanted to add a
different option apart from those provided. Some teachers used this space to write
their opinions or reasons. (See Appendix 1)
Item 1 “I consider that teaching grammar using the deductive approach is efficient.”
(See Graph 2 in Appendix 3)
39
After choosing an answer for the previous statement, teachers were asked to
provide reason(s) for their answer (See Appendix 1). Following, the reasons
provided by the teachers who considered this approach efficient are presented. I
could group those answers into these different categories according to the aspects
that those reasons shared in common. The various categories identified are
presented in the following table:
Category
Summary of comments
a) Difficulty of
Some participants showed their concern about what might be
the grammar
the best for their students; they considered that it is all right to
point.
use the deductive approach if the new grammatical point is quite
difficult for students or if it is causing problems in the students’
performance.
b) Time
Some participants indicated that the deductive approach could
available.
be efficient taking into account that the time available for the
syllabus to be covered is often not enough.
c) Planning.
Other participants thought that the efficiency of the approach
depends on factors that have to be taken into consideration
during the phase of lesson planning, such as the aim of the
lesson, the students’ age and level, etcetera.
d) Adult
Some other participants considered that the deductive approach
learners.
might be efficient with adult students since these types of
learners are often used to follow patterns.
According to the teachers’ answers, I would say that they take into consideration
the advantages that this approach offers when using it to consider it as efficient.
According to Thornbury (1999), there are four great advantages in using this
approach: time saving, respect for the intelligence and maturity of learners
(especially adult learners), students’ confirmation of their expectations about
learning, and teachers’ role in solving problems as they come up instead of
40
anticipating them. I may see that all of these advantages were reflected in the
participants’ answers.
In 3.1.2 I mentioned that one participant did not consider the deductive approach
as efficient. In the following table, I describe this category and the argument that
the participant used to make his/her point.
Category
Comment
a) Students’
The reason that the participant provided was that he/she
involvement.
considered the students’ involvement and interaction in the
grammar rule explanation as an important factor in the learning
process.
I agree with this participant to a certain extent because as a teacher I also consider
it an important factor that students become involved in the lesson. As Thornbury
(1999) claims, using this approach, the teacher goes straight to the rule
explanation and then to the practice of the rule. Therefore, the possibility of
students experimenting that kind of involvement is limited. Nevertheless, I do not
agree with considering it inefficient because I think there are also some
advantages such as the ones mentioned earlier.
Item 2 “Choose from A-D to describe how you feel when you use the deductive
approach” (See Graph 3 in Appendix 3)
After choosing an answer for the previous statement, teachers were asked to
provide reason(s) for their answer (see Appendix 1). I could group the answers into
these different categories according to the aspects that those reasons shared in
common. The various categories identified are presented in the following table:
41
Category
Summary of comments
a) The grammar Participants’ responses referred to the fact that when dealing
rules.
with some grammar rules, it is sometimes easier to write them
on the board and solve the students’ doubts if they have any.
b) Adult
Participants indicated that a number of adult learners often
learners.
prefer to be given structures because in that way those
students feel more confident when expressing ideas.
c) Connecting
Participants indicated that they expect their students to be
the rules.
able to connect the English grammar structure learnt with the
corresponding one in their mother tongue by using their own
language knowledge.
In order to avoid confusion among students, teachers sometimes prefer to
present the rules of complex grammar structures. Thornbury (1999) claims that
by using this approach teachers do not have to worry about guiding students to
discover the grammar rule. They only could go straight to the point and then face
the problems as they come up instead of thinking about them before presenting
the grammar lesson.
I have no experience teaching adult learners because in my short experience as
a teacher I have only taught teenagers. Therefore, I find the answers of these
experienced teachers very useful.
In the same statement, there were participants who did not answer as expected.
They did not choose any of the options provided (see Appendix 1). However, they
answered the next stage of the question in which they had to include reasons. I
could group those answers into this category according to the aspects that those
reasons shared in common. The category identified is presented in the following
table:
42
Category
Summary of comments
a) Depends on
It depends on the successfulness of the lesson and the students’
certain factors.
response. One of these participants simply wrote the words “it
depends”.
Unfortunately, the responses of these participants were very brief, and at the same
time too broad to find out any precise implications from the words “it depends”.
Perhaps participants only decided not to spend a longer time reflecting on the
subject because of their time available, they may think their answers were clear
enough or they may not have interest in providing a longer explanation.
Item 3 “Choose from A-E to describe your students’ response when grammar is
presented in a deductive way” (See Graph 4 in Appendix 3)
In this statement participants were not asked to provide reasons for their answer
(See Appendix 1). Nevertheless, there were participants who included some
statements that tried to explain certain facts. I could group those answers into
these different categories according to the aspects that those statements shared in
common. The various categories identified are presented in the following table:
Category
Summary of comments
a) Keep on
Although students using the deductive approach show a
making
satisfactory response, they easily forget this information and
mistakes.
keep on making mistakes in their work.
b) Depends on
The efficiency of the deductive approach may depend on the
the type of
type of learner.
learner.
In a classroom, teachers commonly have students with different learning styles.
Therefore, when a teacher uses a specific approach, e.g the deductive one, the
information might be difficult to grasp for certain students; the information might be
43
kept only in the short term memory. This kind of approach can be very useful with
visual learners but might be more difficult for tactile learners.
Item 4 “Number the advantages that you notice using the deductive approach. List
them from 1 (most noticeable) to 4 (least noticeable)” (See Graph 1 in 3.1.3.1)
In this statement a space called “other(s)” (see Appendix 1) was provided in case
teachers wanted to add any other advantage. Only two participants used this
space. One of them wrote an opinion about using the deductive approach and the
other one wrote a reason explaining why he/she did not number the advantages.
The information provided was the following:
Category
Summary of comments
a) Opinion about The opinion expressed was that as most of students are used
the deductive
only to work with this approach because of their previous
approach.
schooling experience. Therefore, for teachers might take time
and effort to engage students into a new way of teaching.
b) Reason for
The four advantages addressed in the statement are equally
not numbering
important for him/her and it depends on the situation and the
the advantages.
students’ needs.
Unfortunately, very often the teaching of English as a foreign language is based on
overusing the deductive approach. Thus, students are given information they are
expected to memorize. Hence, if the usual procedure for teaching/learning is
modified, both teachers and students might find the different approach somewhat
challenging at the beginning.
44
Item 5 “Number the disadvantages that you notice using the deductive approach.
List them from 1 (most noticeable) to 4 (least noticeable)” (See Graph 2 in 3.1.3.2)
In this statement a space called “other(s)” (see Appendix 1) was provided in case
teachers wanted to add any other advantage. Only two participants used this
space. One of them used it to explain why he/she decided to give a number to
each disadvantage; the other participant used it to write the reason why he/she did
not number the disadvantages. The criteria used by the participants to provide their
answers were the following:
Category
Summary of comments
a) Reasons for
He/she was aware of these disadvantages; therefore, he/she
the numbering
numbered them in an arbitrary way implying that they are all
used
major disadvantages.
b) Reasons for
This approach includes all the disadvantages mentioned, to the
not numbering
same degree, hence the difficulty in deciding. He/she therefore
the advantages.
adds that the range variation of the disadvantages might
depend on the features of the group such as the students’ age
and level.
Both participants agreed that all of the disadvantages provided in the questionnaire
are equally important. Maybe because it is relatively difficult for them to decide the
numbering of these disadvantages. These participants gave the impression of
being very analytical when answering the questionnaire (both of them are the same
two participants of Item 4 which is similar to this one). I perceive them to be
somewhat unsatisfied with this numbering request because they did not agree to
answer
either
section
(numbering
the
advantages
and
numbering
the
disadvantages) as requested.
45
Item 6 “I consider that teaching grammar using the inductive approach is efficient.”
(See Graph 2 in Appendix 4)
After choosing an answer for the previous statement, teachers were asked to
provide reason(s) for their answer (See Appendix 1). I could group those answers
into these different categories according to the aspects that those reasons shared
in common. The various categories identified are presented in the following table:
Category
Summary of comments
a) A meaningful
The grammar lesson becomes more meaningful and memorable
and memorable
for students, who feel motivated when they discover the rule by
grammar
themselves. Besides, some of the students understand better in
lesson.
that way than only having the teacher’s explanation. Moreover
students can realize that they can learn English without feeling
stressed by the grammar rules.
b) Young
This approach is likely to be successful with young learners.
learners.
c) Planning.
The efficiency of this approach depends on factors like the
purpose of the class; the students’ age and level as these all
have to be taken into consideration during the phase of lesson
planning. Also, participants wanted to clarify that the efficiency
of both approaches depends on the difficulty of the language to
be dealt with.
Children acquire their mother tongue because they are immersed in the proper
context of language learning, associating the real world with the language,
repeating and understanding the structures in a real context instead of memorizing
(Thornbury 1999). We can infer from the term “inductive approach”
that the
teacher attempts to encourage students to the grammar rule discovery without
presenting the structure from the very beginning. This discovery is intended to be
46
reached through exposure of appropriate input showing a variety of examples from
the real world –both spoken and written language- around them which implies
using the grammar structure contemplated in the syllabus content.
Item 7 “Choose from A-D to describe how you feel when you use the inductive
approach” (See Graph 3 in Appendix 4)
After choosing an answer for the previous statement, teachers were asked to
provide reason(s) for their answer (See Appendix 1). I could group those answers
into these different categories according to the aspects that those reasons shared
in common. The various categories identified are presented in the following table:
Category
Summary of comments
a) Students’
As students have to discover the rule, they pay more attention
attention.
to the lesson and are self-rewarded with a feeling of success
when they achieve it.
b) Discovering
Participants stated that most of the students enjoy discovering
the rule.
the rule through the realization of activities that are of their
interest. When students make the discovery, teachers can be
certain that those students achieved the aims of the lesson.
Both categories agreed that to draw the students’ attention to the lesson might be
an important factor in the learning process. The discovery of the rule might keep
students focused on the activities to work on the lesson and give them a feeling of
success when they discover the rule. Making use of a variety of activities might
allow the lesson to be more meaningful for them. This also helps students not to
feel bored of being exposed to the same teaching approaches in every class. In
this case both students and teachers achieve their aims: students learn having fun
and teachers might feel confident that their students are achieving the learning
process.
47
One of the participants said that he/she feels stressed using this approach but
he/she did not write any reasons for this answer. (See Graph 3 in Appendix 4)
Category
Comment
a) stressed
This participant did not provide any comment.
I think that this feeling might be explained if we bear in mind that a suitable lesson
using the inductive approach needs to employ appropriate activities and materials.
These activities and materials should allow the teacher to perform his/her role as a
guide and at the same time provide the necessary input for the students. In this
way, students may find out the rule without becoming confused. Therefore, while
using this approach, students might enjoy themselves and learn the lesson at the
same time. Nowadays teacher educations in ELT as well as the materials
emphasize the role of discovery learning. Most EFL teachers are expected to be
able to deal with various approaches to learning grammar. However, in some
cases, the teacher’s individual characteristics might influence his/her preferences
about one specific approach.
Item 8 ““Number the advantages that you notice using the inductive approach. List
them from 1 (most noticeable) to 5 (least noticeable)” (See Graph 3 in 3.2.1.1)
In this statement a space called “other(s)” (see Appendix 1) was provided in case
teachers wanted to add any other advantage. One participant used this space to
provide his/her personal opinion about using this approach. The information
provided was the following:
Category
Comment
A) Not all
This approach is not good for all the students since not all of
students
them understand equally.
understand
equally
48
He/she considers that this approach might not be appropriate for all the students.
He/she may refer to the fact that there are students who might miss certain
details of the lesson which leads to misusing the structure or pattern taught in the
class.
Item 9 “How do you prefer teaching grammar? Inductively, deductively or using a
combination?” (See Appendix 5)
After choosing an answer for the previous question, teachers were asked to
provide reason(s) for their answer (See Appendix 1). I could group those answers
into these different categories according to the aspects that those reasons shared
in common. The various categories identified are presented in the following table:
Category
Summary of comments
a) Variety in
By using a combination, the class can be more relevant and varied
the lesson.
so students do not expect the same from each class and teachers
can broaden their teaching techniques. In that way teachers can
introduce the class using the inductive approach and then reaffirm
knowledge with the deductive approach.
b) Combining
Using a combination of both approaches, teachers are able to
both
adapt the lesson according to the students’ needs and the aims of
approaches
the course.
It came as no surprise that the participants chose ‘a combination’ as a response.
However, my real interest was to find out what their reasons behind this choice
were. I also wanted to know details about teachers’ perceptions of using a
combination of both approaches. From their answers, I can infer that the benefit of
using both approaches is that, in such a way, teachers can use the advantages of
both approaches. For example, teachers may use each approach at different
stages of the lesson in order to fulfill certain aims. Another possible reason for
49
combining is to avoid predictability in the lesson. The benefit of supplying variety of
input is twofold: learners are exposed to various ways of dealing with the new
language and the learners’ needs may be attended as well.
Teachers might be rewarded with the accomplishment of reaching the intended
aims of the lesson, thus making their task more satisfactory.
Item 10 “Underline the percentage of each approach that you use when teaching
grammar. (The sum of both approaches must be a total of 100%)” (See Graphs 5
and 6 in 3.2.2)
One of the participants did not answer this section as expected (See Appendix 1).
Instead of underlining a percentage of each approach he/she wrote his/her opinion
about what the statement required of him/her. The information provided was the
following:
Category
Comment
a) Students’
This participant stated that he/she makes use of these
needs and
approaches in relation to his/her teaching needs and learners
demands.
demands, not in relation to a number.
Stating numbers or percentages for this item involved making an estimate of how
much time the teacher uses with each approach in the majority of the lessons. That
is to say, it takes into account that the teacher is already familiar with a group and
its characteristics. Teaching in general and teaching English as a foreign language
is often compared to an art rather than to an exact discipline, therefore, there was
no intention whatsoever to measure the teaching activity with a focus on numbers.
In actual fact, we need numbers to establish the timing of the various phases in a
lesson but there are other more subtle aspects that may also need some type of
estimation in terms of depth or duration in order to balance the realization of the
lesson. I agree there is no exact number, like a magic formula, to succeed in
50
teaching grammar. As a matter of fact, I agree with him about the idea that no
matter how carefully a teacher prepares a lesson if students are not able to
achieve the aims, a good teacher needs to be able to change the approach on the
spot.
3.4 Discussion
In the previous section the information gathered from the participants was
presented. Their responses allowed me to make the following considerations
based on this information.
Teacher education
During several decades in Mexico English teachers in general were people who
had learned English from other situations and studies: people who had either spent
time in an English speaking country or were native speakers. These teachers of
English were not always qualified, that is to say, their teacher education was not
that of a professional EFL teacher. Nowadays, there is the possibility of becoming
professional by means of engaging in one of the various types of EFL teacher
programs. These kinds of programs may range from relatively brief seminars,
workshops and specializations to full time highly academic programs such as BAs,
Masters and PhD. degrees. Therefore a large number of English teachers can
become qualified.
Participants’ age and education
Participants from this paper were all qualified English teachers with a great variety
in education (from BAs to PhDs) as well as age. I consider that the great diversity
in age and education among the participants was very helpful for my research.
Hence, I could have a broader outlook of how the deductive and inductive
51
approaches are perceived when using them. Thanks to this variation in age and
education, the teachers’ experience was very helpful for my research since they
shared information that I did not know and that I might not have found in books.
The age and education of participants allowed me to have various interesting
opinions. I could notice how the diversity in years of experience and education
showed in their responses.
For example, I could realize how a teacher with greater experience and higher
education referred to the role of the deductive and inductive approaches in relation
to different teaching environments. That is to say, he/she was able to describe the
possibilities of using the approaches appropriately according to a number of factors
such as age, level, and aims of the course. On the other hand, a participant with
fewer years of experience and lower education shared limited information about
how to manage these approaches. That is to say he/she wrote assertive and
general comments but in most of his/her answers he/she did not make reference to
factors such as age, level, or aims of the course.
Beliefs
I think that the different beliefs of the participants are a reflection of the variation of
age and education. Thanks to this diversity I could obtain a wide range of answers
and opinions with respect to the application of these approaches. There were
comments which were very specific and those helped greatly to develop this paper.
However, there were also a few comments which were expressed in a very general
way (the most common, “It depends”). From my point of view and for my research
interests these kinds of answers were not very helpful. I consider that offering this
sort of response does not help the researcher to find useful information since it
implies something that is difficult or even impossible to interpret.
52
These different kinds of answers could be due to many reasons. I could perceive
some of them, such as the experience participants have had teaching, the interest
in providing relevant information to my research, the time spent answering the
questionnaire and knowledge about the approaches. Although a number of the
ideas were expressed in different ways, somehow the participants ended up
sharing certain aspects: namely, the fact that in general, the use of a combination
of both approaches in the EFL classroom is recommended.
There were teachers that maybe because of their qualifications and experience felt
the need to express comments in some questions, even when they were not asked
to do so. Those comments helped to have a more detailed knowledge of their point
of view. They were also of great help in my own personal development as a
teacher of EFL.
Some participants who answered my questionnaire stated that the successfulness
of the deductive and inductive approaches in a classroom depends on many
different factors. I agree with them: the achievement of presenting a lesson using
either approach may not depend merely on how it is presented. For the success of
the lesson many factors should be taken into consideration as explained in the
qualitative analysis. Some of these factors are the students’ learning styles, the
students’ age, the students’ level, the aim and difficulty of the lesson.
These factors are important to take into account when teaching in order to have a
successful lesson. Sometimes it is not possible to cover all aspects because of the
variety of learning styles that may be found in a classroom but when teachers are
familiar with their group(s), they can notice which aspects of the deductive or
inductive approaches work better for them. Then teachers might take that into
consideration when presenting a grammar lesson. I believe that it is important to
highlight that using a combination of both approaches’ advantages might make a
lesson stronger.
53
Because of the participants’ characteristics –both personal and educational- they
have the capability to handle both approaches. This is not always the case. In
some teaching environments, English teachers may not always be aware of the
importance of all the previously mentioned factors. Therefore I consider the
information obtained for this paper may be useful for prospective, new or young
teachers, as well as for the active teachers who might be interested in improving
their craft.
54
Conclusion
This research enabled me to find out that a number of the participants are aware of
the approaches that can be used when teaching grammar. Working on this paper, I
was also able to realize the extent to which teachers are aware of the advantages
and disadvantages when using one or the other approach in the EFL context.
Regardless of the fact that sometimes teachers do not use the terms deductive and
inductive, they certainly show a mastery of the possibilities of using them in their
everyday work. They may not remember the exact name of the approach but
through use and experience they know how to apply these approaches when
planning a lesson and how to use them in the classroom.
The results only show limited information about these approaches in the teaching
of grammar because this was a very specific area that I wanted to explore. This
paper only intends to show an overview of the English teachers’ perspectives
about how they perceive these approaches. Further investigation could focus on
the specific procedures EFL teachers choose to implement the deductive and
inductive approaches when teaching grammar.
As a result it could be said that in general teachers consider both approaches
efficient for teaching grammar. None of the participants consider it appropriate to
use only one of the approaches in a lesson. I think this statement has to do with
the variety of students’ learning styles among other reasons and the objectives of
the lesson. As both approaches have advantages and disadvantages when
applying them in a lesson, all participants agreed that using a combination of these
approaches according to the students’ needs and the grammar point is the most
appropriate option.
55
I think this information may be useful for other EFL teachers because it can help
them to have a broader idea of the usefulness of these approaches. I believe that
the information provided in this research may be especially helpful for the ones
who have recently obtained BAs as English teachers because many of them may
have limited experience in the teaching of English. Hence, they can have a broader
idea of how these approaches are perceived when applied from the real world
point of view. The experiences provided by the participants may help these new
teachers to have a clearer idea of what approach could be suitable to use with
adult, teens or younger learners. Also new teachers might have a general idea of
what to take into in consideration when presenting a lesson.
Certainly, there is no magic formula for using these approaches and being
successful in teaching grammar. I may only highlight that it is crucial for EFL
teachers to pursue a deeper understanding of the ways in which we can help
students to achieve their English learning goals.
56
References
Anderson, M. and Larsen-Freeman, D. (2011) Techniques and Principles in
Language Teaching. New York: Cambridge University Press.
Crystal, D. (2010) The Cambridge Encyclopedia of Language. New York:
Cambridge University Press.
Davies, P. and Fraenkel, A. (2003) The Language in English Teaching. Mexico:
Richmond.
Drever, E. and Munn, P. (1990) Using Questionnaires in Small-Scale Research: a
teacher’s guide. Great Britain: SCRE Press.
Harmer, J. (2007) How to Teach English. England: Pearson Longman Press.
Madrid, M. T., Personal communication, February 8, 2013.
Nunan, D. (1991) Language Teaching Methodology: A textbook for teachers. New
York: Prentice Hall.
Odlin, T. (1994) Perspectives on Pedagogical Grammar. Cambridge: Cambridge
University Press.
Reid, J. M. (1995) Learning Styles in the ESL/EFL Classroom. New York: Heinle &
Heinle.
Rudin, S. (Producer) and Heckerling, M. (Director). (1995). Clueless (Movie).
United States: Paramount Pictures.
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Spratt, M., Pulvernes, A. and Williams, M. (2005). The Teaching Knowledge Test
Course. United Kingdom: Cambridge University Press.
Swan, M. (2006a) Grammar. Oxford UK: Oxford University Press. Retrieved from
http://fdslive.oup.com/www.oup.com/pdf/elt/catalogue/0-19-437241-3-a.pdf and
http://fdslive.oup.com/www.oup.com/pdf/elt/catalogue/0-19-437241-3-b.pdf
Swan, M. (2006b) Practical Language Usage. New York: Oxford University Press.
Thornbury, S. (2002) How to Teach Vocabulary. England: Pearson Longman.
Thornbury, S. (1999) How to Teach Grammar. England: Pearson Longman.
Ur, P. (1996) A Course in Language Teaching. New York: Cambridge University
Press.
Ur, P. (1988) Grammar Practice Activities. New York: Cambridge University Press.
58
APPENDIX 1
Estimada(o) maestra(o) de la manera más atenta solicito su cooperación para contestar la presente
encuesta. Su información contribuirá de manera importante en la elaboración de mi tesis, la cual aborda
una investigación sobre dos importantes enfoques para la enseñanza de la gramática en los cursos de
inglés como lengua extranjera: deductive and inductive.
La primera parte de la encuesta se refiere al “deductive approach”. La segunda parte se refiere al
“inductive approach”. Le ruego verifique que las dos partes queden contestadas.
PARTE 1
SECCIÓN UNO
Personal information
Qualifications:
BA
MA
Ph.D.
Age:
25-34
45-54
35-44
55-65
66Sex:
M
F
Level(s) of English taught:
Beginners
Lower-Intermediate
Elementary
Intermediate
Other (describe):
_____________________
_____________________
_____________________
Years in teaching experience:
1-4
10-14
15-19
5-9
20-24
25-29
30 or more
Upper-Intermediate
Advanced
SECCIÓN DOS: deductive approach
Deductive approach; implica la presentación de una estructura gramatical dada por el profesor la cual es
seguida por ejemplos en los que se aplica dicha regla. (Thornbury 1999)
1. Have you used the deductive approach with your students?
A) Yes
B) No
2. I consider that teaching grammar using the deductive approach is efficient.
A) Yes
B) No
Provide reason(s) for your answer:
____________________________________________________________________________________
____________________________________________________________________________________
_________________________________________________________________________________
*If the answer is NO, please go to SECCIÓN TRES question number 5
59
3. Choose from A-D to describe how you feel when you use the deductive approach.
A) Confident
B) Relaxed
C) Insecure D) Stressed
Provide reason(s) for your choices.
____________________________________________________________________________________
____________________________________________________________________________________
___________________________________________________________________________________
4. Choose from A-E to describe your students’ response when grammar is presented in a deductive way.
A) Excellent B) Very good C) Satisfactory D) Less than satisfactory E) Poor
SECCIÓN TRES
5. In the following tables read the description of some advantages and disadvantages when using the
deductive approach.
a). Number the advantages that you notice using the deductive approach. List them from 1 (most
noticeable) to 4 (least noticeable).
Advantages of the deductive approach
It goes straight to the point, and can therefore be
It respects the intelligence and maturity of many
time-saving.
students (especially adult).
It confirms many students’ expectations about
It allows the teacher to deal with language points
classroom learning.
as they come up.
Other(s):_________________________________________________________________________________
________________________________________________________________________________________
____________________________________________________________________________________
b). Number the disadvantages that you notice using the deductive approach. List them from 1
(most noticeable) to 4 (least noticeable).
Disadvantages of the deductive approach
It starts the lesson with a grammar presentation may
It encourages a teacher-fronted, transmissions
be off-putting for some students, especially younger
style classroom with the grammar explanation.
ones.
It
is
less
memorable
explanation
than
It encourages the belief that learning a language is
demonstration.
simply a case of knowing the rules.
Other(s):_________________________________________________________________________________
________________________________________________________________________________________
____________________________________________________________________________________
60
PARTE DOS: inductive approach
Inductive approach; implica la presentación de ejemplos donde se usa la regla gramatical y se espera
que el alumno descubra por sí mismo la regla a seguir. Thornbury, S. (1999) How to teach grammar.
SECCIÓN UNO
1. Have you used the inductive approach with your students?
A) Yes
B) No
2. I consider that teaching grammar using the inductive approach is efficient.
A) Yes
B) No
Provide reason(s) for your answer:
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
*If the answer is NO, please go to SECCION DOS question number 5
3. Choose from A-D to describe how you feel using the inductive approach?
A) Confident
B) Relaxed
C) Insecure D) Stressed
Provide reason(s) for your choices:
____________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
4. Choose from A-E to describe your students’ response when grammar is presented in an inductive way.
A) Excellent B) Very good C) Satisfactory D) Less than satisfactory E) Poor
SECCIÓN DOS
5. In the following table read the description of some advantages and disadvantages when using the
inductive approach.
a). Number the advantages that you notice using the inductive approach. List them from 1 (most
noticeable) to 5 (least noticeable).
Advantages of the inductive approach
Learners discover for themselves the rules.
Learners are more actively involved in the learning
Therefore, the rules may become meaningful.
process.
Learners’ abilities for pattern-recognition and
Learners have the opportunity for extra language
problem-solving are favored.
practice.
Learners engage in a process of preparation for
Other/s:____________________________________
greater self-reliance.
__________________________________________
_________________________________________
61
b). Number the disadvantages that you notice using the inductive approach. List them from 1
(most noticeable) to 5 (least noticeable).
Disadvantages of the inductive approach
Learners’ time and energy spent in working out
rules.
Learners may hypothesize the wrong rule.
Learners who would prefer simply to be told the
rule might be frustrated.
Learners’ time taken to work out a rule may be at the
expense on time spent in practicing the rule.
Learners (engaged in) solving activities within the
inductive approach should have teachers capable to
plan suitable lessons.
Other/s:____________________________________
__________________________________________
__________________________________________
_________________________________________
SECCIÓN TRES
En la práctica es poco probable que se utilice un solo enfoque al impartir las clases, lo más común es que
se dé una combinación. Las siguientes preguntas están relacionadas con ello.
1. How do you prefer teaching grammar? Inductively, deductively or using a combination?
Provide reasons.
____________________________________________________________________________________
____________________________________________________________________________________
___________________________________________________________________________________
2. Underline the percentage, of each approach that you use when teaching grammar. (The sum of both
approaches must be a total of 100% approximately).
Deductive approach
Inductive approach
a) 10 to 20%
e) 51 to 60%
a) 10 to 20%
e) 51 to 60%
b) 21 to 30%
f) 61 to 70%
b) 21 to 30%
f) 61 to 70%
c) 31 to 40%
g) 71 to 80%
c) 31 to 40%
g) 71 to 80%
d) 41 to 50%
h) more than 80%
d) 41 to 50%
h) more than 80%
= 100%
Thank you very much
for your time!
62
APPENDIX 2
Personal information
Graph 1
Graph 2
Graph 3
63
Graph 4
Graph 5
64
APPENDIX 3
Deductive approach
Graph 1
Graph 2
65
Graph 3
Graph 4
66
APPENDIX 4
Inductive approach
Graph 1
Graph 2
67
Graph 3
Graph 4
68
APPENDIX 5
69