## CHAPTER ONE THE PROBLEM 1.1 Introduction Mathematics is one

CHAPTER ONE

THE PROBLEM

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1.1     Introduction

Mathematics is one of the core subjects that are
offered in all pre-tertiary institutions in Nigeria. “It is the science of
structure, order and relation that has evolved from elementary practices of
counting, measuring and describing the shapes of objects, it deals with logical
reasoning and quantitative calculation and its development has involved and
increase the degree of idealization and obstruction of its subject matter”
(Encyclopedia Britannica, 2013). Kolawole, Oladosu and Ajetunmobi (2013) opined
that mathematics is an instrument that is used to facilitate the learning of
other formal school subjects, and also very important tool for resolving problem
situations in all disciplines. It is with the realization of the importance of
Mathematics education that compelled the Federal Government of Nigeria made Mathematics
compulsory subject at both primary and secondly levels of the Nigerian
educational system (Mathew and Kenneth, 2013). This compulsory nature of Mathematics
carries with it assumption that the knowledge of the subject is essential for
all members of the society. However, this enables most citizens to acquire the
basic Mathematics knowledge and skills for effective contribution to community
and national development. Okereke (2006) opined that Mathematics competence is
a critical determinant of the post-secondary education and career options
available to young students.

The Nigerian Secondary School Mathematics Curriculum
is developed and structured around six main concepts, namely; Algebra; Number
and Numeration; Geometry; Mensuration; Statistics and Probability; and Trigonometry.
Trigonometry has long been a standard
component of the secondary school curriculum in Nigeria, usually in the latter
half of the secondary years. Table 1.1 shows the Mathematics Curriculum in Nigeria.

Table 1.1 Distributions of the Curricula of
Mathematics at Post-Primary in Nigeria.

Course                                JSI            JSII       JSIII         SSI           SSII           SSIII

Algebra

Geometry

Mensuration

Number and Numeration

Statistics and Probability

Trigonometry

Source: NERDC Abuja (2013) Secondary School Mathematics Curriculum

Trigonometry is an important branch of school Mathematics
that has everyday application in the life of the child, especially in
estimation, construction, technology and astronomical relationships (Sidhu, 2006).
Trigonometry is the aspect of Mathematics involving the measurement of
distances, angles, lines and surfaces. The knowledge of trigonometry assists
the students to appreciate the shapes and situation around their environment
and helps to develop their inductive reasoning skills that become necessary
ingredient for learning Mathematics, unlike geometry, trigonometry constitutes
a substantial part of the senior secondary school Mathematics, which form a
great part in their assessment (Abakpa, 2011).

Despite
the importance attached to trigonometry to our-day-today activities and as
agents of nation’s development and wealth creation, student’s attitude and
performance towards trigonometry has not been encouraging. Many factors have
been identified by Ahmad (2014) as reasons for the poor performance of students
in trigonometry; such factors include government policies, curriculum planners,
examination bodies, teachers’ attitudes, students’ attitudes, home, and lack of
qualified mathematics teachers that will handle the abstract curriculum that
does not address to immediate use of trigonometry in everyday life. Apart from
these, other factors have also been identified, such as poor primary school
background in Mathematics, lack of interest on the part of the students, students’
attitude towards trigonometry, lack of incentives for the teachers, lack of
qualified teachers in primary schools, students’ perception that trigonometry
is difficult, large class size syndrome, psychological fears of the subject and
poor method of teaching. Massive and consistent failures of students in
mathematics have remained a major threat to its learning. Nworgu (2013)
reported that the Federal Government described the poor performance of students
in mathematics as unacceptable and warns that the trend has to be checked if the
country has to move forward. Table 1.2 illustrates the performance of students
in WAEC, 2007-2016

Table 1.2 Performances
of Students in Mathematics in WAEC 2007- 2016

YEAR

Total No. of students Who Sat

No. of Students that Obtained Credit
& Above (A1 – C6)

% of Students with Credit & Above
(A1 -C6)

No. of Students with (D7-F9)

% of Students with (D7- F9)

2007

1,275,330

198,441

15.56

1,076,889

84.44

2008

1,369,142

314,903

23.00

1,054,239

77.00

2009

1,373,009

425,633

31.00

947,376

69.00

2010

1,351,557

453,447

33.55

898,110

66.45

2011

1,540,250

587,630

38.93

952,620

61.07

2012

1,675,224

819,390

49.00

852,834

51.00

2013

1,543,683

555,726

36.00

987,957

64.00

2014

1,692,435

529,732

31.30

1,162,703

68.70

2015

1,593,442

544,638

34.18

1,048,804

65.82

2016

1,544,234

597,310

38.68

946,924

61.32

Source: (WAEC, 2016)

It could be observed from Table 1.2 that the
students’ performance for the period is less than 50% throughout the years with
the exception of 2013 and 2016 in which the performance slightly raised to
64.26 and 52.97 respectively. Bearing in mind the importance attached to
trigonometry the continued low performance would lead to ripple effects which
undermine the future development of the country. Generally trigonometry is
considered by many as uninteresting, boring and difficult.

However, the performance
of students depends largely on the quality of  teacher’s competence and the use of a wide
variety of techniques to change the students’ attitude. In order to complement
other instructional strategies which are being used in the teaching and
learning of mathematics, to this end the researcher is of the opinion that if
Mathematical-Games and Analogical Instructions are incorporated to complement
the conventional method of teaching Mathematics could help in development
positive attitude and improved the academic performance of students.

In every culture children play games as part of
learning to show up in the culture or as a pass-time or leisure. The idea of
using games to engage students in the process of active learning, over the past
several years is well pronounced, Educators have been increasingly
incorporating various games into their teaching curriculum in an effort to
create a fun and engaging learning environment for students. Games have been
used to teach Science and Mathematics in Nigeria (Azuka, 2005). Datun(2005) views
Mathematical games as activities in the form of puzzles, magic tricks,
fallacies, paradoxes or any type of Mathematics which provides amusement or
curiosity. Mathematical games can facilitate the mathematical environment as
they reduce boredom, tension and establish a friendly atmosphere, which allows
for the growth of interest, skills, attitude and knowledge.

Ainsworth and Habgood (2009), opined that when
students are engaged in mathematical activities they can succeed where it count
in applying their skills and reasoning ability to solve real-life problems
requiring, mathematical solutions. One way to arouse students’ interest in
learning mathematics is the integration of mathematical game. Mathematical
games bring joy to the learners and teachers, helps to break resistance or
negative attitude to learning by reducing tension, it also flushes boredom and
providing an environment for learners to develop interest and acquire skills
and competence in mathematics. Games enhance learners to think mathematically, imbibe
the culture of cooperation, competition organization and spirit of individualism
(Okigbo and Okeke, 2011). Games do not only help in reducing tension and
boredom in class, but also provide an environment where the students can
develop their individual and collective skill and acquire more knowledge. Games
and mathematics are related because each has rules which involve experience,
drill and practical application to real life situation.

Analogy is a process of
identifying similarities between two concepts. The familiar concepts are called
the analog and the unfamiliar concepts are called the target (Glynn in Nworgu,
2009). According Ruhl (2003) analogy is a comparison of something unfamiliar
with something familiar in order to explain shared principles. The students
could use this process for comparison between newly introduced concepts
(unfamiliar) with the previous concept (familiar) for better understanding.
Analogy is when some less familiar domains or abstract concept are made more
understandable to the learners are by making references to similar relations
object or situation with which the learners are familiar. Moreover, Sani (2006)
opined that analogy is one the teaching strategies within the constructivist
frame that has evidently proved effective in preventing and overcoming poor
performance and wrong perception of the students towards trigonometry.

Furthermore, Sani (2006)
reported three benefits of the use of analogies as a teaching strategies for
abstract concepts, these are:

i.      it
provides visualization of abstract concepts.

ii.    It
helps compare the similarities of the students’ real world with the new
concepts.

iii.   it has
a motivational function.

Attitudes are psychological orientations developed
as a result of one’s experiences which influences a person’s view of
situations, objects, and people and how to respond to them either positively or
negatively or favourably or unfavourably (Mensah et al, 2013). Attitude is an
organization of beliefs, feelings and behavioral tendencies. In education, attitude has been
identified as one of the important elements which determine students’ success
(Cetingöz and Özkal, 2009). Attitudes affect the students’ interaction with
their friends, families, school and lessons. Therefore, positive students’
attitude towards trigonometry will add to their academic performance.

Academic performance refers to how well
a student is accomplishing his or her task and studies (Scortts 2012). Smith, (2010)
defined Academic performance as a display of knowledge attained or skills
developed in schools subject designated by test and examination scores or marks
assigned by subject’s teachers, therefore, academic performance is the outcome
of education: the extent to which the student, teacher or institution have
achieved their educational goals. In the context of this study, academic
performance refers to observable or measurable behavior of a student in a particular
situation usually an experiment. Kathryn (2010) opined that academic
performance encompasses the students’ ability and performance in all academic disciplines
in a class as well as extracurricular activities.

From the on-going,
teaching strategies and attitude of students may have effects on the academic
performance of students; therefore, the study intends to find out the “effects of Mathematical-games and Analogical instruction
on attitudes and performance in trigonometry among Secondary School Students in
Zaria, Kaduna State”.

1.2
Statement of the Problem

Despite the relative importance of Mathematics in
science and technology, students’ performance in the subject in both internal
and external (WAEC) examination has remained consistently poor (Adolphus, 2011).
Mathematics educators are trying to identify the major problems associated with
the teaching and learning of mathematics in the nations’ schools. Many factors
were identified which includes inadequate facilities instructional material, students
attitudes, poor infrastructure, manpower deficits in schools and the over
population of students are among causes of poor performance of students in WAEC
examination (Alausa, 2013).It is also observed that, students factor is a
direct cause for their success or failure in Mathematics, no matter how
professional the teachers is, no matter the amount of instructional materials
provided without the students to exhibits the right attitude and learn with a
strong determination for success all other efforts become unproductive, thus, the
performance of students in a subject is determined by the students attitude.
The negative attitude of students towards Mathematics and particularly the
concepts of trigonometry tend to create fear and anxiety among students who
continue to perform dismally as they lack the interest, curiosity and patience
needed for learning.

The report of WAEC (2015) Chief Examiner,
Mathematics educators and researchers revealed that most students including
those who passed Mathematics at credit level and those who failed, haphazardly
attempted geometry and trigonometry questions or avoided them completely. Instructional
strategies employed by the teachers’ play an important role in the acquisition of instructional content for
meaningful learning. Nigerian secondary schools classrooms are predominantly
dominated by lecture method of instruction, which does not encourage students’ active participation and interaction. Studies in
many areas of education have shown that the method of teaching utilized by the
teacher is an important factor in students learning and subsequent performance
in examination (Obeka, 2014).

In
view of the above, the researcher intends to use Mathematical-games and Analogical
instructions in teaching some selected concepts in trigonometry in order to
investigate their effects on student’s performance. In other words, could the
use of Mathematical-games and analogical instruction help to enhance student’s attitude
and performance towards trigonometry?

1.3       Objectives of the Study

The major purpose of this
research work is to find out the effects of mathematical-games and analogical
instructions on attitudes and performance in trigonometry among secondary
school students in Zaria. Specifically, the objectives of this Study are to
find out:

1.
the effects
of mathematical-games and analogical instructions on student

performance when taught trigonometry.

2.
the Change
in attitude of students’ towards trigonometry when taught using

mathematical-games and analogical instruction
strategies.

3.
the effects of mathematical games and analogy
instructions on the

performance of male and female students in
trigonometry.

4.
the change
of attitude on students’ gender taught trigonometry with

mathematical    games and analogy instruction strategies.

1.4       Research Questions

Based on the stated objectives, the following
research questions are formulated for answering:-

1.
What is the difference
in the mean performance scores between students taught

trigonometry using mathematical-games, analogical
instruction and those

taught using lecture method?

2.
To what extent
does the attitude of students taught trigonometry using

mathematical-game, analogical instruction differ
from those taught using

lecture method differ?

3.
How does the
mean performance scores of male and female students differ

when taught
trigonometry mathematical-game and analogical instruction?

4.
What are the
differences in attitude change between male and female students

taught
trigonometry using   mathematical-games and analogy instruction?

1.5       Hypotheses

From the research questions four null hypotheses
were formulated and will be tested at P?0.05 level of significance.

H01:     there is no significant
difference in the mean performance scores of students

taught
trigonometry using mathematical-game, analogical instruction and

lecture
method.

H02:     there is no significance
attitude change between students taught trigonometry

using mathematical-game,
analogical instruction and lecture method.

H03:     there is no significant
difference in the mean performance scores of male and

female students
taught trigonometry using mathematical-game and analogical

instruction.

H04:     there is no significant
difference between the attitude of male and female

students
taught trigonometry using mathematical-games and analogical

instruction

1.6       Significance of the Study

The significance of this study lies in its
potentiality of addressing key issues in the teaching and learning of
mathematics as a compulsory discipline as well as being its prerequisites for
further education. It is expected that the findings of this study will
hopefully be useful and uplift the standard of mathematics education.
Specifically, the significance was discussed under the applications and implications
of the research for students, teachers, curriculum planners, the government and
other researchers in the following ways:

Students will hopefully develop
a positive attitude towards mathematics and enable them to know that
mathematics is fun and learners friendly. Thus, have better scores and
performance in mathematics. This study will also be of importance to teachers
of mathematics who will find mathematical-game and analogical instruction
result oriented and applicable in their teaching of trigonometry and
mathematics in general and thus enable them to employ mathematical-game and
analogical instruction as a guide for developing a wide range of classroom
activities which are capable of making teaching and learning of mathematics
more meaningful.

It is also hoped that the study will
help the curriculum experts/planners in plans to improve in the standardization
of educational programmes and hopefully extend the frontiers of knowledge and
stimulate further researches on teaching and learning of mathematics in Nigeria.

Furthermore, it is also
hoped that science and research based organizations like Science Teachers
Association of Nigeria (STAN), Mathematical Association of Nigeria (MAN),
National Educational Research Development Council (NERDC) etc. will find this
study useful and will see the need
emphasize the use of mathematical-game and analogical instruction in
mathematics teaching in secondary schools in Nigeria.

The study is significant to extent it
is hoped that it will help to improve students attitude and performance in mathematics.
The potentiality of mathematical-game and analogical instruction will hopefully
make it easier for teachers to expose pupils to certain mathematical concepts
that are real and meaningful with much emphasis.

It is also hoped that
the study will be of benefit to society in that the study will help to improve
student’s attitude and performance in mathematics. Thereby, the subject and its
allied courses (Engineering, Medicine, and Physics, etc.) will be studied by
many students in institutions of higher learning. This will raise our nation’s potential in the use of Science and Technology
for capacity building and sustainable growth. In increase, researchers can
utilize the findings of the study as a basis for their inquiry. The researcher
believes that the findings of the study will make a modest contribution to the
existing body of knowledge and also be useful for further research in mathematics
education.

1.7       Basic Assumption

For the purpose of this
research, the following assumptions are made, thus:

1.
The selected
topics are appropriate for the level of the students used for the

research.

2.
The
mathematics teachers are familiar with the use mathematical-games and

analogical
instruction in teaching trigonometry.

3.
The Students
have some foundation of trigonometry concept from their

previous
class which is needed for the present study.

4.
Learning by doing
could enhance and motivate students to improve on their

performance
in mathematics.

1.8
Scope/Delimitation of the Study

The research is aimed at
investigating the effect of two teaching strategies, mathematical game and analogical
instruction on the academic performance among senior secondary school students
in the Zaria educational zone. The research is delimited to SSII students of some
selected senior secondary schools in Zaria educational zone because SS II are
familiar with trigonometry concept and more stable class, SS I are just into
the senior secondary and are not familiar with the trigonometry concepts needed
for this study and the SSS III are preparing for their senior secondary
certificate examination (SSCE). The study will cover all aspects of trigonometry
and Mathematics SSII for senior secondary schools. The trigonometry topics
selected for the conduct of this study are:

1.
Pythagoras
theorem

2.
Trigonometric
ratio of special angles

3.
Angles of
elevation and depression

4.
Sine  and Cosine rule

5.
Bearing and
distances

These topics were chosen
because they form part of the SS II syllabus and basic foundation for learning
trigonometry. Also the WAEC (2015) chief examiners report identified these
topics as difficult and students’ lack of understanding of the concepts in
their workings.

The study will use two
instruments, which will be developed by the researcher for data collection.These
are:

1.
Trigonometry
Performance Test (TPT) which is made up of 40 structured multiple choice
questions on trigonometry.

2.
Trigonometry Attitude Questionnaire (TAQ)
is a 20- item questionnaire that will be adapted from Lim and Chapman  (2013) the TAQ will be administered to both
the experimental groups and the control group before and after the treatment to
determine change in attitude of the students towards trigonometry and
mathematics in general .the TAQ will be scored based on Likert five (5) point
scale: strongly agreed (SA), agree (A), undecided (UD) disagree (DA) and
strongly disagree (SD).Period  of the
treatment will last for six weeks

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