CHAPTER ONE

THE PROBLEM

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