COMPARATIVE EFFECTIVENESS OF MATHEMATICAL GAME AND INSTRUCTIONAL ANALOGY AS ADVANCE ORGANIZERS ON STUDENTS’ ACHIEVEMENT AND INTEREST IN MATHEMATICS
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COMPARATIVE
EFFECTIVENESS OF MATHEMATICAL GAME AND INSTRUCTIONAL ANALOGY AS ADVANCE
ORGANIZERS ON STUDENTS’ ACHIEVEMENT AND INTEREST IN MATHEMATICS
ABSTRACT
The aim of
this study was to compare the effectiveness of mathematical game and
instructional analogy on achievement and interest of JS2 mathematics students.
Six research questions and eight null hypotheses provided focus to the study.
Literature confirmed that game activity was more physical (hands-on) than
analogy activity which was more intellectual (minds-on). The design was quasi-
experimental that employed a pre-test, post-test` non-randomized control
groups. A total of 246 mathematics students stratified and randomly selected
from students’ population of 3900 were involved in the study. Two instruments:
Mathematics Interest Inventory (MIntIv) and Mathematics Achievement Test (MAT)
were used for data collection and were validated by the experts and the
reliability established to be 0.85 and 0.89 respectively. Also, mathematical
game, bridging analogy teaching plan and lesson plan were used as instructional
tools. Results were analyzed using mean, standard deviation, 2 x 3 Multivariate
Analysis of Covariance (MANCOVA) and Z- test. From the findings, it was
observed that; game and bridging analogy teaching enhanced both achievement and
interest in mathematics more than lecture method; no significant difference
exists in the achievement and interest of male and female mathematics students
taught with either game or analogy; there was no significant interaction
between teaching methods and gender on students’ achievement in mathematics;
and a non-significant interaction effect was observed between teaching methods
and gender as measured by the students interest in mathematics. Since game and
analogy enhanced achievement and interest of mathematics (male and female)
students equally, by implication teacher effectiveness resulting from the use
of these techniques will affect students in learning mathematics which may
result to a remarkable achievement and sustenance of learners interest. The
study recommended that mathematics teachers should provide instructional
activities such as games and bridging analogy teaching before, within and after
a mathematics lesson in order to relate mathematics to real life; and to ensure
that mathematics teachers grasp the tenets of the two techniques, pre-service
mathematics teachers should be trained on their uses during their training
process and the in-serving mathematics teachers also re-trained.
Background
to the Study
For science
and technology to successfully achieve the goals of sustainable development in
any country, there is need to engage creatively in science and mathematics
education. Bajah (2000) noted that no nation can make any meaningful progress
in the information technology age, particularly in economic development without
technology which has science and mathematics as its foundations. This is
because the level of Science, Technology and Mathematics Education (STME) of
any nation has been widely accepted to be indicative of that nation’s
socio-economic and geo-political development.
In the
National Policy on Education, Federal Republic of Nigeria (2004), mathematics
is one of the core subjects to be offered by all students up till the tertiary
levels of education. This compulsory nature of mathematics carries with it the
assumption that the knowledge of the subject is essential for all members of
the society. In fact, mathematics competence is a critical determinant of the
post- secondary education and career options available to young people
(Okereke, 2006). Stressing on the importance of mathematics, Ukeje (1986)
described the subject as the mirror of civilization in all the centuries of
painstaking calculation and the most basic discipline for any person who would
be truly educated in any science and in many other endeavours.
Despite the
importance placed on mathematics, it is very disappointing to note that
students’ performance in the subject at both internal and external examinations
has remained consistently poor. Also, statistics show that mass failure in
mathematics examination is real and the trend of students’ performance has been
on the decline (Betiku, 2002; Maduabum & Odili 2006; WAEC, 2008; NECO,
2009).
Many
variables had been identified by Betiku (2002) as responsible for the poor
performance of students in mathematics. Such variables include governments,
curriculum, examination bodies, teachers, students, home, and textbook. The
government failed to train and recruit more qualified mathematics teachers with
a teacher: student ratio of 1:80 that will handle the abstract curriculum that
does not address to immediate use of mathematics in everyday life. Some of the
available few mathematics teachers give the students impression that
mathematics is meant for special people. Apart from these variables, some
specific variables have been identified by Udeinya & Okabiah (1991) and
Amazigo (2000) to include: poor primary school background in mathematics, lack
of interest on the part of the students, lack of incentives for the teachers,
incompetent teachers in primary schools, students not interested in hard work,
perception that mathematics is difficult, large class syndrome, psychological
fear of the subject, poor methods of teaching, and lack of qualified
mathematics teachers, which results in teaching of the subject by unqualified,
untrained and inexperienced auxiliary teachers. The poor performance in
mathematics also emanated from anxiety and fear. Phobia has been observed by
Aprebo (2002) to be an academic disease whose virus has not yet been fully
diagnosed for an effective treatment in the class and the symptoms of this
phobia are usually expressed on the faces of mathematics students in their
classes. He further pointed out that the final output of this fear is spread to
all subjects that relate to mathematics and this may result in learners
refusing to improve their interest in mathematics. The WAEC Chief Examiner’s
Report (2005) suggested that students’ performance in mathematics could be
improved through meaningful and proper teaching. According to the report,
teachers should help students develop interest in mathematics by reducing the
abstractness of mathematics, and thence remove their apathy and fears of the
subject. Thus it becomes pertinent to look for interventions that could be
manipulated in order to find their effects on learning outcomes. This could
address the problems of teaching and learning of mathematics in schools. Based
on this, the researcher used mathematical games and analogies as advanced
organizers in teaching mathematics students two units of JS2 mathematics
contents and compared their effects with teaching without advanced organizer
(using modified lecture method).
Mathematical
games and instructional analogy are types of advance organizer learning
strategies advocated by Ausubel (1962). Ausubel in Onwioduokit & Akinbobola
(2005) described advance organizer learning strategy as a pedagogic strategy
for implementing the programme principles of progressive differentiation and
integrative reconciliation which involves appropriately linking the known with unknown.
It is used to provide a conceptual framework which students can use to clarify
the task ahead.
Obodo (1997)
described mathematical games as activity in form of puzzles, magic tricks,
fallacies, paradoxes or any type of mathematics which provides amusement or
curiosity and stimulates mathematical thinking, excitement and spirit of
competition and co- operation. Many reasons abound for using mathematical
games. The games help to reduce the level of abstraction involved in teaching
and learning a concept in mathematics, capturing the learner’s interest and
providing for active participation of the students. Obodo further stressed that
games do not only help in releasing tension and boredom in class but also
provide an environment where the children can develop their individual and
collective skills and acquire more knowledge.
Harrison
& Treagust (1993) see analogy as synonymous with similarity and
instructional analogy which they refer to as instances in instruction in which
some less familiar domains or abstract concepts are made more understandable to
the learner by making references to similar relations, objects or situations
with which the learner is familiar. Researchers (Goswami, 1992; Bassok, 2001)
across disciplines have shown that analogical reasoning may be central to
learning of abstract concepts, procedures, novel mathematics and the ability to
transfer representations across contexts.
Lecture
(expository) method of teaching is a teacher-centered, student-peripheral
teaching approach in which the teacher delivers a pre-planned lesson to the
students with or without the use of instructional materials (Nwagbo, 1999).
According to her, in using this method, the teacher ‘talks about the subject’
while the students ‘read about the subject’. However, the modified lecture
method used in this study involves more than ‘talking’ and ‘reading’ about
mathematics for it allows some interactive between the teacher and the students
in terms of asking and being asked questions on the topic of discussion. Thus
to some extent this interaction can help to improve the achievement and
interest of mathematics students.
Although
mathematics is recognized as abstract subject that can easily be learnt by high
achievers only, literature (Ezenwa, 1996 and Nworgu, 2005) had shown that
mathematics is more of boys’ than girls’ favourites. Strategies such as the use
of mathematical games and analogies as advance organizers in teaching could
help to enhance mathematics learning, appreciation and achievement. Hence the
study intends to compare the effectiveness of mathematical game and
instructional analogy as advance organizers on achievement and interest of male
and female mathematics students.
Statement of
the Problem
Evidence of
poor performance shown by researchers (Okereke 2006; WAEC, 2005-2009, NECO,
2009) points to the fact that the current methods of teaching mathematics may
not be exciting to the students. This may lead to students’ lack of
understanding of the concepts, functionality and application of mathematics ideas.
The WAEC Chief Examiners (2007, 2008 & 2009) consistently reported that
students dodge questions on number and numeration and algebra and when an
attempt is made they show lack of understanding of the concepts in their
workings. The reports also show a general poor performance in the subject.
Based on the
forgoing, the researcher decided to use games and analogy as advance organizers
in teaching some concepts in mathematics in order to observe their effect on
students’ achievement and interest. In other words ‘could the use of
mathematical games and
analogy as
advance organizers in teaching mathematics enhance achievement and interest of
mathematics students?’
Purpose of
the Study
The purpose
of this study is to investigate the effects of mathematical game and
instructional analogy as advance organizers on the achievement and interest of
junior secondary school students in mathematics.
Specifically,
the study is designed to:
Investigate
the extent to which the use of mathematical games and Instructional analogy as
advance organizers will enhance the achievement of mathematics students.
Compare the
achievement of the students when taught mathematics with mathematical games, analogies,
and when taught with modified Lecture method (without advance organizers).
Find out if
there is a significant change in interest of the students when taught
mathematics using mathematical games, instructional analogy and modified
lecture method.
Compare the
achievement of male and female students taught with mathematical games and
analogies (advance organizers).
Compare the
interest of male and female mathematics students taught with mathematical games
and analogies (advance organizers).
Significance
of the Study
The findings
from this study are beneficial to many people through improving the poor
performance of mathematics learners. These people include; teachers, learners,
curriculum planners, textbook writers, government and the society at large.
The study
will help the teacher in proper implementation of the curriculum. From the
advantages of mathematical games and instructional analogy, their use in
mathematics classroom will motivate the teachers in handling the subject well
by directing the students on how to apply mathematics in their day-to-day
living. This is because the two strategies could help the teacher in entry
behaviour testing, introducing novel concepts, teaching difficult concepts and
provision for active involvement of the learners.
The findings
of this study will help secondary school students to remove some of the social
apathy towards mathematics and that their achievement depends on their own
active participation not only their teachers. Thus, the students will appreciate
the need for their involvement in mathematics activities in their classroom and
this may help them to acquire both mathematics skills and mathematics knowledge
which will enhance capacity building and sustainable development. In other
words, the students will be enabled towards achievement of national goals for
mathematics education.
The
knowledge of the use of mathematical games and bridging analogy teaching will
help the curriculum planners to apply the strategies when reviewing mathematics
curriculum. Thus the curriculum should be organized in such a way that it will
enhance capacity building and sustainable development. Also the goals of the
curriculum planners will be re-directed towards more on acquisition of
performance skills in mathematics than on acquisition of knowledge. To achieve
this aim, government and other education authorities will realize the
importance of organizing seminars and regular workshops on mathematics to
educate the in-service teachers on this need.
It is
expected that the results of this study would be helpful to mathematics
textbook writers to design and apply the use of mathematical games and analogy
in structuring their textbook. In this way the teachers will use them when seen
in the teacher’s guide to improve their knowledge of the two strategies. The
textual materials would gain an appeal and efficacy if adequate number of
suitably structured mathematical games and analogies are used by the text- book
writers at strategic positions in their texts.
Finally, the
society will benefit from the study because if the study helps to improve
students’ achievement and interest in mathematics, then the subject and its
allied courses (engineering, pharmacy, industrial physics, etc) will be studied
by many students in institutions of higher learning. If students study
mathematics and its allied courses, our dream in the use of science and
technology for capacity building and sustainable development will be fully
realized.
Scope of the
Study
The study
concentrated on the effect of two teaching strategies (mathematical game and
bridging analogy teaching) on achievement and interest of Junior Secondary Two
(JS2) mathematics students. The study also looked into how the effect of the
use of two advance organizers in teaching is reflected on gender of the
students.
More so, the
content of the teaching covers two major units in junior secondary school
mathematics syllabus namely: Number and numeration
Algebraic
expression
Each unit is
broken down into topics as follows:
Number and
numeration
Whole
numbers and decimal numbers
Fractions
Approximation
Multiplication
and division of directed numbers
Algebraic
expression
Algebraic
equations
Solving
simple algebraic equations
Factorization
of algebraic equations
Word
problems on algebraic fractions
These topics
were chosen because they form part of the basic foundations for learning any
other concepts in secondary school mathematics. Also WAEC Chief Examiners
2005-2009 identified these areas as difficult and students’ lack of
understanding of the concepts therein in their workings.
Research
Questions
The
following research questions provided focus to this study.
What are the
standard deviation and mean gain scores in achievement of students taught
mathematics through the use of mathematical game, instructional analogy and
modified lecture method?
What are the
standard deviation and mean gain scores in interest of students taught
mathematics using mathematical game, instructional analogy and modified lecture
method?
What are the
standard deviation and mean gain scores in achievement of male and female
mathematics students taught mathematics with mathematical game?
What are the
standard deviation and mean gain scores in achievement of male and female
mathematics students taught mathematics with instructional analogy?
What are the
standard deviation and mean gain scores in interest of male and female
mathematics students taught mathematics with mathematical games?
What are the
standard deviation and mean gain scores in interest of male and female
mathematics students taught mathematics with instructional analogy?
Research
Hypotheses
Based on the
research questions, eight null hypotheses were formulated and tested at 0.05
level of significance
There is no
significant difference in the mean achievement scores of students taught
mathematics using mathematical game and those students taught with
instructional analogy and modified lecture method.
There is no
significant change in interest amongst students taught mathematics with
mathematical game, instructional analogy and lecture method.
There is no
significant difference in the mean mathematics achievement scores of male and
female students taught mathematics using games.
There is no
significant difference in the mean mathematics achievement scores of male and
female students taught mathematics using analogy.
There is no
significant change in the mean interest scores of male and female students
taught mathematics with games.
There is no
significant change in the mean interest scores of male and female students
taught mathematics with analogy.
There is no
significant interaction between gender and teaching methods as measured by the
mean scores in Mathematics Achievement Test (MAT).
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