# 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.

## Chapter One

### Introduction

#### 1.1 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.

#### 1.2 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?’

#### 1.3 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).

#### 1.4 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.

#### 1.5 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.

#### 1.6 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?

#### 1.7 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).

**Comparative Effectiveness Of Mathematical Game And Instructional Analogy As Advance Organizers On Students’ Achievement And Interest In Mathematics **

**Comparative Effectiveness Of Mathematical Game And Instructional Analogy As Advance Organizers On Students’ Achievement And Interest In Mathematics**

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