INFLUENCE OF CONCRETE MANIPULATIVE TACTICS ON OUTLOOK, RETENTION AND PERFORMANCE IN GEOMETRY AMONG JUNIOR SECONDARY SCHOOL STUDENTS IN BENUE STATE, NIGERIA
This study investigated the Effect of Concrete Manipulative Approach on Attitude, Retention and Performance in Geometry among Junior Secondary School Students in Benue State, Nigeria. Quasi-experimental research design was used for the study. The total population of the study consisted of 6230 Junior Secondary School Two Students in Benue State, Nigeria. A sample of 211 students was drawn from the population for the study using a stratified proportionate random sampling technique. The instruments used to collect data
were: Students’ Geometry Attitude Questionnaire, Geometry Performance Test and the Instructional Instrument (Lesson Plans).The Questionnaire and the test instruments were validated by three experts and had a reliability of coefficient of 0.90 and 0.71 respectively. Five research questions were raised and five hypotheses were formulated to guide the study. The research questions were answered using the mean and standard deviation while the hypotheses were tested at 0.05 level of significance using Mann-Whitney U-test and ttest statistical tools. The results of this study indicated that (1) Students’ attitude was rated positive in the Geometry concepts taught due to the use of Concrete Manipulative Approach. (2) Concrete Manipulative Approach was not gender bias in attitude formation. (3) The Concrete Manipulative Approach improved the performance of students taught Geometry concepts in Mathematics. (4) Female students exposed to the Concrete Manipulative Approach, performed equally with their males counterparts. (5) The retention ability of students exposed to Concrete Manipulative Approach was found to be better than that of the students’ exposed to the Conventional Lecture Method. Based on the findings from this study, it was recommended that:(1) The Concrete Manipulative Approach be used by Students of Geometry in learning as it helped to form positive attitude inlearning Geometry. (2) It was also recommended that the Concrete Manipulative Approach be used by Teachers of Mathematics, as the use of it aid students to retain much of what was learnt. (3) It was recommended that the Concrete Manipulative Approach be used to teach Junior Secondary School Students in order to clear the beliefs that the study of Geometry is masculine. (4) It was also recommended that Concrete Manipulative Approach be incorporatedin the juniorsecondary school curricular.
Geometry is the study of space and spatial relationship. As one of the longest-established branches of Mathematics, it is widely applied in various applications, such as Computer Aided Design (CAD), Geometric modeling, robotics, medical imaging, computer animation and visual presentation (Chan, Tsai and Huang, 2006; Hannafin, Truxaw, Vermillion and Liu, 2008; Rafi, Samsudin and Said, 2008). Other areas where Geometry problems arise are in Computer Graphics, Architecture, Chemistry, Material Physics,
Biology, Geographic Information Systems (GIS) and most fields of engineering (Chang, Sung and Lin, 2007). Its recalling powers has made policy makers to consider it as an important and essential branch of Mathematics curriculum at all grades levels in Nigeria (Federal Ministry of Education, 2006). The ability to apply geometric concepts and reasoning is the life wire of many occupations. For example, in satellite dish building, acquiring the practical knowledge in deriving the area of a square (A= 4 x 4 = 16 or in general A = X x X = X2), a foundation is been laid for the satellite dish builder as this function is the same with that of a parabolic function Y = X2/A used in making satellite dish shape while that of a rectangle (A = xy) is a good example of a utility function for consumers.
Furthermore, the study of Geometry provides the learner with a vehicle for enhancing logical reasoning and deductive thinking for modeling abstract problems. It helps to develop the mind in determining differences especially at early stages of our life as in games where children are made to place different shapes (squares, rectangles, triangles among others) in the right positions or slots. These help the toddlers to make deductions that expand their mind and this served as their first exposure to Geometry.
The importance of geometry lies also within the fact that geometry is not only relating to Mathematical courses, but also concerned with the development of students‟ cognitive, affective and psychomotor skills, such as investigating, criticizing, creative thinking, illustrating what students have learnt and self-expression (Erdogan, Akkaya and Akkaya, 2009). Geometry is necessary to our life and various professions because shapes and objects learnt from geometry are also available in our world (Cherney, 2008).
Nevertheless, geometry looks like Mathematics, which may be difficult to most people (Andersson, 2008).
In view of this wide use, research in geometry is becoming an important and essential area in current research all over the world for better performance in geometry (Guven and Kosa, 2008; Walker, Winner, Hetland, Simmons & Goldsmith, 2011; Meng and Idris, 2012 and Darwish, 2014). With a desire to continue the teaching and learning of Geometry and the development of spatial abilities (understanding relations visually, making changes on shapes, rearranging and interpreting them) as well as acquisition of practical skills that are expected to be of use to the learner and the society, the Federal and State Government of Nigeria and other bodies like National Mathematics Centre, Abuja, Mathematics Association of Nigeria (MAN), National Teachers Institute (NTI) and Science Teachers Association of Nigeria (STAN) among others have invested huge amounts of money and time in training and retraining of teachers who are expected to bring about the desired educational change. However, no significant changes seem to have been recorded (Emaikwu and Nworgu, 2005). Students still continue to record poor performance at both internal and external examinations in Mathematics. This poor performance is incontrovertibly attributable to poor students‟ attitude towards the subject; the types of instructional materials used and wrong teaching methods (Emaikwu and Nworgu, 2005; Baram, 2004, Eze, 2011).
The inadequacy of the Conventional Lecture Method (CLM) to improve students‟ attitude, retention and performance in Mathematics especially geometry has become a source of concern to Mathematics educators, curriculum planners, secondary school teachers and even the students‟ themselves. Conventional Lecture Method which is a collection of teaching methods other than the concrete manipulative approach has its main characteristics as verbal presentation of ideas about the topics. It is a teaching procedure in which there is a one – way channel of communication where the teacher makes an oral presentation of the subject matter content and students react by silently listening and taking notes. In this method also the teacher gives out all the facts he wants the students to know and master, caring very little if at all whether or not, the students are actively participating and contributing to the success of the lesson (Cohen and Manion, 2006). The method reduces learners to mere note – takers and passive listeners. Learner‟s perception and assimilation of the subject matter is slow. Conventional Lecture Method often inhibits active participation of students in the classroom and teacher dependence on the part of students (Ransdem, 2009). Tom (2011) was of the view that students should be well equipped with the necessary experiences needed in learning school subjects if they are to learn maximally. Instructional strategies adopted in teaching influence the cognitive, affective and psychomotor outcomes of learning (Micklich, 2012).
Concrete Manipulative Approach as a student‟s centered method of learning is a strategy that draws its inspiration from the concrete operational stage as well as part of the formal operational stage of the Piaget‟s learning theory of cognitive development. These two stages are concretetized to cover ten to fifteen year old students in this study. This was because the approach needs reference to familiar actions using concrete manipulatives or observable properties and simple relationships in learning geometry. In addition to this, learners will need a practical interaction with concrete manipulatives before the meaning of a concept and a phenomenon is understood. The approach helps students acquire qualities like conservation, orderliness and irreversibility properties that helps students form positive attitude and creates‟ geometric images that will remain more permanently in students for good performance and retention in geometry. Performance which is the psychomotor educational outcomes of the students‟ has to do with the use of environment in learning. It is a better way of transferring procedural skill to students than students given abstract manipulation thought.
Retention in Geometry on the other hand is the ability to keep or retain the knowledge of the subject learnt as well as ability to recall it whenever required while attitude refers to the students‟ character towards the learning of Geometry. The role attitude plays in teaching and learning of Geometry cannot therefore be over emphasized. Bayram (2004); Etukudo (2006); Odeleye, Oluwatimilehin and Okereke (2009) believed that positive attitude of learner towards a subject and the teaching strategy employed by the teacher enhanced meaningful learning and thus better concept formation. It is therefore pertinent to search for ways of encouraging positive attitude in learners towards learning in order to improve the learning of Mathematics generally and for the study of Geometry in particular.
In another development, gender based studies like Becker, (2005); Kajuru and Kauru, (2010) show that there are under-representation and inconsistencies as to the nature, extent and sources of the differences in the attitude and performance of males and females in geometry. Earlier, the International Mathematics Study (SIMS, 1982-1983) shows that gender differences do not appear in mathematical learning except in the poorly taught areas, such as geometry and measurement. In these areas, prior out-of-class experience is significant. In many societies, girls often do not play games that enhance their visual and spatial knowledge. According to Hyde and Mertz, (2009) girls are therefore disadvantaged when these topics are taught in class. This gives reasons why a large body of literature reported that gender should be included as a variable in analysis, even if it is not the main focus of the study (Santos, Ursini, Ramirez and Sanchez, 2006). With this inconsistencies and significant methodological flaws observed, more empirical researches are needed to investigate the existence of gender differences in the classrooms. It is based on this background that the researcher investigated the Effect of Concrete Manipulative Approach on Attitude, Retention and Performance in Geometry among Junior Secondary School Students in Benue State, Nigeria.
1.2 Statement of the Problem
The alarming rate of students‟ poor performance in Basic Education Certificate Examinations (BECE) in Mathematics and the Benue State Examination Board (BSEB) chief examiners report on students‟ weakness in Geometry is of great concern to mathematics educators, teachers, parents, students, researchers, non-governmental organizations and in fact, the entire nation. BSEB Chief Examiners Report in Mathematics of 2007-2014 theory papers reviewed that many of the students avoided geometry questions and the few that attempted did not perform well. This by implication means the students did not have an appropriate pedagogy while learning the Geometry concepts taught. The researcher therefore carried out the study on the Effect of Concrete Manipulative Approach on Attitude, Retention and Performance in Geometry among Junior Secondary School Students in Benue State, Nigeria.
1.2 Objectives of the Study
The objective of this study is to determine the effect of concrete manipulative approach on attitude, retention and performance in Geometry among Junior Secondary School Students in Benue State, Nigeria. The Specific objectives of the study were to:
- investigate the atitudinal change of students towards the learning of geometry.
- ascertain whether there was gender difference in the attitude of Junior Secondary School Students towards the learning of geometry
- investigate whether Junior Secondary School students improved in their academic performance in the learning of geometry
- ascertain whether there was any gender difference in the Junior Secondary School students academic performance in the learning of geometry
- determine whether Junior Secondary School students improved in their retention of the geometry concepts taught.
1.4 Research Questions
This Study sought to answer the following research questions:
- What are the effects of attitude changes on Junior Secondary School students taught geometry using Concrete Manipulative Approach and Conventional Lecture
- What are the effects of attitude changes on Junior Secondary School male and female students‟ taught geometry using Concrete Manipulative Approach?
- What are the effects of mean academic performance scores on Junior Secondary School students taught geometry using Concrete Manipulative Approach and
Conventional Lecture Method?
- What are the effects of mean academic performance scores on Junior Secondary School male and female students taught geometry using Concrete Manipulative Approach?
- What are the effects of mean retention scores of Junior Secondary School students taught geometry using Concrete Manipulative Approach and Conventional Lecture
1.5 Null Hypotheses
The following null hypotheses were formulated and tested at P ≤ 0.05 level of significance
- There is no significant difference between the attitude changes of Junior Secondary
School students taught geometry using Concrete Manipulative Approach and Conventional Lecture Method.
- There is no significant difference in the attitude changes of Junior Secondary
School male and female students taught geometry using Concrete Manipulative Approach.
- There is no significant difference between the mean academic performance scores of Junior Secondary School students taught geometry using Concrete Manipulative Approach and Conventional Lecture Method.
- There is no significant difference in mean academic performance scores of Junior Secondary School male and female students taught geometry using Concrete Manipulative Approach.
- There is no significant difference between the mean retention scores of Junior Secondary School students taught geometry using Concrete Manipulative Approach and Conventional Lecture Method.
1.6 Significance of the Study
It is hoped that the findings from this study will help students, secondary school teachers, Mathematics educators, curriculum planners and higher institution lecturers and various associations like the Science Teachers Association of Nigeria (STAN) and
Mathematics Association of Nigeria (MAN) among others to articulate the Concrete Manipulative Approach.
The students will be able to learn meaningfully using concrete manipulatives and be able to read geometric shapes and bring out their relationships and properties for decision making. The Concrete Manipulative Approach as a student centered approach can be adopted by students for learning geometry concepts in the classrooms. This is significant in the sense that students will use manipulatives that will assist them see the need to apply their cognitive, affective and psychomotor factors in their learning. The students will exercise most especially their affective and psychomotor skills which will in turn improve their attitude and academic performance. It is also hoped that this research will serve as a stepping stone for other researchers‟ to carry out their research. Teachers can now identify the steps of learning to serve as a guide for selecting appropriate instructional plans.
Therefore, this study is significant based on the following implications:
- Learning will be faster as students associate it with concrete manipulatives and reason from unscientific to scientific ways of doing geometry.
- Students taught Geometry using Concrete Manipulative Approach will be more involved in the learning and as such will help the students‟ develop good attitude in
what they learn.
- The approach encourages the interplay of thoughts and actions between the three educational domains. Students become more alert and can respond to difficult problems on their own, and would be able to solve geometric problems with confidence.
- The implication for teachers is that, the teacher will now make available and relevant manipulatives in teaching geometry at Junior Secondary Schools level to enhance performance.
The applications for Mathematics educators and curriculum planners are obvious. Institutions responsible for teachers‟ professional development like National Teachers Institute (NTI), Nigerian Educational Research and Development Council (NERDC) would also find the results of this study useful, thereby incorporating the findings into their curriculum design processes and instruction innovation programmes in mathematics and create more awareness.
The findings of this study will provoke further research in order to make a wakeup call for the depressed state of Geometry learning in particular and Mathematics in general in Nigerian Secondary Schools. This present study will also add new information to all existing literatures when published.
- Scope/Delimitation of the Study
The study was specifically focused on the JSSII students who were being prepared for the Basic Education Certificate Examination in Benue State, Nigeria. This class was preferred because it was not an examination class and has already acquired substantial knowledge of Geometry at JSSI. The schools that were covered for this study comprised both the Federal, State and Missionary owned secondary schools in the state.
The content scope include: the properties of polygons, perimeter of a square and a rectangle. The area of a square, a rectangle, a parallelogram, a trapezium, a triangle and a circle were also considered. Others are the circumference of a circle, angle properties of parallel lines, properties of an angle at a point of intersecting straight lines and at a point and construction of triangles. These areas are considered because they are part of the fundamental concepts of Mathematics in JSS II syllabus.
The delimitation of this study was that the researcher did not consider any other class than the JSSII students as well as 3D shapes topics.
- Basic Assumptions
The following are the basic assumptions for the study:
- The Concrete Manipulative Approach was within the reach of the students for the topics in Geometry. The selected topics are appropriate for the level of the subjects used for the study.
- The students in the study sample have acquired basic JSSII geometry concepts through Conventional Lecture Method but not exposed to Concrete Manipulative Approach.
- The selected concepts for the study are appropriate for the level of the students targeted for the study.
- The schools used for the study are true representations of secondary schools in
INFLUENCE OF CONCRETE MANIPULATIVE TACTICS ON OUTLOOK, RETENTION AND PERFORMANCE IN GEOMETRY AMONG JUNIOR SECONDARY SCHOOL STUDENTS IN BENUE STATE, NIGERIA