EFFECTS OF ADVANCE ORGANIZER AND CONCEPT ATTAINMENT MODELS ON THE ACHIEVEMENT AND RETENTION OF PRE-NCE STUDENTS IN GEOMETRY

Abstract

This study investigated the effectiveness of two instructional models – the Concept Attainment Model (CAM) and Advance Organiser Model (AOM) on the achievement and retention of Pre-NCE students in geometry. Four research questions and six hypotheses guided the study. The design of the study was pre-test pos-test equivalent control group design or quasi experimental design. The study was carried out in Kogi and Benue States in the present North Central Zone of Nigeria. The population of the study was 1100 Pre-NCE students in both the State and Federal-owned colleges of education in the two states. Three out of the four public colleges of education in the two states were randomly selected for the study. The total number of students in their intact classes who offered Pre-NCE geometry in these colleges was 830. This formed the sample for the study. 402 (48.4%) of the students were male and 428 (51.6%) were female. The instrument used for data collection was Pre-NCE Geometry Achievement Test (PNGAT). PNGAT had two versions Pre-PNGAT and Post- PNGAT which were the same except for the swapping of some of the questions. PNGAT was subjected to both face and content validation and item analysis. Using Kuder Richardson (K-R) 20, the internal consistency was found to be 0.74. Using Pearson r, the test retest stability measure was found to be 0.96. Pre- PNGAT was administered on the groups before treatment started while Post- PNGAT was administered at the end of the 5 week treatment period. After 2 weeks of administration of Post-PNGAT, it was again administered on the groups as a retention test. Scores from Pre-PNGAT, Post- PNGAT and the retention test were analysed using means and analysis of covariance (ANCOVA). Some of the major findings from the analysis were (i) AOM and CAM were more effective than the conventional method for achievement (ii) CAM was more effective than AOM for achievement; (iii) CAM and AOM were more effective than conventional method for retention (iv) CAM was more effective than AOM for retention. Based on the findings, the implications were highlighted and recommendations were made towards better achievement and retention of Pre-NCE students in geometry.

INTRODUCTION

CHAPTER ONE

Background to the Study

Mathematics is often defined or described from the point of view of its utility, especially by those who only make use of the subject. However, a simple definition which seems to capture the overall essence of the subject of mathematics is that it is the study of quantity, structure, space and change (Agwagah, 2008). Mathematics is one of the core subjects in primary and secondary school levels of education in Nigeria. Performance in mathematics at the Senior Secondary School Certificate Examination (SSCE) is used to determine those who are qualified to enter the tertiary levels of education especially those taking courses in the sciences and science related disciplines like engineering, survey, medicine and so on.

Many institutions of higher learning have introduced post-Joint Admission and Matriculation Board (Post-JAMB) screening examination into their admission policy. In many of such screening exercises, mathematics features among the subject areas where candidates are tested. In some Colleges of Education running Preliminary Nigerian Certificate in Education (Pre- NCE) programme, admission into the programme is through screening examination in which mathematics forms part of the examination. The NCE certificate is awarded by Colleges of Education on successful completion of a 3-year programme. It is the minimum teaching qualification in Nigeria for primary and junior secondary school levels of education (Federal Republic of Nigeria, 2004).

The Pre-NCE programme is a remedial outfit mounted by National Commission for Colleges of Education, (NCCE) and run by some Colleges of Education. It is designed to redress the deficiencies of candidates who either cannot make the required number of credit passes (including Mathematics and English) at SSCE for direct entry into the NCE programme or for candidates who have the required number of passes at SSCE but cannot pass the screening exercise for entry into the NCE programme. The Pre-NCE programme is for duration of one academic session. The progamme is aimed at addressing the challenges of weak students in colleges of education (Junaid, 2008).

The Pre-NCE programme is widely spread across colleges of education in the country. During the one year programme, students are exposed to prescribed number of courses that can remedy their deficiencies for entry into the NCE programme. Furthermore, following the recently introduced policy by JAMB that all Pre- NCE students must write the Unified Entrance Examination, the Pre- NCE programme is now saddled with additional responsibility of preparing the students in the various subject areas. From the foregoing, it is clear that mathematics plays enormous role in the affairs of humanity. But despite this role of mathematics, researches have showed that performance of students in the subject is generally poor (Okereke, 2006; Uloko and Usman, 2007; Galadima and Yusha’u, 2007). Recent performance statistics of students in mathematics emanating from WAEC (see Appendix I) is indicative that performance of students in the subject remains all-time low.It is therefore clear that mathematics is given huge consideration and plays prominent role at all levels of education system. One may ask: why are we so concerned about mathematics? Of all the disciplines in school curricula, why are we so concerned about the failure and/or success of our children in mathematics? The answer is premised on the fact that it is one of the subjects that pervades all endeavours of humanity – sciences, arts, engineering, medicine, astronomy, etc. It is in consideration of the versatility of mathematics that James (2005) asserted that it is not only an academic, a scientist, an engineer that needs mathematics but that even a shop keeper, a housewife, a sportsman, etc. needs it. Thomaskutty and George (2007) agreed with James when the authors asserted that mathematics should not be seen as a classroom discipline only. From the point of view of science and technology, mathematics takes a unique position. In fact, the tremendous achievement of science and technology towards industrialized economy and human survival seems to be buoyed up by many far reaching mathematical contributions.

The scenario, certainly, is assuming alarming and scandalous proportion, resulting into a situation where more candidates opt for Pre-NCE programme than those going straight into NCE and degree programmes. This situation is, however, not peculiar to Nigeria; every country seems to be infected by the poor performance syndrome. Close to two decades ago in Britain, Bow (1993) feared that the worry about poor enrollment in physics and chemistry seemed to be overshadowed by the concern for a bleaker future of mathematics. In America, Raizen and Michelsohn (1994) reported that in comparism with other countries, American children lag behind in achievement tests especially in mathematics and science areas.

As if the general poor performance in mathematics is not worrisome enough, another dimension to the problem is students’ performance in geometry which is one of the major components of secondary school and Pre-NCE mathematics. Over the past two decades or so, WAEC has been disturbed about students’ performance in geometry. WAEC (2000,2003,2005,) reported that students did not only perform poorly in geometry questions but avoided questions in geometry in certificate examinations. The worry heightened and assumed attitudinal dimension when WAEC (2005) reported that geometry is one of the topics in secondary school mathematics towards which students have shown negative attitude.

The situation at the Pre-NCE level is very similar if not worse. This is obvious because, as has been noted earlier, the Pre-NCE is a representation of mainly weak students The four courses in mathematics offered at this level are Number and Numeration, Algebra, Geometry and Statistics. The researcher, at one time or the other has taught all these courses. Over the years, the internal examination records have always indicated that students perform relatively poorly in geometry (see appendix J). From Appendix J, it is obvious that geometry poses a problem for the Pre- NCE students. Since a pass in mathematics is one of the conditions for placement into NCE programme, there is the fear that the poor performance in geometry may be partly responsible for non-placement of many Pre-NCE candidates. The need therefore arises to probe into a better technique in the teaching of geometry at this level to ameliorate the problem.

Geometry, as a branch of mathematics, is not only crucial in understanding properties and relationships of points, lines and figures in space but its study can enhance the understanding of many phenomena in several other areas of knowledge, especially in the sciences. This, perhaps, informs the inclusion of geometry in the Pre-NCE mathematics curriculum by National Commission for Colleges of Education (NCCE). Educational researchers have attempted to probe into the causative factors of poor performance of students in mathematics. While some researchers have reported that hard curriculum content is a causative factor, others reported deficiencies in the teacher factor. For example, Habor-Peters (2003) reported lack of mastery of mathematics contents by mathematics teachers while Adeniyi (1998) and Ojo (2002) reported that poor quality of instructional techniques was responsible for the poor performance of students. Agashi (2005) reported that hard content of the curriculum and teacher ineffectiveness were partly responsible for the poor performance of students. A good number of these findings are teacher related and this casts some doubts on the effectiveness of the mathematics teacher especially in the area of instructional techniques.

There are ample research evidence supporting various instructional techniques as enhancing teaching and learning and better achievement of students in mathematics (Harbor-Peters, 2003; Okigbo, Osuafor, 2008;  Eze, 2008; Bawa and Abubakar,2008; Tyarbee and Imoko,2009). There may be no doubt that some of such techniques are being used in our schools by some mathematics teachers. But despite the reported efficacy of such techniques and the possibility of their use in instruction, the poor performance syndrome persists.

This situation may not be unconnected with the fact that over the years educational psychologists have been worried over all manner of instructional techniques many of which are teacher – centred and address only the cognitive behaviour of the learner at the expense of the affective and psychomotor domains. The traditional method of teaching is characterized by this major flaw. The concept of traditional method or conventional method of instruction is derived from the concept of traditional education. The chief business of traditional education is to transmit to a next generation those skills, facts and standards of moral and social conduct that adult deem to be necessary for the next generation-s materials and social success (Dewey, 1938). As beneficiaries of this scheme, which educational progressivist John Dewey described as being imposed from above and from outside, the students are expected to docilely and obediently receive and believe these fixed answers. Teachers are the instruments by which this knowledge is communicated and these standards of behaviour are enforced.

Traditional education is communicated through various modes or techniques. Historically, the primary educational techniques of traditional education were simple oral recitation and rote memorization (memorization with no effort at understanding the meaning). From this brief description of traditional education and the technique of communication, one can observe that it is teacher-centered and leaves no room for students’ active participation in the learning process. It is widely criticized for its focus on teaching instead of learning. From the earlier primary traditional techniques of simple recitation and rote memorization other techniques which are equally characterized by students’ passivity in the learning process have been in use over the years. All these techniques which main focus is teacher as chief information giver and students as passive recipients may be said to be traditional or conventional method of instruction. In the context of this work, the conventional method is any other method used in teaching mathematics at the Pre-NCE level except the CAM and AOM.

The conventional method of teaching has therefore been widely criticized by the progressive psychologists. These psychologists advocated that effective learning can hardly take place under such a setting. For instance, Jerome Bruner emphasized the importance of understanding the structure of a subject being studied, the need for active learning as the basis for true understanding and the value of inductive reasoning in learning. Bruner believed students must actively identify key principles for themselves rather than relying on teachers’ explanations. Teachers must provide problem situations, stimulating students to question, explore and experiment, a process called discovery learning. Thus Bruner (1966) believed that classroom learning should take place through inductive reasoning, that is, by using specific examples to formulate a general principle. It is at this point of inductivism that David Paul Ausubel (Brunner’s contemporary) disagreed.

Ausubel (1960) believed that people acquire knowledge primarily through reception rather than discovery; thus learning should progress not inductively from examples to rules but deductively from the general to the specific or from the rules to examples. Ausubel’s strategy always began with an advance organizer – a technique which this work addresses – which is a kind of conceptual bridge between new material and students’ current knowledge. In a concerted effort to ‘decode’ the work of Bruner, Ausubel and other leading educational psychologists, Joyce and Weil (1980) developed more than 20 models of teaching in an attempt to chart a new course to instruction. Educational researchers in mathematics do not seem to have adequately explored these models in terms of their efficacy in instruction. This has created the need for this study with a focus on the relative efficacy of these models in teaching geometry at the Pre-NCE level.

The Advance Organizer Model (AOM) is a teaching model credited to the theory of David Paul Ausubel. Ausubel (1960) maintained that the primary process in learning is subsumption in which new material is related to relevant ideas in the existing cognitive structure on a substantive, non-verbatim basis. Mayer (2003) defined advance organizer as information that is presented to organize and interpret new incoming information. Advance organizers may be described as statements or devices used in the introduction of a topic which enable learners to orient themselves to the topic, so that they can locate where any particular bit of input fits in and how it links with what they already know. Advance organizers are introduced in advance of learning itself and are also presented at a higher level of abstraction, generality and inclusiveness. These core components of advance organizer are indicators of the emphasis this strategy places on the development of the cognitive structure of the learner and that it serves as an umbrella which houses all the components of the lesson. The substantive content of a given organizer or series of organizers is selected on the basis of its suitability for explaining, interpreting and interrelating the materials they precede. This strategy therefore satisfies the substantive as well as the programming criteria for enhancing the organization and strength of cognitive structure (Ausubel, 1963).

Ausubel and Fitzgerald (1962) believed that slow learners benefit most from the use of advance organizer. Such students require additional assistance in learning how to structure their thinking. There may be no doubt that a good number of Pre-NCE students fall into this category of learners given the general deficiency in mathematics. Secondly, Ausubel (1963) discovered that organizers are more useful when working with factual materials than they are when dealing with abstraction. Thirdly, Ausubel (1963) believed that advance organizer enhances retention. These reasons may have informed the need for this study involving advance organizer as a teaching model.

The Concept Attainment Model (CAM) is credited to the theory of Jerome Brunner and its design is to help students learn concepts through systematic categorization and classification of learning materials or objects in an attempt to determine the rationale behind the categories. By using this method, students will learn the material much better as the learners figure it out for themselves. As well as learning the material better and remembering it longer, the students will learn how to learn by using this model. It encourages creative thinking, communication and independent learning (Bruner, 1966).

From the descriptions of Advance Organiser Model (AOM) and Concept Attainment Model (CAM) above, it is clear that they are constructivist-oriented. Constructivism is built on the philosophy and cognitive psychology that human beings are not passive recipients of information.  Learners actively take knowledge, connect it to previously assimilated knowledge and make theirs by constructing their own interpretation (Cheek, 1992). It is also clear from the descriptions that their use in instruction may enhance retention, which is one of the variables of interest in this study. The Encarta Dictionaries defines retention as “the ability to remember things” In education, these “things’ are the values, attitudes, skills acquired by the learner in the process of learning. Educational psychology is so much concerned about retention of what has been learned as it serves as a basis for sustaining the desired change in the behaviour of the learner. This underscores the reasons why retention of knowledge has become an important area of research in education, as it has the potential to inform instructional practices and school learning goals (Bahrick, 2000). Implicit in Bahrick’s submission is the fact that instructional techniques are determinants of the extent of retention of knowledge. Semb and Elli (1994) were of the same view that one factor that determines retention of school knowledge is the nature of the instructional approach. It is clear therefore that retention and achievement of students are related variables and this informs the rationale of this study to investigate which of the two models is better in terms of these variables.

One other variable that is of interest to this study is gender. Gender is an ascribed attribute that differentiates feminine from masculine socially (Lee, 2001). Gender difference in mathematics in particular and science in general has over the years become such a controversial issue that educational researchers have become so weary about and have no common ground to land. For example, Ezeugo and Agwagah (2000), Okereke (2001), Steen (2003); Onwiodukit and Akinbobola (2005), Eriba (2005), Abuh (2005), Okereke, (2006), Ogunkunle (2007), Uloko and Imoko (2007), Nzewi (2009) reported that males are superior to females in mathematics in terms of achievement. Others (e.g. Ozofor, 2001; Kurumeh, 2004) sharply disagreed contending that females are superior. There is, however, research evidence (Okigbo and Osuafor, 2008) that improved instructional techniques can close the gender gap in achievement in mathematics. Can the use of AOM and CAM close this gap in the study of geometry at the Pre-NCE level? This question forms part of the focus of this study.

Statement of the Problem

The ugly scenario of poor performance in mathematics in SSCE has resulted into a situation where some candidates wishing to pursue NCE programme are compelled to undergo Pre-NCE programme in Colleges of Education to remedy their deficiency. Over the years, experience and available records have indicated that after the one year Pre-NCE programme, many candidates still do not qualify for placement into the NCE programme on grounds of failure to pass prescribed examinations in critical areas like mathematics and English. This situation seems to have contributed to so many social problems of candidates and the society, apart from negating the necessity for the programme. Furthermore, records indicate that poor performance in geometry is partly responsible for the poor performance in mathematics and non-placement of candidates. Why the problem of poor performance in mathematics at the SSCE and Pre-NCE levels persists, there is the need for increased production of NCE mathematics teachers for the UBE programme.

Research evidence indicates that out of the many distractions and impediments in the study of mathematics in general and geometry in particular, poor instructional techniques play a major role. Despite some efforts that have been made by researchers to remedy the situation, there seems to be no evidence that performance in geometry has improved. Over the years, educational psychologists have frowned at instructional techniques that are teacher-centred, a situation bereft of active participation and high achievement of the learner. Among the educational psychologists that hold this view are David Ausubel and Jerome Bruner. Ausubel’s summative ideas and work on effective teaching resulted in a teaching model called Advance Organize Model (AOM) while the Concept Attainment Model (CAM) resulted from the work of Jerome Brunner.

There is however inadequate documented information in research conducted in Nigeria on the effects of AOM and CAM in the teaching of mathematics in general and geometry in particular at the Pre-NCE level. The problem of this study, therefore, is: What are the effects of AOM and CAM on the achievement and retention of Pre-NCE students in the study of geometry?

Purpose of the Study

The main purpose of the study was to investigate the relative efficacy of the advance organizer model and concept attainment model with respect to the achievement and retention of Pre-NCE students in geometry. In specific terms, the study attempted to find.

1. The mean achievement scores of Pre-NCE students taught with CAM, AOM and conventional method in geometry.
2. The mean achievement scores of male and female students taught with CAM, AOM.
3. The mean retention scores of students taught with CAM, AOM and conventional method.
4. The mean retention scores of male and female students taught with CAM, AOM.

Significance of the study

This study on the efficacy of the two models in teaching geometry will be of immense theoretical and practical significance to education, teachers, students, professional bodies, researchers and other stakeholders in education industry. On the theoretical significance, the study will provide an insight on the theories of Bruner (1966) and Ausubel (1960) which have been acclaimed as promoting teaching and learning. On the practical significance, the study will popularize the two models under investigation and mathematics teachers in Nigeria will come to understand and maximize their use in teaching mathematics in general and geometry in particular. Mathematics teachers will be exposed to the models through conferences, seminars and workshops to be organized by professional bodies such as Mathematical Association of Nigeria.  Furthermore, the study will be of benefit to mathematics teachers as it will serve as a road map in the choice of a more efficacious model for instruction and in the process, the teacher will acquire more capacity to deliver and impart mathematics knowledge to the students.  The teacher will also benefit from the study as it will indicate the relative efficacy of the two models with respect to gender and student’s retentive ability and in the process the teacher will be guided in his choice of a better instructional strategy.  The benefit of the study to the teacher will translate into better achievement of students in the study of geometry because with the knowledge of better instructional strategy, there will be improved teaching and learning leading to better achievement of students.

Furthermore, the study will be of significance to professional bodies like Mathematical Association of Nigeria and Science Teachers’ Association of Nigeria as it will serve as a source of theme for conferences, seminars/ workshops and in the process their members will benefit.

Finally, the findings of the study will be of benefit to researchers as it will serve as a yardstick for making comparison with similar studies outside Nigeria with a view at stimulating internationalization of studies in this area of education. In addition, it will add to the existing pool of knowledge on gender studies in mathematics and provide an anchor upon which further studies may be carried out, thereby leading to increased pool of knowledge.

Research Questions  

The study was guided by the following research questions.

1. What are the mean achievement scores of students taught with CAM, AOM and conventional method?
2. What are the mean achievement scores of male and female students taught with CAM and AOM?
3. What are the mean retention scores of students taught with CAM, AOM and conventional method?
4. What are the mean retention scores of male and female students taught with CAM and AOM?

Hypotheses

At 5% probability level, the following null hypotheses were formulated to guide the study.

1. There is no significant difference in the mean achievement scores of students taught with CAM, AOM and conventional method.
2. There is no significant difference in the mean achievement scores of male and female students taught with AOM and CAM.
3. There is no significant interaction effect of gender and instructional models on the achievement of students in Pre-NCE geometry.
4. There is no significant difference in the mean retention scores of students taught with CAM, AOM and conventional method.
5. There is no significant difference in the mean retention scores of male and female students taught with AOM and CAM.
6. There is no significant interaction effect of gender and instructional models on the retention of students in Pre-NCE geometry.

Scope of the study

The study was carried out in three randomly selected colleges of education in North Central Nigeria. The choice of the zone was informed by the fact that Pre-NCE programme is common in Northern part of Nigeria. The Pre-NCE students in the three colleges were used for the study and the course covered by the study is geometry-one of the courses offered in Pre-NCE mathematics. The choice of this course was informed by the continued abysmal poor performance in this area of mathematics. The course outline include angles, plane shapes and their properties, length of chords and arcs, circle theorems, areas of plane shapes and surface areas and volumes of solid shapes

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