EFFECT OF APPLIED ORIENTATION AND MOBILITY PROGRAMME ON ATTITUDE AND ACHIEVEMENT IN GEOMETRY OF LEARNERS WITH VISUAL IMPAIRMENT IN ABUJA AND GINDIRI, NIGERIA

 

ABSTRACT

Geometry and on larger scale mathematics was not taught to learners with visual impairment and so they do not write public examinations in the area of mathematics (geometry) in Nigeria. This study is on effect of applied orientation and mobility programme on attitude and achievement in geometry of learners with visual impairment in Abuja and Gindiri. The specific aim of the research is to find out if applied orientation and mobility programme as an adapted teaching strategy will give access and enhance task performance of learners with visual impairment in geometry; and its effect on the attitude and age at onset of the impairment of the learners towards geometry. The research design used was experimental design. The pre-test post test design was used. Two schools were used; schools for blind children Jabi-Abuja and Gindiri with the population of one hundred and fifty seven children. Proportional stratified random sampling method was used.  The sample size was ten in classes four and five of each of the schools making a total of 20 samples. The samples were stratified based on age at onset of impairment and grouped into experimental and control groups. Two instruments were used: Attitude to Geometry Scale (AGS) and Adapted Geometry Task Performance Test (AGTPT). Three research questions and five hypotheses were used. The research questions were analysed by the use of simple percentage and mean. An independent tTest was employed in testing the hypotheses. The findings of this study were that the new adapted teaching strategy developed; applied orientation and mobility programme gave access to learners with visual impairment to participate in geometry and it enhanced task performance of the learners in geometry. The high performance in geometry tasks changed from negative to positive attitude of the learners towards geometry. The study showed that the adapted strategy had no effect on task performance and attitude towards geometry on the basis of age at onset of visual impairment. The implications of the findings of this study are: Access and high task performance in geometry and mathematics in general will qualify the learners‟ entrance into tertiary institutions since today mathematics is used as a filter for entrance into tertiary institutions. Some will read mathematics as a course of specialisation and obtain certificate in it and many will read science, technology and engineering courses or professions in future as a result of skills in geometry and mathematics. Much of the working of the adapted teaching strategy involved interaction with the environment thereby resulting in skills in spatial concepts. Therefore the adapted strategy will enhance skills and knowledge in most of the subjects taught in school which involve spatial process and its applicability cuts across all subjects. The study revealed that age at onset in learners does not matter in task performance and attitude towards geometry. This disproof the deficiency inefficiency theory or controversy that has existed in special education for long which states that congenitally visually impaired persons perform lower in spatial concepts than adventitiously visually impaired or sighted persons.

 

CHAPTER ONE

INTRODUCTION

1.1       BACKGROUND OF THE STUDY

The teaching and learning of mathematics and especially geometry to learners with visual impairment in Nigeria has remained a great challenge to both the teachers and their children. Learners with visual impairment (LWVI) in most cases are exempted from offering mathematics and the case of geometry is worse. The few schools that attempted teaching the subject to learners with visual impairment faced a lot of problems. The main problem faced is that teachers lack the adapted strategy or methodology to use in teaching the learners geometry. They also lack adapted materials or assistive devices they would use in teaching the subject and the skills to operate the devices.  These materials include adapted geometry kits with embossed protractors, TSquares, rulers, rubber mat and polythene sheet for drawing. This has resulted in low participation or non participation in mathematics especially the geometry aspect by learners with visual impairment in Nigeria.

What learners with visual impairment require in their education is the modification or adaptation of the strategies or teaching methods and devices their teachers apply on them to enable them develop their full potential. This group of learners live in a three Dimensional world. Even their system of writing the Braille, has to be three dimensional in nature. The traditional oral method of instructions and writing on the board in mathematics lesson are difficult to be used with them.

In comparing the results of learners with visual impairment with their sighted peers in Nigeria, the West African Examination Council (WAEC) (2013) reported that although learners with visual impairment had better results than their sighted peers, in its

2012 examinations, learners with visual impairment did not write mathematics in the examination. Similarly in November/December 2012 results, WAEC reported that only 37.97% (150,615) sighted candidates pass with five credits including English and mathematics. Their peers with visual impairment in the same year and the same examination had 46.93% (49) pass which was a higher percentage result than their sighted peers.  These 46.93% (49) candidates with visual impairment who obtained five credits including English language unfortunately did not sit for mathematics and science practical in the WAEC examination (Research Development Institute Inc [RDII] , 2013). This situation of learners with visual impairment not writing mathematics in such a national examination has been on for quite some times in the country. When teachers omit learners with visual impairment from offering mathematics as is the case often, they have omitted them from the regular syllabus.

Mathematics is one of the prominent subjects in school. It has a lot of use-values with respect to life in its totality. Mathematics is a daily experience or actions exercised on things in the environment. Geometry as a subset of mathematics is more practical than most aspects of mathematics. It involves a lot of mental constructions which are derived from actions performed on or with materials which may be concrete, semiabstract or abstract progressively as the learner matures and the concept becomes complex (Gupta, 1992). What learners with visual impairment experience are that they are often fed with symbolic materials through text-books where available or the teacher talks. The consequence is that concepts are not properly formed. Learners with visual impairment in Nigeria, therefore, have not been given the proper, relevant and adequate exposure to teaching and learning of geometry that will enable them to have concepts and skills especially in descriptive geometry. The researcher is of the view that applied orientation and mobility programme (APOMP) as an adapted strategy full of geometry concepts that could first be presented practically via orientation and mobility skills gives the learner the opportunity to access the environment and objects around it to obtain information about the characteristics of the objects through other sensory modalities and eventually transfer these information through embossed form to abstract form or mental imagery for better task performance in geometry/mathematics.

It was becoming normal expectation in Nigeria for children with visual impairment not to offer mathematics. To suggest teaching geometry to learners with visual impairment was like talking about impossibility.  This situation became a cause of worry to the Nigerian federal ministry of education. The federal government had to send letters to all heads of special integrated primary and secondary schools and teacher colleges stating that mathematics had been made compulsory for ―blind‖ students (Federal Ministry of Education (FMOE), personal communication, February 27, 1987). This was to compel teachers and learners with visual impairment to take deliberate steps to teaching and learning mathematics. The letter further stated that learners with visual impairment must have a pass in the subject before they were admitted into any tertiary institution. After many years now this order from federal government could not be complied with.

The initial concept of learners with visual impairment not offering mathematics was first conceived because the first Nigerian with visual impairment to enter secondary school did not offer mathematics. Subsequent students with visual impairment in the country followed his footsteps by not offering mathematics too. The late Professor

Bitrus Gani the pioneering learner with visual impairment in secondary school wrote

WAEC in 1962, came out with ―Division One‖ he did not offer mathematics at that time, it became normal for others with visual impairment in the country not to offer mathematics. This became a belief that learners with visual impairment do not offer mathematics in Nigeria. It became an attitudinal problem which as usual has a wider implication on performance in mathematics and is difficult to change.

Attitude could be seen as the major root cause of problems of learners with visual impairment in life and in learning mathematics and geometry in particular. Historically, they have been viewed negatively. People believe that learners with visual impairment cannot do mathematics especially geometry and some of the learners with visual impairment equally think that they cannot cope with the subject. The possibility of learning of mathematics or geometry by learners with visual impairment is often questioned. Worse are areas in mathematics like geometry which demand for so much visual tasks. However many of such visual ideas can be converted into tactual practical experience to get the required learning experience in geometry.

Worried also by none participation in mathematics by learners with visual impairment, the Gindiri material centre for visually impaired (GMCVH) embarked on a five year programme of visit to schools. They interacted and encouraged learners with visual impairment to offer science and mathematics and practically engaged them with some geometry drawings. They organized series of workshops for the teachers, parents and the students. During that time, they found out that in some states, teachers, parents, the public and the learners with visual impairment in Nigeria saw the inclusion of learners with visual impairment in the teaching and learning of mathematics as complete impossibility. Therefore the attitude of the public and especially the learners with visual impairment themselves seem to make the teaching and learning of mathematics challenging in special schools. The same attitude if not worse is shown to teaching geometry to learners with visual impairment.

In a nationwide research, National Education and Research Development

Council [NERDC] (2009) found out that in twenty-four selected special residential schools, mathematics was not offered by learners with visual impairment. By implication geometry is not taught or offered by learners with visual impairment in special residential schools. Special residential school is a special school that caters for the needs of special kind of learners. It considers visual impairment as requiring special attention so it has the best experts usually with the best experience and skills in teaching them.

Special school imparts not only academic education but also aims at developing compensatory or self help skills. The school is supposed to handle tougher areas that regular teachers cannot handle like special subject areas including: Science, mathematics, Braille, rehabilitation skills, sports and recreation or leisure. Special attention is provided them in the area of feeding, provision of special materials and specially trained or experienced teachers who also are often provided residential quarters within the school premises together with them. It gives room for involving them in extracurricular activities like sports, clubs, and time for preparation yet mathematics is found not taught in many of such schools. Gindiri and Abuja are residential special schools solely for learners with visual impairment. The rests are either units in regular schools and the learners are day students or they are special residential schools that cater for other types of disabilities too. The Abuja and Gindiri residential special schools have no definite adapted strategy of teaching and learning of mathematics in the schools.

Recently learners with visual impairment that were newly admitted into the University of Jos were refused registrations into their departments for lack of mathematics either at a pass or credit levels. The learners complained either to national university commission (NUC) or the minister of education in Abuja saying that they had never been taught mathematics. Either the minister or NUC pleaded with the university for exemption since learners with visual impairment were never taught the subject let alone write a national examination in the subject. An education without mathematics in this century will cause some hardship to learners with visual impairment especially now that mathematics is demanded in science, technology and social science related professions. Instead of excusing them from offering mathematics, there is the need to search into adapted strategies that will make it possible to teach them mathematics/geometry. Applied orientation and mobility programme is one of the strategies that enabled learners with visual impairment access geometry in particular and mathematics in general but has never been used.

Mathematics is simply concerned with the science of structure, order, numbers, space and quantity. It is concerned with the elementary practice of counting, measuring and describing of shapes and objects. Descriptive geometry is a branch of mathematics which deals with the study of properties of figures and shapes, and the relationship between them. Basic geometry allows us to determine properties such as the areas and perimeters of two-dimensional shapes and the surface areas and volumes of threedimensional shapes. However such concepts can only be known to a person with visual impairment through direct contact.

There are people who are congenitally visually impaired. There are those that are adventitiously impaired. The difference at the onset of visual impairment can affect both orientation and mobility skills and mathematics concepts and skills especially in geometry. Those who are born totally visually impaired may not have any previous concept on which to build on in the area of orientation and mobility and mathematics particularly in geometry concepts and skills. Incidentally most school age children are congenitally visually impaired. In such a case it may be more challenging teaching the child geometry or even orientation and mobility skills. Orientation and mobility like geometry is about order, space, shapes, measuring, counting of objects etc in space as the individual manoeuvres through the space.

People giving and undergoing training in orientation and mobility started suspecting mathematical concepts embedded in orientation and mobility. This led to a strong speculation that there is a relationship between performance in orientation and mobility skills, which are more within the psychomotor domain, and achievement in academic subjects like mathematics for learners with visual impairment. The researcher in search for evidence of geometry in orientation and mobility went through primary school mathematics textbooks and books written on orientation and mobility and found out that there were geometry concepts in orientation and mobility concepts and skills in quite a number of mathematics textbooks and books on orientation and mobility which could be used as strategy for teaching geometry to learners with visual impairment.

 

1.2       STATEMENT OF THE PROBLEM

The teaching of geometry/mathematics can take several forms and can be carried out through different experiences and situations. Unfortunately sometimes lessons depend too much on exposition from the teacher‘s part and a passive style of learning from the part of the students which promotes rote learning or non participation in the subject (Tanti, 2012). We experience mathematics in our daily activities and the application of the simplest operations and results in mathematics are many. Therefore Tanti stated that to teach geometry/mathematics to learners with visual impairment, it requires experience with concrete objects for manipulation with hands and fingers, the use of embossed diagrams and the opportunity to experience the concept in real life. This involves the use of adapted strategies or methodologies and devices. Unfortunately the restriction visual impairment imposes on the life of learners with visual impairment makes their contact with the environment difficult. Teachers hardly understand or take the risk of exposing the learners to the environment to experience and manipulate concrete objects for the purpose of teaching and learning geometry/mathematics.

Similarly teaching method can cause mathematics anxiety in children. Learners with visual impairment like their sighted peers have negative attitude towards mathematics and perform poorly in the subject. This was due to the fact that they were exempted from offering the subject. They also strongly believe that they cannot do mathematics since as earlier stated; the first student with visual impairment to write a national examination made a Division 1 in his West African School Certificate (WASC) did not offer mathematics. However he did not escape geometry because he eventually read physiotherapy in Britain, a profession full of geometry concepts and skills.

An earlier experience of not offering mathematics by learners with visual impairment or any earlier encounter of difficulty in teaching mathematics especially geometry to learners with visual impairment results in attitude problem thereby thinking that learners with visual impairment will not be able to offer the subject. A missionary mathematics teacher in Boys Secondary School (BSS) Gindiri attempted involving learners with visual impairment in her mathematics class. One of the learners with visual impairment in the school was overheard saying that a mad white woman wanted to introduce them to mathematics. He further added that ―blind boys‘ brain can‘t do mathematics, everyone knows that‖. The attitude of believing that learners with visual impairment cannot offer mathematics has hindered the learners from opening up their minds to offer the subject.

Mathematics anxiety which is an attitude issue simply refers to feelings of tension and fear that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations.

Mathematics anxiety could also be seen as the feeling of tension, nervousness, or fear that disrupts mathematics performance (Jain, & Dowson, 2009; Ma & Xu, 2004). Mathematics anxiety is related to negative attitudes towards mathematics. It is related to

mathematics avoidance and poor mathematics performance. Highly anxious mathematics learners avoid mathematics which in turn results in less competency, exposure and mathematics practice and mathematically unprepared to achieve (Hembree, 1990).

Anxious mathematics students feel negative towards mathematics. This affects confidence and motivation negatively in mathematics (Ashcraft, 2002). In a research after using brain scans, scholars confirmed that the anticipation or the thought of solving mathematics actually causes mathematics anxiety. The brain scans showed that the area of the brain that is triggered when someone has mathematics anxiety overlaps the same area of the brain where bodily harm is registered (Harms, 2012). To look into geometry (mathematics) issues, mathematics anxiety which is an attitude problem cannot be left out.

Orientation and mobility has basic concepts that are related to concepts in descriptive geometry. It is concerned with shapes and objects in space, their positions, quantity, distances, locations, angles etc and how one can identify or locate them through the senses, and how to move around those structures in the space safely and gracefully. Basic orientation and mobility relates to the knowledge of space and the relationship of objects to each other and to the person. Example of the use of concepts in orientation and mobility that are geometry related include: maintaining directional orientation using perpendicular or parallel alignment for straight line travel; executing 90⁰ and or 180⁰ turns; recognizing characteristic of objects around the space or landmarks eg shapes, horizontal sides, vertical sides, parallel sides etc

 

At the conference of international council for people working with visual impaired (ICEVI) held in Malaysia, 2006, one of the issues discussed was the need to research into the possibility of using orientation and mobility skills and concepts to teach mathematics to learners with visual impairment. There was a plea for people to increasingly do empirical research in special education and especially on the relationship between mathematics for the learners with visual impairment and orientation and mobility concepts and skills. Unfortunately, there is no curriculum developed in Nigeria for teaching learners with visual impairment orientation and mobility. There is no regular or consistent teaching of orientation and mobility skill in special schools that teach the subject as to expose them to some of the experiences of geometry skills that are embedded in orientation and mobility.

In a similar situation, the national council for teachers of mathematics (NCTM) in America admonished that the field of orientation and mobility (O&M) can provide experiences that help students with visual impairments and blindness to develop the conceptual framework for understanding mathematics (as cited by Smith,  2006 p. 161). Unfortunately this admonition has not been taken seriously as to use orientation and mobility skills as intervention programme to activate the skills dormancy that exist in teaching and learning geometry with learners with visual impairment.  The problem of the study therefore is: Can applied orientation and mobility programme be used as an adapted strategy or teaching method enhance tasks performance and change attitude of learners with visual impairment towards geometry? Can it affect attitude direction and task performance based on age at onset of visual impairment?  Can there be any utility value in the use of applied orientation and mobility programme as is used to enhance skills in geometry of learners with visual impairment?

 

1.3       PURPOSE OF THE STUDY

The purpose of this study is to examine the effects of applied orientation and mobility programme (APOMP) on the attitude, task performance and utility value in geometry of learners with visual impairment in residential special schools for blind children in Jabi-Abuja Federal Capital Territory (FCT) and Gindiri in Plateau state of Nigeria. Specifically the objective of the study is to:

1. Analyse the extent to which the task performance of learners with visual impairment in geometry using applied orientation and mobility programme

will be.

2. Compare the task performance in geometry of learners with congenital visual impairment and learners with adventitious visual impairment using applied orientation and mobility programme.
3. Determine the usability value of applied orientation and mobility programme in enhancing task performance in geometry to learners with visual impairment.
4. Identify the nature and direction of attitude of learners with visual impairment towards geometry.
5. Compare the nature and direction of attitude of learners with congenital and those with adventitious visual impairment.

 

1.4       RESEARCH QUESTIONS

The following research questions were investigated and answered in this research study:

• What is the nature of geometry task performance of learners with visual impairment?
• To what extent can Applied Orientation and Mobility Programme (APOMP) be of utility value to learners with visual impairment in learning geometry?
• What is the nature and attitude direction of learners with visual impairment to descriptive geometry aspect of mathematics?

 

1.5     HYPOTHESES

The following hypotheses were formulated and tested at 0.05 level of

significance:

1. There is no significant difference in extent of geometry tasks performance of learners with visual impairment trained in the use of applied orientation and mobility programme skills and those not trained.
2. There is no significant difference in extent of geometry tasks performance of learners with congenital visual impairment and those with adventitious visual impairment trained in applied orientation and mobility programme skills.
3. There is no overall significant difference in value in the use of applied orientation and mobility programme skills in training learners with visual impairment in geometry tasks and those not trained.
4. There is no significant difference in the attitude towards geometry tasks of learners with visual impairment trained in applied orientation and mobility skills and those not trained.
5. There is no significant difference in attitudes towards geometry tasks of learners with congenital visual impairment and those with adventitious visual impairment trained in applied orientation and mobility programme.

 

  1.6       SIGNIFICANCE OF THE STUDY

This study was conducted to benefit learners with visual impairment, the government, and the educational system. Others are parents, teachers, curriculum experts; examination bodies, orientation and mobility experts and textbook writers. The result of the study showed that learners with visual impairment achieved high in geometry tasks performance which is an aspect of mathematics through the use of applied orientation and mobility programme (APOMP). Applied orientation and mobility programme therefore could be used to open doors for job opportunities for learners with visual impairment in the fields of science, technology and engineering and to achieve various economic and domestic benefits both at home and abroad. Applied orientation and mobility programme has just been developed and has never been used. It could serve as one of the convenient methods for teaching geometry/mathematics to learners with visual impairment to impart in them the skills, habit and knowledge of geometry/mathematics.

Attitude determines performance in mathematics. Equally when learners perform poorly in mathematics, they develop negative attitude towards the subject. When applied orientation and mobility was used as an adapted method of teaching geometry for learners with visual impairment, it enhanced task performance in mathematics and the learners achieved highly. This resulted in developing positive attitude towards geometry (mathematics).

The study is significant to teachers and learners with visual impairment because the need was seen for the learners to offer mathematics and orientation and mobility. Teachers were trained in the area of using adapted methods and materials to teach learners with visual impairment geometry/mathematics and also in the area of orientation and mobility. The applied orientation and mobility skills taught broke the barrier of restriction in the life of a child with visual impairment due to the effect of blindness. It gave the child access to the environment and the opportunity to explore things in the environment.

The research findings will help curriculum experts in developing and adapting curriculum for learners with visual impairment. This will lead to planning better to meet both regular and unique curricula to meet the special needs of children with visual impairment. The result of the study involving orientation and mobility concepts and skills revived the teaching and learning of orientation and mobility and skills in daily living skills.

The result of the research will hopefully prepare examination bodies like west African examination council (WAEC), national examination council (NECO), and joint admission and matriculation board (JAMB) etc to understand the unique needs of learners with visual impairment in the area of giving extra time, use of adapted materials, provision of embossed diagrams and graphs and brailing of mathematical and science examination questions. Learners with visual impairment will participate in national examinations in mathematics as currently they do not write mathematics. Textbook writers also will be encouraged in integrating orientation and mobility concepts in writing and illustrating books for children with visual impairment. They would produce books on the effect of psychomotor skills on the academic areas.

It is however disturbing that in many special schools and integrated institutions in Nigeria and in many other developing countries academic pursuit receives great emphasis while the teaching of orientation and mobility receives peripheral or casual attention. The study will make the teaching and learning of orientation and mobility important in Nigeria such that curriculum might be developed for it since it could be adapted and used to enhance teaching and learning of geometry and mathematics in general.

 

1.7   THEORETICAL/CONCEPTUAL FRAMEWORK

The theoretical framework for this study is derived from two theories. The Piaget‘s theory of genetic epistemology also referred to as theory of cognitive development. The second theory used is the theory of deficiency and inefficiency derived from John Lock‘s theory which states that child mind is a ‘blank slate’ (tabula rasa).  Piaget identified four basic stages in the development of mental structures.

The first stage is the sensori-motor stage. This is pre-verbal and pre-symbolic period.  The child does not use words or symbols to represent things, instead it uses action. (eg. sucking, looking, grasping etc). The actions are uncoordinated, inherited reflexes and gradually the actions become coordinated habit gradually converting to cognition or intelligence. The environment for the actions or activities is the child‘s own body and later the child extends the actions to the environment. Applied orientation and mobility programme (APOMP) is concerned with the environment of the child both within his body and his surrounding environment. Activities of APOMP within the body includes identifying and naming the learner‘s different body parts and using non standard means of measuring the body parts which include the use of arm span, finger pacing, waist height, leg pacing etc. The non standard measurement starts from the different parts of the body and is extended to objects around the environment. APOMP eventually uses standard measurement of body parts using adapted rulers, measuring tapes and meter rules. APOMP activities within the environment involve taking and reading of measurement of lengths, distances or circumferences, identifying length of various shapes. Therefore basic concepts in measurements start with using non standard measurement involving the child‘s body parts and objects in the environment.

The second stage is the preoperational stage. This is the stage of representation or symbolism. The child presents his thought through the use of words to represent things through imagining. Applied orientation and mobility programme (APOMP) involves identification of landmarks within the environment. Landmarks refer to objects within the environment so that the child will hold, feel, touch, grasp, smell, identify their features and characteristics and manipulate them by either weighing, measuring, identification of shapes, sizes, distances eventually construct the mental images of  the objects and their features or characteristics.

The third stage is the concrete operational stage. The child at this stage is said to be operational in his thinking. It is concrete operational because the necessary logical thought is based on the physical manipulation of objects in the environment. Basic mathematics concepts are better introduced to children first through manipulating objects around the environment.

The fourth stage is the Formal Operation. The child hypothesises with symbols or ideas rather than needing objects in the physical world as a basis for his thinking. Applied orientation and mobility programme based on the various contact with the environment, gives chance for the child with visual impairment to practically and theoretically be involved with geometry activities. The child identifies characteristics of objects within the environment eg shapes. The child identifies embossed shapes in two dimensional forms and draws embossed lines, quadrilaterals, polygons, angles, cardinal points, using rubber mat etc.

Piaget‘s theory of cognition covers the whole complex system of human mental abilities. Cognitive areas are: perception, attention, learning, memory, and reasoning.

Others are conception, imagery, assimilation and accommodation (Advani, 1992). Perception is an important part of cognition that helps in variety of tasks. Cognition involves the use of knowledge in reasoning and problem-solving tasks.

 

Piaget stated that intellectual development takes place through the process of assimilation and accommodation. Assimilation is when an already learnt stimulus brings to mind a respond, and accommodation on the other hand is when a child adds a new activity to his repertoire. Memory is an important part of cognitive process. There is short- term memory which Baddeley (1990) refers to as working memory. The short term or working memory has a limited capacity system being responsible for the manipulation and storage of information during the performance of cognitive tasks such as comprehension learning, problem solving, and reasoning. When one is under taking an activity, such an activity is also held in the mind. At the same time, there is manipulating, and integrating information in memory. Short term or working memory refers to the ability to hold information in mind while manipulating, and integrating other information in the service of some cognitive goal (Kane & Engle, 2002; Roberts & Pennington, 1996).

There are some considerable evidences suggesting that short term memory may be important for geometry or mathematics learning and problem solving. In solving a geometry/mathematical problem often it involves remembering the totals of certain calculations while performing other mathematical operations and then combining the outcomes. For example, Adams and Hitch (1998) suggested that mental arithmetic performance relies on the recourses of short term memory. Holmes and Adams, (2006) reported a significant association between children’s short term memory ability and their mathematics attainment. Holmes and Adams further found that there was no significant difference between short term memory capacity of children with visual impairment and their sighted peers. Geometry/mathematics tasks executed through applied orientation and mobility programme (APOMP) involves short term and long term memory. In another study, Pooryal, Hassan and Farzad (2011) discovered that students with low short term memory have less achievement in mathematics performance. Geometry/mathematics tasks executed through applied orientation and mobility programme (APOMP) require short term and long term memory which eventually result in high task performance in geometry/mathematics.

 

Stephens noted that Piaget stresses the importance of the child‘s interaction with his environment in all his stages of cognitive development (as cited by Advani, 1992, p. 32). The interaction with the environment leads to perception and perceptual interaction with the environment is necessary for cognitive growth.  No child skips any of the stages. This is a normal progression of cognitive development, and any deviation from normal development may impede an individual‘s cognitive growth (Hupp, 2003).

According to Copeland (1979) concrete operation stage is important mathematically. Many of the operations are mathematical in nature. Piaget lists some of the operations to include: classification, ordering, construction of the idea of number, spatial and temporal operations and conservation. Others are elementary logic of classes and relations of elementary mathematics and geometry and physics. This is the stage of mathematical structure, Piaget calls ―grouping‖ putting objects together to form a class, separating a collection into subclasses, ordering elements in some way, ordering events in time etc. All these forms of classifications depend on sensory experience. Applied orientation and mobility programme (APOMP) avails the child with the opportunity of grouping objects within the environment as stated by Piaget based on their contact with objects within the environment through the use of their remaining senses.

Conception is basic to cognitive development. Concepts are building blocks of thought.  A fundamental ability required for concept formation is classification too. This involves noting similarities, disregarding insignificant differences and also ability to note significant differences. Classification depends to a very large extent on sensory experience. Any deficit in sensory experience produces deficit in concept formation. Most often learners with visual impairment receive a great deal of information through words, it is found that their object concepts are defective due to lack of contact with objects in the environment. They use a number of words in the wrong context. They also may use words of whose meaning they do not know precisely (verbalism). Verbalism is the use of words without knowing the precise meaning (NIVH, 1992). Applied orientation and mobility programme (APOMP) prevents defective object concepts and verbalism through concrete presentation of the objects from the environment to the learner with visual impairment.

Piaget‘s theory of cognition seems to outline a lot of complications in the life of learners with visual impairment. They tend to have problems with cognitive development. According to Lowenfeld (1974) visual impairment imposes three general restrictions in the life of children with visual impairment in relation to cognitive development. They are range and variety of experience, ability to get about control of environment and self-in-relation to environment. All of these have effect on cognitive development. Warren is of the view that there could be delay in the process of cognitive development of a child with visual impairment due to limited critical interaction with the external world (as cited by Advani, 1992, p.32). The child will lack the sensory continuity afforded by visual stimulation. This lack of continuity hinders the integration of the child‘s sensory motor experience. Although auditory cues help learners with visual impairment in attaining a degree of spatial orientation, their inconsistency must make the process exceedingly difficult. Applied orientation and mobility programme (APOMP) makes contact with the environment and uses all the remaining senses in the child with visual impairment. Therefore the child with visual impairment will have better concept development and spatial orientation.

Contrary to the views that visual impairment encounters problem with the process of cognitive development, there are researches that have shown that interaction with the environment as emphasized in Piaget‘s theory of cognitive development is important with children with visual impairment. Easton, Greene, and Svinis (1997) found a child with visual impairment with a much better developed ability to ―link‖ information. They referred to it as structural priming. The child was able to semantically link information in the process of concept formation and it resulted in ability to think divergently, or in a creative manner. Wyver and Markham (1999) defined divergent thinking to mean ―the ability to find multiple solutions to a single problem‖. They considered this ability to be an important component in creativity and cognitive flexibility. Morgan (1999) described how a sample of learners with visual impairment was able to form a three-dimensional cognitive map based on auditory information. These individuals used this cognitive map to assist them in moving about, or orienting, to the physical world. Morgan concluded that learners with visual impairment often compensate for their lack of vision with over-developed abilities in other sensory functions. Learners with visual impairment need to make the best possible use of their non-visual senses like in the case of applied orientation and mobility programme (APOMP) which results in the learners with visual impairment developing cognitive map due to much development of their remaining senses as a result of opportunity to interact with the environment.

There are instances where learners with visual impairment were able to solve geometry/mathematical problems, although their approach and way of solution was a bit different from approach of the sighted persons. Where it involves geometry, most sighted learners draw a picture by solving given problems of analytical and Euclidean geometry. On the other hand, learners with visual impairment had to use imagination and objects (solids and plane figures). They first touched and then stored the images before they drew the pictures. Geometry is for them a kind of adaptation to the environment. This research work uses applied orientation and mobility programme (APOMP), as an adapted strategy, first to provide an avenue for the child with visual impairment to have access to the objects in the environment and interact with the environment thereby breaking the initial consequence of visual impairment which is restriction. Applied orientation and mobility programme uses all the remaining senses in the child with visual impairment to interact with the environment an act which Piaget emphasises for cognitive development.

Attitude is an important concept for learning mathematics; also it is a mental set or disposition of readiness to respond to the subject. Hembree (1990) found that mathematics anxiety is related to poor performance on mathematics. One of the components of attitude is cognitive component. This is opinion information or strength of belief or disbelief of the subject (Guimaraest, 2005). Therefore attitude is an aspect of cognitive constructs, and cognition is about Piaget‘s theory. Mathematics anxiety has been directly or indirectly, affecting all aspects of mathematics education as one of the most commonly investigated constructs in mathematics education. Some of the symptoms of mathematics anxiety are a ‗blank‘ mind, inability to hear the teacher or lack of noise sensitivity, and inability to concentrate (Kitchens, 1995). All these are within the characteristics of cognitive process. When applied orientation and mobility programme (APOMP) enhances performance, there is the possibility of mathematics anxiety being reduced in the life of persons with visual impairment. This simply means that APOMP can change negative belief of learners towards geometry/mathematics to positive attitude (cognitive aspect of attitude) which often results in high task performance or achievement in geometry/mathematics.

According to Poorya1, Hassan, and Farzad (2011) they found out that a lot of failure in the previous mathematics examination and inferior achievement which are products of intelligence cause the feeling that achievement of good mathematics result is not so important. Attitude can influence performance in mathematics and performance in mathematics can in turn influence performance too. Intelligence quotient an aspect of cognition and motivation are said to be variables that determine the outcome of mathematics attitude and achievement (Kabiri & Kiamanesh, 2004; Bull & Scerif, 2001; Yunus & Ali, 2009). Applied orientation and mobility programme (APOMP) can serve as a motivation for doing geometry/mathematics which leads to achievement in the subject thereby resulting in high mental performance and the product is high intelligence quotient.

The second theory used in this work is the theory of inefficiency and deficiency. John Locke believed that our minds originated as a ‘blank slate’ (tabula rasa) and that all concepts we have are derived from our sensory experiences. Thus a congenitally blind person would only have tactile impressions of objects, and these could not automatically allow him to recognise the same objects by sight. It is only by integrating experiences from different senses that we build up abstract concepts. In view of this assertion by Locke, Millar asked; If one perceptual modality (i.e. vision) is missing, what (if any) effect does this have on our knowledge of the world? Three answers were proposed for this question resulting in three theories. They are theories of deficiency, inefficiency and difference in spatial tasks of congenitally visually impaired learners (Andrews, 1983; Fletcher, 1980). The first theory the deficiency theory states that lack of visual experience may result in a total lack of spatial understanding. The second theory is the inefficiency theory. The theory states lack of visual experience may result in spatial abilities which are similar to, but necessarily less efficient than, those of sighted people. The third theory, the difference theory may result in abilities which are qualitatively different from, but functionally equivalent to, those of sighted people. The first of these positions came up from the work of von Senden in 1932 who argued that spatial concepts are impossible in people who have been blind from birth, and that visual experience during some early period is essential for even a minimal understanding of space (Ungar, 2000). This research work compares task performance or achievement and attitude direction of learners who are congenitally visually impaired and those that are adventitiously visually impaired.

In a study by Hupp (2003) on cognitive differences between congenitally and adventitiously blind individuals, the findings suggested that congenitally blind individuals develop alternate methods of cognitively processing nonverbal, abstract, or complex information, especially information involving a high degree of spatial orientation. Ungar (2000) in review of literatures in spatial concepts with learners with visual impairment revealed that there are factors to consider when dealing with spatial cognition of learners born with visual impairment. There are environmental spaces or objects that are presented to them that are referred to as near or far spaces. Near space refers to small – scale or manipulatory space or areas that can be explored without changing the location of the body. Far space relates to medium or large scale space; areas in which movement is required for exploration.

In small scale, both tactile and haptic exploration with the hands and arms is used.  In any task the learner can perform based on spatial relation that has been directly experienced and will require only coding or task that can require inferring the new relation based on direct experience task that will require transformation of the coded information. Applied orientation and mobility programme (APOMP) involves the use of the concept of both far and near space (environmental exploration and tactile drawings) as found by Ungar. There is the need for environmental experience and providing models or tactile maps for learners with visual impairment especially those that are congenital.

External cues could be of advantage when experiencing complex task with a learner born blind. (1988) working on spatial development called convergent active processing in interrelated networks (CAPIN) stated that information from each of the different senses is specialised, and are complementary and overlapping. Because of this, spatial information is not the exclusive domain of one sensory modality. Spatially relevant information is available through senses other than vision (e.g., through hearing, touch and movement) and this information can form the basis for spatial coding. Congenitally visually impaired learners tend to code spatial relations egocentrically because this type of strategy generally works best for them (Ungar, 2000).

Processing of spatial information by congenitally visually impaired learner may not be less efficient than sighted or adventitiously visually impaired as the inefficiency theory proposes. According to Ungar, it is misleading looking at efficiency rather than on the nature of coding used by the learners. Tactile maps in conjunction with direct experience of the environment will optimise spatial knowledge in both congenitally and adventitiously visually impairment learners (Millar, 1988; Ungar, 2000). The use of applied orientation and mobility programme (APOMP) creates the opportunity for direct experience of the environment which gives opportunity for both congenitally and adventitious visually impaired to have contact with the environment to optimise spatial knowledge in them and also excel in geometry and mathematics.

 

1.8       DELIMITATIONS OF THE STUDY

The study was carried out in only two residential special schools. The schools were school for blind children Jabbi in Abuja and school for blind children Gindiri. The school in Abuja belongs to the Federal Capital Territory administration while the school in Gindiri belongs to the Church of Christ in Nations (COCIN). While the school in Abuja is located in the nation‘s capital, the school in Gindiri is located in Gindiri a rural town in Mangu Local Government area of Plateau State. Gindiri is renowned for hosting many educational institutions from primary, secondary to tertiary levels since the 1950s. Gindiri School for blind children was the first school for blind children to be established in 1953 in Nigeria.

The study did not look at all aspects of orientation and mobility and geometry. In the area of orientation and mobility, the study only looked at aspects of concepts and skills that are embedded with geometry concepts and skills. For example, there is measurement in orientation and mobility skills involving ascertaining the exact or approximate dimensions of an object or space, using a given unit. In basic sighted guide, one of the skills is for the learner‘s upper and lower arm form an angle approximately 90⁰ with the forearm pointing forward. The study is only concerned with descriptive geometry. This aspect of geometry is concerned with the study of the angles, shapes, lines, surfaces and solid objects in space.

The study did not involve all categories of children with visual impairment. It did not involve children with multiple disabilities. For example learners with visual impairment that have deafness in addition (deafblind). They are referred to as Multiply Disabled Visually Impaired (MDVI). It did not involve learners with additional intellectual impairment.

Although the world talks much of inclusive setting today, the research work could not be done under such setting. This is because inclusive programme in Nigeria has not taken off officially. The special residential schools are used for the research.

 

1.9       OPERATIONAL DEFINITIONS OF TERMS

Achievement: In this study, achievement refers to task performance in geometry Age at onset of visual impairment: This refers to when learner with visual impairment first acquired the impairment or damage to the organ of vision. It can occur before or at birth call congenitally impaired or later in life known as adventitiously impaired. The age range as used in defining congenitally impaired in this study is (before, during and immediately) after birth is 0-7 years. Adventitious visual impairment as applied to this study is 8 years and above but within the primary and secondary school age.

Applied Orientation and Mobility Programme (APOMP): This refers to a programme/adapted strategy (teaching method) designed with geometry concepts and skills embedded in orientation and mobility concepts and skills. It is used for training in geometry skills to enhance task performance in geometry concepts and skills. It is used as a treatment (intervention) for awakening dormant geometry skills that are found in orientation and mobility skills for learners with visual impairment which they could use in geometry task and enhance their task performance in geometry. The geometry skills and concepts can be demonstrated practically with orientation and mobility methods or skills which are then transferred through embossed form practically. Some of the geometry concepts in applied orientation and mobility programme APOMP include:

Spatial concepts, turns, shapes, measurement etc.

Attitudes toward Geometry: This simply refers to the beliefs, feelings and behaviour of learners with visual impairment towards the study of geometry as a subject. It includes geometry or mathematics anxiety which influences task performance in geometry of learners with visual impairment. It shows the direction of the attitude as being negative or positive which eventually influences their task performance in geometry, as measured by attitude to geometry scale (AGS) in this study.

Effects of Applied Orientation and Mobility Programme: This refers to the outcome or results of the use of applied orientation and mobility programme (APOMP) as an intervention to change attitude and also to enhance task performance in geometry of learners with visual impairment. It refers to changes that may occur in their attitudes and task performance in geometry that may be exclusively tied to exposure to applied orientation and mobility programme.

Geometry: This refers to descriptive geometry concepts and skills that are found embedded in orientation and mobility skills which are also found in spatial process within the environment. The descriptive geometry can be practically demonstrated in the cause of demonstrating skills in orientation and mobility in space and translated in written form as tactile or embossed diagrams or shapes for learners with visual impairment. The descriptive geometric concepts include: spatial concept by establishing and maintaining direction and maintaining distance and straight line and locating specific objects. This involves concepts like: Spatial concepts: parallel, perpendicular, around, diagonal, horizontal, vertical. Spatial concepts dealing with action: Turns, 45⁰ turn, ¼ turn, right angle turn, whole turn etc. Concepts of Shapes: Primary shapes: round, triangle, circle, rectangle, square, Secondary shapes: Octagon, hexagon, pentagon, parallelogram etc. Concept of measurement: distance, amount, time, weight and volume and their presentations in tactile forms.      

Learners with Visual Impairment: This refers to those who lost their sight either totally or they have some remaining sight, they may be born (congenital, 0 – 7 years) with it or they acquire it (adventitious, 8 and above years) at later age. They are studying in primary or secondary institutions. They can use all the apparatus involved with applied orientation and mobility programme.

Adapted Geometry Task Performance Test: This refers to skills in orientation and mobility embedded with geometry task performance of learners with visual impairment in geometry test developed and validated by the researcher. It is one of the two instruments used; it was used as pre-test and post-test in the study

Residential Special School: Learners with visual impairment are considered to need special care so residential special schools are provided where they have hostel accommodation, equipment and teaching and learning materials are provided and trained or experienced teachers and supportive staff are provided. It has wide environment for demonstrating applied orientation and mobility programme. The residential special schools referred in this study are the ones in Gindiri and Jabi-Abuja which are solely for learners with visual impairment.

Treatment: This simply refers to interventions given to learners with visual impairment in the study.

EFFECT OF APPLIED ORIENTATION AND MOBILITY PROGRAMME ON ATTITUDE AND ACHIEVEMENT IN GEOMETRY OF LEARNERS WITH VISUAL IMPAIRMENT IN ABUJA AND GINDIRI, NIGERIA