LEARNING STAGES IN MATHEMATICS
Alexander M.0 (1954) said that leering stages in Mathematics can be divided into three sections namely: (a) The of role play that is (Intuitive learning)
(b) The role of structured experience
(c) The role of application and practice.
Intuitive learning, According to Dr. A.R.O. Sule, is the acquiring of knowledge by chance of circumstances situations on problems or the truth of certain events came to light spontaneously without vigorous reflections of events, so, the role of play in the teaching of mathematics is an integral part of children’s activities, - collection and pouring of water on sand into different containers, drawing of geometrical figures in the sand Estimation of lengths and distances with foot, span and sticks.
This is first step in learning and recording a mathematical-concepts. The children can be asked to lift different objects with their hand and also, they can be asked to pour some quantity of water from one container to other container of different sizes.
The role of structured experience is the number system like addition, subtraction multiplication and division that is the study of measurement and estimation, the use of pictorial representation, intuitive geometry, relations and functions. These concepts provide a firm foundation for the children future works in mathematics i.e. the application and practice stage. This is the thinking stage."
The second stage is very important and it affects the conservation of the concepts if poorly handled therefore the teacher should be a guide and not an instructor of teeming situation. Due to improper application of the concept by the children they resulted in memorizing a host of abstract formulae and figures which effects the conservation.
VOLUMES:
 According to oxford Advance Learners Dictionary of current English by A.S. Hornby pg 96 the term of volume is referred to as amount of space expressed in cubic meters occupied by substance, liquid or gas, cubic content of container WILLIAM LITTLE, at al shorter oxford Dictionary Pg 2289) referred to Volume as the bulk, size or dimension of a thing It is often determined by length X breadth X height e.g. the volume of water in a jar or bucket. The volume of a liquid is measured in liters, this is defined as the volume occupied by a mass of lkg of pure water at its temperature of maximum densify and under standard atmospheric pressure,
In the SI system, the cubic meter (M3) is the unit of volume water that has a density of 100kg/M3 in Si units. (equivalent == IgKM3).
A solid is a three-dimensional object, that is an object that can be viewed lengthwise, breadth wise and heigh wise for example boxes, suit case book shelf or a brick and so on. Though the one is some solid without specified length nor breadth nor height. But in any case, we can always fund the volume, that is the amount of space occupied by a solid. Any solid with equal edges is called cube and the volume assuming the length is 2cm equals 8cm3
But, for solid without specified length or breadth to find the volume, you use graduated bucket or container full of water (pure), then drop the solid into the container, subtract your final volume of the water from the initial volume, the difference in volumes is the volume of the irregular shaped object.
filled with pure water irregular shape object
Then, the final volume 3,4cm3 subtracted from the initial volume 5cm3 we have 1.6cm3 as the volume of the irregular object.
 
WEIGHT:
This is the gravitational force with which a body tends towards the centre of the world. How heavy a thing is the force of gravity on a body varies slightly from place to place on the earth for two reasons and its rotation on it access and secondly the shape of the earth. The earth is not a perfect sphere but bulges at the equator the distance free the centre of the earth to the polar region will decrease; consequently, the weight of any object. According to Newton's gravitational law the gravitational pull on its will gets more, The weight of a body is force if exerts on anything which freely support it and normally, it exerts this force among because it is being attracted towards the earth by the force of gravity. The unit weight is in Newton (N). An important distinction between mass and weight is that the mass of a boy does not depend on where the body is, whereas weight of a body can varies from place to place because of gravitational force acting on it.
CONCEPTS AND CONSTRUCTS: A concept is an abstraction from observed events, it is a word that represents the similarities or common aspects of objects or events that are otherwise quite different from one another. The purpose of a concept is to simplify thinking by including a number of events uncher one general loading some concepts owe quite close to the events they represent. Thus, for examples illustrated to a Junior Secondary School Children by pointing to different objects and asked them to lift them with their hands and say which is heavier between the two the concept is an abstraction of the characteristic of all objects have in common - characteristics that are directly observable. However, terms such as motivation, justice, honesty and problem-solving ability cannot be easily illustrate by pointing to specific objects or events. These higher-level abstractions one referred to as constructs. In the same way that we construct a house by putting together wood and other materials in a purposeful pattern, we create con-structs by combining concepts and less complex constructs in purposeful patterns. Constructs are useful interpreting empirical data and in building theory they are Used to account for observed regularities and relationships.
 
Constructs are created in order to summarize observations and to provide explanations. A construct is abandoned when a better way of explanation and summarizing observation replaces it. This construct was abandoned when more useful explanations of the process of burring were developed.
CONCEPTUAL LEARNING: 
By responding to various objects as both similar an: different, the individual is able to organize his environment. If a child is able to categorise meaningfully, such a child has formed a concept about learning. This is inevitable for every, or else would have to face each new situation a fresh.
Gestalt field also talked about the ability of the learner to orgarise his environment into meaningful end. Hemce, concept formation enable the children to generalize, discriminate and label things appropriately. Children learn concepts best when they are given wide range of experiences with the objects and situations that their developing vocabulary expresses. with the ability of classify objects in their environment which is essential concept formation.
Before coming to school, concept such as magnitude and time had been understood by the student, left with abstract concept such as honest and courage that are probably not well developed on in the developing stage in Junior Secondary class. Although culturally, disadvantaged children are shower or shallow in conceptualization than middle class children because the latter heave played those kinds of games more often.
Student may appear to have developed the concert of "conservation of weight" but will temporarily "close" the concept when by trickery the experimented, falsifies the data presented to them for observation showed by Jan Sinedslund. Therefore, conceptualization is not an all or none proportion, but a gradual attainment with experience.
A pertinent question to ask now is, why is it that certain concepts fail to acquire further meaning with the passage of time. First, we have to consider the number of concept that the students, age could assimilate. Secondly the assumption that student earning the concept when they have just succeeded in memorializing it, Contrary to William Browell indication that "concept are far more than word or
Arbitrary associations.
The question "how of the conceptual learning bears directly on teaching. The kind of concept that will be given for child will determine by the number and kinds of experiences the child has had with referents of that concept to child may be courageous in one situation and not courageous in another. If this happens; if means that the child has not learnt the concept because he cannot discriminate and generalize.
In conclusion, for better conservation of the concept of volume and weights in Junior secondary School Children the teacher must devise many activities that will give concrete experience along with verbal instruction to the students.
FACTORS AFFECTING MENTAL DEVELOPMENT
  Developmental stages in student are somehow difficult to temper with, not withstanding, teacher should ready in providing appropriate needful activities and in asking question otherwise, the children may be delay in developing in any of the stages. There are four factors that affects mental development, two of which are strongly affected by teachers. The first two or four listed below. Experience and social interaction organic and equilibration.
ORGANIC GROWTH FACTOR: Organic factor consists of opening up new possibilities and is a necessary but not sufficient condition for the development of certain behaviour at about four and half months, the organic condition for usual perception are not fully relaxed until adolescence, there are some fact that the brain can accommodate time.
EXPERIENCE FACTOR: There are two types of experience that are different from psychological point of view namely the physical experiment and logical mathematical experience.
The act of weighing two objects to determine, if they have the same weight would be a physical experience. While for example the student can be asked to weigh three object: A; B and C this is a physical experiment but if B is 1-1, heavier than A and C is heavier then B, can the child predict which is heavier C or A will he have to weigh C A again?
The logical or mathematical structure of transit unity is necessary to realise that C must be heavier than A Although we can provide a physical environment and physical knowledge by having children weigh the objects. The mathematical structure of transivity is not "taught".
SOCIOAL TRANSMISSION FACTOR: The impacting of knowledge by language is very important, but only when the child has a "structure" that allows him to understand the language being used. And it is at this point that a child often become cost, the teacher not realising that he does not yet have the necessary structures. For instance, the relation uncle of may mean something different to the student if he wants to relate is to himself because he sees the person as uncle to him but the reversibility of the nephew of is not yet understood. The student can think in only one direction. This is social transmission factor.
CLASSIFICATION OF OBJECT: The idea of multiple classification for example classifying on object into two or more sets simultaneously is a mathematical intersection and in logic conduct in this also affect the student and should be taken into consideration.
EQUILIBORATION FACTOR: This fourth factor is self-regulation is the fundamental one, according to Piaget on of the form of equilibration is the coordination of the first three factors. In other way the student having passed through the stages of maturation and has given two clay molded Balls of the same size. If the teacher hastens the and ask the student to flatten the other and ask which one is more than the other. If is only after the student has molded the ball back, he would know that they are of the same size and ten realised the reversibility action that heads to reformation do not change the amount of the clay.
CONSERVATION OF NUMBER AND CONSERVATION OF EQUIVALENCE To relate the idea of conservation of number that is (comparing two sets each containing the same number of objects. In one row to see if the child realised the number is the same in both rows) to other types of conservation to be considered on measurement on metric geometry, it is worth noting that the various types of conservation do not occur at the same time in children thinking. They do occur in the same order usually from for example A clay ball Hatened and remold into rectangular cube might seems puzzle in the sight of five years old children, to determine which one is more but if is it done in their presence and the question is
then asked which one is more. Then it is only few that would not think that would wait to discriminate.
So also, for children above seven years old they are matured enough and except the duller among them that would be deceived by the bigness of the container any liquid is taken.
IMPLICATION FOR TEACHING 
For student in Junior Secondary Schools they are children averagely in their formal. Operational stage. They need many experiences in comparing equal sets in which the configuration of one set is changed to see if they can conserve the numbers of idea involved, Also showing of one set of concept in various configurations and it braking the highly necessary. Although they have mastered the idea of the conservation or invariance of number and are ready for more highly structured type of mathematical activities normally. Therefore, the children needed more experience with physical objects. to abstract and the number given ideas even if they were ready. That is formal operational.
HYPOTHESIS FOR THE STUDY
These are the hypothesis for the study;
(1) That the teacher's qualification affects His/Her ability to organise suitable atmosphere for the conservation of concept of volume and weight among Junior Secondary Schools.
(2) That teachers are overloaded with many classes to take them mathematics which result in ineffectiveness,
(3) That the use of concrete teaching aid will go a long way in fostering right attitudes of the student and classroom atmosphere.
(4) The children needs stimulation and multination towards the learning of the concept of volume and weights since it deals with day to day life situation.