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Nature of Mathematics: The nature of Mathematics can be made explicit by analyzing the chief characteristics of Mathematics. (i) Mathematics is a science of Discovery: E.E.Biggs states that, "Mathematics is the discovery of relationships and the expression of those relationships in symbolic form – in words, in numbers, in letters, by diagrams (or) by graphs."
Problem solving – a sort of healthy mental exercise. (iii)Mathematics deals with the art of drawing conclusions: One of the important functions of the school is to familiarize children with a mode of thought which helps them in drawing right conclusions and inferences. According to Benjamin Pierce, "Mathematic is the science that draws necessary conclusions." In Mathematics, the conclusions are certain and definite. Hence, the learner can check whether (or) not he has drawn the correct conclusions, permit the learner to begin with simple and very easy conclusions, and gradually move over to more difficult and complex ones.
Mathematics is a tool subject: Mathematics has its integrity, its beauty, its structure and many other features that relate to Mathematics as an end in it. However, many conceive Mathematics as a very useful means to other ends, a powerful and incisive tool of wide applicability. In the article "Mathematics & the Teaching Sciences", John. J. Bowem pointed out that, "Not all students are captivated by the internal consistency of Mathematics and for everyone who makes it a career; there will be dozens to whom it is only an elegant tool." As Howard. J. Fehr says, "If Mathematics had not been useful, it would long ago have disappeared from our school curriculum as required study."
Mathematics involves an intuitive method: The first step in the learning of any mathematical subject is the development of intuition. This must come before rules are stated (or) formal operations are introduced. The teacher has to foster intuition in our young children, by following the right strategies of teaching. Intuition when applied to Mathematics involves the concretization of an idea not get started in the form of some sort of operations (or) examples. Intuition is to anticipate what will happen next and what to do about it. It implies the act of grasping the meaning (or) significance (or) structure of a problem without explicit reliance on the analytic mode of thought. It is a form of mathematical activity which depends on the confidence in the applicability of the process rather than upon the importance of right answers all the time. It is up to the teacher to allow the child to use his natural and intuition way of thinking, by encouraging him to do so and honoring him when he does.
Mathematics as a science of Logical Reasoning:
Mathematics is the science of precision & accuracy: Mathematics is known as an exact science because of its precision. It is perhaps the only subject which can claim certainty of results. In Mathematics, the results are either right (or) wrong, accepted (or) rejected. There is no midway possible between right and wrong. Mathematics can decide whether (or) not its conclusions are right. Even when there is a new emphasis on approximation, mathematical results can have any degree of accuracy required. It is the teacher's job to help the students in making decisions regarding the degree of accuracy which is most appropriate for a measurement (or) calculation. (vii)Mathematics is the subject of logical sequence: The study of Mathematics begins with few well – known uncomplicated definitions and postulates and proceeds step by step to quite elaborate steps. Mathematics learning always proceeds from simple to complex and from concrete to abstract. It is a subject in which the dependence on earlier knowledge is particularly great. Algebra depends on Arithmetic, Calculus depends on Algebra, Dynamic depends on Calculus, Analytical Geometry depends on Algebra and Elementary Geometry and so on. Thus gradation and sequence can be observed among topics in any selected branch of Mathematics. (viii)Mathematics requires the application of rules and concepts to new situations: The study of Mathematics requires the learners to apply the skill acquired to new situations. The students can always verify the validity of mathematical rules and relationships by applying them to novel situations. Concept and principle become more functional and meaningful only when they are related to actual practical applications. Such a practice will make the learning of Mathematics more meaningful and significant.
Class: B.Ed. II Sem
Science is defined in several different ways by different individuals.
1. Science is a subject that explains the cause and effect relationship of many incidents
2. Science is a subject that explains various components and the characteristics of nature.
3. Science is both a body of knowledge and the process of acquiring and refining knowledge From the various definitions of science, a comprehensive views "Science as a body of knowledge, a way of investigation and a way of thinking in the pursuit of an understanding of nature.
Nature of Science Science is a dynamic, expanding body of knowledge covering ever new domains of experience. Broadly speaking, it involves several interconnected steps: observation, looking for regularities and patterns, making hypotheses, devising qualitative or mathematical models, deducing their consequences: verification or falsification of theories.
Nature and Scope of Science observations and controlled experiments and thus arriving at the principles, theories and laws governing the physical world. There is no strict order in these various steps. Sometimes, a theory may suggest a new experiment; at other times an experiment may suggest a new theoretical model. Speculation and conjecture also have a place in science, but ultimately, a scientific theory, to be acceptable, must be verified by relevant observations and /or experiments. The laws of science are never viewed as fixed external truths. Even the most established and universal laws of science are always regarded as provisional, subject to modification in the light of new observations, experiments and analysis. The methodology of science and its demarcation from other fields continue to be a matter of philosophical debate. Its professed value neutrality and objectivity have been subject to critical sociological analyses. Moreover, while science is at its best in understanding simple linear systems of nature, its predictive or explanatory power is limited when it comes to dealing with non linear complex systems of nature. Yet, with all its limitations and failings, science is unquestionably the most reliable and powerful knowledge system about the physical world known to humans. But science is ultimately a social endeavor. Science is knowledge and knowledge is power. With power can come wisdom and liberation. Science has the potential to be beneficial or harmful emancipative or oppressive. History, particularly of the twentieth century, is full of examples of this dual role of science. In a progressive forward- looking society, science can play a truly liberating role, helping people out of the vicious circle of poverty, ignorance and superstition. In a democratic political framework, the possible aberrations and misuse of science can be checked by the people themselves. Science, tempered with wisdom, is the surest and the only way to human welfare. This conviction provides the basic rationale for science education.
Scope of Science Science is a way of making sense of the natural world. Scientists seek to describe its complexity, to explain its systems and events, and to find the patterns that allow for predictions. Science is the basis for the design of the technologies that solve real world problems. Not all students will become scientists or engineers. But science and technology occupy ever- expanding places in our everyday lives.
Nature & Scope of Physics
Physics studies matter, energy, force, and their interactions, aiming to understand the universe's fundamental laws from subatomic particles to galaxies, bridging classical (mechanics, optics, heat) and modern (quantum mechanics, relativity) realms, and driving technology by explaining natural phenomena through simple, testable principles. Its scope is vast, covering everything from everyday motion to black holes, using quantitative laws to explain and predict natural occurrences.
Nature of Physics
- Study of Nature: Physics, from the Greek physis (nature), is the most fundamental science, seeking to understand the universe's workings and natural phenomena.
- Matter, Energy, Force, Time: It focuses on the interactions between energy, matter, space, and time.
- Fundamental Laws: It aims to uncover basic, quantitative laws (like conservation of energy, momentum) that explain diverse phenomena.
- Experimental & Theoretical: It uses observation, experiments, and reasoning to develop and test theories, which are refined or replaced if contradicted by evidence.
Scope of Physics
Physics is broadly divided into two domains:
- Macroscopic (Classical Physics): Deals with large-scale phenomena.
- Mechanics: Motion, forces (Newton's Laws).
- Thermodynamics: Heat and energy transfer.
- Electromagnetism: Electricity, magnetism, light.
- Optics: Light and vision.
- Microscopic (Modern Physics): Deals with atomic and subatomic scales.
- Quantum Mechanics: Behavior of atoms, molecules, particles.
- Relativity: Space, time, gravity at high speeds (Einstein).
- Nuclear & Particle Physics: Structure of the nucleus, fundamental particles.
Systems Approach
The input-process-output model of a system also brings out another dimension of the systems approach. It is a way of looking at things, processes or problems. Instead of attacking the problem in an arbitrary manner, the systems approach helps solve the problem systematically. So, the systems approach is a tool to be used for solving educational problems more efficiently and effectively, Systems approach can also be looked upon as a mode of thinking that emphasizes problem identification and problem resolution. It enables an individual to &fine the problem precisely, consider the alternative available and to choose the most efficient alternative (on the basis of the performance criteria) to solve the problem and achieve the goal(s). As systems approach is basically a mess of problem solving, it can be applied to many areas in the field of education, such as instruction, research, management of educational institutions, curriculum development and so on. One may apply it to any problem situation as the process and the mode of thinking remains the same.
Suppose we wish to develop a new course or instructional unit according to the system concept. We should begin with a survey and analysis of subject - matter identifying the skills to be learnt and the characteristics of the learners. The specific objectives, learning outcomes and performance criteria should then be formulated. An inventory of human, technological and financial resources must be made besides considering the limitations or constraints like, time, money, facilities etc. This is the stage at which we are concerned with media along with other materials. No doubt, course construction and software production can begin only after completion of content, method and media strategies. Available materials must be reviewed and examined. When no suitable materials are available, we must prepare a 'package' in the form of good kits. Field testing and validation provide opportunities to try out newly developed instructional packages with a representative sample of students. While a full scale try out is underway, we must observe closely all aspects and note further adjustments that may be needed. Implementation is the final step of putting the validated materials into full scale operation. Continuous feedback should be obtained from the learners at every stage which should lead to a further cycle of updating and modification. The least effective methods are recycled out and better materials are incorporated.
ADVANTAGES OF SYSTEM APPROACH
1. It provides a conceptual framework on which to build plans for implementing change for education.
2. It helps to identify the suitability or otherwise of the resource material to achieve the specific goals.
3. It helps to assess the resources needs, their sources and facilities in relation to quantities, time and other factors
4. Technology advances could be used to provide integration of machines, media and people for attaining the definite goal.
5. It permits an orderly introduction of components demonstrated to be required for systems success in terms of student learning.
6. Rigidity in plan of action is avoided as continuous evaluation affords desired beneficial changes to be made.
CONCLUSION
The development and use of a technology in the field of education is viewed in different ways by different people. Some claim it as the basis of a revolution in the educational system aimed at improving the effectiveness and efficiency of education at different levels. On the other hand, some castigate it as a movement aimed at replacing the traditional teacher from the educational scene by sophisticated machines and gadgets. But, in reality the function of an educational technology lies in structuring the environment for learning, by the use of modern methods, techniques, approaches, media etc. In simple words, educational technology is concerned with the development, application and evaluation of systems, techniques and aids to improve the process of human learning. Thus, we can conclude that system approach helps in optimising the effectiveness of use of educational technology. It helps in all the three phases, i.e. designing, implementing and evaluating phases of educational technology.
SUMMARY
System approach has been introduced in the field of education to manage, control and improve the process and products of education. It acts as a link between hardware and software approach. The system approach to design and analysis of teaching/learning situations is the basis of the great majority of modern educational technology related development. System approach is a rational problem-solving method of analyzing the educational process and making it more effective. The system approach in instruction is an integrated, programmed complex of instructional media, hardware and personnel whose components are structured as a single unit with a schedule of time and sequential phasing. Thus, system approach is a systematic attempt to coordinate all aspects of a problem towards specific objectives. It helps to assess the resources needs, their sources and facilities in relation to quantities, time and other factors In education, this means planned and organised use of all available learning resources to achieve the desirable learning objectives. In the context of education, the system is a unit as a whole incorporating all its components and parts namely, pupils, teachers, curriculum, content, audio visual media and evaluation of instructional objectives. Flow Diagram is a collective term for a diagram representing a flow or set of dynamic relationships in a system. It is used to structure and order a complex system, or to reveal the underlying structure of the elements and their interaction.