Chapter-I INTRODUCTION Background of Study
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Chapter-I INTRODUCTION Background of Study The term ‘Mathematics’ has been interpreted and explained in various ways. According to Oxford Dictionary, “Mathematics is the science of number and space’’. A famous 20th century mathematician Albert Einstein defined, ‘Mathematics is a free invention of human intellect. Similarly, Sidhu ( 2002, pg.2) writes, “Mathematics is the numerical and calculation part of man’s life and knowledge. It helps the man to give exact interpretation to his ideas and conclusions. It deals with quantitative facts and relationship as well as with problems involving space and form. Thus, mathematics as an expression of the human mind and reflects the active will the contemplative reason, and desire for aesthetic perfection. Mathematicians seek out patterns and formulate new conjunctives. Mathematician reside the truth or falsity of conjunctives by Mathematical proof”. Basnet, D.B. (2003 pg.3) writes, “Mathematics has been used throughout the world as an essential tool in many fields, including natural science, engineering, medicine and social science. Applied mathematics (the branch of mathematics concerned with application of mathematical knowledge to other field) inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical discipline such as statistics and a game theory”. Similarly, Gautam, D. (2005 pg.2) writes, “Mathematics also engages pure mathematics or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical application for what began as pure mathematics are often discovered. Mathematics and mathematics education are too separate disciplines in the field of education. Mathematics primarily focuses on the process and products of 1 what mathematician does. This is the obstruction of thinking and process as mathematician applies in creating mathematics. The focus of mathematics in on creating mathematics with understanding is its basic structure. It does not give much concern about the mathematics should be thought, who can learn mathematics and why one cannot learn mathematics like issues. Mathematics education deals with mathematics from prospective of education. It is concerned with the development and implementation of appropriate curriculum and with all issues associated with the teaching and learning mathematics. Mathematics education covers the learners of all ages and at all levels from early childhood to adult. Thus, mathematics education is not solely concerned with curriculum, classrooms teachers and learners in school, nevertheless issues associated with school mathematics will be a major focus. The areas of mathematics education are curriculum, teaching, learning, and education. Five foundations:- Philosophy, Psychology, Sociology, Mathematics and technology guide, these are the areas. Improvement of school mathematics education is the primary concern of mathematics education, but it does not mean that it is limited to school education. What mathematics, what teaching methods and what learning strategies for the students of higher education would be appropriate are also the area of mathematics education. Hence, mathematics education is an applied discipline that deals with the wider application of mathematics is different sectors and fields”. “The main objective of mathematics education is to prepare well-qualified mathematics teachers in both methods and contents. Mathematics education is the synthesis of what (content) and how (method). A mathematics education cannot afford the luxury of being a student of subject matter only, or students of the process transmitting subject matter only. We cannot concern ourselves with one of these to exclusion of the other. We must concern ourselves with both the process and product, the how of teaching and what of teaching. 2 Geometry is one of the most useful and important branch of mathematics. Geometry includes an enormous range of ideas and can be viewed in many different ways. It has been interlocked with many other subjects and different views of human activity. The basic ideas of mathematics system originated in geometry some 22 or 23 hundred years ago” (Kelly & Ladd, 1989). Furthermore, Kelly & Ladd writes, “It is not certain who first had the ideas of typing to prove mathematics rule by reasoning rather than typing to prove it in different cases. Although both Thales (640-546 BC) and Pythagoras (Born 572 BC) have been given credit for the idea, originated in Greece around the sixth century BC, once the idea of this mathematical method has been discovered or invented the mathematics of geometry grew with astonishing speed. By 300 BC, a large body of geometric knowledge was in existence. At this time, the mathematician Euclid brought together and unified this knowledge by constructing the first definite, formal system of mathematics in his treaties ‘The Element’. It is probable that ‘Euclid’s Elements’ is highly successful of earlier writers; Euclid’s Element is not devoted theory and geometric algebra. The work is composed of 13 books with 465 propositions (Eves, 1986)”. Geometry concerned with the properties of configurations of geometric objects, points, lines and circles. The word ‘Geometry’ is derived from the Greek word ‘Geomertorn’ that means geo (Earth) and metron (Measure), which points to its practical roots. According to Oxford Advanced Learners Dictionary (7th Ed.) ‘Geometry is the branch of mathematics that deals with the measurement and relationships of lines, angles, surfaces and solids. Similarly, Pandit (2002, pg3) noted, “Geometry is the growing body knowledge with ever widening applications and inherent beauty in its systematic structure and organization”. Furthermore, shorting the importance of geometry, Malkevith(1998) writes, “Geometry considered a tool for understanding, describing, and interacting with the space in which we live , in perhaps the most intuitive, concrete and reality linked part of mathematics. On the on hand geometry as discipline, rest 3 on an expensive formulization process which has been carried out for over 2000 years at increasing levels of rigor, abstraction and generally thus, geometry is the best means of stimulating the spirit of inquiry and intuition. It is one of the most universal and useful tool in all parts of mathematics. It is also vital catalyst for effective use or study of any branch of mathematics”. In Nepal, Mathematics has been taught as one of the major subjects in secondary education since the beginning of modern education. Secondary education level general mathematics has three components: Arithmetic, Algebra, and Geometry. In the past, these three components of mathematics taught separately. Now, there are more than these three areas such as Arithmetic, Algebra, Geometry, Trigonometry, Statics and Linear Programming. “School mathematics curricula of Nepal have given emphasis on Geometry learning from beginning of school. The curricula aimed at developing students understanding of intended geometric concepts at primary, lower secondary and secondary level” (Luitel, 2005 pg.4). Similarly, according to NCTM, “geometry is one of the content standards of school mathematics, which aims at developing spatial reasoning, problem solving skills, and communication”. Moreover, about the important of thinking skills in geometry, A vision for School Geometry (2005) writes, “reasoning is fundamental to mathematical activity. Active learners question, examine conjecture and experiment. Mathematics programs should provide reasoning skills. Learners need varied experiences to construct arguments in problems settings and to evaluate the arguments of others” (VSG, 2005). Furthermore, MALATI believes “Geometry offers an excellent context for learners to experience, mathematical activity and that can be done at primary and secondary levels (Smith, 1997)”. Thus, geometry is regarded as a core content area of school mathematics program. It is the most important and integral part of school mathematics curricula. 4 Showing the importance of geometry, Vance (1973) writes, “it is a way of modeling our physical environment and because there is a great abundance of models suitable for all levels, from kinder garden through graduate school. Geometry is a natural vehicle for developing intuition, creativity and a spirit of inquiry. Furthermore, geometry is a fertile source for interesting and challenging problems and geometrical methods are powerful tools in problems solving”. Schacht (1996) put this idea in this way; perhaps the most important value of geometry for all students is the experience they get in building a logical system of thought. Learning to use correct reasoning in solving geometric problems should help to improve thinking habit generally. Similarly, Koman at al. (1986) characterized the place of geometry as uniting and making more precise all the objective approaches to mathematical knowledge. The geometry, therefore, plays a significant role in school mathematics. Moreover, it is our belief that geometry teaching for school students should be based on psychological, theoretical and practical considerations. Therefore, it is important that the subject matter presented to the pupils should be attractive and interesting to them. The content and methods of work in geometry should be influenced bye some practical motives. Supporting this idea, Chernysheva et al. (1986) states “Geometry has many aspects which are directly linked with the