Mathematics

History

Elementary Mathematics was part of the education system in most Ancient Civilisations, including Ancient Greece, the Roman Empire, Vedic Society and Ancient Egypt. In the Renaissance the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European Universities, it was seen as subservient to the study of Natural, Metaphysical and Moral Philosophy.

This trend was somewhat reversed in the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in University of Oxford in 1619 and the Lucasian Chair of Mathematics being established by the University of Cambridge in 1662.

By the Twentieth Century Mathematics was part of the core curriculum in all developed countries and currently mathematics is part of curriculum of any teaching.

Importance

Mathematics is the queen of science and the language of nature. Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance; and for personal decision-making. Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics. It is essential in public decision-making and for participation in the knowledge economy.

Mathematics equips pupils with uniquely powerful ways to describe, analyze and change the world. It can stimulate moments of pleasure and wonder for all pupils when they solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Pupils who are functional in mathematics and financially capable are able to think independently in applied and abstract ways, and can reason, solve problems and assess risk.

Mathematics is a creative discipline. The language of mathematics is international. The subject transcends cultural boundaries and its importance is universally recognized. Mathematics has developed over time as a means of solving problems and also for its own sake.

Objectives

• The teaching of basic numeracy skills to all pupils.
• The teaching of practical mathematics (arithmetic, elementary algebra, plane and solid geometry, trigonometry) .
• The teaching of abstract mathematical concepts (such as set and function) at an early age.
• The teaching of selected areas of mathematics (such as Euclidean geometry) as an example of an axiomatic system and a model of deductive reasoning.
• The teaching of selected areas of mathematics (such as calculus) as an example of the intellectual achievements of the modern world.
• The teaching of advanced mathematics to those pupils who wish to follow a career in Science, Technology, Engineering, and Mathematics (STEM) fields.
• The teaching of heuristics and other problem-solving strategies to solve non-routine problems.
• The teaching of various tricks and tips those are helpful in solving the problem fast, sometime without use of pen and paper. These include calculation strategies provided by Vedic mathematics are creative and useful, and can be applied in a number of ways to calculation methods in arithmetic and algebra, most notably within the education system.

Mathematics as a Career

Those who qualify in mathematics are in the fortunate position of having a wide range of career choices. The abilities :

1. To use logical thought ,
2. To formulate a problem in a way which allows for computation and decision ,
3. To make deductions from assumption ,
4. To use advanced concepts,

are all enhanced by a mathematics degree course. It is for this reason that mathematician are increasingly in demand. With a mathematics degree, you should be able to turn your hand to finance, statistics, engineering, computers, teaching or accountancy with a success not possible to other graduates. This flexibility is even more important nowadays, with the considerable uncertainty as to which areas will be the best for employment in future years.

The most recent surveys show graduates in mathematicians and computer science at the top of the earning lists six years after graduation.]Computer science has a considerable mathematical component, which is becoming more important as the designers of software are required to prove that the software meets its specification. This kind of rigour is one of the basic techniques of mathematics, and can be learned only through a mathematics course.

Quality Perspective

UPPER PRIMARY

• The emphasis in the designing of the material is on using a language that the child can and would be expected to understand herself and would be required to work upon in a group.
• The entire material would be immersed in and emerge from contexts of children. There would be expectation that the children would verbalise their understanding, their generalizations, and their formulations of concepts and propose and improve their definitions.
• There needs to be space for children to reason and provide logical arguments for different ideas. They are also expected to follow logical arguments and identify incorrect and unacceptable generalizations and logical formulations.
• Children would be expected to observe patterns and make generalisations. Identify exceptions to generalisations and extend the patterns to new situations and check their validity.
• Need to be aware of the fact that there are not only many ways to solve a problem and there may be many alternative algorithms but there maybe many alternative strategies that maybe used. Some problems need to be included that have the scope for many different correct solutions.
• There should be a consciousness about the difference between verification and proof. Should be exposed to some simple proofs so that they can become aware of what proof means.
• Mathematics should emerge as a subject of exploration and creation rather than finding known old answers to old, complicated and often convoluted problems requiring blind application of un-understood algorithms.
• The purpose is not that the children would learn known definitions and therefore never should we begin by definitions and explanations. Concepts and ideas generally should be arrived at from observing patterns, exploring them and then trying to define them in their own words. Definitions should evolve at the end of the discussion, as students develop the clear understanding of the concept.
• Children should be expected to formulate and create problems for their friends and colleagues as well as for themselves.

Higher Secondary and Senior Secondary

This syllabus continues the approach along which the syllabi of Classes VI to VIII have been developed. It has been designed in a manner that maintains continuity of a concept and its applications from Classes IX to XII.

The salient features of the course are the following :

• The development and flow is from Class I upwards, not from college level down.
• The time given for developing a concept/series of concepts is allowing for the learner to explore them in several ways to develop and elaborate her understanding of them and the inter-relationships between them. While transacting the syllabus, we expect that the learner would be allowed a variety of opportunities for exploring mathematical concepts and processes, to help her construct her understanding of these.
• The focus is on developing the processes involved in mathematical reasoning. Accordingly, the learner requires plenty of opportunity and enough time to develop the processes of dealing with greater abstraction, moving from particular to general to particular, moving with facility from one representation to another of a concept or process, solving and posing problems, etc.
• Linkages with the learner’s life and experiences, and across the curriculum, need to be focused upon while transacting the curriculum. The idea is to allow the learner to realize how and why mathematics is all around us.
• We note that it is at the secondary stage, the child enters into more formal mathematics. She needs to see the connections with what she has studied so far, consolidate it and begin to try and understand the formal thought process involved. With this in view two areas, related to mathematical proofs/reasoning and mathematical modeling, have been introduced from Class IX to XII, in a graded manner.