Aims and objectives of mathematics
The aims of teaching and learning mathematics are to encourage and enable students to:
- recognize that mathematics permeates the world around us
- appreciate the usefulness, power and beauty of mathematics
- enjoy mathematics and develop patience and persistence when solving problems
- understand and be able to use the language, symbols and notation of mathematics
- develop mathematical curiosity and use inductive and deductive reasoning when solving problems
- become confident in using mathematics to analyse and solve problems both in school and in real-life situations
- develop the knowledge, skills and attitudes necessary to pursue further studies in mathematics
- develop abstract, logical and critical thinking and the ability to reflect critically upon their work and the work of others
- develop a critical appreciation of the use of information and communication technology in mathematics
- appreciate the international dimension of mathematics and its multicultural and historical perspectives.
A. Knowledge and understanding
Knowledge and understanding are fundamental to studying mathematics and form the base from which to explore concepts and develop problem-solving skills. Through knowledge and understanding students develop mathematical reasoning to make deductions and solve problems.
At the end of the course, students should be able to:
- know and demonstrate understanding of the concepts from the five branches of mathematics (number, algebra, geometry and trigonometry, statistics and probability, and discrete mathematics)
- use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations including those in real-life contexts
- select and apply general rules correctly to solve problems including those in real-life contexts.
B. Investigating patterns
Investigating patterns allows students to experience the excitement and satisfaction of mathematical discovery. Mathematical inquiry encourages students to become risk-takers, inquirers and critical thinkers.
Through the use of mathematical investigations, students are given the opportunity to apply mathematical knowledge and problem-solving techniques to investigate a problem, generate and/or analyse information, find relationships and patterns, describe these mathematically as general rules, and justify or prove them.
At the end of the course, when investigating problems, in both theoretical and real-life contexts, student should be able to:
- select and apply appropriate inquiry and mathematical problem-solving techniques
- recognize patterns
- describe patterns as relationships or general rules
- draw conclusions consistent with findings
- justify or prove mathematical relationships and general rules.
C. Communication in mathematics
Mathematics provides a powerful and universal language. Students are expected to use mathematical language appropriately when communicating mathematical ideas, reasoning and findings—both orally and in writing.
At the end of the course, students should be able to communicate mathematical ideas, reasoning and findings by being able to:
- use appropriate mathematical language (notation, symbols, terminology) in both oral and written explanations
- use different forms of mathematical representation (formulae, diagrams, tables, charts, graphs and models)
- move between different forms of representation.
Chapter # 2 Differentiation
Introduction : The ancient Greeks knew the concepts of area, volume and centroids etc.Which are related to integral calculus .Later on in the seventeenth century, Sir Isaac Newton, an English mathematician and Gottfried Whilhelm Leibniz, a German mathematician,considered the problems of instantaneous rates of change. They reached independently to the invention of differential calculus.After the development of calculus, mathematics become a powerful tool for dealing with rates of change and describing the physical universe. :