This framework gives an overview of the principles of an effective mathematics programme which is applicable to all levels. It gives the direction for the Mathematics teaching, learning, and assessment to the students. Mathematical problem solving is central to mathematics learning. This learning is also given by many tuition centres in Singapore. In the case of Math tuition in Singapore price is little expensive. But it involves the teaching of acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real-world problems. The mathematical problem-solving ability is based on five inter-related components, and they are, Concepts, Skills, Processes, Attitudes and Meta-cognition.
Mathematical concepts cover numerical, algebraic, geometrical, statistical, probabilistic, and analytical concepts. Students should develop and realize that mathematics is an integrated whole, not a merely isolated piece of knowledge. They should make sense and help them to develop their understanding of various connections and applications, as it will help to participate actively in learning mathematics and to become more confident in exploring and applying mathematics. The use of manipulative (concrete materials), practical work, and use of technological aids should be part of the learning experiences of the students.
Mathematical skills include calculation of numerical, manipulation of algebraic, analysis of data, mathematical tool usage, and estimation. The development of skill proficiencies in students is essential in the learning and application of mathematics. Although students should become able to understand and apply various mathematical skills, applying mathematical procedural skills without understanding should be avoided. Skill proficiencies include the ability to use technology confidently, where appropriate, for exploration and problem-solving.
A mathematical process is nothing but the process details of acquiring and applying mathematical knowledge. This includes the following,
• Communication and connections
• Thinking skills and heuristics
• Application and modelling.
Reasoning, communication and connections:
Mathematical reasoning refers to the ability to analyse maths related situations and to construct logical and clear arguments. Communication refers to the ability to use and express mathematical ideas and arguments clearly, shortly and logically. It helps to develop their own mathematical understanding and develop their mathematical thinking. Connections are the ability to see and make links among various mathematical ideas, and between maths and other subjects, and between mathematics and everyday life. This helps students make sense of what they learn in mathematics. Mathematical reasoning, communication and connections should be encouraged among all levels of mathematics learners from the primary to A-levels.
Thinking skills and heuristics:
Students should use various thinking skills and heuristics to solve mathematical problems. Thinking skills are skills which can be used in classifying, comparing, sequencing, analysing, pattern identifying and induction, deduction and visualisation. Some examples of heuristics are listed below and grouped into four categories according to how they are used:
• To give a representation,
• To make a calculated guess
• To go through the process
• To change the problem
Application and modelling:
Application and modelling help students in the mathematical understanding and to develop competencies. Students should apply mathematical problem-solving skills and reasoning skills to overcome a variety of problems. Mathematical modelling is the process of formulating a mathematical model to solve real-world problems. It helps students to learn and to use a variety of representations of data, and apply suitable mathematical methods and related tools for solving real-world problems.
Attitudes refer to the effective aspects of mathematics learning such as:
• Beliefs about mathematics and its usefulness
• Interest and enjoyment in learning mathematics
• Appreciation of the beauty and power of mathematics
• Confidence in using mathematics
• Perseverance in solving a problem
Making the mathematics learning fun, meaningful and useful goes a long way and helps to develop a positive attitude towards the subject.
Metacognition is nothing but “thinking about thinking”, the ability to control one’s thinking processes, like the selection and use of problem-solving strategies. It includes monitoring of self-thinking and self-regulation of learning. There is much best Math tuition Centre in Singapore to develop the children self-confidence and self-thinking. Care and attention should be given to the design of the learning activities, to build confidence in and develop an appreciation for the subject.