What Is Singapore Mathematics?
WHY THE SINGAPORE MATHEMATICS METHOD.
THE HISTORY OF SINGAPORE MATHEMATICS
Before the 1980s, Singapore imported its math textbooks from other countries and its students were ranked in the lower half of countries in mathematics. In the beginning of 1980, Singapore started developing its own primary and secondary textbooks, The Curriculum Development Institute of Singapore published its first math program in 1982. In 1995, Singapore's students were ranked first in the Trends in International Mathematics and Science Study (TIMSS). Since then, Singapore's students have been consistently ranked among the top.
THE SINGAPORE MATHEMATICS FRAMEWORK
The Singapore Mathematics framework was developed on the basis that mathematical problem solving is central to learning math. It involves the acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real-world problems. The development of mathematical problem solving ability is dependent on five inter-related components, namely, Concepts, Skills, Processes, Attitudes and Metacognition.
CONCEPTS/ CONCRETE LEARNING
Mathematical concepts covers numerical, algebraic, geometrical, statistical, probabilistic and analytical concepts. Students would be given a variety of learning experiences to enable them to develop a good understanding of mathematical concepts and their connections and applications. Concrete materials (manipulatives) such as cubes, blocks, place value mats, geometric figures and practical work are used as part of the learning experience.
The Singapore Mathematics method in elementary grades uses the concrete to pictorial to abstract learning approach to encourage active thinking, understanding and communication of mathematical concepts and problem solving. Singapore Mathematics also emphasizes mental math and model drawing. This approach helps students transition better to more complex mathematical problems and algebra.
Singapore Mathematics emphasizes the "why" before the "how". At the concrete stage our center uses manipulatives such as cubes, blocks, place value mats and geometric figures to model each mathematical concept.
PICTORIAL LEARNING APPROACH
At this stage, the concrete model is transformed into a pictorial level. This may involve model drawing, drawing circles, dots or number bonds.
Model drawing is an excellent approach solving word problems. Model drawing is versatile can be used for first grade addition problems or 5th grade pre-algebra. Not only can this be used as a visual aid, but a teacher can use the same model to extend learning and ask questions such as: What is the ratio of the amount of money Kathy's has to the amount of money Lucy has? or How much more money does Kathy have than Lucy?
ABSTRACT LEARNING APPROACH
At this stage, the teacher models mathematical concepts at a symbolic level using numbers, notations and math symbols. Students are encouraged to reflect on mathematical attributes and relationships.
Mathematical skills include procedural skills in numerical calculation, algebraic manipulation, spatial visualization, data analysis, measurement and estimation.
Understanding underlying mathematical principles is emphasized before developing students to be competent in mathematical skills.
Mathematical processes refer to process skills and includes reasoning, communication and connections, thinking skills and heuristics, application and modelling.
Being able to use mathematical language to express mathematical ideas and arguments clearly and logically helps students sharpen their mathematical thinking. Students should be able to make linkages between mathematics and everyday life and other subjects.
Singapore Mathematics encourages students to use thinking skills and heuristics to solve mathematical problems. Under the framework, heuristics are grouped in four categories according to how they are used.
1) To give a representation (e.g. draw a diagram or use equations)
2) To make a calculated guess (e.g. look for patterns or make suppositions)
3) To go through the process (e.g. work the problem backwards)
4) To simplify or restate the problem.
Application and modelling play an important role in developing understanding and competence in mathematics. In mathematical modelling, students learn to use a variety of data representations and apply appropriate methods and tools to solve real-world problems.
Singapore Mathematics makes math fun. meaningful and relevant to foster positive attitudes towards mathematics.
Metacognition or "thinking about thinking", refers to the one's awareness and ability to control the thinking process and selection and use of strategies to solve mathematical problems. By providing students with the metacognitive experience, students are empowered to develop their own problem solving skills.
Some activities used to encourage metacognition awareness include:
1) Encouraging students to think aloud during the problem solving process.
2) Encouraging students to find and discuss alternative methods of solving a mathematical problem and check to see if the answer is appropriate and reasonable.
3) Exposing students to general problem solving and thinking skills and heuristics and apply it to problem solving.