Soundview School is implementing and following the Singapore Mathematics curriculum syllabus and as well as International Baccalaureate Primary Years mathematics scope and sequence. Soundview School’s philosophy and belief on mathematics concur with the philosophy of Singapore Mathematics. Our math program is consistent grade-to-grade from preschool through 8th grade. This consistency is very important for developing confidence and mastery for fundamental number concepts and mathematical reasoning. With the IB curriculum, math is also integrated with transdisciplinary themes and students are applying mathematic minds and skills to solve real-life problems.

After completing Singapore Math in the primary and middle years programmes, Soundview students are confident math students that embark on Algebra 2 in high school with strong number concepts, problem solving skills, algebraic concepts and other important mathematical foundations.
Singapore Math is a national math curriculum for Singapore. Soundview School has adopted the mathematics framework from Singapore for many years. The framework is defined by the Singapore Ministry of Education.

Singapore Math is a national math curriculum for Singapore. Soundview School has adopted the mathematics framework from Singapore for many years. The framework is defined by the Singapore Ministry of Education.

The following statements are excerpts from Singapore Mathematics Syllabus published by the Ministry of Education in Singapore:
 
The framework of Singapore Math curriculum emphasizes the essence of mathematics teaching and learning in schools. The learning of mathematics at all levels involves more than the basic acquisition of concepts and skills. It also crucially involves an understanding of the underlying mathematical thinking, the general strategies of problem solving and positive attitudes to and appreciation of mathematics as an important and powerful tool in everyday life.
 
Care has been taken to ensure that there is continuity from the primary to the secondary levels. Using a spiral design of the curriculum, each topic is revisited and introduced in increasing depth from one level to the next. This enables students to consolidate the concepts and skills learned and then further develop them. The concrete-pictorial-abstract development of concepts is advocated and this is evident in the teaching and learning approaches in the Singapore math textbooks and workbooks.

The content for Mathematics includes all the topics covered from 1-6th grade. The content for Foundation Mathematics repeats some of the important topics covered from 1-4th grade. This is to ensure that students doing Foundation Mathematics have a good understanding of basic mathematical concepts covered in 1-4th grade. The pace of the Foundation Mathematics curriculum is also slower, giving more time and emphasis on hands-on activities to provide the concrete experience in the concrete-pictorial-abstract learning sequence.
 
The curriculum is developed with the interests and abilities of the students uppermost in mind. Teachers exercise flexibility and creativity when using the Singapore Math textbooks. They are encouraged to use a wide variety of strategies and resources to meet students’ diverse range of abilities and needs, and to enhance the learning of mathematics.

Mathematics is an excellent way for the development and improvement of a person’s intellectual competence in logical reasoning, spatial visualization, analysis and abstract thought. Students develop numeracy, reasoning, thinking skills, and problem solving skills through the learning and application of mathematics. These are valued not only in science and technology, but also in
everyday living and in the workplace. The development of a highly skilled scientifically- and technologically-based manpower requires a strong grounding in mathematics. An emphasis on mathematics education will ensure that we have an increasingly competitive workforce to meet the challenges of the 21st century.

Mathematics is also a subject of enjoyment and excitement, which offers students opportunities for creative work and moments of enlightenment and joy. When ideas are discovered and insights gained, students are spurred to pursue mathematics beyond the classroom walls.

AIMS OF MATHEMATICS EDUCATION IN SCHOOL

Mathematics education aims to enable students to:

(1) Acquire the necessary mathematical concepts and skills for everyday life, and for continuous learning in mathematics and related disciplines.

(2) Develop the necessary process skills for the acquisition and application of mathematical concepts and skills.

(3) Develop the mathematical thinking and problem solving skills and apply these skills to formulate and solve problems.

(4) Recognize and use connections among mathematical ideas, and between mathematics and other disciplines.

(5) Develop positive attitudes towards mathematics.

(6) Make effective use of a variety of mathematical tools (including information and communication technology tools) in the learning and application of mathematics.

(7) Produce imaginative and creative work arising from mathematical ideas.

(8) Develop the abilities to reason logically, communicate mathematically, and learn cooperatively and independently.

MATHEMATICS FRAMEWORK

This framework shows the underlying principles of an effective mathematics program that is applicable to all levels, from the primary to secondary level. It sets the direction for the teaching, learning, and assessment of mathematics.

Mathematical problem solving is central to mathematics learning. 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

Mathematical concepts cover numerical, algebraic, geometrical, statistical, probabilistic, and analytical concepts.

Students should develop and explore the mathematics ideas in depth, and see that mathematics is an integrated whole, not merely isolated piece of knowledge.

They should be given a variety of learning experiences to help them develop a deep understanding of mathematical concepts, and to make sense of various mathematical ideas, as well as their connections and applications, in order 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.

SKILLS

Mathematical skills include procedural skills for numerical calculation, algebraic manipulation, spatial visualization, data analysis, measurement, use of mathematical tools, and estimation.

The development of skill proficiencies in students is essential in the learning and application of mathematics. Although students should become competent in the various mathematical skills, over-emphasizing procedural skills without understanding the underlying mathematical principles should be avoided.

Skill proficiencies include the ability to use technology confidently, where appropriate, for exploration and problem solving. It is important also to incorporate the use of thinking skills and heuristics in the process of developing skill proficiencies.

PROCESSES

Mathematical processes refer to the knowledge skills (or process skills) involved in the process of acquiring and applying mathematical knowledge. This includes reasoning, communication and connections, thinking skills and heuristics, and application and modeling.

Mathematical reasoning refers to the ability to analyze mathematical situations and construct logical arguments. It is a habit of mind that can be developed through the applications of mathematics in different contexts.

Communication refers to the ability to use mathematical language to express mathematical ideas and arguments precisely, concisely and logically. It helps students develop their own understanding of mathematics and sharpen their mathematical thinking.

Connections refer to the ability to see and make linkages among mathematical ideas, between mathematics 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 pervade all levels of mathematics learning, from the primary to A-levels.

Thinking Skills and Heuristics

Students should use various thinking skills and heuristics to help them solve mathematical problems. Thinking skills are skills that can be used in a thinking process, such as classifying, comparing, sequencing, analyzing parts and wholes, identifying patterns and relationships, induction, deduction and spatial visualization. Some examples of heuristics are listed below and grouped in four categories according to how they are used:

• To give a representation, e.g. draw a diagram, make a list, use equations

• To make a calculated guess, e.g. guess and check, look for patterns, make suppositions

• To go through the process, e.g. act it out, work backwards, before-after

• To change the problem, e.g. restate the problem, simplify the problem, solve part of the problem

Application and Modeling

Application and modeling play a vital role in the development of mathematical understanding and competencies. It is important that students apply mathematical problem-solving skills and reasoning skills to tackle a variety of problems, including real-world problems.

Mathematical modeling is the process of formulating and improving a mathematical model to represent and solve real-world problems. Through mathematical modeling, students learn to use a variety of representations of data, and to select and apply appropriate mathematical methods and tools in solving real-world problems. The opportunity to deal with empirical data and use mathematical tools for data analysis should be part of the learning at all levels.

ATTITUDES

Attitudes refer to the affective 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

Students’ attitudes towards mathematics are shaped by their learning experiences. Making the learning of mathematics fun, meaningful and relevant goes a long way to inculcating positive attitudes towards the subject. Care and attention should be given to the design of the learning activities, to build confidence in and develop appreciation for the subject.

METACOGNITION

Metacognition, or “thinking about thinking”, refers to the awareness of, and the ability to control one's thinking processes, in particular the selection and use of problem-solving strategies. It includes monitoring of one's own thinking, and self-regulation of learning.

The provision of metacognitive experience is necessary to help students develop their problem solving abilities. The following activities may be used to develop the metacognitive awareness of students and to enrich their metacognitive experience:

 • Expose students to general problem solving skills, thinking skills and heuristics, and how these skills can be applied to solve problems.

• Encourage students to think aloud the strategies and methods they use to solve particular problems.

• Provide students with problems that require planning (before solving) and evaluation (after solving).

• Encourage students to seek alternative ways of solving the same problem and to check the appropriateness and reasonableness of the answer.

• Allow students to discuss how to solve a particular problem and to explain the different methods that they use for solving the problem.