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# Teaching Secondary School Singapore Express Maths - Focusing on getting Students to Understanding Mathematical Processes

Mathematics is a key skill to be thought to the new generation to equip them to be productive in our modern knowledge based economy. Since independence in 1965, Singapore has put great emphasis on mathematics education and Singapore mathematics education has now gained international recognition with successive good results in The Trends in International Mathematics and Science Study (TIMMS). Singapore mathematics curriculum targets to teach all students a level of maths mastery which will serve them well in the career as well as daily lives. Today, compulsory mathematics education takes up around 1600 hours of total curriculum time and since 1995, Singapore has ranked within the top 3 positions in TIMMS with the exception of Primary 4 Science (ranked 7th) in 1995.

The mathematics syllabuses in Singapore, for schools, are issued by the Ministry of Education in collaboration with University of Cambridge Local Examinations Syndicate.Every six years or so, the syllabuses undergo a periodic review to ensure that they remain relevant so as to prepare pupils for the challenges and opportunities of the future and also to be in line with the national objectives.

There are 4 alternative courses available at Singapore secondary school, known as streams: Integrated Programme, Express, Normal (Academic) and Normal (Technical). Most students in Singapore secondary education system qualifies to express stream, one of these four tracks, depending on their Primary School Leaving Examination (PSLE) results held at the end of Primary 6. This stream is designed to make students achieve their “O” level in four years and to attend to junior colleges and centralized institutes.

The Singapore maths teaching focuses on some contemporary principles which emphasizes understanding and applying mathematics rather than memorizing and forgetting it after school. This type of mathematics knowledge is achieved by focusing on three phases of mathematics learning in the classroom as well as getting students to understanding mathematical processes. Teaching secondary school Singapore Express maths as in other levels are based on these concepts and in this post, we will cover both principles of mathematics teaching and mathematical processes in detail.

Principles of Mathematics Teaching

Teaching Secondary School Singapore Express Math is founded on three principles of mathematics teaching as well as three phases of mathematics learning in the classroom.

Principles of mathematics teaching sets the direction towards understanding not memorizing, step-by-step, hierarchical mathematics knowledge building and applying mathematics knowledge to real-world problems.”

Mathematics teaching principle 1 says “teaching is for learning; learning is for understanding; understanding is for reasoning and applying and ultimately for problem solving”. According to this principle, learning of mathematics should focus on understanding, not memorizing. This means, problem solving is the focus in Singapore Express Maths curriculum.

Mathematics teaching principle 2 says “teaching should build on student’s knowledge; take cognisance of student’s interests and experiences; and engage them in active and reflective learning”. This principle takes the hierarchical nature of mathematics into account. Mathematics is largely hierarchical and higher concepts and skills are built on more foundational ones. This requires a sequential learning and it is important for teachers to check students’ understanding before introducing new concepts and skills.

In reality, the math syllabuses adopt a spiral approach and are a guide for teachers to plan their mathematics and science instructional programmes.Teachers are not bound by the sequence of topicsbut ensure that the hierarchy and linkage aremaintained.

Mathematics teaching principle 3 says “teaching should connect learning to the real-world, harness Information and Communication Technology (ICT) tools and emphasise 21st century competencies”. This enables Singapore students to not only learn maths as an abstract topic but apply mathematics knowledge to real world problems. The advanced technology and ICT tools enabled more readily application of mathematics to real-world and Singapore maths education encourages teachers to apply ICT tools in teaching.

According to phases of the learning theory, effective instruction of a unit involves readiness, engagement and mastery.

Student’s readiness to learn (Phase 1) is vital and in this phase, teachers prepare students so that they are ready to learn by taking into account prior knowledge, motivating contexts and learning environment.

The 2nd Phase of learning, engagement, is also the main phase of learning where students are engaged into learning new concepts and skills. The most common used pedagogical approaches used are activity-based learning (learning by doing and mostly effective in lower secondary), teacher-directed inquiry (teacher leading students to explore, investigate and find answers on their own)and direct instructions (explicit teaching where teachers introduce, explain and demonstrate new concepts and skills).

In Phase 3, mastery, includes motivated practice (students need to practice to achieve mastery), reflect on their learning (reflective review). Students who are mathematically inclined are also encouraged to extend their learnings.

**Mathematical Processes**

Teaching Singapore secondary school, Singapore Express Maths focuses on getting students to understanding Mathematical Processes. In Singapore maths, mathematical processes refer to the knowledge or process skills involved in the process of acquiring and applying mathematical knowledge. The mathematical processes include reasoning, communication and connections, thinking skills and heuristics, and application and modelling.

The Secondary Express Math syllabus is also organized along 3 content strands: Number and Algebra, Geometry and Measurement and Statistics and Probability. Mathematical processes cut across these 3 strands.

**Reasoning, communication and connections** focuses on mathematical reasoning (ability to analyze mathematical situations and construct logical arguments), communication (ability to use mathematical language to express mathematical ideas and arguments) and connections (ability to see and make linkages among mathematical ideas, between mathematics and other subject or everyday life).

In this process, the students are thought to reason inductively and deductively like explaining a mathematical statement, drawing logical conclusions, making inferences and writing mathematical arguments as well as using appropriate representations, mathematical language and technology to present and communicate mathematical ideas.

**Thinking skills and heuristics** are various skills and technics developed to help students to solve mathematical problems. Thinking skills such as classifying, comparing, sequencing, generalization etc. can be used in a thinking process and heuristics such as drawing diagrams, looking for patterns and work-backward can be used in different situations to solve a mathematical problem.The students are also thought to use a problem-solving model like Polya’s model.

Application and modelling refers to the application of mathematical problem-solving skills to a variety of problems, including real world problems, by the students. The students are also expected to formulate and improve a mathematical model to represent and solve a real-world problem using mathematical modelling.

In the secondary school, students are expected to give more attention to applications and modelling since they are more mature at this phase and more aware of their immediate environment. Students are guided by their teacher to develop an awareness and understanding of the mathematical processes. This involves working on real world problems individually or as a member of a group and giving opportunities to students to apply mathematical solving and reasoning skills to a variety of problems, including open ended and real-world ones.

When students are moved to secondary school, emphasizes moves to deductive arguments and justifications. Students are expected to justify or disprove a mathematical statement using logical reasoning chain or counter example.

**Teachers, Parents and Students**

“Every child is precious” approach is the key to Singapore education. The child is the focus of the school system and no child is deprived of opportunities and resources. The rewards are based on merits and parents are key stakeholders of the schools and the most responsible party when it comes to the education of the students.

Teachers have high expectations oftheir students and parents also have highexpectations of their children. Singapore society values education as itallows people to improve theirsocial status. This creates a competitive environment but in Singapore, parents as the responsible parties, put effort and resources for their children to catch up and rise. Even if a student may find himself or herself falling behind the topics, not understanding the content and also performing poorly in exams; there are ways to help him / her such as putting extra hours of study, either by a maths tuition teacher or parents themselves.

**Summary**

School mathematics curriculum, emphasizes a balancebetween mastery over basic skills and concepts and theapplication of higher order thinking skills to solve mathematical problems.

In teaching secondary school Singapore Express math, the key concept are the modern mathematics teachings principles and phases applied. Focusing on getting students to understanding Mathematical Processes, namely reasoning, communication and connections, thinking skills and heuristics, and application and modelling, will equip the students with necessary skills to use mathematics in their 21st century jobs and daily lives.