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# Mathematics Department

### Vision

TO be a value-added department, nurturing young minds to be creative problem solvers.

### Mission

To be a caring, competent and cohesive team of teachers nurturing students to be connective, creative and confident problem solvers.

### Curriculum

The Mathematics syllabus aims to enable all students to:
acquire mathematical concepts and skills for continuous learning and to support learning in other subjects;

• develop thinking, reasoning, communication, application and metacognitive skills through a mathematical approach to problem-solving;
• connect ideas within mathematics and with other subjects through the applications of mathematical concepts;
• build confidence and foster interest in mathematics.

### Special Programmes

Mathematical Modelling

Mathematical modelling is incorporated in our Secondary One to Three curriculum to develop 21st century competencies such as collaborative learning, critical thinking and real-world problem solving skills. In mathematical modelling, students are guided to experience the process of formulating and improving a mathematical model as they solve real-world problems.

Steps in Mathematical Modelling

1. Formulate by representing the problem mathematically and making necessary assumptions
2. Solve using mathematical concepts and tools
3. Interpret mathematical solution in the context of the real-world problem
4. Reflect on the reasonableness of the solutions and checking for alternative strategies and solutions Teacher giving an Outline on Mathematical Modelling Students working collaboratively on a Math Modelling Task

The main objective Secondary 1 Math Modelling Task is for students to use critical thinking to solve real-world problem using the skills that they have learnt in the classroom.

Working in pairs, students are given a task about planning a class outing to go for a river cruise. The task requires the students to come up with multiple solutions and choose the most effective solution. This task allows students to learn that most real-life problems have more than one solution and the final solution chosen has to be backed up with good reasons. Students will also understand that some assumptions have to be made and many factors have to be considered when solving real world problems.

The Secondary 3 Math Modelling Task aims to sharpen students’ skills in critical thinking and to allow students to apply the skills that they have learnt in the classroom to solve real-life problems which they can identify with.

To gradually build up the skills necessary for students to develop a mathematical model effectively, students are first taught the fundamentals of mathematical modelling through an example task which requires students to design the most economical box for packing soft toys. After which, the students will be given two practice tasks which are similar to the example task to practise in their groups. Comments will be given to the groups after each practice task to ensure that students are able to apply the skills that they have learnt. For the final task, a formative assessment based on the four fundamental steps of Mathematical Modelling (Formulating, Solving, Interpreting and Reflecting) will be used to help students grasp and internalise these skills.

Focus: Critical Thinking, Real-world Problem Solving and Collaborative Learning

Gaming in Mathematics

The teaching and learning of Trigonometry in Crescent are brought to a new dimension through the 46-inch HeuMi multi-touch tables which function like giant-sized tablets. In the game Submariner, our Secondary Three students work collaboratively as they navigate the submariner to annihilate invading ships. In the process of playing the game, the students get to apply the mathematical concepts such as bearings and angle of elevation in a simulated real-world situation. Students explaining the Submariner game at MOE Excel Fest 2013

Secondary 1 Integrated Curriculum

For the Secondary 1 Integrated Curriculum, students are given a task that integrates Mathematics, Science and Geography. The whole integrated curriculum is based on the main theme of Environment and students are to choose a place in the school where they can conserve energy by reducing the school’s electrical consumption.

Students are given real statistical data to prove that electrical consumption has been increasing over the years and they also look for authentic data from the internet to show that some building installations can conserve electrical consumption over a period of time. The students also use their Science and Geography knowledge to solve the problem.

The Integrated Curriculum allows students to see the link between different subjects and how to utilise their knowledge from these 3 subjects to solve an issue.

Focus: Performance Task - Data Analysis for Math

Secondary 2 Maths Bridging Course on Indices

The main aim of this course is to enable students to draw connections between indices in Maths and that in Additional Maths. In Maths, an index is a number that is written on the right and top of a base number, to show how many times the base numbers are to be multiplied. Indices are the plural of index. Indices are helpful because they enable us to display the numbers in standard form and they have number properties.

In Maths, students learn basic rules for operations with indices and handles mostly numerical indices. In Additional Maths, students learn to manipulate both indices and logarithms as well as indices and surds. The manipulation of indices and surds can be a powerful tool for evaluating and simplifying expressions.

Focus: Indices

Secondary 3 Maths Talent Development Programme

Students learn basic concepts and applications in Graph Theory.  In Graph theory, mathematical structures are used to model pairwise relations between objects. A "graph" in this context is made up of "vertices" or "nodes" and lines called edges that connect them. Graphs are one of the prime objects of study in discrete mathematics. These graphs are not to be confused with the graphs of functions.

Graph theory can be used to model many types of relations and process dynamics in physical, biological, social and information systems. Graph theory is also used to study molecules in chemistry and physics. Likewise, graph theory is useful in biology and widely used in sociology.

In mathematics, graphs are useful in geometry and certain parts of topology, e.g. Knot Theory.

Focus: Graph Theory and some of its real world applications

### Achievements

2016
Australian Mathematics Competition 2016
• 2 High Distinctions
• 75 Distinctions
Singapore Mathematical Olympiad 2016 (Senior Section):
• 1 Silver
• 3 Bronzes
• 2 Honourable Mentions
Singapore Mathematical Olympiad 2016 (Junior Section):
• 1 Silver
• 2 Bronzes
• 3 Honourable Mentions
Singapore Mathematical Olympiad 2016: School Award
• Commendation
Singapore and Asian Schools Math Olympiad (SASMO) 2016
• 3 Golds
• 10 Silvers
• 30 Bronzes
Singapore International Mathematics Olympiad Challenge 2016
• 3 Bronzes
World Mathematics Invitational 2016
• 1 Excellent Award
• 1 Bronze
Singapore Math Kangaroo Contest 2016
• 28 Golds
• 25 Silvers
• 24 Bronzes
Hwa Chong Institution Maths Quest 2016
• 9th and 10th (Individual)
Ngee Ann Polytechnic Maths Challenge 2016 (Day 1)
• Champion (Team)
• 1st, 2nd (Quiz Category) South Zone Mastermind Competition Participants