**Mathematics Programme**

**Curriculum 课程内容**

The Mathematics programme in Dunman High School spans across six years. Our content is aligned to ensure that students move from Junior High to Senior High seamlessly and the content coverage extends beyond the basic syllabus in breadth and depth.

本校6年数学课程不但连贯初中与高中，在内容上也比一般基础课程更深广。

In Junior High, the curriculum is built upon the major strands of Mathematics such as Numbers and Algebra, Trigonometry, Geometry, Calculus, Graphing Techniques and Statistics.

在初中部分，数学课程是围绕主要的数学领域所设计，例如数目和代数、三角、几何、微积分学、制图技巧和统计学。课程注重数学概念的理解和问题解答，从而让学生体味数学的奥妙，并探索数学与其他学科（如物理，美学等等）的密切关系。

Students would be able to appreciate the beauty of Mathematics in the various strands through derivation and understanding of concepts. They would also make connections across Mathematical topics and the other disciplines through integration with subjects such as Physics and Aesthetics. In addition, the curriculum seeks to engage students in the application of Mathematics in real life situations so as to enrich their appreciation of the subject. This is done through Mathematical Modeling, a process which requires students to represent or describe real world problems mathematically. The aim is to find a real world solution or gain a better understanding of the problem. At the end of Junior High, students develop the skills to reason, to communicate mathematically, and to learn cooperatively.

At Senior High, our students have the option to offer H1 Mathematics or H2 Mathematics for their GCE ‘A’ Level examinations. The curriculum continues to develop our students’ mathematical thinking and problem solving skills, with an emphasis on conceptual understanding and skills in reasoning, applications and modelling with the use of technology. Students will have opportunities to conjecture, discover and reason in mathematics. For those who show passion and the aptitude to go further in Mathematics, they can choose to offer MOE-H3 Mathematics or NUS Linear Algebra. These programmes allow students to further develop their mathematical modelling and reasoning skills. Students will also learn the process of mathematical modelling for real-world problems, which involves making informed assumptions, validation and prediction.

Through our collaborations with organizations such as the Gifted Education Branch, Ministry of Education, Singapore Mathematics Society and our overseas partners, students have opportunities to undergo tailored training programmes and participate in various international and nation-wide mathematics competitions, such as the Singapore Mathematics Olympiad, American Mathematics Competition, Australian Mathematics Competition, Singapore Mathematical Society Project Festival.

Apart from the Mathematics Curriculum, all Upper Secondary students also attend compulsory Financial Literacy lessons structured within their formal curriculum time. Through these lessons, students learn about the importance of financial literacy. They will be taught good financial habits and these invaluable life skills can prepare the students to acquire sound values which will take them through life as responsible adults and active citizens. They are also exposed to the basic concept of time value of money and the fundamentals of the foreign exchange market. At the end of the Financial Literacy modules, students are also given the opportunity to embark on a trip to Asia countries to learn more about finance and entrepreneurship.

### Curriculum Content

The topics offered at Junior High are shown in the following:

Lower Secondary | Upper Secondary | Upper Secondary |
---|---|---|

Mathematics |
Mathematics 1 |
Mathematics 2 |

1. Integers | Indices and Surds | Quadratic Functions and Inequalities |

2. Factors and Multiples | Linear Inequalities | Polynomials |

3. Fractions and Decimals | Quadratic Expressions and Equations | Functions |

4. Estimation and Approximation | Simultaneous Equations | Trigonometric Ratios and Graphs |

5. Real Numbers | Coordinate Geometry | Trigonometric Equations and Identities |

6. Basic Algebra and Algebraic Manipulation | Graphs of Functions | Further Trigonometric Identities |

7. Linear Algebraic Equations | Similarity and Congruency | Exponential and Logarithmic Functions |

8. Pythagoras’ Theorem | The Modulus Function | The Linear Law |

9. Area and Perimeter of Plane Figures | Applications of Trigonometry | Differentiation |

10. Volume and Surface Area (Mensuration) | Angle Properties of Circle | Application of Differentiation |

11. Rate, Ratio and Proportion | Vectors in 2 dimensions | Partial Fractions |

12. Percentage | Binomial Theorem | Integration |

13. Data Handling and Analysis | Probability | Applications of Integration |

14. Geometric Construction | Circular Measure | - |

15. Angle Properties of Parallel Lines and Polygons | - | - |

16. Standard Notation | - | - |

17. Law of Indices | - | - |

18. Algebraic Expansion and Factorization | - | - |

19. Quadratic Equations | - | - |

20. Graphs in Practical Situations | - | - |

21. Linear and Quadratic Graphs | - | - |

22. Simultaneous Equations | - | - |

23. Algebraic Manipulation | - | - |

24. Trigonometry | - | - |

25. Set Theory | - | - |

此外，为了更好地让学生把握数学课程，本部门通过开展“数学建模”的项目，让学生在现实生活中应用数学。这个项目让学生尝试通过数学方式的呈现来解决现实世界中的问题并对其有更深入的认识。在初中结束时，学生不但能培养逻辑推理思维，也能学习如何以数学的方式进行沟通，并且进行合作式的学习。

在高中部，学生可选修‘A’水准的H1或H2课程。课程将延续初中部的教学理念，通过数学概念、推理、技巧和数学科技建模的管道，继续培养和提高学生思考和解题能力。他们将有机会利用相关知识对数学问题进行推测、探讨和论证。能力较强并有兴趣的学生，也可以选择内容更丰富和具挑战性的H3数学课程或国大的线性代数。这些课程旨在让学生更进一步提升他们的数学建模和推理能力。值得一提的是，学生将通过以现实生活为背景的建模过程，学习如何更好地做出明智的假设、验证和预测。

在我校与教育部高材部门、新加坡数学协会和其他海外合作伙伴的配合下，学生将有机会接受为他们量身定做的培训课程，并参与各种国际和全国性的数学比赛，如新加坡奥林匹克数学比赛，美国数学竞赛，澳大利亚数学竞赛，新加坡数学协会展览会等等。

除了正式课程外，所有初中高年级学生也必须参加金融知识课程。这些涵盖在正式课堂时间的课程将让学生学习金融知识的重要性。学生将学习良好的理财习惯，而这些宝贵的生活技能将培养学生正确的价值观，使他们在未来能成为积极和负责任的公民。学生也将接触到金钱的时间价值的基本概念和外汇市场的基本原理。课程结束后，学生也会有机会到亚洲国家学习更多有关金融和创业的知识。

**课程内容**

在初中所学习的数学内容包括：

低年级 | 高年级 | 高年级 |
---|---|---|

数学 |
数学1 |
数学2 |

1. 整数 | 指数和不尽根 | 二次函数与不等式 |

2. 系数和倍数 | 线性不等式 | 多项式 |

3. 分数和小数 | 二次表达式和方程 | 函数 |

4. 估计和近似 | 联立方程 | 三角比和图形 |

5. 实数 | 坐标几何 | 三角恒等式和方程 |

6. 基本代数和代数表达式 | 功能图 | 进阶三角恒等式和方程 |

7. 代数方程 | 相似性和一致性 | 指数和对数函数 |

8. 毕达哥拉斯定理 | 模功能 | 直线法 |

9. 面积和周长 | 三角学的应用 | 微分 |

10. 体积和表面积 | 圆形的角特性 | 微分的应用 |

11. 比率，比值和比例 | 二维的向量 | 部分分式 |

12. 百分比 | 二项式定理 | 积分 |

13. 数据处理和分析 | 可能性 | 积分的应用 |

14. 几何建筑 | 圆形测量 | |

15. 平行线和多边形的角特性 | - | - |

16. 标准符号 | - | - |

17. 指数法 | - | - |

18. 代数扩张和分解 | - | - |

19. 二次方程 | - | - |

20. 实际情况中的图表 | - | - |

21. 线性和二次图 | - | - |

22. 联立方程 | - | - |

23. 代数运算 | - | - |

24. 三角学 | - | - |

25. 集合论 | - | - |

**Pedagogy 教学法**

The Mathematics Programme tailors our teaching environment and practices to cater for different learning experiences for our students. By integrating out-of-class experiences and different subject disciplines in our programme, it encourages the investigation of real-life problems.

本校以具区分性的教学环境和方式让学生们有不同的学习经验。课程融合课堂以外的学习和其他不同的学科知识，来鼓励学生对现 实生活中的问题进行探索。

Students are given opportunities for discovery learning and open-ended problem solving to enable them to develop higher level thinking skills in our six-year course. In Lower Secondary, various games and activities are also incorporated into the pedagogical methodologies in order to better engage students and allow them to develop appreciation for the subject. As most of these and many other Math-related projects involve group work, students are also given the opportunity to learn collaboratively. These collaborations are not only learning opportunities, they are also good platforms for our students to develop an invaluable skill of being able to work in teams.

Our programme aims to develop the essential process, mathematical thinking and problem solving skills that students require to solve problems. They are taught to recognize and use connections among mathematical ideas and to develop a positive attitude towards Mathematics. We make use of a variety of information and communication technology tools in our lessons to further enhance students’ learning.

Being a school offering an Integrated Programme allows us to have holistic and comprehensive programmes in the teaching and learning of Mathematics. We fully explore the advantages of spiral-building up of skills in Mathematics throughout the six years and provide opportunities for students to see the applications of Mathematics in their daily lessons. Talented students explore research projects and participate in national competitions that require knowledge spanning across the two disciplines.

他们也可在这6年里有许多发掘学习和解答开放式问题的机会，从而培养更强的思考能力。我们也在初中低年级的课程里融入了各种游戏和活动，以提升学生的参与度和让他们对科目有更好的认识。由于大多数的数学专题作业都是以小组形式进行，因此学生不仅能学习知识，也可以加强他们在团队合作时所需的各种技巧。

本学科旨在培育数学思考和问题解决的技能。学生除了学习识别和应用不同数学课项之间的存在关系外，也同时加深对数学的喜好。除此之外，课程也广泛地运用多种信息和通讯技术来提升学生的学习效率。

身为直通车计划的学府之一，我校秉持着为学生提供一个更全面的教育体验的使命，数学部也不例外。本部门利用螺旋式的课程架构，在六年内为学生打下良好的数学基础，并让他们亲身体验数学在日常生活的应用。此外，我们也提供机会让有才华的学生参与跨学科的探索研究活动以及全国比赛等。

**Assessment 评估与测试**

Other than pen-and-paper tests, the Mathematics Programme places emphasis on alternative assessment which focus on the conceptual understanding of what has been learned.

除了例常笔试外，本课程的评估方式也包涵其他类型，以更全面地测试学生对所学概念的理解。

In the midst of their learning, students are also given authentic tasks which allow them to apply what they have learnt in the classroom to the world outside.

Examples of alternative assessment include interdisciplinary projects such as creating a rain gauge or cereal box, Viva Voce (Oral presentation), creative problem posing and solving as well as mathematical games and modelling. Other examples include writing a proposal for a modified Health and Fitness Indicator, and using a software to determine the minimum surface area of a solid figure.

一些跨学科的真实评估包括雨量计和麦片盒的制作，口述报告，创意问题的提问与解答，以及各类数学游戏和建模活动等。其他例子还包括为改良后的健康和体能指示器草拟计划书，以及使用软件来鉴定一个固体的最小面积。