Mathematics has been described as the study of structure, order and relation that has evolved from the practices of counting, measuring and describing objects. Mathematics provides a unique language to describe, explore and communicate the nature of the world we live in as well as being a constantly building body of knowledge and truth in itself that is distinctive in its certainty. These two aspects of mathematics, a discipline that is studied for its intrinsic pleasure and a means to explore and understand the world we live in, are both separate yet closely linked.
Summary of the courses available
Individual students have different needs, aspirations, interests and abilities. For this reason there are two different subjects in mathematics, each available at SL and HL
These courses are designed for different types of students: those who wish to study mathematics as a subject in its own right or to pursue their interests in areas related to mathematics, and those who wish to gain understanding and competence in how mathematics relates to the real world and to other subjects. Each course is designed to meet the needs of a particular group of students. Mathematics: analysis and approaches and Mathematics: applications and interpretation are both offered at SL and HL. Therefore, great care should be taken to select the course and level that is most appropriate for an individual student.
In making this selection, individual students should take into account the following factors:
• Their own abilities in mathematics and the type of mathematics in which they can be successful
• Their own interest in mathematics and those particular areas of the subject that may hold the most interest for them
• Their other choices of subjects within the framework of the DP
The structure of IB DP mathematics courses, with two different routes to choose from, recognizes the two different aspects of mathematics discussed in the introduction.
Mathematics: Analysis and Approaches is for students who enjoy developing their mathematics to become fluent in the construction of mathematical arguments and develop strong skills in mathematical thinking. They will also be fascinated by exploring real and abstract applications of these ideas, with and without technology. Students who take Mathematics: analysis and approaches will be those who enjoy the thrill of mathematical problem solving and generalization.
Mathematics: Applications and Interpretation is for students who are interested in developing their mathematics for describing our world and solving practical problems. They will also be interested in harnessing the power of technology alongside exploring mathematical models. Students who take Mathematics: applications and interpretation will be those who enjoy mathematics best when seen in a practical context.
Both subjects are offered at higher level and SL. There are many elements common to both subjects although the approaches may be different. Both subjects will prepare students with the mathematics needed for a range of further educational courses corresponding to the two approaches to mathematics set out above.
Format of the Syllabus
There are five topics and within these topics there are sub-topics. The five topics are:
• Number and algebra
• Geometry and Trigonometry
• Probability and statistics
The aims of all DP mathematics courses are to enable students to:
• Develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power
• Develop an understanding of the concepts, principles and nature of mathematics
• Communicate mathematics clearly, concisely and confidently in a variety of contexts
• Develop logical and creative thinking, and patience and persistence in problem solving to instill confidence in using mathematics
• Employ and refine their powers of abstraction and generalization
• Take action to apply and transfer skills to alternative situations, to other areas of knowledge and to future developments in their local and global communities
• Appreciate how developments in technology and mathematics influence each other
• Appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of mathematics
• Appreciate the universality of mathematics and its multicultural, international and historical perspectives
• Appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course
• Develop the ability to reflect critically upon their own work and the work of others
• Independently and collaboratively extend their understanding of mathematics.
Problem solving is central to learning mathematics and involves the acquisition of mathematical skills and concepts in a wide range of situations, including non-routine, open-ended and real-world problems. Having followed a DP mathematics course, students will be expected to demonstrate the following:
• Knowledge and understanding: Recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.
• Problem solving: Recall, select and use their knowledge of mathematical skills, results and models in both abstract and real-world contexts to solve problems.
• Communication and interpretation: Transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized n otation; use appropriate notation and terminology.
• Technology: Use technology accurately, appropriately and efficiently both to explore new ideas and to solve problems.
• Reasoning: Construct mathematical arguments through use of precise statements, logical deduction and inference and by the manipulation of mathematical expressions.
• Inquiry approaches: Investigate unfamiliar situations, both abstract and from the real world, involving organizing and analyzing information, making conjectures, drawing conclusions, and testing their validity.