There are two courses available at DP level, each available at SL and HL. These two courses might approach mathematics from different perspectives, but they are connected by the same mathematical body of knowledge, ways of thinking and approaches to problems. The differences in the courses may also be related to the types of tools, for instance technology, that are used to solve abstract or practical problems.
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.
AIMS
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 instil 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.
OBJECTIVES
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 notation; 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 analysing information, making conjectures, drawing conclusions, and testing their validity.
Structure of the course
Students will be studying the following units over 2 academic years:
- Number and Algebra,
- Functions,
- Geometry and Trigonometry,
- Statistics and Probability and
- Calculus.
They will also need to work on a Mathematics exploration which is like a research paper of around 3000 words which they need to write about a topic of their choice.
Theory of knowledge questions usually accompany the lessons, and they enable students to think deeply about the matter. The questions look like the following: Should Mathematics be defined as a language? Is there a distinction between truth and certainty in Mathematics?
Mathematics: analysis and approaches
The IB DP Mathematics: analysis and approaches course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. The focus is on developing important mathematical concepts in a comprehensible, coherent and rigorous way, achieved by a carefully balanced approach.
Students are encouraged to apply their mathematical knowledge to solve abstract problems as well as those set in a variety of meaningful contexts. Mathematics: analysis and approaches has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.
Students should expect to develop insight into mathematical form and structure, and should be intellectually equipped to appreciate the links between concepts in different topic areas. Students are also encouraged to develop the skills needed to continue their mathematical growth in other learning environments.
The internally assessed exploration allows students to develop independence in mathematical learning. Throughout the course students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas.
Assessment at a glance
Assessment – SL
External assessment (3 hours)
Paper 1 (90 minutes) No technology allowed. (80 marks)
Section A Compulsory short-response questions based on the syllabus.
Section B Compulsory extended-response questions based on the syllabus
Paper 2 (90 minutes) Technology required. (80 marks)
Section A Compulsory short-response questions based on the syllabus.
Section B Compulsory extended-response questions based on the syllabus
Internal assessment
This component is internally assessed by the teacher and externally moderated by the IB at the end of the course. Mathematical exploration Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. (20 marks)
Assessment – HL
External assessment (5 hours)
Paper 1 (120 minutes) No technology allowed. (110 marks)
Section A Compulsory short-response questions based on the syllabus.
Section B Compulsory extended-response questions based on the syllabus
Paper 2 (120 minutes) Technology required. (110 marks)
Section A Compulsory short-response questions based on the syllabus.
Section B Compulsory extended-response questions based on the syllabus.
Paper 3 (60 minutes) Technology required. (55 marks)
Two compulsory extended response problem-solving question
Internal assessment
This component is internally assessed by the teacher and externally moderated by the IB at the end of the course. Mathematical exploration Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. (20 marks)