Mathematics Applications and Interpretations SL/HL

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.

Mathematics is driven by abstract concepts and generalization. This mathematics is drawn out of ideas, and develops through linking these ideas and developing new ones. These mathematical ideas may have no immediate practical application. Doing such mathematics is about digging deeper to increase mathematical knowledge and truth. The new knowledge is presented in the form of theorems that have been built from axioms and logical mathematical arguments and a theorem is only accepted as true when it has been proven. The body of knowledge that makes up mathematics is not fixed; it has grown during human history and is growing at an increasing rate.

The side of mathematics that is based on describing our world and solving practical problems is often carried out in the context of another area of study. Mathematics is used in a diverse range of disciplines as both a language and a tool to explore the universe; alongside this its applications include analyzing trends, making predictions, quantifying risk, exploring relationships and interdependence. While these two different facets of mathematics may seem separate, they are often deeply connected. When mathematics is developed, history has taught us that a seemingly obscure, abstract mathematical theorem or fact may in time be highly significant.

On the other hand, much mathematics is developed in response to the needs of other disciplines. The two mathematics courses available to Diploma Programme (DP) students express both the differences that exist in mathematics described above and the connections between them. 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. The next section will describe in more detail the two available courses.

This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics. The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.

The assessment objectives for biology, chemistry and physics reflect those parts of the aims that will be formally assessed either internally or externally. These assessments will centre upon the nature of science. It is the intention of these courses that students are able to full-fill the following assessment objectives:

The aims of all DP mathematics courses are to enable students to:

• • 1. develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power
  • 2. develop an understanding of the concepts, principles and nature of mathematics
  • 3. communicate mathematics clearly, concisely and confidently in a variety of contexts
  • 4. develop logical and creative thinking, and patience and persistence in problem solving to instil confidence in using mathematics
  • 5. employ and refine their powers of abstraction and generalization
  • 6. 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
  • 7. appreciate how developments in technology and mathematics influence each other
  • 8. appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of mathematics
  • 9. appreciate the universality of mathematics and its multicultural, international and historical perspectives
  • 10. appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course
  • 11. develop the ability to reflect critically upon their own work and the work of others
  • 12. independently and collaboratively extend their understanding of mathematics.