The mathematician G.H. Hardy gave a very clear definition of mathematics when he wrote, "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."
However, the much more common view of mathematics is that it consists of the techniques to solve quantitative problems. The two viewpoints are linked together by the idea that mathematics is about solving problems. Hardy's patterns are generated in the process of problem solving and mathematics is more about this process than it is about calculating answers to questions using an established set of rules and formulae.
The preamble to AIS-R's mathematics curriculum document lists a number of essential agreements that underpin the teaching of mathematics in the High School. These include the implementation of a challenging instructional program, the creation of classroom environments that engage students in learning mathematics and assessing students' learning and providing them with feedback on their progress. In addition to recognizing the importance of students mastering essential numeric and algebraic skills we want them to be able to use appropriate technologies to enhance their problem solving skills and to make connections between mathematics and other subjects that they study. We want our students to be able to solve problems both individually and cooperatively and to be able to communicate their results clearly.
AIS-R's mission is to produce students who are "responsible, productive and ethical global citizens with the skills and passion to think creatively, reason critically, communicate effectively and learn continuously". This can be considered as having a fractal relationship with the Mathematics Department's aims. [fractal: a geometrical shape whose structure is such that magnification by a given factor reproduces the original object.] This also fits in with the IBO's mission to develop lifelong learners through challenging programs and rigorous assessment.
The goals of mathematics at AIS-R is to help students develop their abilities to explore and solve mathematical problems, think critically, reason and represent their mathematics, make connections, and communicate their ideas clearly. These skills will allow students to be more successful in situations that require them to apply what they know to transfer their knowledge and ultimately more comfortable taking risks. Students will be expected to learn through collaboration, investigation, modeling, conjecture and proof.