Mathematics teaching and learning
practices range from Practising mathematical routines to
develop procedural fluency, through to investigating scenarios,
modelling the real world, solving problems and explaining reasoning.
When students achieve
procedural fluency, they carry out procedures flexibly, accurately and
efficiently.
When factual knowledge and concepts come to
mind readily, students are able to make more complex use of knowledge to
successfully formulate, represent and solve mathematical
problems. Problem-solving helps to develop an ability to transfer
mathematical skills and ideas between different contexts. This
assists students to make connections between related concepts and adapt
what they already know to new and unfamiliar situations.
With
appropriate effort and experience, through discussion, collaboration and
reflection of ideas, students should develop confidence and
experience success in their use of mathematics.
The major domains of mathematical knowledge in Specialist Mathematics
are Vectors and Matrices, Real and Complex Numbers, Trigonometry,
Statistics and Calculus. Topics are developed systematically, with
increasing levels of sophistication, complexity and connection, building
on functions, calculus, statistics from Mathematical Methods, while
vectors, complex numbers and matrices are introduced.
Functions
and calculus are essential for creating models of the physical world.
Statistics are used to describe and analyse phenomena involving
probability, uncertainty and variation. Matrices, complex numbers and
vectors are essential tools for explaining abstract or complex
relationships that occur in scientific and technological endeavours.
Students who undertake Specialist Mathematics will develop confidence
in their mathematical knowledge and ability, and gain a positive view
of themselves as mathematics learners. They will gain an appreciation of
the true nature of mathematics, its beauty and
its power.
Assumed knowledge, prior learning or
experience Specialist Mathematics is designed to be taken in conjunction
with, or on completion of, Mathematical Methods. It is assumed that
work covered in Mathematical Methods will be known before it is required
in Specialist Mathematics.
Assumed knowledge refers to the
subject matter that teachers can expect students to know prior to
beginning this subject. Emphasis is placed on the mastery of content,
ensuring key concepts or procedures are learnt fully so they will not
need reteaching.
Students need to have attained an A or B level in Extension Maths.