Advanced Programme Mathematics

Advanced Programme Mathematics

The advanced level of Mathematics (Advanced Programme Mathematics) is designed for students who have a real passion for the subject.  It is a three-year course, designed for students who enjoy and achieve excellent results in Mathematics and would like more challenges in the subject.
A learner must have displayed an ability to apply mathematical concepts in unknown situations. A good understanding of mathematical concepts is required as well as the ability to make logical deductions. No girl should consider participating in Advanced Programme Mathematics unless she has a positive attitude; a positive mathematical self-image; determination to succeed; perseverance and self-discipline and the willingness to take responsibility for her own achievements.  A work ethic of a very high standard is clearly essential.  As Advanced Programme Mathematics is an extra subject, it demands more work and more time.
At the end of Grade 9, girls will be invited into the Advanced Mathematics Programme.  If a girl is unable to maintain a Mathematics average above 70%, she will be requested to return to Core Mathematics only.  This can happen at the end of Grade 10 and again at the end of Grade 11. 

Compulsory Component:
Algebra, Calculus, Radian Measure

Elective:
St Mary’s DSG’s chosen elective is Matrices and Graph Theory.  The other options for the elective are Finance and Modelling or Statistics and Probability, but these are not taught at St Mary’s DSG.

Assessment and Examination:
Assessments in Advanced Programme Mathematics are rare.  Students are normally only tested under examination conditions.  This is purely because of time constraints – testing is time consuming, and the teachers have very little time to teach the content of this subject.

Contact Time:

Grade 10:
One hour session once a week.

Grade 11:
One evening session (1 ½ hours) and one hour session each week.

Grade 12:
One evening session (1 ½ hours) and one hour session each week, plus 3 hour Saturday workshops in Term 1 and Term 2 on elected Saturdays (reflected in the school calendar)

(Information taken from the National Curriculum Statement Grades 10–12 (General) Advanced Programme Mathematics (previously known as Additional Mathematics)

DEFINITION
Advanced Programme Mathematics is an extension of Mathematics and is similarly based on the following view of the nature of the discipline. Advanced Programme Mathematics enhances mathematical creativity and logical reasoning about problems in the physical and social world and in the context of Mathematics itself. All mathematics is a distinctly human activity developed over time as a well-defined system with a growing number of applications in our world. Knowledge in the mathematical sciences is constructed through the establishment of descriptive, numerical and symbolic relationships. Advanced Programme Mathematics also observes patterns and relationships, leading to additional conjectures and hypotheses and developing further theories of abstract relations through rigorous logical thinking. Mathematical problem solving in Advanced Programme Mathematics enables us to understand the world in greater depth and make use of that understanding more extensively in our daily lives. The Mathematics presented in Advanced Programme Mathematics has been developed and contested over time through both language and symbols by social interaction, and continues to develop, thus being open to change and growth.
 
Learning Outcome 1:  Calculus
The learner is able to establish, define, manipulate, determine and represent the derivative and integral, both as an anti-derivative and as the area under the curve, of various algebraic and trigonometric functions and solve related problems with confidence.

Learning Outcome 2: Algebra
The learner is able to represent investigate, analyse, manipulate and prove conjectures about numerical and algebraic relationships and functions, and solve related problems.

Learning Outcome 3: Statistics
The learner is able to organise, summarise, analyse and interpret data to identify, formulate and test statistical and probability models, and solve related problems.

Learning Outcome 4: Mathematical Modelling
The learner is able to investigate, represent and model growth and decay problems using formulae difference equations and series.

Learning Outcome 5: Matrices and Graph Theory
The learner is able to identify, represent and manipulate discrete variables using graphs and matrices, applying algorithms in modelling finite systems.

COURSE REQUIREMENTS

PURPOSE
In a society that values diversity and equality, and a nation that has a globally competitive economy, it is imperative that within the Further Education and Training band learners who perform well in Mathematics or who have a significant enthusiasm for mathematics are offered an opportunity to increase their knowledge, skills, values and attitudes associated with Mathematics, and so put them in a position to contribute more significantly as citizens of South Africa. The study of Advanced Programme Mathematics contributes to the personal development of high performing Mathematics learners by providing challenging learning experiences; feelings of success and self-worth; and the development of appropriate values and attitudes through the successful application of its knowledge and skills in context, and through the collective engagement with mathematical ideas.

SCOPE
Advanced Programme Mathematics is aimed at increasing the number of learners who through competence and desire enter tertiary education to pursue careers in Mathematics, engineering, technology and the sciences. Advanced Programme Mathematics is an extension and challenge for learners who demonstrate a greater than average ability in, or enthusiasm for Mathematics. The greater breadth of mathematical knowledge gained and the deepening of mathematical process skills developed through being exposed to Advanced Programme Mathematics enhances the learner’s understanding of Mathematics both as a discipline and as a tool in society. This broadens the learner’s perspective on possible careers in Mathematics and develops a passion for and a commitment to the continued learning of Mathematics amongst mathematically-talented learners. This assists in meeting their needs and encourages more mathematically-talented learners to pursue careers and interests in mathematically related fields.

The studying  of Advanced Programme Mathematics will also further the appreciation of the development of Mathematics over time, establishing a greater understanding of its origins in culture and in the needs of society.

Advanced Programme Mathematics enables learners to:
• extend their mathematical knowledge to solve new problems in the world around them and grow in confidence in this ability; 
• use sophisticated mathematical processes to solve and pose problems creatively and critically;
• demonstrate the patience and perseverance to work both independently and co-operatively on problems that require more time to solve;
• contribute to quantitative arguments relating to local, national and global issues;
• focus on the process of Science and Mathematics, rather than on right answers;
• view Science and Mathematics as valuable and interesting areas of learning;
• become more self-reliant and validate their own answers;
• learn to value Mathematics and its role in the development of our contemporary society and explore relationships among Mathematics and the disciplines it     serves;
• communicate mathematical problems, ideas, explorations and solutions through reading, writing and mathematical language;
• enable students to become problem solvers and users of Science and Mathematics in their everyday lives. The study of Advanced Programme Mathematics    should encourage students to talk about Mathematics, use the language and symbols of Mathematics, communicate, discuss problems and problem solving,    and develop competence and confidence in themselves as Mathematics students.

EDUCATIONAL AND CAREER LINKS
Advanced Programme Mathematics is valuable in the curriculum of any learner who intends to pursue a career in the physical, mathematical, financial, computer, life, earth, space and environmental sciences or in technology. Advanced Programme Mathematics also supports the pursuance of careers in the economic, management and social sciences. The knowledge and skills attained in Advanced Programme Mathematics provide more appropriate tools for creating, exploring and expressing theoretical and applied aspects of the sciences. The subject Additional Mathematics in the Further Education and Training band provides the ideal platform for linkages to Mathematics in Higher Education institutions. Learners proceeding to institutions of Higher Education with Advanced Programme Mathematics will be in a strong position to progress effectively in whatever mathematically-related discipline they decide to follow. The added exposure to modelling encountered in Advanced Programme Mathematics provides learners with deeper insights and skills when solving problems related to modern society, commerce and industry. Advanced Programme Mathematics, although not required for the study of Mathematics, engineering, technology or the sciences in Higher Education, is intended to provide talented Mathematics learners an opportunity to advance their potential, competence, enthusiasm and success in Mathematics so that it is more likely that they will follow mathematically-related careers.

In particular; the following are some of the career fields that demand the use of high level Mathematics:
• Actuarial Science
• Operations research
• Mathematical modelling
• Economic and industrial sciences
• Movie and video game special effects
• Engineering
• Computational Mathematics
• Theoretical and applied physics
• Statistical applications
• Academic research and lecturing in Mathematics, Applied Mathematics, Actuarial Science and Statistics