Mathematics HL Course Outline 2017
Table of Contents Course Overview... 2 Mathematics HL Outline... 2 Aims and Objectives... 3 Assessment... 4 Links to Theory of Knowledge... 5 Extended Essay... 5 Approaches to Learning... 6 International Mindedness... 7 Learner Profile... 7 Resources... 8 Year 12 2017 (Year 1 Mathematics)... 9 Year 13 2017 (Year 2 Mathematics)... 11 1
Course Overview By studying mathematics students develop the ability to think creatively, critically, strategically, and logically. They learn to structure and to organise, to carry out procedures flexibly and accurately, to process and communicate information, and to enjoy intellectual challenge. Students can also develop other important thinking skills. They learn to create models and predict outcomes, to conjecture, to justify and verify, and to seek patterns and generalisations. They learn to estimate with reasonableness, to calculate with precision, and to infer with an appreciation of variation. Mathematics HL caters for students with a good background in mathematics who are competent in a range of analytical and technical skills and who display considerable interest in the subject. The majority of these students will be expecting to include mathematics as a major component of their university studies. Others may take the subject because they have a strong interest in mathematics and enjoy meeting its challenges and engaging with its problems. The course focuses on developing important mathematical concepts in a comprehensible, coherent and rigorous way. Students are encouraged to apply their mathematical knowledge to solving problems set in a variety of meaningful contexts. Development of each topic should feature justification and proof of results. Mathematics HL Outline The six Higher Level topics are split across a two-year course. Students undertake class formative assessments at the end of each topic to gauge their progress, with a formal end of year exam in Year 12. The Exploration (IA) is introduced at the end of Year 1 and completed dureing the first term of Year 2. YEAR 1 TOPICS 1. Functions, Equations and Graphs 2. Circular Functions and Trigonometry 3. Calculus 4. Core Descriptive Statistics 5. Core Probability YEAR 2 TOPICS 1. Vectors 2. Complex Number 3. Mathematical Exploration 4. Option Topic Statistics and Probability Use of calculators Students may have a GDC on their laptop but all students must have a Casio GDC in class at all times. Formulae Booklet and Statistical Tables Students will receive a copy of this booklet at the start of the course. All students must have a clean copy of this booklet during the examination. 2
Aims and Objectives The aims of all mathematics courses in group 5 are to enable students to: 1. enjoy mathematics, and develop an appreciation of the elegance and power of mathematics 2. develop an understanding of the principles and nature of mathematics 3. communicate clearly and confidently in a variety of contexts 4. develop logical, critical and creative thinking, and patience and persistence in problem-solving 5. employ and refine their powers of abstraction and generalization 6. apply and transfer skills to alternative situations, to other areas of knowledge and to future developments 7. appreciate how developments in technology and mathematics have influenced each other 8. appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics 9. appreciate the international dimension in mathematics through an awareness of t he universality of mathematics and its multicultural and historical perspectives 10. appreciate the contribution of mathematics to other disciplines, and as a particular area of knowledge in the TOK course. 3
Assessment External assessment 5 hrs 80% The external assessment consists of three written papers, Papers 1, 2 and 3, which are externally set and externally marked. Written papers Paper 1 (No Calculator permitted) 2 hrs 30% Section A Compulsory short response questions based on the whole syllabus Section B Compulsory extended-response questions based on the whole syllabus Paper 2 (GDC required) 2 hrs 30% Section A Compulsory short response questions based on the whole syllabus Section B Compulsory extended-response questions based on the whole syllabus Paper 3 (GDC required) 1 hr 20% Compulsory extended-response questions based on the option syllabus Internal assessment 10 hours in lessons 20% 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 HL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics (20 marks) Internal assessment is an integral part of the course and is compulsory for all students. It enables students to demonstrate the application of their skills and knowledge, and to pursue their personal interests, without the time limitations and other constraints that are associated with written examinations. The internal assessment should, as far as possible, be woven into normal classroom teaching and not be a separate activity conducted after a course has been taught. The internally assessed component in this course is a mathematical exploration. This is a short report written by the student based on a topic chosen by him or her, and it should focus on the mathematics of that particular area. The emphasis is on mathematical communication (including formulae, diagrams, graphs and so on), with accompanying commentary, good mathematical writing and thoughtful reflection. A student should develop her own focus, with the teacher providing feedback via, for example, discussion and interview. This will allow the students to develop area(s) of interest to them without a time constraint as in an examination, and allow all students to experience a feeling of success. The final report should be approximately 6 to 12 pages long. It should be word processed and shared with the teacher to allow for monitoring of student progress. Students should be able to explain all stages of their work in such a way that demonstrates clear understanding. While there is no requirement that students present their work in class, it should be written in such a way that their peers would be able to follow it fairly easily. The report should include a detailed bibliography, and sources need to be referenced in line with the IB academic honesty policy. Direct quotes must be acknowledged. Students must ensure the School s Academic Honesty Policy is adhered to. 4
Links to Theory of Knowledge TOK is central to the diploma and needs to play a part in the teaching and learning in Mathematics HL. Throughout the course students should be asked to justify their answers by answering HDIKT? (How do I know that?), reflect on their thought processes and evaluate different approaches to solving a problem. They will be encouraged to develop a spirit of enquiry and investigation. Interesting discussions can develop from questions such as: Is maths invented or discovered? Why does maths describe reality? Are the mathematical equations of Newton and Einstein inventions to describe reality, or did they exist prior to their discovery? If equations exist independent of discovery, then where do they exist and in what form? Some mathematical constants (ππ, e, Fibonacci numbers) appear consistently in nature, what does this tell us about mathematical knowledge? Mathematics and music. Music can be expressed using mathematics. Does this mean that music in mathematical, mathematics is musical or that they are both reflections of a common truth? Do different measures of central tendency express different properties of the data? Are these measures invented or discovered? Could mathematics make alternative, equally true, formulae? What does this tell us about mathematical truths? How easy is it to lie with statistics? Extended Essay An extended essay in mathematics provides students with an opportunity to demonstrate an appreciation of any aspect of the subject, whether it is: - the applicability of mathematics to solve both real and abstract problems - the beauty of mathematics as in, for instance, geometry or fractal theory - the elegance of mathematics in the proving of theorems as in, for example number theory - the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years - the way that a branch of mathematics has been born, or flourished, as a result of technology. These are just some of the many different ways mathematics can be enjoyable or useful, or, as in many cases, both. The extended essay may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself. Students will normally be expected either to extend their knowledge beyond that encountered in the Mathematics HL course they are studying, or to apply techniques used in their mathematics course to modelling in an appropriately chosen topic. 5
Some samples of extended essay are: Prime numbers in cryptology Other ways of measuring the size of the earth What role mathematics played in ending the controversy surrounding the flat earth vs the round earth paradigms Differential equations in simple harmonic motion Using graph theory to minimise cost Approaches to Learning The learning of mathematics for real understanding relies on a wide range of teaching and learning approaches and experiences. The processes of mathematical inquiry, mathematical modelling and applications and the use of technology should be introduced appropriately. These processes should be used throughout the course, and not treated in isolation. Communication: In addition to the acquisition of a significant number of subject specific terms and appropriate mathematical notation, students need to be able to discuss, question and justify their findings with concise mathematical reasoning. This may take the form of class discussions, problem solving or the written development, explanation and justification of their Exploration. Thinking: Students learn mathematics by being active participants in learning activities rather than recipients of instruction. Teachers provide students with opportunities to learn through mathematical inquiry, by making and testing a conjecture or by developing and testing a model. Students are constantly challenged to apply their knowledge to varied and meaningful situations. Technology: Technology is a powerful tool in the teaching and learning of mathematics. Technology can be used to enhance visualization and support student understanding of mathematical concepts. It can assist in the collection, recording, organisation and analysis of data. Technology can increase the scope of the problem situations that are accessible to students. The use of technology increases the feasibility of students working with interesting problem contexts where students reflect, reason, solve problems and make decisions. Self-Management: Students need to be able to manage their time effectively as they move through the two year course, as it is vital that they undertake home learning to consolidate their understanding. A high level of self discipline and personal organisation is essential and students will need to develop these qualities in order to gain top marks. Research Skills: Students will utilise their research skills when planning their Exploration; it will be important for them to be able to discern the quality of material they source and to be able to use this material appropriately in the development of their own mathematical investigation. 6
International Mindedness The aim of all IB programmes is to develop internationally minded people who, recognising their common humanity and shared guardianship of the planet help to create a better and more peaceful world. The teacher can exploit opportunities to achieve this aim by discussing relevant issues as they arise and making reference to appropriate background information. For example, it may be appropriate to encourage students to discuss: differences in notation the lives of mathematicians set in a historical and/or social context the cultural context of mathematical discoveries how the attitudes of different societies towards specific areas of mathematics are demonstrated the universality of mathematics as a means of communication. Learner Profile The aim of all IB programmes is to develop internationally minded people who, recognizing their common humanity and shared guardianship of the planet, help to create a better and more peaceful world. As IB learners in Mathematics we strive to be: Inquirers Knowledgeable Thinkers Communicators Principled Open-minded Caring Risk-takers We nurture our curiosity, developing skills for inquiry and research. We know how to learn independently and with others. We learn with enthusiasm and sustain our love of learning throughout life. We develop and use conceptual understanding, exploring knowledge across a range of disciplines. We engage with issues and ideas that have local and global significance. We use critical and creative thinking skills to analyse and take responsible action on complex problems. We exercise initiative in making reasoned, ethical decisions. We express ourselves confidently and creatively in more than one language and in many ways. We collaborate effectively, listening carefully to the perspectives of other individuals and groups. We act with integrity and honesty, with a strong sense of fairness and justice, and with respect for the dignity and rights of people everywhere. We take responsibility for our actions and their consequences. We critically appreciate our own cultures and personal histories, as well as the values and traditions of others. We seek and evaluate a range of points of view, and we are willing to grow from the experience. We show empathy, compassion and respect. We have a commitment to service, and we act to make a positive difference in the lives of others and in the world around us. We approach uncertainty with forethought and determination; we work independently and cooperatively to explore new ideas and innovative 7
Balanced Reflective strategies. We are resourceful and resilient in the face of challenges and change. We understand the importance of balancing different aspects of our lives intellectual, physical and emotional to achieve well-being for ourselves and others. We recognize our interdependence with other people and with the world in which we live. We thoughtfully consider the world and our own ideas and experience. We work to understand our strengths and weaknesses in order to support our learning and personal development. Resources Pearson Baccalaureate Higher Level Mathematics 2013 Edition Mathematics HL Pearson with HL Options Statistics and Probability Mathematics HL resources Delta Mathematics Sigma Mathematics Mathematics for the International Student Mathematics HL (Core) (Urban et al) 8
Year 12 2017 (Year 1 Mathematics HL) Term 1 Dates Year One Notes/School Assessment Activities Week 0 25 27 Jan Teacher Only Day (Thurs) Week 1 30 Jan 3 Feb Functions & Equations Anniversary day (Mon) School starts Tuesday Week 2 6 10 Feb Waitangi day (Mon) Athletics day (Fri) Swimming Sports Week 3 13 17 Feb Week 4 20 24 Feb Swimming Finals Teacher Only Day (Fri) Week 5 27 Feb 3 EOTC Week Mar Week 6 6 10 Mar Exponents & Logarithms Week 7 13 17 Mar Week 8 20 24 Mar Permutations & Combinations Week 9 27 31 Mar Binomial Expansion Summer Tournament Week Week 10 3 7 Apr Mathematical Induction Week 11 10 14 Apr Good Friday Functions, Exp & Log, Perm & Com and Bin Exp Test Term 2 Week 1 1 5 May Sequences & Series Week 2 8 12 May School Ball (Sat) Week 3 15 19 May Week 4 22 26 May Trigonometry Week 5 29 May 2 June Birthday Concert (Mon) Week 6 5 9 June Queen Birthday (Mon) Week 7 12 16 June Week 8 19 23 June Week 9 26 30 June Week 10 3 7 July Induction, Seq & Series and Trigo Test Term 3 Week 1 31 July 4 Core Descriptive Statistics Aug Week 2 7 11 Aug House Music (Thu) Week 3 14 18 Aug Core Probability Week 4 21 25 Aug Week 5 28 Aug 1 Sept Differential Calculus Week 6 4 8 Sept Winter Tournament Week Statistics, Probability and part of Differential Test 9
Week 7 11 15 Sept AIMS tournament Week 8 18 22 Sept Senior School Exam Week 9 25 29 Sept Review for Exam Term 4 Week 1 16 20 Oct Week 2 23 27 Oct Integral Calculus Labour day (Mon) Week 3 30 Oct 3 Nov Week 4 6 Nov 10 Nov Week 5 13 17 Nov Week 6 20 24 Nov IB Exploration Week 7 27 Nov 1 Dec (Introduction) Differential and Integral Test 10
Year 13 2017 (Year 2 Mathematics HL) Term 1 Dates Year Two Notes/School Activities Assessment Week 0 25 27 Jan Teacher Only Day (Thurs) Week 1 30 Jan 3 Feb Vector Anniversary day (Mon) School starts Tuesday Week 2 6 10 Feb Waitangi day (Mon) Athletics day (Fri) Swimming Sports Week 3 13 17 Feb Week 4 20 24 Feb Swimming Finals Teacher Only Day (Fri) Week 5 27 Feb 3 EOTC Week Mar Week 6 6 10 Mar Week 7 13 17 Mar Complex Number Week 8 20 24 Mar Week 9 27 31 Mar Summer Tournament Week Week 10 3 7 Apr Vector and Complex Test Week 11 10 14 Apr Good Friday IB Exploration (Draft) Term 2 Week 1 1 5 May Option Statistics and Probability Week 2 8 12 May School Ball (Sat) Week 3 15 19 May Week 4 22 26 May Week 5 29 May 2 Birthday Concert (Mon) June Week 6 5 9 June Queen Birthday (Mon) Week 7 12 16 June Statistics and Probability Test Week 8 19 23 June IB Exploration (Final) Week 9 26 30 June Week 10 3 7 July Term 3 Week 1 31 July 4 Aug Revision for Exam Week 2 7 11 Aug House Music (Thu) Week 3 Week 4 14 18 Aug 21 25 Aug Week 5 28 Aug 1 Sept Week 6 4 8 Sept Winter Tournament Week Week 7 11 15 Sept AIMS tournament Week 8 18 22 Sept Senior School Exam Week 9 25 29 Sept Review for Exam Term 4 11
Week 1 16 20 Oct IB Study Leave Week 2 23 27 Oct Labour day (Mon) Week 3 30 Oct 3 Nov IB Exams Start Week 4 6 Nov 10 Nov Week 5 13 17 Nov IB Exams Finish Week 6 20 24 Nov Week 7 27 Nov 1 Dec Week 8 4 8 Dec 12