Mathematics: AI-SL Handbook
Table of Contents
Applications and Interpretations Aims
The aims of 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 instill 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
By the end of the course, students are expected to reach the following assessment objectives.
1. Knowledge and understanding: Recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.
2. Problem solving: Recall, select and use their knowledge of mathematical skills, results and models in both abstract and real-world contexts to solve problems.
3. Communication and interpretation: Transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized notation; use appropriate notation and terminology.
4. Technology: Use technology accurately, appropriately and efficiently both to explore new ideas and to solve problems.
5. Reasoning: Construct mathematical arguments through use of precise statements, logical deduction and inference and by the manipulation of mathematical expressions.
6. Inquiry approaches: Investigate unfamiliar situations, both abstract and from the real world, involving organizing and analyzing information, making conjectures, drawing conclusions, and testing their validity
Assessment objectives in practice
External Assessment Outline - SL
External Assessment Details
Purpose of internal assessment
Internal assessment is an integral part of the course and is compulsory for both SL and HL 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 internal assessment requirements at SL and at HL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. It is marked according to five assessment criteria.
Guidance and authenticity The exploration submitted for internal assessment must be the student’s own work. However, it is not the intention that students should decide upon a title or topic and be left to work on the internal assessment component without any further support from the teacher. The teacher should play an important role during both the planning stage and the period when the student is working on the exploration.
It is the responsibility of the teacher to ensure that students are familiar with:
• the requirements of the type of work to be internally assessed
• the IB academic honesty policy available on the programme resource centre
• the assessment criteria; students must understand that the work submitted for assessment must address these criteria effectively.
Collaboration and teamwork
Collaboration and teamwork are a key focus of the approaches to teaching in the DP. It is advisable that the teacher uses the available class time to manage student collaboration. While working on their exploration students should be encouraged to work collaboratively in the various phases of the process,
for example: • generating ideas
• selecting the topic for their exploration
• sharing research sources
• acquiring the necessary knowledge, skills and understanding
• seeking peer feedback on their writing. The Approaches to teaching and learning (ATL) website on the programme resource centre provides an excellent source for developing collaborative skills in students.
Time allocation Internal assessment is an integral part of the mathematics courses, contributing 20% to the final assessment in the SL and the HL courses. This weighting should be reflected in the time that is allocated to teaching the knowledge, skills and understanding required to undertake the work, as well as the total time allocated to carry out the work. It is recommended that a total of approximately 10-15 hours of teaching time should be allocated to the work.
This should include:
• time for the teacher to explain to students the requirements of the exploration
• class time for students to work on the exploration and ask questions
• time for consultation between the teacher and each student
• time to review and monitor progress, and to check authenticity.
Requirements and recommendations
Students can choose from a wide variety of activities: for example, modelling, investigations and applications of mathematics. To assist teachers and students in the choice of a topic, a list of stimuli is available in the teacher support material. However, students are not restricted to this list.
In developing their explorations, students should aim to make use of mathematics learned as part of the course. The mathematics used should be commensurate with the level of the course–that is, it should be similar to that suggested in the syllabus. It is not expected that students produce work that is outside the syllabus–however, this will not be penalized. Ethical guidelines should be adhered to throughout the planning and conducting of the exploration. Further details are given in the Ethical practice in the Diploma Programme poster on the programme resource centre.
The following details should be stated on the cover page of the exploration:
• title of the exploration
• number of pages. The references are not assessed. However, if they are not included in the final report it may be flagged in terms of academic honesty.
The specific purposes of the exploration are to:
• develop students’ personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematics
• provide opportunities for students to complete a piece of mathematical work over an extended period of time
• enable students to experience the satisfaction of applying mathematical processes independently
• provide students with the opportunity to experience for themselves the beauty, power and usefulness of mathematics
• encourage students, where appropriate, to discover, use and appreciate the power of technology as a mathematical tool
• enable students to develop the qualities of patience and persistence, and to reflect on the significance of their work
• provide opportunities for students to show, with confidence, how they have developed mathematically.
Internal Assessment Criteria
The “presentation” criterion assesses the organization and coherence of the exploration.
A coherent exploration is logically developed, easy to follow and meets its aim. This refers to the overall structure or framework, including introduction, body, conclusion and how well the different parts link to each other.
A well-organized exploration includes an introduction, describes the aim of the exploration and has a conclusion. Relevant graphs, tables and diagrams should accompany the work in the appropriate place and not be attached as appendices to the document.
Appendices should be used to include information on large data sets, additional graphs, diagrams and tables.