1. Introduction to Mathematics IA The Exploration

2. Internal assessment in mathematics SL is an individual exploration
Internal assessment in mathematics SL 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.

3. Internal assessment is an integral part of the mathematics SL course, contributing 20% to the final assessment in the course. It is expected that a total of approximately 10 teaching hours 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 • time for consultation between the teacher and each student • time to review and monitor progress, and to check authenticity.

4. 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 his or 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 can be either word processed or handwritten. 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

5. 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. The exploration should not normally exceed 12 pages, including diagrams and graphs, but excluding the bibliography. However, it is the quality of the mathematical writing that is important, not the length.

6. Requirements and recommendations
The teacher is expected to give appropriate guidance at all stages of the exploration by, for example, directing students into more productive routes of inquiry, making suggestions for suitable sources of information, and providing advice on the content and clarity of the exploration in the writing-up stage. Teachers are responsible for indicating to students the existence of errors but should not explicitly correct these errors. It must be emphasized that students are expected to consult the teacher throughout the process.

7. Requirements and recommendations
All students should be familiar with the requirements of the exploration and the criteria by which it is assessed. Students need to start planning their explorations as early as possible in the course. Deadlines should be firmly established. There should be a date for submission of the exploration topic and a brief outline description, a date for the submission of the first draft and, of course, a date for completion

8. Requirements and recommendations
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 by the syllabus. It is not expected that students produce work that is outside the mathematics SL syllabus—however, this is not penalized

9. Developing The Exploration
The topic is one that interests you. (It is easier to stay motivated and work hard)
While deciding the topic of the exploration a student should keep in mind that there is enough scope of Mathematical analysis in the topic.

10. Timeline – Developing The Exploration
Process
Date begun
Date ended
Progress check
Think about a stimuli
Choose a topic
Oct 3rd
Oct 10th
Draft exploration
Nov 11th
 Nov 14th
Introduction
Outline the aim and purpose in a clear and succinct manner.
Justify the exploration choice
Briefly discuss the area of mathematics that will be used.
Evidence of some research.

11. Timeline – Developing The Exploration
Body/Mathematical Exploration
Describe the method, followed by an investigation
Record your results (tables, lists etc)
Analyse the results (graphs, diagrams, calculations etc) and form conjectures.

12. Timeline – Developing The Exploration
Conclusion and Bibliography
Summarise your findings in response to your aim. Restate any rules, conjectures or models that you found.
Comment on any limitations to your approach, or to your findings.
Comment on possible extensions and real life connections. Relate it to your personal knowledge and to your previous knowledge.
Including a reflection on what you have learned and what you have taken away from this experience will reflect personal engagement.

13. Timeline – Developing The Exploration
First Draft Due date
Nov 25th
Teacher to review & comment on draft
Meet with teacher
Dec 1st
Dec 3rd
Final writing
Revise draft
 Dec 15th
 Dec 16th
Final version due date: Dec 18th

14. Planning – Mind Mapping

15. Stimuli sport archaeology computers algorithms cell phones music sine
musical harmony
motion e
electricity
water
space
orbits
food
volcanoes
diet
Euler
games
symmetry
architecture
codes
the internet
communication
tiling
population
agriculture
viruses
health
dance
play π
geography
biology
business
economics
physics
chemistry
information technology in a global society
psychology

16. Choose a stimulus and create your own mind map here.

17. The Assessment Criteria

18. The Assessment Criteria
Your teacher expects these skills and strategies from you:
Choosing a topic
Identifying an appropriate topic
Developing a topic
Devising a focus that is well defined and appropriate
Ensuring that the topic lends itself to a concise exploration

19. The Assessment Criteria
Communication
Expressing ideas clearly
Identifying a clear aim for the exploration
Focusing on the aim and avoiding irrelevance
Structuring ideas in a logical manner
Including graphs, tables and diagrams at appropriate places
Editing the exploration so that it is easy to follow
Citing references where appropriate

20. The Assessment Criteria
Mathematical presentation
Using appropriate mathematical language and representation
Defining key terms, where required
Selecting appropriate mathematical tools (including information and communication technology)
Expressing results to an appropriate degree of accuracy

21. The Assessment Criteria
Personal engagement
Working independently
Asking questions, making conjectures and investigating mathematical ideas
Reading about mathematics and researching areas of interest
Looking for and creating mathematical models for real-world situations
Considering historical and global perspectives
Exploring unfamiliar mathematics

22. The Assessment Criteria
Reflection
Discussing the implications of results
Considering the significance of the exploration
Looking at possible limitations and/or extensions
Making links to different fields and/or areas of mathematics

23. The Assessment Criteria
Use of mathematics
Demonstrating knowledge and understanding
Applying mathematics in different contexts
Applying problem-solving techniques
Recognizing and explaining patterns, where appropriate
Generalizing and justifying conclusions

24. The Assessment Criteria

25. The Assessment Criteria

26. The Assessment Criteria

27. The Assessment Criteria

29. As part of the learning process, teachers can give advice to students on a first draft of the exploration. This advice should be in terms of the way the work could be improved, but this first draft must not be heavily annotated or edited by the teacher. The next version handed to the teacher after the first draft must be the final one.

30. Authenticity
Authenticity may be checked by discussion with the student on the content of the work, and scrutiny of one or more of the following: • the student’s initial proposal • the first draft of the written work • the references cited • the style of writing compared with work known to be that of the student

31. Self-Assessment
When completing your self assessment, use the language of the rubrics and the teacher expectations to comment on why you have given yourself this particular grade. Set goals for yourself for each criterion.

32. Checklist Item Yes No Is the work entirely yours?
Partially No
Is the work entirely yours?
Have you chosen a topic that you are interested in and developed your own ideas? Is it evident in your exploration?
Have you explained the reason why you have chosen your topic in your exploration?
Is the aim of your exploration included in your introduction?
Do you have an introduction and conclusion? Is your exploration organized?
Have you defined key terms/variables?
Have you used appropriate mathematical language (notation, symbols and terminology) consistently throughout your exploration?
** Calculator/computer notation should not be used. **

33. Checklist
Have you used more than one form of mathematical representation? Are all graphs, tables and diagrams sufficiently described and labeled?
Are formulae, graphs, tables and diagrams in the main body of the text? No full-page graphs and no separate appendices.
Have you used technology to enhance your exploration?
Have you explained what you are doing at all times? Explanatory comments should be seen throughout your exploration?
Have you used mathematics that is commensurate with the Standard Level course (or beyond)?
Is the mathematics in your exploration correct?
Have you reflected on your finding at appropriate places in your exploration, particularly in your conclusion?
Have you considered limitations and extensions in your reflection?
Have you considered the assessment criteria when writing your exploration? Have you self assessed your exploration?

34. Checklist Is your exploration approximately 6 to 12 pages long?
Have you referenced your work in a bibliography?
Have you had someone else read your exploration to ensure that the communication is good? Does it have flow and coherence? Is it easily understandable? Does it read well?
Have you completed your self-assessment?
Have you submitted a first draft to your teacher and used the feedback to improve your report?

35. Authenticity
Plagiarism
This includes copying quotes, information and ideas, directly or paraphrased, from books and websites.
Collusion
This includes working closely with another student such that the work between the two students is similar.
Ensuring academic honesty
To prevent plagiarism, you need to cite your sources correctly and include any sources in your bibliography. If you have questions on how to properly cite your sources, seek advice from your teacher or from the school librarian.
To prevent collusion, you should discuss ideas with other students, but you should never giver another student your work, either in print or electronically.

36. Recommended Technology
Some examples of technology include:
any kind of calculators, the internet, data logging devices
word processing packages, spreadsheets, graphics packages
statistics packages or computer algebra packages.
Great software for working with graphs, diagrams, functions, spreadsheets, statistics, calculus and much, much more.

37. A modern, easy-to-learn, programming language that is great for writing simulations. There are loads of tutorials available: just google “python tuts”.
An online graph plotter with graphing capabilities similar to those of your graphical calculators.

38. A really powerful search engine
A really powerful search engine. (For example, type “find antiderivative of f(x) = 3x” into the search bar.)