1. The Math Studies Project for Internal Assessment   Personal research   Relate to student’s own interest   Use mathematical tools from the syllabus   No restriction on the area of interest : sport, art, finance…

2. A good project should be able to be followed by a non-mathematician and be self explanatory all the way through. BE CLEVER ! BE CLEAR ! Your teacher will be here to help at any time

3. Organisation (1) 1 st stage : discussion in class/ Examine others projects/think about a topic   choose a subject before September 30 2 nd stage : organize the data collection/ make appointments/ Collect the data IT IS A TIME CONSUMING STAGE 3 rd Stage : analyse the data : be critic !

4. Organisation (2) 4 th Stage : perform the math analysis 5 th Stage : first conclusions and first “boucle de rétroaction”  DO YOU NEED MORE DATA ??? DO YOU NEED OTHERS MATH PROCESSES ? 6 th Stage : final draft

5. Organisation (3) Recommendation : At each stage : write a draft that will help you : To precise your own ideas To explain the way you think to your teacher To write the final draft Try to write it as close as possible to the final draft

6. Requirement (1) Length The project does not have a word limit. It is the quality of the mathematics and the processes used and described that is important, rather than the number of words written. However : to have an idea, a 10 to 15 pages project (including appendices) is an average.

7. Requirement (2) Commitment : The project is a substantial piece of work (20 hours class time plus several more hours outside the class) The project should demonstrate a commitment of time and effort by the student

8. Choice of Topic (1) The choice of topic must give students sufficient scope to demonstrate their mathematical ability. Statistical Chi-Squared test for Independence Correlation/Linear regression Student ‘t’ test Spearman’s rank order correlation

9. Choice of Topic (2) Algebraic Modelling Quadratic Exponential Trigonometric Calculus i. Optimization Problems ii. Modelling

10. Choice of Topic (3) Number and algebra i Sequences and series ii Linear programming Sets, Logic and Probability i Venn diagrams ii Probabilities Financial Mathematics

11. Examples of previous projects Do people choose a free newspaper at random or is there a relationship with their age and gender ? how does music change the mathematical ability of students ? What influence does doing nothing and listening to music have on perception of time ? The perceived value of a coin or a bill depends on its familiarity Statistical relationship and correlation between subject appreciation and political opinion Do student rank in the family/Number of siblings affect the IB grade ?

12. Assessement 7 Criteria A : Introduction (3) B: Information/Measurement (3) C: Mathematical processes (5) D : Interpretation of results (3) E : Validity (1) F : Structure and communication (3) G : Notation and Terminology (2)

13. Preliminary The Project must have a clear title Other information   Candidate’s name   Candidate’s number   Date   Subject   Teacher’s Name + Table of contents

14. A: Introduction Title Task:What is the aim of the project?   distinct objective +clear hypothesis or direction   must be clearly stated Plan:How to achieve this aim?   Data : describe data collection /sampling techniques   Math process : describe which process and the reason for choosing these processes

15. B: Information / Measurement The information/measurements collected :   may come from a survey, internet, calculation, etc   must be sufficient in quantity (especially if used in tests –Chi2- 50 pieces of data will be necessary)   must be relevant   must be organised (table, sorting, chart …)   Should be given in appendix (questionnaire if any + raw data + processed data : table, diagram …)

16. C: Mathematical Processes (1) Start with simple and relevant processes (diagram, mean…)   Explain the mathematical technique   why it is useful for your project : relevance/validity   For each formula, always do one calculation “by hand” then use the GDC or EXCEL for further calculations.   Always check the accuracy of your results   Interpret results/draw conclusions from the results of the calculations Ex : A simple process can help recognize “incorrect” data or a problem in your survey. Or can prove that you need more data.

17. C: Mathematical Processes (2) Apply relevant sophisticated processes as thoroughly as for simple process. Interpret results/draw conclusions from the results of the calculations Comment on validity of results Check the accuracy of the results For Chi-squared tests to be valid: Frequencies must be used, not raw data or percentages No more than 20% of the expected cells should have a number less than 5 No expected cells should have a number less than 1 For Linear correlation : do not calculate R if the scatter graph shows no correlation !

18. D: Interpretation of results Always give a thorough and detailed analysis and discussion of results : Show how smart you are !

19. E: Validity Examinators know you cannot produce a complete job : be aware of the limits of your project : Limit in your data collection Validity of mathematical processes used Validity of results obtained from these processes

20. F: Structure and Communication The project should :   include the discussion in the body of the work   always uses appropriate mathematical language   be presented correctly and in a systematic manner : paragaph   acknowledged all sources   include website addresses in bibliography   include raw data in appendix (preferably) and processed data in the body.

21. Special recommendation : Conclusion Did the data and calculations support your task? Discuss limitations in its applicability within the project. Scope for improvement /extension of the project

22. G: Notation and Terminology Means that the student :   Uses correct terminology   Uses mathematical notation   Explicitly defines variables

23. Bibliography State websites State websites Footnotes as necessary Footnotes as necessary Other sources of information Other sources of information

24. Appendices  Raw data collected can be placed here