The Math Studies Project for Internal Assessment

1. The Math Studies Project for Internal Assessment A good project should be able to be followed by a non-mathematician and be self explanatory all the way through.

2. 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.

3. Commitment • The project is a substantial piece of work (counts for 20% of the final IB grade) • The project should demonstrate a commitment of time and effort by the student

4. Choice of Topic • 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

5. Choice of Topic • Algebraic Modelling • Quadratic • Exponential • Trigonometric • Calculus • i. Optimization Problems • ii. Modelling

6. Choice of Topic • Number and algebra • i Sequences and series • ii Linear programming • Sets, Logic and Probability • i Venn diagrams • ii Probabilities • Financial Mathematics

7. Title page • The Project must have a clear title • Candidate’s name • Candidate’s number • Date • Subject • Teacher’s Name

8. Table of contents • Page numbering where each part of the project can be found

9. A: Introduction • Task: What is the aim of the project? • The task must focus on a distinct objective with a clear hypothesis or direction • The task must be clearly stated • Plan: What must be done to achieve this aim? • Include as much detail as is necessary to be clear • Include a description of method of data collection including any sampling techniques, this will be useful for validity • Include a description of the mathematical processes to be used and the reason for choosing these processes

10. B: Information / Measurement • The information/measurements collected may come from a survey, internet, calculation, etc • The information/measurements must be sufficient in quantity • When the information/measurements is to be split, as in the chi squared test, more than 50 pieces of data is necessary to avoid small expected values, rendering the test invalid. • The information/measurements must be relevant • The information/measurements must be organised • The information/measurements should be reorganised each time, to suit calculations being done eg. Male, female categories • If a questionnaire is used then include this in the project • A questionnaire should be designed to collect multidimensional mathematical data • Raw data must be included to determine the accuracy of calculations

11. C: Mathematical Processes • Always include some relevantsimple math processes • What is the mathematical process used? Explanation of mathematical technique • Why is this particular procedure useful? Relevance/validity of mathematical technique • Always state formulae used and do one calculation by hand. The GDC can be used to perform further similar calculations • Always check the accuracy of your results • Interpret results/draw conclusions from the results of the calculations • (Standard deviation is often calculated but not used or commented on.)

12. C: Mathematical Processes • 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 • There is no point in finding the correlation coefficient or regression line if the scatter graph shows that there is no correlation

13. D: Interpretation of results • Always give a thorough and detailed analysis and discussion of results

14. E: Validity • Validity of mathematical processes used • Validity of results obtained from these processes

15. F: Structure and Communication • The project should include the discussion in the body of the work • Appropriate mathematical language should always be used • The project should be presented correctly and in a systematic manner. • All sources should be acknowledged • Include website addresses in bibliography • Include raw data in body of document or in appendix

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

17. Bibliography • State websites • Footnotes as necessary • Other sources of information

18. Appendices • Raw data collected can be placed here