PART 1: Critical Thinking: 1. What is argument?; 2. Recognising arguments; 3. Responding to arguments; 4. Analysing arguments; 5. More complex arguments; 6. Claims; 7. Conclusions; 8. Drawing conclusions; inference; 9. Assumptions; 10. Sound or unsound?; 11. Finding Flaws; 12. Challenging an argument; 13. Lending support; 14. Explanation; 15. Looking at evidence; 16. More evidence; 17. Case study; Who's telling the truth; 18. Case study: Collision course; 19. Introducing longer arguments; 20. Applying analysis skills; 21. Critical evaluation; 22. Further argument; 23. The appliance of science; 24. Conditions; 25. Principles; 26. An argument under the microscope; 27. Synthesis; 28. Critical marking; PART 2: Problem Solving: 1. What do we mean by a 'problem'?; 2. How do we solve problems?; 3. Selecting and using information; 4. Processing data; 5. Finding methods of solution; 6. Solving problems by searching; 7. Spatial reasoning; 8. Recognising patterns; 9. Making choices and decisions; 10. Using models; 11. Combining skills - using imagination; 12. Using other mathematical methods; 13. Use of more complex diagrams; 14. Modelling and investigating; 15. Analysis: hypotheses, reasons and inference; 16. Have you solved it?; Solutions to problems; Glossary; Index.