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Problem Solving: From General to Specific

Learn how to solve problems by moving from a general perspective to a specific one. Develop problem-solving skills and apply them in various situations. Inductive and deductive reasoning.

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Problem Solving: From General to Specific

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  1. What We Will Learn: – Problem Solving Perspective – General  Specific – Problem Solving Sample General  Specific

  2. People, in the real world, pay you money to solve problems. The better your problems solving skills, the more demand for your services and the more money they will pay you. General  Specific

  3. Problem solving is a learned skill. Some individuals will be better at it than others, but it is still a LEARNED skill. Like any other learned skill, you have to work at it to get good at. Someone has to expose you to the tools of problem solving and then YOU have to apply those tools ON PURPOSE to learn how to solve problems. The problems could be it social, mechanical, biological, structural, mathematical, etc. General  Specific

  4. In your classes, you will be exposed to HOW your teachers solve problems. Their way is not the only way, but their way is a good place for you to start LEARNING HOW SOLVE PROBLEMS. After awhile, you will develop your own methods of solving problems that will be composed of how your teachers solve problems tempered with your own unique way of looking at the world. General  Specific

  5. GeneralSpecific The double arrow is a logic term that means a bijection (movement in both directions). It means the general implies the specific and the specific implies the general. GENERAL SPECIFICandSPECIFIC  GENERAL Deductive Reasoning Inductive Reasoning In this course, you determine when, where, and how much of each is used in the solution of a problem. Many problems will require you to use both. General  Specific

  6. A generalrelationship example is the area of a circle is equal to pi times the radius squared. A specific relationship would be a circular irrigation plot that has a radius of 150 feet. A =  r2 A =  1502 General  Specific

  7. The following problem is an example of solving a problem from a general statement of what you want to solve. After the solution, you want to see if the solution has a pattern you can discover that may apply to other similar problems. General  Specific

  8. You are to ride one of the new three wheeled motorcycles (two wheels in front) to a town one-hundred miles away. The motorcycle has two spare tires. The problem posed to you is that by the time you get to the town, all five motorcycle tires have to have the same mileage. You can stop as many times as you need to change out the tires. General  Specific

  9. If this is the first time you have worked a problem like the one just stated, your first thought is probably, “How in the world do I even start?” A lot of times it is more important to get started than it is to actually start at the exact right place, take the prescribed steps to solve the problem, and arrive at a point where the problem is “Solved.” Real life doesn’t happen that way. General  Specific

  10. Sometimes we make false starts, we go down promising paths that turn out to be wrong, we make false assumptions, we see things that are not true, we don’t collect the right data, we misunderstand the problem, and the list goes on. Someone dinged Thomas Edison after his 1000th attempt to make a light bulb, and told Edison that he failed and still did not know how to make a light bulb. He said, “No! I know a 1000 ways how NOT to make a light bulb.” He learned from his mistakes, did not repeat his mistakes, and he did not stop. He kept his eye on the prize. General  Specific

  11. Now, how are you going to solve the stated problem? You are to ride one of the new three wheeled motorcycles (two wheels in front) to a town one-hundred miles away. The motorcycle has two spare tires. The problem posed to you is that by the time you get to the town, all five motorcycle tires have to have the same mileage. You can stop as many times as you need to change out the tires. General  Specific

  12. AFTER THE PROBLEM IS SOLVED What general rule (we are trying to use induction) can you determine from this problem that would apply to a car with four wheels and a spare tire and ALL tires must have the same mileage when you get to the town? General  Specific

  13. What about a car with four wheels and you have three spare tires? Can this rule be used in any other situation other than situations similar to the preceding situations? General  Specific

  14. You are the manager of the laptop computers in your organization. You are tasked to ensure the batteries of each laptop are used equally (this is so they will all reach their projected useful lifespan at the same time for tax purposes). You have fifteen computers and you have determined that no more than ten are used on any given day. The computers run four hours each day and must be charged afterwards. General  Specific

  15. You need to develop a scheme that will keep the usage of the computers fairly consistent so that the computer reach their projected lifespan together. What do you do? General  Specific

  16. What do we know? 15 computers total. 10 used each day for four hours each (one recharge cycle). There are 5 workdays a week. I want some schedule that will repeat, after an undetermined amount of time, so that it will be easy for me to schedule and manage the laptop computer usage. You have to start somewhere, soooo… “Do I want to cycle the computers every day?” General  Specific

  17. Assume I want to swap out the computers every day. Since I have to loan out 10 everyday, what kind of schedule would I have? M T W T F 1-10 6-15 11-5 1-10 6-15 But this does not use all computers equally. Now what? What if we extent it one more week? General  Specific

  18. M T W T F 1-10 6-15 11-5 1-10 6-15 11-5 1-10 6-15 11-5 1-10 6-15 11-5 1-10 6-15 11-5 Still not equal usage Therefore, if you swap out five computers everyday, you can be assured that the computers will be used equally over a three week period. How many hours is each computer used each three week period? What if you tried this and decided that you did not want to swap out the computers every day. Could you do it on a two day cycle? General  Specific

  19. MT WT FM TW TF 1-10 6-15 11-5 1-10 6-15 11-5 1-10 6-15 11-5 1-10 6-15 11-5 1-10 6-15 11-5 The previous example swapped out the laptops everyday and took three weeks to complete a cycle. How many weeks does it take to complete this cycle? How many hours is each laptop used during this time period? Can you see a pattern here? General  Specific

  20. What We Have Learned – Problem Solving Perspective – General  Specific –Problem Solving Sample General  Specific

  21. End of Line General  Specific

  22. General  Specific

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