Published on November 19, 2007
Analytical Thinking &Problem Solving: Analytical Thinking & Problem Solving The University of Tennessee Student Academic Support Services Overview: Overview Creative Problem Solving Critical Thinking- Attitude Models and methods on problem solving Challenges and exercises on problem solving Introduction: Introduction Intelligence = Good Thinking Skills “Thinking is the operating skill with which intelligence acts upon experience for a purpose.” Operating skill + intelligence + experience PMI : PMI P plus or good points M minus or bad points I interesting points Two or three minutes to deliberately think through a problem or situation. Creative Problem Solving: Creative Problem Solving Recognize the problem Define the problem Gather ideas or data Rank ideas Test the ideas Draw conclusions Evaluate conclusions Attitudes Plus Action Equals Success: Attitudes Plus Action Equals Success The Attitudes Greet problems as challenges and not as threats Tolerate uncertainty Engage in self-evaluation and criticism Engage in divergent thinking Persevere Systematically and deliberately approach task Are Flexable Attitudes Plus Action Equals Success: Attitudes Plus Action Equals Success The Actions Brainstorm and search all possibilities Attend to details Set plans of action Question continuously Check for accuracy Break problems into pars Avoid Guessing DeBono’s Characterization of a Good Thinker: DeBono’s Characterization of a Good Thinker Confident in his/her thinking Not that he/she is right or even that he/she can find the answer but that he/she can turn on his/her thinking at will and deliberately focus it in any direction he/she wants. In control of his/her thinking Does not drift from idea to idea or emotion to emotion Has a clear idea of what he/she wants to do Defines the thinking task and then sets out to carry it out DeBono’s Characterization of a Good Thinker: DeBono’s Characterization of a Good Thinker Has a clear focus and a broad view of the situation Values wisdom over cleverness Likes thinking even when it isn’t particularly successful Confident and decisive but humble DeBono’s Characterization of a Good Thinker: DeBono’s Characterization of a Good Thinker Robust in thought but practical were this is demanded Doesn’t wallow in over-intellectualization, nit-picking or a dither of indecision Able to discern his/her progress after thinking Practices and observes thinking Levels of Thinking: Levels of Thinking Knowledge: recalling information; repeating information with no changes (ex: recalling dates; memorizing definitions for a history exam) Comprehension: Understanding ideas; using rules and following directions (ex: explaining a mathematical law; knowing how the human ear functions; explaining a definition in psychology) Application: Applying knowledge to a new situation (ex: using knowledge to solve a new physics problem) Levels of Thinking: Levels of Thinking Analysis: Seeing relationships; breaking information into parts; analyzing how things work (ex: comparing two poems by the same author) Synthesis: Putting ideas and information together in a unique way; creating something new (ex: designing a new computer program) Evaluation: Making judgments; assessing value or worth of information (ex: evaluating the effectiveness of an argument opposing the death penalty) Selecting a problem solving method: Selecting a problem solving method 1. You should apply already-learned concepts to fill in the gaps from information provided in the passage. Only use principles, definitions, equations, theories, and laws to integrated within the passage. 2. You should apply the newly-learned concepts from the passage as and when appropriate after a thorough understanding. 3. When working with mathematics problems watch for consistency in units and conventions, and always start from the given data. 4. Use only relevent facts. Selecting a problem solving method: Selecting a problem solving method 5. Use proportional reasoning as and when required to compare various options. 6. Evaluate designs, methods, phenomena, and their effects in a logical and systematic way. Do not get persuaded by the writer’s arguments if you discover technical flaws or problems. These problems may not require any mathematical operations to solve, only analytical/logical reasoning will suffice. 7. You should also use integrated reasoning in looking at pieces of evidence, parts of instruments, steps in procedures and various actions in phenomena. You should evaluate and interpret particular perspectives including technical views and opinions of scientists. Selecting a problem solving method: Selecting a problem solving method 8. Always try to get the answer in the form presented, especially in data analysis problems. Organize and interpret your data so it is directly linked to the format of the answers presented. 9. You should learn how to test the responses against your answer and make sure to follow basic logic. 10. Pick up various strategies and approaches to solve the problem in any order as long as they are well connected and sequential in solving the problem. Problem Solving Model: Problem Solving Model Use your own experience or similar situation to help you mentally see the given information. Actually create a tough sketch of the information. Mark inner problem cues which link new information with known concepts. Actually create a rough sketch of the information. Try to condense the information in the question as much as possible. What is the question? Isolate and examine the limitations and assumptions in the question stem. Select the best problem solving method for the question. Examine whether or not your answer makes sense. Problem Solving Methods: Problem Solving Methods Make a Diagram Cathy knows French and German. Sandra knows Swedish and Russian. Cindy knows Spanish and French. Paula knows German and Swedish. If French is easier than German, Russian harder than Swedish, German easier than Swedish, and Spanish is easier than French, which girl knows the most difficult language? Problem Solving Methods: Problem Solving Methods Make a Chart Paula, Joanne, and Mary own a total of 16 dogs, among which are 3 poodles, twice as many cocker spaniels, and the remainder German Shepherds and collies. Joanne despises poodles and collies, but owns 4 cocker spaniels and 2 German Shepherds, giving a her a total of 6 dogs. Paula owns 1 poodle and only 2 other dogs, both German Shepherds. Mary owns 3 collies and several other dogs. What other dogs and how many of each does Mary own? Problem Solving Methods: Problem Solving Methods Go Through the Actions You are facing east, you make an about-face, and then you turn left. Which direction is now on your left? Draw a Picture Belvedere Street is parallel to St. Anthony Street. Davidson is perpendicular to River Street. River Street is parallel to St. Anthony Street. Is Davidson Street parallel or perpendicular to Belvedere? Problem Solving Methods: Problem Solving Methods Write It Out On a certain day, I ate lunch at Tommy’s, took out two books from the library (The Sea Wolf and Martin Eden, both by Jack London), visited the museum and had a cavity filled. Tommy’s is closed on Wednesday, the library is closed on weekends, the museum is only open Monday, Wednesday, and Friday, and my dentist has office hours Tuesday, Friday, and Saturday. On which day of the week did I do all these things? Problem Solving Methods: Problem Solving Methods Use a Venn Diagram The government wants to contact all druggists, all gun store owners, and all parents in a town. How many people must be contacted, using these statistics? Druggists 10 Gun Store owners 5 Parents 3000 Druggists who own gun stores 0 Druggists who are parents 7 Gun store owners who are parents 3 Checklist For Problem Solving: Checklist For Problem Solving Inaccuracy in Reading: Inaccuracy in Reading Reading material without concentrating strongly on the meaning. Didn’t constantly ask, “Do I understand that completely?” Reading material too rapidly; at the expense of comprehension. Misreading one or more words; not careful enough. Missing one or more facts or ideas; not careful enough. Not spending enough time rereading a difficult section to clarify it meaning. Inaccuracy in Thinking: Inaccuracy in Thinking Not placing a constant high premium on accuracy. Performing operations with out sufficient care or observation. Interpreting words or performing operations inconsistently. Not checking the correctness of an answer or conclusion. Not checking the appropriateness of a formula or procedure before utilizing it. Working too rapidly. Visualizing a description or relationship inaccurately. Drawing a conclusion from the middle of a problem rather than reading it through and giving it sufficient thought. Weakness in Problem Analysis: Inactiveness: Weakness in Problem Analysis: Inactiveness 1. Not breaking a complex problem into parts. 2. Not drawing upon prior knowledge and experience in trying to make sense of ideas which were unclear. 3. Skipping unfamiliar words or phrases, rather than trying to gain good understanding through context. 4. Not translating an unclear word or phrase into one’s own words. Weakness in Problem Analysis: Inactiveness (cont’d): Weakness in Problem Analysis: Inactiveness (cont’d) 5. Not using a dictionary when necessary. 6. Not actively constructing (mentally or on paper) a representation of ideas described in the text. 7. Not evaluating a solution or interpretation in terms of its reasonableness. Lack of Perseverance : Lack of Perseverance 1. Making little attempt to solve the problem through reasoning because of lack of confidence in one’s ability to deal with this type of problem. 2. Choosing to answer based on only a superficial consideration of the problem. 3. Solving the problem in a mechanical manner, without much thought. 4. Reasoning the problem part way through, then giving up and jumping to a conclusion. Failure to Think Aloud: Failure to Think Aloud 1. Not vocalizing one’s thinking in sufficient detail while working the problem. Question: Question You have only an 8-liter jug and a 3-liter jug. Both containers are unmarked. You need exactly 4 liters of water. How can you get it, if a water faucet is handy? Question: Question Three handsome geniuses all wanted to marry the beautiful heiress. The wealthy father told them, “I have three red hats and two white hats. I will blindfold all of you then choose three of the five hats to put on your heads. After the hats are on your heads, I will take off your blindfolds. The first man to tell me the color of his own hat without looking at it will marry the heiress.” The father did as he had said. The man said he couldn’t tell the color of his hat. The second man said he couldn’t tell, either. But the third man, who was blind, correctly told the color of his hat. What color was it, and how did he know?