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TITLE: IMPROVING DEDUCTIVE REASONING SKILLS AUTHOR: Paul Allan, Palmer High School, Palmer, Alaska GRADE LEVEL/SUBJECT: 7-12, Math or Science (but may be extended) OVERVIEW: Throughout the year in all of my math and science classes I stress problem solving. Students develop a strategy list for problem solving by working with different types of problems. One unit that I have developed is based upon developing and enhancing deductive reasoning skills. I introduce deductive reasoning, through the use of Mind Bender puzzles, at the beginning of the year because it requires little traditional math knowledge and because it is the perfect situation to teach and practice cooperative grouping techniques. For most of the activities in this unit students are in heterogeneous groups of 4, usually selected by me. The unit is generally spread out over 2-3 weeks and student produced puzzles can be generated and used for extra credit throughout the year. PURPOSE: To enhance student problem solving strategies and increase student ability to solve deductive reasoning problems. To bring a sense of fun and accomplishment to math and science class problem solving. OBJECTIVES: Students will be able to: 1. Recognize problems that may be solved using deductive reasoning. 2. Develop aids to help them in solving deductive reasoning problems. 3. Successfully solve deductive reasoning types of problems. 4. Produce their own deductive reasoning puzzles for other students to solve. RESOURCES/MATERIALS: At the beginning of the unit I use materials from Mind Benders (Midwest Publications Co.) copied onto overheads and "help charts" copied on paper for each group. ACTIVITIES AND PROCEDURES: 1. Students are reminded of the deductive reasoning skills used by Sherlock Holmes to solve his mysteries. The teacher should read some exerts from Sherlock Holmes stories. 2. Students are divided into small groups and asked to solve a deductive reasoning type of puzzle. They are given no help as to how to solve the puzzle. After the groups have worked for a while, the class should be brought back together to discuss the strategies employed to solve the puzzle. 3. Once the better strategies have been determined, give the students another puzzle in their groups and allow them to work. 4. Over a time period of one or two weeks, give the students puzzles of varying degrees of difficulty. Allow them to use help charts (as provided in the Mind Benders materials) sometimes but have them develop the ability to produce their own charts to facilitate their problem solving.
TYING IT ALL TOGETHER: The real fun in this unit starts when the students produce their own puzzles. They have by now experienced 8 - 12 deductive reasoning puzzles and have seen how the charts can be used as an aid. Ask each student to produce a simple puzzle of his or her own making. The results are really remarkable. Some students start very simply, but then they discover that it is not too hard to make the puzzle special by adding things that are important to them. Have the students share their puzzles with other students, copying them on overheads for class work or onto paper for individual work. An example of a puzzle produce by a student that is autobiographical follows: (The student fits the characteristics of Frank, before he moved to Alaska.) Frank's Puzzle Don, Frank, Jenny, and Ken each come from one state, either Alaska, Maine, Montana, or Oklahoma. They each speak one primary language, either English, French, Russian, or Spanish. And they each have one of four pets, a chinchilla, a dog, a hamster, or a turtle. 1. Frank needed a language book to write to the Alaskan. 2. The kid from Oklahoma has a mammal for her pet. 3. The Alaskan found his pet outside his door in a snow bank. 4. The French speaking boy lives east of Oklahoma. 5. The Russian speaking boy wants to write to the kid from Montana, but he doesn't speak his language. 6. Don bought his pet in Peru. 7. Ken does not own a hamster. 8. The dog's owner wrote a letter in Russian to the kid in Oklahoma, but she couldn't understand it. 9. Don had to travel west to meet Jenny. 10. Frank is learning Spanish at school.
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