PROBLEM SOLVING • NANA AMOA • FRAN GREENE • PRADEEP BHATTA • SAFIYE EDGUER TUESDAY, 5TH OCTOBER 1999
PRESENTATION CONTENT • INTRODUCE PROBLEM SOLVING METHODS • WORKSHOP • BREAK UP INTO GROUPS • DISCUSS THE THREE PRISONERS PROBLEM • FORMAL SOLUTION OF PROBLEM TO ILLUSTRATE PERTINENT PROBLEM SOLVING TECHNIQUES • DISCUSSION OF OPEN ENDED PROBLEMS • CONCLUSION
TEACHING WITH PROBLEM SOLVING METHODS • WHAT DO WE ACHIEVE WITH PROBLEM SOLVING EXERCISES ?
PROBLEM SOLVING IS A STUDENT CENTERED APPROACH !E STUDENTS APPLY AND USE ACQUIRED KNOWLEDGE ALLOWS STUDENT TO PARTICIPATE OBTAIN FEED BACK ON STUDENT COMPREHENSION LEVEL ALLOWS FOR STEPWISE LEARNING PROCESS
OPTIONS AVAILABLE TO INSTRUCTOR • PRESENT CLEARLY ILLUSTRATED SOLUTION WITH STUDENTS AS SPECTATORS • EXPLICIT GUIDELINES • IMPLICIT GUIDELINES • INTERACTIVE PROBLEM SOLVING • ALLOW STUDENTS TO PRESENT AND ACT AS AN INTELLIGENT SCRIBE.
PROBLEM STATEMENTThere are three men in a low security jail.Two of them can see and the third is blind.The warden of the prison having a slow day decides to allow them to play a gameHe decides that these are the conditions.He puts them in a room and behind them lines up 5 hats. He tells them that three of them are blue and the other two are white… They are not allowed to look behind them
At random he takes a hat and places it on their heads. They are not allowed to see the hats on their own heads They are allowed to see the hat on each others heads if they can indeed see. If anyone is able to guess correctly the hat on his head, he walks free. If on the other hand he guesses wrong, he is summarily executed. Deciding not to gamble means that the status quo remains. The first sighted man given the first go didn't know what hat he was wearing The second sighted man given the second go thought about it but was also at a loss The blind guy waiting last for his turn knew straight away what hat he had on and walked free Assuming that the prisoners are rational human beings and of reasonable intelligence What color hat did the blind guy have on and how did he know it !!!
Instructor’s preparation • Completely solve the problem beforehand. • Time management. • Prepare hand-outs. • Keep out of class resources ready.
Selecting the Problem • Base on prior knowledge of students. • Note common pitfalls. • Incorporate problems from real life. • Include problems that may introduce new concepts than ones covered in the lecture/recitation.
Solving the Problem: First steps • Clearly state the problem. • Mention real world relevance, if appropriate. • Allow enough time to read /comprehend /solve the problem. • Trigger the thinking process.
And…. • Explicitly list all data. • Diagrams & Illustrations. May be some photos from real life. • Break a big problem into parts.
Student interaction • Develop group work strategies, if appropriate. • Encourage question asking. • Act as a scribe. • Ask students to solve problems on the board.
Additional comments • Make students aware of multiple approaches, if they exist. • Review all steps. • Identify and discuss common pitfalls. • Design homework assignments appropriately.
OPEN ENDED PROBLEMS • Multiple solutions • More difficult problems which require longer duration of time • Requires a greater level of thinking • Requires teamwork • Examples: projects, case studies, research, etc.
PRESENTING OPEN ENDED PROBLEMS • Create teams • Present an overview and prerequisites • Be general • Allow students to brainstorm • Ensure complete accessibility to resources
AND • Require progress reports • Do not solve problem for the students • Require final report with all relevant materials
SUMMARY • Be prepared • Encourage Class Participation • Allow the students to comprehend the problem and the solution(s) • Choose problems that are relevant and challenging • Remember there is no wrong answer
LAST WORD Problem solving is a symbiotic relationship