Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA PROBLEM SOLVINGSUMMARY (Even when we distinguish between exercises and problems, problem solving couldserve as the heart of teaching.Problems can pump life intodrill, serve as a vehicle for introducing new ideas and typesof problems, give a basis for transfer, motivate at least somestudents, and above all, put the teaching of problem solving processes into its propersetting--the solving of problems.ODDS AND ENDS ABOUT PROBLEM SOLVINGThis subsection contains a varietyof suggestions and research findingsoriented to the two aspects of a problem:(a) the student must want asolution, but (b)the student must overcomesome block to the solution.The student wants a solution.Let'sacknowledge that many students work problemsonly because that is what is expectedin mathematics classes.Perhaps someof the following will create an interestin the problems themselves.PROBLE."" :STUDEt-lT WAt-lTS SOLUTIOtJBUT OOES t-lOT RE:ALIZE HOWTO REACH IT.Ol-l,OH'IVE GOT APROBLEM.DESIREDSOLU,IOIU• We might poll the class to see what their interests are ("Give 5 things youlike to do," "What are your favorite pastimes--foods, hobbies, TV shows, singinggroups, possessions?") and then try to build problem situations on theseinterests. Listen to the students' topics of conversation in the hallways orbefore class.• Ask each student to submit one mathematics "problem" each week, based on inclasstopics or out-of-school events, and use some of these.• Some teachers find that having the students guess an answer leads to greaterinterest since they then have made a definite "conunitment."• On occasion, a problem can be dramatized by class members (e. g., two "interviewers"questioning a factory owner about pollution control, or two coachestrying to choose the "best" team from given statistics).• Using students' names in problems usually gains some interest if not over-done.Basing problems on things unique to each student (e.g., MuscleFatigue in MATHEMATICS AND BIOLOGY) also "personalizes" the topic.• Problems taken from foreign textbooks or old U.S.to any, may provoke interest.textbooks, if youhave accesc28