Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA PROBLEM SOLVING• Problems based on things close to the students' world can be interesting,although Johnson and Rising offer this opinion: "For most students it is notnecessary to take problems from their immediate environment. Often, studentsare less interested in grocery bills than in cannibals and missionaries, lessinterested in the volumes of oil tanks than in walks through K15nigsberg."[1972, p. 240]• Familiarity may improve the chances of success for some students. For example,Lyda and Church [1964] found that lower ability students in particular were moresuccessful on word problems dealing with situations they were familiar with.Help to overcome the block: general remarks. The major reason for givingattention to the problem-solving processes is that these may make us more selfsufficient.Students need to become more independent and more confident of theirability to do things for themselves. Other people won't always be around! Recentresearch has been investigating systematic instruction in problem-solving processes(e.g., Vos, 1973). Nelson's work [1975] indicated that teaching the use of diagramsimproves problem-solving performance (he also advocates presenting some problems indiagram form).Students with some background in problem-solving processes can beencouraged" to review their own use of the processes ("What approach have Itried?What haven't I tried?"). In any case, attention to processes may help to change theusual student's view that the only concern is The Answer.Middle schoolers may not be confident problem solvers.Having hints in mindis a good idea, although knowing when the students are claiming frustration for thesake of getting a hint and when they are genuinely stuck is a bit of an art;study with ninth graders [Akers, 1975] indicated that having answers accessibletended to increase the time students spent on problems (exercises?); thus, in situationswhere the answer does not reveal how the problems are solved, having answersavailable may lead to greater persistence on the part of the students.OneHaving smallgroups attack problems offers a chance for the students to learn others' approachesand may build up some degree of confidence.Groups usually are more successful onproblems, although there does not seem to be a great carry-over to later, individualwork. lHudgins, 1960] Blomstedt [1974] found that having middle schoolers agree onapproaches to word problems by consensus did seem to enhance their performance onword problems, perhaps because of the immediate feedback and reinforcement fromclassmates."Real" problems will not be solved quickly.for some middle schoolers to accept.time for attempted solutions.This is perhaps the hardest lessonBe sure to point this out, and allow plenty ofA phenomenon you may have noticed in your own problem29