Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA PROBLEM SOLVING• To help students to attack problems, we might •--emphasize and practice problem-solving processes,--provide encouragement, hints, peer support, and adequate time,--work on defeatist attitudes,--do what we can to guard against students' developing mind sets,--give attention to translations among mathematical and English sentences and pictorialand concrete representations,--use an approach which fosters the writing of mathematical sentences, and--nourish our students' abilities to process and present word statements of problems.1. Here is a method of combining drillwith problem solving. [Wirtz, 1975JThe object is to start at a ringednumber and find a path through allthe other numbers, ending at theother ringed number. The path mustgo through adjacent squares. Forexample, starting at 6 we can add5 (adjacent diagonal squares are allright) to get to the 11. Subtractionis also allowed.~ 7 47 If.•I~3 5 1110 2-®3 ~5- r=-U10 '2.®Continuing, we can get a completepath as to the right.Try these after the students have theidea; you do not have to indicate thestarting and stopping points. Eachnumber is to be used once and only once.a..2- .3 @b..2- .tt.8 1.0 .6c. Make up one of these by penciling inthe path first, putting in suitablenumbers and then erasing the path.Use whole numbers, fractions ordecimals..8 1 ./4..7 3 G).'2. .3 .3.9 .2- :7d. Modify the idea to use multiplicationand division.e. Modify the idea to allow any combinationof operations.35