Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA PROBLEM SOLVING8. The size or type of the numbers in some story problems sometimes seems to overwhelmstudents' thinRing. Accordingly, some teachers' suggest that the studentssubstitute small whole ilUmbers (or "easy" fractions or decimals), see how tosolve this new problem; and then'proceedin the same way with the original problem.Try this technique on some Word problems from your textbook to seeho~youlike it.9. Where can the following contribute to problem'-centered instruction?a. questioning (See the Questioning section in the resource Geometry andVisualization. )b. discovery lessons (See the section Goals through Discovery Lessons in theresource Geometty and Visualization.)c. laboratory lessons (See the section Teaching Via Lab Approaches in theresource Mathematics, in Science and Society. 210. Suppose you have only containers (unmarked) with the capacities given in each rowand you want the quantities' given in the last column. How would you get thosequantities?H~eW=ta. 29 unit, 3 unitb. 21 unit. 127 unit, 3 unitc. 14. 163, 25d. 18, 43. 10e. 9, 42, 6f. 20. 59, 4g. 23, 49, 3h. 15, 39, 31. 28, 76, 3j. 18, 48, 4k. 14, 36, 8t. 5, 25, 10m. 3, 65, 2920 units, 100 units9952131201825226o3These items were used by Luchins and Luchins [1950J in their work on mental set.It would not be unusual if you used an unnecessarily complicated procedure onparts g, h, j and k. And even college students approachedt and m in a remarkably"set" way. You may wish to give your students a-i. say. from the list (thestereotyped procedure does not work on i). Tell the students not to erase anyof their work.11. How do you teach students to write an equation for the usual word problem?12. Under the tell-the-action approach. it is not the order of appearance of the datain the word presentation but the action and its order in the actual problem settingthat are to be reflected in the equation. For the problem. "Joe got $3.75for his birthday. Then he had $5.25. How much money did he have before his birthday?"one would write n + 3.75 = 5.25 to parallel the actual situation exactly.Write the equations which best parallel these word problems.a. Kay had $6 when she went shopping. When she got home she had $4.15. Howmuch did she spend?b. Dick spent $2.25 at the camporee. He had $1.45 when he got back. How muchmoney did he take to the camporee?37