Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA PROBLEM SOLVING13. What sort of "action" is involved in a percent problem? Look through a textbook (.for other topics for which the "action" is somewhat abstract.14. Mr. Denson:You:"I've tried assignments with more thanthem. The kids just couldn't do them.with only one type."one type of word problem inSo now I use assignments15. Teacher: "Whether you call problem solving the star of the curriculum or theheart of teaching, fancy (and mixed) metaphors don't make problemsolving any easier. I've found that my students can't do word problemsat all, so I just skip them. The kids can learn how to do wordproblems in high school."You:16. Talton [1973] suggests stressing these reading skills to improve performance onword problems: selecting main ideas, making inferences, constructing sequences,following directions for simple and complex choices, and reading maps and graphs.Plan how you might stress some of those skills. (See also Reading in Mathematiasin the resource Ratio, Proportion and Scaling, Mathematics Resource Project.)17. Schwieger [1974] has listed eight components which he believes to be basic insolving mathematics problems. Examine some problems to see whether his componentswould yield a solution. Here is his list:a. CIassify: to recognize pertinent characteristics and attributes of mathematicalproblems or expressions and to specify the class or classes to whichthey belong.b. Deduce: to relate a set of statements so that acceptance of the statementsand their interrelationships dictates a particular conclusion.c. Estimate: to use available mathematical information to make a judgement ofm;a~ent or of a result of calculation.d. Generate Pattern: to put known or available mathematical data into a systematicarrangement.e. Hypothesize: to recognize or to generate conditional relationships betweenmathematical statements.f. Translate: to substitute for one mathematical form, an equivalent representation.g. Trial and Error: to apply knowledge to a mathematical problem in an unorganized'manner.h. Verify: to apply data to a hypothesis in testing its validity.. Ipp. 38-5'9J(References and Further ReadingsAkers, Betty. "The relationship of given answers to persistence and achievement whenattempting solutions to mathematical problems." (Memphis State University,1975), Dissertation Abstracts International, Vol. 36A (November, 1975), p. 2688.38Ammon, Richard. "An analysis of oral and written responses in developing mathematicalproblems through pictorial and written stimuli." (The Pennsylvania State ( ..University, 1972), Dissertation Abstracts International, Vol. 34A (September,1973), pp. 1056-1057.