# Enhancing Learning and Thinking

By Robert F. Mulcahy; Robert H. Short et al. | Go to book overview

Script Implicit
 1 At first the wolf caught 41 chickens. The wolf caught 69 more chickens. The fox picked 38 ducks altogether (SIR). The wolf sighted 83 more chickens (SR). How many birds did the animal catch? 2 Tom had 78 cats. Tom had 47 dogs. Tom helped 32 seals. Tom desired 47 rabbits. How many pets did Tom have? 3 The man rented 12 houses. The woman rented 78 houses. The bank sold 86 houses. The worker fixed 63 houses. How many houses did the people rent? 4 Mrs. Green caught 35 sharks. Mrs. Brown caught 65 trout. Mrs. Smith saw 87 frogs. Mrs. Watson cooked 55 salmon. How many fish did the women catch?

MATHEMATICAL OPERATION AND COMPUTATION LEVEL

Two types of problems have been used to define the number and type of operation contained in the problems: direct and indirect. The operations in the direct problems are either addition or multiplication, or both addition and multiplication. A direct question is found when only definite quantifiers are used in the word problems. On the other hand, indirect questions have indefinite quantifiers incorporated into one of the preliminary statements. This change results in a shift in the required operation to either subtraction or division, or both subtraction and division.

Three variations in computational level are found: single digit, double digit, and single/double digit combinations. For the single digit problems, the digit 1 was omitted since it is logically impossible to have the result of one, given the plural nature of the required answers (e.g., one horses is illogical). All digits were used in the other computational levels. The difference between the last two cases was that regrouping was required at least once during the calculation of the final answer in the second case and was never necessary in the first instance.

REFERENCES

Anderson C. W. ( 1987). "Strategic teaching in science". In B. F. Jones, A. S. Palincsar, D. S. Ogle, & E. G. Carr (eds.), Strategic teaching and learning: Cognitive instruction in the content areas. Elmhurst, Ill.: North Central Regional Educational Laboratory.

Bachor D. G. ( 1979). "Using work samples as diagnostic information". Learning Disabilities Quarterly, 2, 45-52.

-----. ( 1985). "Questions for and by the learning disabled student". In J. F. Cawley (ed.), Cognitive strategies and mathematics for the learning disabled. Rockville, Md.: Aspen.

-----. ( 1987). "Towards a taxonomy of word problems". In J. Bergeron, N. Herscovics, & C. Kieran (eds.), Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education. Vol. 2. Montreal: PME.

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