Effects of Differential Arithmetic Practice on Children's Solutions of Mathematical Word Problems

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Word problems are difficult. Although children eventually master computational skills, problem solving skills remain poor through adulthood. Two different types of manipulations were attempted to affect rates of successful word problem solution. First we made changes to the word problems themselves to make them more comprehensible for students, and therefore easier to solve. Second, students were given one of two types of arithmetic practice and were compared with a third group of students who received no additional practice to determine whether such practice could assist students with solving arithmetic word problems. First- and second-grade students were tested on three different types of single-step arithmetic word problems: a set of Compare problems, a set of six typically worded Change problems and a set of six Change problems whose wording was clarified with simple temporal, semantic and referential clarifications. These changes were intended to make the action in the problem easier to follow so students could model the problems more successfully. The percentage of students answering correctly on different problems was compared. Students were then randomly assigned to one of two different arithmetic worksheet conditions or to a third no practice condition. Worksheets consisted of either standard arithmetic practice or computational practice requiring students to solve for something other than the result. After completing all of the worksheets, students were tested on a set of word problems arithmetically identical to those presented five months earlier. Results of clarification were mixed. Students had somewhat more difficulty with solve-for-result problems which are traditionally the type of word problems at which students perform best. Students were more successful at solving clarified solve-for-start-set problems. There was also a curious trend for students to be more successful at subtraction problems than addition problems of the same type. This was more pronounced with clarified problems. Second-grade students showed no effect of worksheet condition. First-grade students who were assigned to the non-canonical worksheet condition demonstrated a marked improvement on typically worded change problems. Reasons why the arithmetic practice did not also have an effect on clarified problems need to be explored further.

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Michael J. Spivey, Chair; James Cutting; Robert Johnston; Marianella Casasola

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mathematics; word problems; problem solving; arithmetic practice


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Government Document




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dissertation or thesis

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