Sentence reading time of multiplicative word problem text : influence of problem structure, mathematical operation, and number type

Abstract

Two experiments were conducted to test the influence of different types of mathematical word problem texts on reading performance and mathematical operation choice. Data from 48 college students in Experiment 1, and those from 35 college students in Experiment 2 were analyzed using a 2 x 2 x 2 within-subjects design. The independent variables were problem structure (mapping rule vs. multiplicative compare), mathematical operation (multiplication vs. division), and number type (integer vs. decimal fraction less than 1). The three independent variables were varied orthogonally, and eight problem categories were defined. The dependent variables were reading time to each sentence in the problem text and the correctness of subject’s mathematical operation choice. The materials were 40 multiplicative problems, 5 from each of the eight problem categories. For the mathematical operation choice task, four alternatives (i.e., addition, subtraction, multiplication, and division) were provided for each problem in a multiple-choice format. The subjects were tested individually in front of a computer screen. In Experiment 1, each sentence in a problem text was presented one at a time, with a new sentence replacing the previous one. In Experiment 2, the previously presented sentence!s) remained on the screen and a new sentence was added one at a time. Following reading of the problem text, the subject was asked to choose the appropriate mathematical operation among the four alternatives. The results showed that problem sentences were read faster in mapping rule problems than in multiplicative compare problems, faster in multiplication than in division, and faster with an integer than with a decimal fraction. A predicted Problem Structure x Mathematical Operation interaction was not found. Mathematical operation choice accuracy was greater for multiplication than for division, and with an integer than with a decimal fraction. Accuracy was greater for multiplicative compare than mapping rule for multiplication, but the order reversed for division. Integer vs. decimal fraction difference was greater for division than for multiplication. In general, longer reading times corresponded to lower accuracy of operation choice, suggesting that more difficult problem information was being processed.