The acquisition of addition facts was investigated in a practice study. Participants were 103 Grade 1 children who practiced simple addition problems with three different methods: (a) writing down the answer, (b) choosing between two alternative answers, and (c) filling in the second missing addend. On a test with simple addition problems,…

Transfer of strategies between problems sharing the same formal structure is facilitated by a semantic recoding that makes evident the structural similarities between the problems. Two experiments were carried out among 4th and 5th grade pupils, with an experimental group trained to compare strategies in order to reinterpret an arithmetic word…

Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with four types of illustrations with increasing…

Effects of guided (GI) and direct instruction (DI) in solving subtraction problems for mathematically low performers in regular schools were compared. In the GI condition, self-development of solution procedures was encouraged whereas in the DI condition one prescribed strategy was to be used. Forty children (M[subscript age] = 9.3 years) were…

This study investigated the role of different modes of representation, i.e., verbal description, decorative pictures, informational pictures and number line, in solving additive change problems. Data were collected from 1447 students in Grades 1, 2, and 3. Structural equations modelling affirmed the existence of four first-order…

This study focused on the extent to which the comparison of isomorphic problems might enrich subjects' representations and solving strategies. Results with 166 sixth graders solving isomorphic problems show that comprehension increased as problems were processed and that simultaneous presentation of all problems was more favorable than successive…

Traditional assessment methods are not always suitable for diagnosing learners' knowledge structures at different levels of their expertise. This paper describes an alternative schema-based rapid assessment technique and its application in the area of arithmetic word problem solving. The technique is based on an assessment of the extent to which…

Mental arithmetic strategies were studied with 91 Dutch third graders who computed by splitting off 10s and units in both numbers or counting by 10s up or down from the first unsplit number. Results reveal flexibility in changing between and within strategy use. Implications for instruction are discussed. (SLD)