Theories of psychology and mathematics education recommend two instructional approaches to develop students' mental representations of number: The "exact" approach focuses on the development of exact representations of organized dot patterns; the "approximate" approach focuses on the approximate representation of analogue magnitudes. This study…

Comparing common mathematical errors to correct examples may facilitate learning, even for students with limited prior domain knowledge. We examined whether studying incorrect and correct examples was more effective than studying two correct examples across prior knowledge levels. Fourth- and fifth-grade students (N = 74) learned about decimal…

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,…

This study examined the development of indirect addition as an alternative for solving multidigit subtractions, by means of two learning environments in traditionally schooled third-graders in Flanders (Belgium). Thirty-five third-graders, who did not demonstrate mastery of indirect addition, participated in an Explicit (n = 20) or Implicit (n =…

To examine the cross-lagged relationships between children's task motivation in mathematics and literacy, and their related performance, 139 children aged 5-6 years were examined twice during their kindergarten year. The results showed that only math-related task motivation and arithmetic performance showed cross-lagged relationship: the higher…

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…

This article reports results of a four-year longitudinal study that investigated the impact of specific and non-specific precursors on mathematical school achievement. Preschool quantity-number competencies (QNC) predicted mathematical achievement in primary school. Furthermore, basic arithmetic fact retrieval in Grade 1 had an impact on early…

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…

Research on dimensional comparison processes has shown that comparing one's own verbal achievements with poorer results in math leads to a higher self-concept of verbal ability. It has been argued that when observers make inferences about a student's academic self-concept, they do not usually have access to dimensional information. In the present…

This study investigated ability-related differences in strategy use and development in the domain of simple arithmetic, in terms of the model of strategic change, using the choice/no-choice method and the chronological-age/ability-level-match design. Twenty-six second-graders with strong mathematical abilities (MA), 25 second-graders with weak MA,…

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)