Given that both children and adults struggle with fractions in mathematics education, we investigated the processing of nonsymbolic fractions in a continuous form of part-of-the-whole. Continuous features of nonsymbolic numbers (e.g., the size of dots in an array) were found to influence numerosity judgment, but it should be noted that the…

Humans perceptually extract quantity information from our environments, be it from simple stimuli in isolation, or from relational magnitudes formed by taking ratios of pairs of simple stimuli. Some have proposed that these two types of magnitude are processed by a common system, whereas others have proposed separate systems. To test these…

Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…

The relations among various spatial and mathematics skills were assessed in a cross-sectional study of 854 children from kindergarten, third, and sixth grades (i.e., 5 to 13 years of age). Children completed a battery of spatial mathematics tests and their scores were submitted to exploratory factor analyses both within and across domains. In the…

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

This study examined how four domain-specific skills (arithmetic procedural skills, number fact retrieval, place value concept, and number sense) and two domain-general processing skills (working memory and processing speed) may account for Chinese children's mathematics learning difficulties. Children with mathematics difficulties (MD) of two age…

This appendix provides the details that underlie the analyses reported in the evaluation brief, "After Two Years, Three Elementary Math Curricula Outperform a Fourth." The details are organized in six sections: Study Curricula and Design (Section A), Data Collection (Section B), Construction of the Analysis File (Section C), Curriculum…

Three experiments were conducted to examine children's use of multiplying and proportionality rules in judgments of area. In the first two experiments, 7- through 8-year-olds were asked to judge the area of rectangles. In the third, 8- through 11-year-olds were tested on ratio of a rectangle compared to a horizontal line. Results indicated…

Three levels of mathematical concepts and three theoretically corresponding levels of cognitive development were posited. Children's test results were consistent with predictions for each age group, leading to the conclusion that, for concept attainment at each level, a minimum information-processing capacity is a necessary, but not sufficient,…

Children from grades 2, 3, 4, 6, and 8 made speeded, bimanual parity (odd/even) judgments of numerals. Response times indicated that from fourth grade on, parity information was retrieved directly from memory. By grade 3, children represented magnitude information as a left-to-right number line which was accessed obligatorily and, by grades 6 and…

Explored relations between measuring procedures and reasoning about amount on the part of 36 children of 3-8 years in 2 studies. Transformation on a relevant measurement procedure predicted difficulty of transformation for a domain. (RJC)

Building on previous research on the tendency in students of diverse ages to overrely on proportionality in different domains of mathematics (e.g., geometry, probability), this study shows that--when confronted with missing-value word problems--Flemish primary school pupils strongly tend to apply proportional solution strategies, also in cases…

In this article, data from a study of the mental computation competence of students in grades 3 to 10 are presented. Students responded to mental computation items, presented orally, that included operations applied to fractions, decimals and percents. The data were analysed using Rasch modelling techniques, and a six-level hierarchy of part-whole…

The estimation processes used by fifth through eighth grade students as they responded to computational estimation test items were examined. Interview-based process descriptions were cross-validated using large group test data from an open-ended test and a multiple choice test. Five question formats were used to test different estimation…

This study investigated whether young, poor, inner-city children are deficient in the mathematical skills and concepts necessary for later success in school arithmetic. Children of pre-kindergarten and kindergarten age, black or white, and lower class or middle class, were given a wide variety of mathematical tasks, including Piagetian measures,…