Developing algebraic thinking is a key factor in learning mathematics. Despite its importance, many students still struggle with algebraic concepts. This research investigates students' achievements in algebraic thinking using Demetriou's test across 7th (approximately 12-13 years old), 8th (approximately 13-14 years old), and 9th (approximately…

A pretest-training-posttest design assessed whether training to improve spatial skills also improved mathematics performance in elementary-aged children. First grade students (mean age = 7 years, n = 134) and sixth grade students (mean age = 12 years, n = 124) completed training in 1 of 2 spatial skills--spatial visualization or form…

A pretest-training-posttest design assessed whether training to improve spatial skills also improved mathematics performance in elementary-aged children. First grade students (mean age = 7 years, n = 134) and sixth grade students (mean age = 12 years, n = 124) completed training in 1 of 2 spatial skills-spatial visualization or form…

For learning math, non-symbolic quantity skills, symbolic skills and the mapping between number symbols and non-symbolic quantities are all important precursors. Little is known, however, about the interrelated development of these skills. The current study focuses on numerical development by: (a) investigating the structure of non-symbolic,…

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…

In a recent study, Gevers and colleagues (2010, "Journal of Experimental Psychology: General," Vol. 139, pp. 180-190) showed that the SNARC (spatial numerical association of response codes) effect in adults results not only from spatial coding of magnitude (e.g., mental number line hypothesis) but also from verbal coding. Because children are…

Four experiments examined children's understanding of the inverse relationship between the number of parts into which a quantity is divided and the size of each part. Found that children tended to judge that bigger shares resulted from sharing with more recipients. Seven-year olds performed correctly on a simplified equal-sharing task. Five-year…

Examined role of spontaneous gesture in 2- to 4-year-olds' counting and assessment of counting accuracy. Found that correspondence of children's speech and gesture varied systematically across age. Children adhered to one-to-one correspondence principle in gesture prior to speech. Counting accuracy related to correspondence of speech and gesture,…

Elementary school children were tested individually on their learning of mathematics and on Piagetian tests of concrete operations. Younger children were found to be inferior to older children in their success on learning tasks. (ST)

Examined whether preschoolers could recognize numerical equivalence for comparisons involving sequentially presented sets. Found that children recognized numerical equivalence for static sets earlier than for sequential sets. Memory of the number of sequentially presented objects emerged earlier than memory for the number of sequential events.…

Examined whether 5- and 6-year-olds understand that addition and subtraction cancel each other and whether this understanding is based on identity or quantity of addend and subtrahend. Found that children used inversion principle. Six- to eight-year-olds also used inversion and decomposition to solve a + b - (B+1) problems. Concluded that…

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,…

Considers how students' mathematical thinking evolves as a result of their actions and everyday experiences and from increasing reliance on introduced mathematical principles and representations. Exemplifies how 8- to 10-year-olds' personal representations come to face with representations involving algebraic concepts. Explores implications for…

This study examined above-grade-level abstract reasoning abilities of 150 students (grades 2-6). Understanding of abstract concepts varied by age for only four of eight subscales or concepts: probability, proportion, momentum, and frames of reference. Performance varied widely within age level for the understanding of volume, correlation,…