Prior research suggests that human children lack an aptitude for tool innovation. However, children's tool making must be explored across a broader range of tasks and across diverse cultural contexts before we can conclude that they are genuinely poor tool innovators. To this end, we investigated children's ability to independently construct 3 new…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining…

Students with cerebral palsy (CP) without severe intellectual impairments often experience difficulties in mathematics performance. Given the high prevalence of learning difficulties in students with CP, few studies have examined interventions to improve the math competency of these students (Jenks et al., 2009). A single-subject reversal design…

Third, fifth, and seventh graders selected the best strategy (rounding up or rounding down) for estimating answers to two-digit addition problems. Executive function measures were collected for each individual. Data showed that (a) children's skill at both strategy selection and execution improved with age and (b) increased efficiency in executive…

Examined the relationship between 6- to 8-year olds' conceptual understanding of additive composition, commutativity, and associativity principles and addition problem-solving procedures. Results revealed that conceptual understanding was related to using order-indifferent, decomposition, and retrieval strategies and speed and accuracy in solving…

Used Wynn's (1992) procedure in 3 experiments to test 5-month-olds' looking-time reactions to correct and incorrect results of simple addition and subtraction transformations. Found non-systematic evidence of either imprecise or precise adding and subtracting in young infants. Results suggest that infants' reactions to displays of adding and…

Asserts that findings on whether young infants look longer at incorrect addition and subtraction have been inconsistent or negative. Hypothesizes that imprecise ordinal calculating with very small numbers of objects develops in late infancy and that precise calculating develops in early childhood. (Author/KB)

This paper proposes a semantic analysis in which meanings of word problems are structures that include class and order relations, and suggests a hypothesis of developmental levels that can account for children's performance of these problems at various ages. The different kinds of problems vary in the complexity of semantic structures and the…

Reports on two studies that use new tasks to compare English children's use of strategies that reverse the order of addends in solving addition problems. Shows that knowledge of commutativity among young children is widespread, but does not establish a direct link between this knowledge and children's choice of addition strategies. (DSK)

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…

The article reviews the development of mathematics error analysis as a means of diagnosing students' cognitive reasoning. Errors specific to addition, subtraction, multiplication, and division are described, and suggestions for remediation are provided. (CL)

The procedures used by first- and second-grade children in solving addition problems are investigated. The subjects were 56 pupils from a parochial school in Ithaca, New York. The data indicate that first graders add by counting, while second graders use both counting and noncounting methods. (MP)

The effects of problem size on judgments of commutativity by 51 moderately and mildly retarded students were investigated. Results indicated that many retarded students who are given computational practice recognize the general principle that addend order does not affect the sum. (Author/DB)

Discussed are the results of the second National Assessment of Educational Progress (NAEP) mathematics assessment concerning children's ability to solve verbal problems. The data indicate that the commonly held view that children cannot solve word problems may be an oversimplification. (Author/TG) Aspect of National Assessment (NAEP) dealt with in…

Examined effects of problem size in mental addition among elementary children in China (n=104) and Missouri (n=105) and among undergraduates in China (n=26) and Missouri (n=35). For all Missouri subjects and Chinese through first grade, larger-valued numbers took longer and induced more errors. (Author/NBI)