Off-task activity is ubiquitous in classrooms, yet little understood. Building on recent work that illustrates the utility of off-task activity to disrupt relations of power among students, this article explores the potential functions of off-task participation during collaborative mathematics problem-solving. We examined 56 instances of off-task…

Children in the elementary grades are expected to solve equations to demonstrate prealgebraic proficiency. Prealgebraic differences may emerge based equation type (i.e., standard vs. nonstandard), the operation shown or required for solution (i.e., addition or subtraction), and the position of the unknown. Prealgebraic differences may also be…

Arithmetic word-problem solving is an important component of elementary mathematics curricula that links school mathematics to real-life problem solving. The present 3-year longitudinal study examined children's arithmetic word-problem solving through understanding its 2 component processes: number-sentence construction and computation. Chinese…

Using a randomized placebo controlled design, we examined the direct and follow-up effects (at 6 and 12 months) of a mathematics tablet intervention. Math training focused primarily on basic arithmetic (addition and subtraction facts up to 12), and secondarily on number knowledge and word problems. We investigated the moderating effects of IQ and…

Research shows that multiple external representations can significantly enhance students' learning. Most of this research has focused on learning with text and 1 additional graphical representation. However, real instructional materials often employ multiple "graphical" representations (MGRs) in addition to text. An important open…

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

Individual differences in strategy use (choice and accuracy) were analyzed. A sample of 362 Grade 6 students solved complex division problems under 2 different conditions. In the choice condition students were allowed to use either a mental or a written strategy. In the subsequent no-choice condition, they were required to use a written strategy.…

The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains,…

The mathematical performance of 182 third and fourth graders in 8 different areas of mathematics was examined. The children belonged to 4 achievement groups: children with mathematic difficulties (MD only), children with both mathematic and reading difficulties (MD-RD), children with reading difficulties (RD only), and normally achieving children…

Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for the development of higher order mathematics skills, including solving word problems. Research indicates equal-sign instruction…

Whether hierarchical ordering among fraction identification problems reflects the replacement of simple rules by complex rules was investigated. Latent class techniques revealed that children applied rules that were adequate for simple problems but had to be replaced to solve more complex problems. (Author/GK)

Following trials in which children self-administered prizes, subjects in the stringent-demand group performed significantly better, during both the incentive and the extinction conditions, on time at task, number of correct problems, and number of problems attempted, than did subjects in lenient-demand and control groups. (Author/CP)

Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting third graders' development of mathematics problem solving. In the fall, 122 third-grade students were…

A test of whether metacognition is a separate factor from cognition was conducted by measuring the effects of metacognitive factors in problem solving, while attempting to hold relevant cognitive factors constant. Learning disabled subjects were less skilled in metacognition with respect to knowledge about cognition and regulation of cognition.…