In this paper we present a novel adaptation of a tri-phase assessment tool, originally devised to investigate students' linear equations-related strategy flexibility, to evaluate Danish grade-six students' multidigit arithmetic-related strategy adaptivity and flexibility. Participants, 731 students, median age 12 years and drawn from 20…

In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn from twenty demographically different schools. Drawing on a tri-phase assessment tool, each student completed…

Drawing bar diagrams has been shown to improve performance on mathematical word problems wherein the relational keyword is consistent with the required arithmetic operation. This study extends this by testing the effectiveness of bar diagram drawing for word problems with an inconsistent keyword-arithmetic operation mapping. Seventy-five fifth…

The statistical properties of data are not present in any individual value, but rather, emerge only by perceiving the set as a whole. Summarizing the statistical properties of sets (e.g., creating ensembles) is ubiquitous in cognition, yet one unanswered question is how this process changes over development. The properties of number sets (e.g.,…

For students to advance beyond arithmetic, they must learn how to attend to the structure of math notation. This process can be challenging due to students' left-to-right computing tendencies. Brackets are used in mathematics to indicate precedence but can also be used as superfluous cues and perceptual grouping mechanisms in instructional…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

Prior work exploring preschool-aged children's reasoning with repeating patterns has shown that patterning ability is an important predictor of math achievement; however, there is limited research exploring older children's growing pattern task performance. The current study tested whether presentation format impacts performance on growing pattern…

We examined the contribution of a major predictor of basic literacy ability--phoneme awareness--to individual differences in two arithmetic computation tasks: a speeded task consisting of simple computation problems (arithmetic fluency) and an untimed, more complex computation task involving multi-digit operands (numerical operations). The…

The research examined the calculation methods used by pupils in Grades 3-6 when they were presented with problems that could be worked out efficiently and flexibly by applying number sense. The study was conducted with a convenience sample of 179 pupils between the ages 7 years and 10 months to 12 years and 10 months. in mainstream education in…

Instruction geared toward priming the underlying problem structures was suggested as an evidence-based practice for students with a learning disability. Schema-based instruction is one intervention aligned with this principle. We extended prior work by: (1) using a teacher as the implementer; (2) providing teacher flexibility in intervention…

Mathematics instruction -- and interventions to support mathematics teaching -- for students with intellectual disability is important yet underexamined. This study explored a graduated instructional sequence referred to as the virtual-representational (VR) as a mathematical intervention. Researchers taught four students with disabilities what…

5th graders (n=527) were randomly assigned to self-explain worked examples (WE) or solve problems during a yearlong study. WE students learned more algebra skills when given algebra worked examples on an end-of-year transfer measure. Comparing attempts, conceptual, and mechanical correctness by condition, results demonstrated that the condition…

Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal…

Research has suggested that different strategies used when solving fraction problems are highly correlated with students' problem-solving accuracy. This study (a) utilized latent profile modeling to classify students into three different strategic developmental levels in solving fraction comparison problems and (b) accordingly provided…

This study aimed to examine the relations among property strategies, working memory, and multiplication tasks with 101 Chinese fourth-grade students. Two multiplication property strategies (associative and distributive) were compared with no strategy and demonstrated differentiated effects on students' accuracy and reaction time. Associative…