Learning curves are an important tool in cognitive diagnostics modeling to help assess how well students acquire new skills, and to refine and improve knowledge component models. Learning curves are typically obtained from a model estimated on real data obtained from a finite, and usually limited, sample of students. As a consequence, there is…

A correlation coefficient taking positive values is introduced. It is more easily understood than other correlation measures especially in social science contexts. Estimation issues are addressed. A data application is given.

While much research has focused on understanding the process by which young children learn to count, little work has explored the effects of direct instruction on this process. In the current study, we explored the impacts of training children in an explicit counting procedure on two distinct cardinality tasks. Two- to 5-year-old children first…

In basic regression discontinuity (RD) designs, causal inference is limited to the local area near a single cutoff. To strengthen the generality of the RD treatment estimate, a design with multiple cutoffs along the assignment variable continuum can be applied. The availability of multiple cutoffs allows estimation of a pooled average treatment…

In basic regression discontinuity (RD) designs, causal inference is limited to the local area near a single cutoff. To strengthen the generality of the RD treatment estimate, a design with multiple cutoffs along the assignment variable continuum can be applied. The availability of multiple cutoffs allows estimation of a pooled average treatment…

Two experiments examined whether concrete models support place value learning. In Experiment 1 (N = 149), 7-year-olds were trained with either a) symbols alone or b) symbols and base-10 blocks. Children in both groups showed significant growth overall, but there were specific effects favoring one training type over another. Symbols-only training…

Research Findings: In this research we explore the relationship between young children's number knowledge and their measurement of length. First, we examined 4- to 5-year-olds' (kindergartners') understanding of and preference for using standard or nonstandard units to measure length. Second, we investigated whether the following tasks were…

Children who struggle in mathematics have a limited understanding of the foundational processes of mathematics. A lack of conceptual understanding causes students to fall behind as they progress through the core curriculum. Children at high risk for developing mathematics disabilities fail to gain numeracy knowledge. The purpose of this case study…

Russian higher education institutions' tradition of teaching large-enrolled classes is impairing student striving for individual prominence, one-upmanship, and hopes for originality. Intending to converting these drawbacks into benefits, a Project-Centred Education Model (PCEM) has been introduced to deliver Computational Mathematics and…

The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing…

Math skills are critical for children's future success in school, as school-entry math knowledge is the strongest predictor of later academic achievement. Although there is a recent increase of literature on math with young children, there is a scarcity of research related to young children with disabilities. This quasi-experimental study with 50…

Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…

Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

The current study employed a randomized controlled trial to evaluate the use of peer tutoring and fluency-based instruction to increase mathematics fluency with addition and subtraction computation skills. Forty-one elementary school students between the ages of eight and 12 years participated in the 8-week study using cross-age peer tutoring, Say…

Purpose: The purpose of this descriptive study is to investigate why some elementary children have difficulties mastering addition and subtraction calculation tasks. Design/methodology/approach: The researchers have examined error types in addition and subtraction calculation made by 697 Portuguese students in elementary grades. Each student…