This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the…

Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

Purpose: Most educational assessments tend to be constructed in a close-ended format, which is easier to score consistently and more affordable. However, recent work has leveraged computation text methods from the information sciences to make open-ended measurement more effective and reliable for older students. This study asks whether such text…

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

The Common Core Standards require demonstration of conceptual knowledge of numbers, operations, and relations between mathematical concepts. Supplemental instruction should explicitly guide students with specific learning disabilities (SLD) in these skills. In this article, we illustrate implementation of the concrete-representational-abstract…

The majority of large-scale assessments develop various score scales that are either linear or nonlinear transformations of raw scores for better interpretations and uses of assessment results. The current formula for coefficient alpha (a; the commonly used reliability coefficient) only provides internal consistency reliability estimates of raw…

The teaching and learning in algebra has been much debated. Traditionally early algebra has relied heavily on arithmetic. Recently our focus has changed to teaching algebraic thinking with arithmetic thinking. This paper explores the models that assist young students generalise the patterns of arithmetic compensation. A teaching experiment was…