Geometry is one of the basic areas of school mathematics education, and it is important for elementary students. However, students with mathematics learning disabilities (MLD) struggle with geometry learning. Research has demonstrated that concrete-representational-abstract (CRA) teaching is an effective practice for students with learning…

Semiotics is simply defined as the sign-using to represent a mathematical concept in a problem-solving. Semiotic reasoning of constructing concept is a process of drawing a conclusion based on object, representamen (sign), and interpretant. This paper aims to describe the phases of semiotic reasoning of elementary students in constructing the…

The purpose of the study was to determine whether individual differences in at-risk 4th graders' language comprehension, nonverbal reasoning, concept formation, working memory, and use of decimal labels (i.e., place value, point, incorrect place value, incorrect fraction, or whole number) are related to their decimal magnitude understanding.…

This paper describes an emerging approach to the design of task sequences to promote reflective abstraction. The approach aims at promoting particular mathematical understandings. Central to this approach is the identification of available student activities from which students can abstract the intended ideas. The approach differs from a…

Spatial discontinuity between causes and effects is a feature of many scientific concepts, particularly those in the environmental and ecological sciences. Causes can be spatially separated from their effects by great distances. Action at a distance, the idea that causes and effects can be separated in physical space, is a well-studied concept in…

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…