When, how, and why students use conceptual knowledge during math problem solving is
not well understood. We propose that when solving routine problems, students are more …

We propose that integrated number sense, the ability to fluidly translate and compare
magnitudes within and across notations, is central to understanding of rational numbers …

Mounting evidence points to the predictive power of cross-notation rational number
understanding (eg, 2/5 vs. 0.25) relative to within-notation understanding (eg, 2/5 vs. 1/4) in …

The association between children's fraction relational reasoning and their algebraic thinking
has not been explored longitudinally. This study used incremental importance analysis and …

Decimal numbers are generally assumed to be a straightforward extension of the base-ten
system for whole numbers given their shared place value structure. However, in decimal …

The adoption of intelligent tutoring systems (ITSs) worldwide has led to a considerable
accumulation of process data as students interact with different learning topics within these …

Background Recent research showed that cross‐notation magnitude knowledge of fractions
and decimals was related to better performance in fraction arithmetic, but it remains unclear …

Understanding the magnitude of rational numbers is crucial for mathematical development.
However, children do not readily integrate the quantity of fractions and decimals and are …

Rational numbers are important for advanced math outcomes but pose challenges for many
children. Although a fair amount is known about how children understand fractions and …

Rational numbers pose a significant challenge in mathematics education. A recent
suggestion was to facilitate learning by designing a curriculum that introduces the different …