Douglas W. Van Dine

TL;DR: For example, this article evaluated and refined a previously developed learning trajectory in early length measurement, focusing on the developmental progressions that provide cognitive accounts of the development of children's strategic and conceptual knowledge of measure.

TL;DR: The findings confirm and extend earlier results that seeing a complete record of the structure of the 2D array—in the form of a drawing of organized rows and columns—supported children’s spatial structuring and performance.

TL;DR: In this article, the effects of three interventions designed to support Grades 2-5 children's growth in measuring rectangular regions in different ways were examined, and it was found that creating a complete record of the structure of the 2D array, by drawing organized rows and columns of equal-sized unit squares, best supported children in conceptualizing how units were built, organized, and coordinated, leading to improved performance.

TL;DR: It was found students could follow and rehearse a rationale for the validity of the circle area formula with substantive opportunities for movement and figural operations with units, or with decompositions from unit images that coordinated circle and rectangle images.