This paper highlights the pedagogical importance of gaps in mathematical proofs to foster students' learning of proofs. We use the notion of 'gap-filling' (Perry & Sternberg, 1986) from literary theory to analyze a task based on a Proof Without Words, which epitomizes the notion of gaps. We demonstrate how students fill in gaps in this…

The introduction conveys some data on learning in India and on designing Geography textbooks in this country. The present paper is reliant on four Geography textbooks, ranging from the 9th to the 12th grade. As regards each textbook, the study considers their learning units, then analyses their structure, the unitary way of designing them, the…

Context-aware ubiquitous learning has been recognized as being a promising approach that enables students to interact with real-world learning targets with supports from the digital world. Several researchers have indicated the importance of providing learning guidance or hints to individual students during the context-aware ubiquitous learning…

According to a 2010 report by ACT, "Only 31 percent of students are performing at a college-and-career reading level with respect to successfully understanding complex text" (p. 5). This statistic demonstrates what educators know: Middle and high school students face numerous challenges in reading, understanding, connecting to, and…