This paper investigates the interplay of words and expressions with students' efforts to indicate times on a clock. We consider how elementary students interpret precise times (e.g., 2:30, 4:30) as compared to relative times (e.g., half past 11) as they describe this intangible quantity using a clock. Interviews with students in grades 2 and 4 (n…

In this article, the authors first present the Hands Together! task. The mathematics in this problem concerns the relationship of hour and minute durations as reflected in the oft-overlooked proportional movements of the two hands of an analog clock. The authors go on to discuss the importance of problem solving in general. They then consider…

This article reports on elementary students' understanding of time in the context of common classroom manipulatives and notational systems. Students in Grades 2 (n = 72) and 4 (n = 72) participated in problem-solving interviews involving different clocks. Quantitative results revealed that students' performances were significantly different as a…

Time is an area of measurement that is difficult for children. This interview study addresses the question: What are children's solution approaches to position the hands of an analog clock? To explore this, we investigated problem solving when using a clock manipulative with mechanically linked hands. We compare overall success rates among…

This paper presents assessment study results addressing the question: Do students treat elapsed time problems differently if phrased as "half an hour" versus "thirty minutes"? A paper-and-pencil assessment was given to second (n = 292) and fourth (n = 205) grade students in six New England elementary schools. I compare…

Algebra instruction has traditionally been postponed until adolescence because of historical reasons (algebra emerged relatively recently), assumptions about psychological development ("developmental constraints" and "developmental readiness"), and data documenting the difficulties that adolescents have with algebra. Here we…