About time: Syntactically-guided reasoning with analog and digital clocks

ABSTRACT Around the globe, young students are expected to learn about time, yet how is it that they themselves make sense of this topic? From a sociocultural perspective, sense-making about time emerges in relation to properties of available tools and representations, such as analog clocks or digital notation. Such interactions with the symbols and structural properties of clocks are examples of syntactically-guided reasoning, a key domain of early algebra. In this paper, I focus on how students’ syntactically-guided reasoning emerged when reasoning about non-routine time problems with different clocks, whether or not such reasoning was consistent with accepted conventions of time measure. I present three case studies of typical Grade 2 students describing time on a particular clock (analog or digital) as they solved tasks related to time identification and elapsed time. I describe how symbolic properties of clocks enabled pathways of thinking about time-related ideas in relation to that particular clock. Implications for the treatment of time in elementary mathematics are discussed.