Making Time: Words, Narratives, and Clocks in Elementary Mathematics

Abstract

This article investigates the interplay of time words with how children position hands on an analog clock. Using a mathematics discourse framework (Sfard, 2008), we analyzed how students interpreted precise (e.g., 2:30) and relative (e.g., half past 11) times, finding that particular words are dynamically interwoven with activity. Interviews with students in Grades 2 and 4 revealed that different prompts led to different narrative descriptions about time on the clock, with precise times leading to whole-number descriptions and relative times to part-whole descriptions consistent with fractions. Subsequent analysis of assessment performance for students across Grades 2–5 corroborated that specific time prompts led to particular clock interpretations. Implications for theory and the K–12 treatment of time measure are discussed.

Cronbach’s alpha in mathematics education research: Its appropriateness, overuse, and alternatives in estimating scale reliability

“…Using coefficient alpha in this way should ordinarily be tolerable except that some mathematics education researchers misrepresent the meaning of internal consistency. On the one hand, there are some researchers (e.g., Kop et al, 2020;Earnest and Chandler, 2021) that equate internal consistency with scale reliability. The case of these researchers is like the indiscriminate use of coefficient alpha 10.3389/fpsyg.2022.1074430 as an estimate of scale reliability that was treated in the last section.…”

“…The most common misuse of coefficient alpha in mathematics education research is using statistics to gauge scale reliability without paying attention to conditions under which the coefficient is trustworthy. For instance, all the articles published in the Journal for Research in Mathematics Education (JRME) between 2021 and April 2022 that reported coefficient alpha as a measure of reliability did so without any information on crucial assumptions of essential tau-equivalence and uncorrelated errors of the scale items ( Battey et al, 2021 ; Earnest and Chandler, 2021 ; Lubienski et al, 2021 ; Santana et al, 2021 ). This indiscriminate use of coefficient to gauge scale reliability is not limited to published papers in JRME but widespread in papers published by other top mathematics education journals (e.g., Dowker et al, 2019 ; Regier and Savic, 2020 ; Saadati et al, 2021 ; Wang et al, 2022 ).…”