Testing a Theoretical Assumption of a Learning-Trajectories Approach in Teaching Length Measurement to Kindergartners

Abstract

We tested a specific theoretical assumption of a learning trajectories (LTs) approach to curriculum and teaching in the domain of early length measurement. Participating kindergartners (n = 189) were assigned to one of three conditions: LT, reverse-order (REV), or business-as-usual (BAU). LT and REV students received one-on-one instruction using the same activities from a length LT, while the REV condition reversed the LT order. At posttest, LT and REV children exhibited significantly greater learning relative to BAU peers. But importantly, LT children outperformed their REV peers. We conclude that instruction following LTs (i.e., providing instruction just beyond a child’s present level of thinking, progressing through the levels in order as the child advances) may promote more learning than an equivalent amount of instruction using the same activities but that are not theoretically sequenced.

Promoting understanding of measurement and statistical investigation among second-grade students with mathematics difficulties.

“…Supporting students’ mathematical competence in early measurement concepts and skills, for example, provides them a foundation for grasping how measurement tools function, understanding the attribute being measured, and making comparisons of the measured attribute relative to a particular unit (Goldenburg & Clements, 2014). Strong problem-solving skills around foundational concepts of measurement can also help lay the foundation for working with more advanced mathematics (Clements et al, 2018; Doabler, Clarke, Kosty, et al, 2019; Frye et al, 2013; Parmar et al, 2011; Sarama et al, 2021; Vasilyeva et al, 2020). For example, understanding that length is continuous and can always be partitioned into smaller lengths is key background knowledge for fractions (Beckmann, 2008).…”

Quantification in Empirical Activity

“…We take a broad view of quantification (or mathematization), 2 drawing from Jin et al's (2019) learning progression, descriptions of scientists' activity (Chang, 2004;Gooding, 1990;Kline, 1980), and classroom-based research on the intertwined development of attributes, measures, and understandings (Lehrer & Schauble, 2015;Sarama et al, 2021). Further, we conceptualize scientific work as a modeling enterprise, one that involves constructing and revising systems of models (e.g., equations, conceptual models of entities and relations, simulations, statistical models, and empirical models such as experiments) (Giere 1990;Nersessian, 2012;Rouse, 2015).…”

“…Young children are intuitively sensitive to quantity and comparison, but do not recognize specific attributes, conceptualizing them generally, such as "small" and "big." They can be supported to discriminate and name attributes through comparing and aligning objects along a particular dimension (Sarama et al, 2021). They can be further supported to understand units of measure, iteration, and ways of developing informative comparisons (Cobb et al, 2001;Sarama et al, 2021).…”

“…They can be supported to discriminate and name attributes through comparing and aligning objects along a particular dimension (Sarama et al, 2021). They can be further supported to understand units of measure, iteration, and ways of developing informative comparisons (Cobb et al, 2001;Sarama et al, 2021). Early introduction of standard tools and procedures (e.g., rulers) without the development of conceptual understandings of attributes and measures can lead to rote use.…”

Teacher Beliefs and Perspectives of Practice: Impacts of Online Professional Learning

“…It is recommended that mathematics instruction should be incorporated into early childhood classrooms to support young children's mathematical development [6], and research has shown that this focus can improve young children's opportunity gaps [7,8]. Furthermore, research supports that time spent engaging children in specific mathematics activities based upon developmental progressions bolsters their understanding [8][9][10]. A critical step in improving learning is ensuring that teachers are afforded tools and strategies to engage young children with rich, developmentally appropriate mathematics experiences everyday [9].…”