Abstract
The importance and complexity of young children's mathematical thinking and learning warrants high-quality, research-based resources that help teachers and caregivers understand and support children's development from birth through the primary grades. The authors discuss young children's potential to think mathematically, the criticality of early math, and the need for a learning trajectories approach to early math. Describing existing risks to young children's experience of high-quality math, the chapter offers solutions to these risks in systematic research and development of technology-based resources for early math using learning and teaching with learning trajectories ([LT]2, at LearningTrajectories.org) as an example. Further, the authors advocate for a lens of equity, inclusion, and accessibility in the development of these technologies. Finally, a vision is described for increasing access to high-quality math through adaptive technologies that use the learning trajectories of early math for in-person and online activities.
TopBackground: Young Children And Mathematics
With opportunities, young children can learn an informal knowledge of mathematics that is amazingly broad, complex, and sophisticated (e.g., Baroody et al., 2019; Clarke et al., 2006; Clements & Sarama, 2021; Fuson, 2004). For example, toddlers independently enjoy composing three-dimensional shapes (e.g. playing with boxes) or noticing differences in size (e.g. putting baby dolls with a larger mama doll). Preschoolers can learn to invent solutions to solve simple arithmetic problems (Sarama & Clements, 2009a). Also, almost all children engage in substantial amounts of pre-mathematical activity in their free play. They explore patterns, shapes, and spatial relations; compare magnitudes; and count objects. This is true regardless of the children’s income level or gender (Seo & Ginsburg, 2004). That is especially important, because all children have the capacity and motivation to incorporate math into such play and engage in mathematical thinking, but not all are given the opportunity to do so (Engel et al., 2016). Given that early math knowledge is a strong predictor of later achievement (Krajewski, 2005; National Mathematics Advisory Panel, 2008), such learning opportunity gaps are pernicious (Claessens et al., 2007; Horne, 2005; National Mathematics Advisory Panel, 2008).
Key Terms in this Chapter
Learning Trajectories: An approach to teaching and learning involving the integration of a learning goal, a developmental progression, and aligned instruction.
Accessibility: Applied to people with disabilities, accessibility allows people to participate with activities and content, including being able to perceive, understand, navigate, and interact with technology.
Access: Applied universally, access is an outcome in which race, ethnicity, language, gender, ability, socioeconomic status, or other personal characteristics do not limit the opportunity to resources such as learning resources.
Building Blocks: An evidence-based curriculum that utilized the learning trajectories approach.
Equity: The condition of fairness and justice based on everyone getting what they need, often contrasted with equality, a condition in which everyone gets the same thing regardless of need.
Developmental Progression: Paths of learning and ways of thinking through which children typically develop.
Curriculum Research Framework: A method for developing curriculum based on ten phases across categories of a priori foundations, a learning model, formative evaluation, and summative evaluation.
Inclusion: An outcome of intentional efforts to make participation inviting to diverse populations in which such populations feel welcome and comfortable.