A rising epistemological paradigm in the cognitive sciences – embodied cognition – has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experiences of enacting or witnessing particular movement forms, even before these movements are explicitly signified as illustrating target content. Putting these theories to practice, new types of learning environments are being explored that utilize interactive technologies to initially foster student enactment of conceptually oriented movement forms and only then formalize these gestures and actions in disciplinary formats and language. In turn, new research instruments, such as multimodal learning analytics, now enable researchers to aggregate, integrate, model, and represent students’ physical movements, eye-gaze paths, and verbal–gestural utterance so as to track and evaluate emerging conceptual capacity. We – a cohort of cognitive scientists and design-based researchers of embodied mathematics – survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning as dialogic multimodal activity, and we synthetize a set of principles for educational practice.

Excerpt: Inthis chapter, we review research on how perceptual and interactive features of manipulatives afford actions and on how those actions connect to target concepts. We acknowledge there are many other factors that may influence the effectiveness of manipulatives, including features of the instruction (e.g., Carbonneau & Marley 2015), children’s prior experience with the manipulatives (e.g., Mayer, 2003), and the ways in which the manipulatives are introduced (Donovan & Alibali, 2021). In this chapter, we focus on characteristics of the manipulatives themselves, specifically the perceptual and interactive features of manipulatives and the affordances, or possibilities for action, they offer. We argue that considering manipulatives in terms of affordances can provide new insights into the varying effectiveness of manipulatives in different contexts. We close by discussing implications for the design of lessons that use manipulatives for math instruction. For the purpose of this chapter, the term “manipulatives” refers to physical objects that can be touched and moved with the hands during problem solving and learning. Some example manipulatives include blocks, chips, Dienes blocks, Geotiles, balance scales, paper clips, popsicle sticks, and beanbags. A growing body of work focuses on computer-based, virtual manipulatives (Moyer-Packenham & Westenskow, 2013; Stull et al., 2013; Suh & Moyer, 2007), which hold promise because technology offers unique affordances for action. However, in this chapter, we focus on manipulatives as objects that can be physically manipulated with the hands. Manipulatives vary along many dimensions, and some of these variations have implications for how learners perceive and interact with the manipulatives. In the following sections, we consider the perceptual and interactive features of manipulatives in turn.

Spontaneous gestures that accompany speech are related to both verbal and spatial processes. We argue that gestures emerge from perceptual and motor simulations that underlie embodied language and mental imagery. We first review current thinking about embodied cognition, embodied language, and embodied mental imagery. We then provide evidence that gestures stem from spatial representations and mental images. We then propose the gestures-as-simulated-action framework to explain how gestures might arise from an embodied cognitive system. Finally, we compare this framework with other current models of gesture production, and we briefly outline predictions that derive from the framework.

This opening chapter provides an introduction to the book. It also introduces a theme that integrates many of the contributions from the remaining chapters: we adopt Kant’s perspective for merging rationalist and empiricist philosophies on the construction of knowledge. In particular, we focus attention on ways that biologically based abilities and experience in the world (coordinations of sensorimotor activity) each contribute to the construction of number. Additional themes arise within the content chapters and the commentaries on them.

Key words: embodied cognition, epistemology, numerical development, radical constructivism, sensorimotor activity.