**Embodied Design**

The phrase “embodied design” was first introduced into the Learning Sciences by Abrahamson. Embodied design is an approach to the construction of pedagogical materials and activities that enables learners to objectify their tacit knowledge in cultural forms relevant to disciplinary content (Abrahamson, ESM 2009). Later Abrahamson elaborated thus: “Embodied design is a pedagogical framework that seeks to promote grounded learning by creating situations in which students can be guided to negotiate tacit and cultural perspectives on phenomena under inquiry; tacit and cultural ways of perceiving and acting” (IDC 2013). [**read more**]

**Attentional Anchor**

An *attentional anchor *is a real or imagined object, area, or other aspect or behavior of the perceptual manifold that facilitates goal-oriented motor-action coordination. The attentional anchor may be discovered or suggested. As scholars of mathematics cognition and instruction, the construct of an attentional anchor is enabling us to apply the theory of ecological dynamics to research on embodied interaction in ways that reveal the emergence of concepts from actions. [**read more**]

**Apprehending Zone**

The *apprehending zone* is a model of student learning in social contexts. The AZ model informs implementation of constructivist philosophy in the form of objects, activities, and facilitation emphases. The AZ model foregrounds the complementarity of personal and interpersonal aspects of classroom learning processes. Abrahamson developed the AZ model as part of his dissertation project to investigate the evolution of proportional reasoning by monitoring a classroom's discourse as they discuss mathematical stories and diagrams. This work led to a conviction that implicit embodied forms of reasoning and learning are under-theorized in the mathematics-education literature. [**read more**]

**Embodied Spatial Articulation**

*Embodied spatial articulation* is an individual's design-facilitated negotiation between personal and cultural resources pertaining to the visuo–spatiality of mathematical situations and representations. The personal resources are proto-mathematical action-based images, and the cultural resources are the appropriate seeing-in-using of classroom spatial–numerical artifacts. Embodied spatial articulation, I conjecture, underpins human interacting with epistemic artifacts historically, developmentally, in the designer's workshop, and in classroom space–time. [**read more**]

**Learning Axes & Bridging Tools**

*Learning axes and bridging tools* (Abrahamson and Wilensky, 2007) is a pedagogical design framework grounded in the philosophy and theory of educational research. In applying this concept, we begin by conceptualizing a mathematical idea as a conceptual composite comprising: (a) naturaistic sensorimotor engagement; and (b) formal analysis. These two aspects subtend a *learning axis*, and the problem of learning the idea is considered the curricular *learning issue*. We then create a source situation to think about as well as a *bridging tool*, which is quasi-mathematical representation that both solicits inuitive responses and instantiates formal analysis for the same situation, thus inviting negotiation and reconciliation. [**read more**]

**Platonic (Adjusted) Sample Space**

Drawing a sample from a random generator could be imagined as randomly selecting an event from its sample space. So, flipping a fair coin could be construed as choosing one of the two items in the [Heads; Tails] space. [read more]

**Semiotic Leap**

The construct "semiotic leap" emerged during collaboraitve microgenetic analysis of empirical data gathered in the Seeing Chance project. The construct attempts to characterize an aspect of student insightful behavior during facilitated engagement with a mathematical activity, particulalrly an activity involving both a realistic problem situation and a formal model of that situation built as a means of establishing a solution. The leap captures the moment when the student comes to see the formal model as as signifying the inference from the situation. [**read more**]

**Stratified Learning Zone**

A *stratified learning zone* is an undesirable classroom dynamic that may emerge in the implementation of collaborative construction projects. In the SLZ, labor is divided and associated with individual students such that they become "type cast" into a particular task that may or may not foster the development of mathematical knowledge. [**read more**]