Bringing forth mathematical concepts: signifying sensorimotor enactment in fields of promoted action

Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the methodological utility of design-research as an approach to such theory development. Building on constructs from ecological psychology, cultural anthropology, studies of motor-skill acquisition, and somatic awareness practices, we develop the notion of an “instrumented field of promoted action”. Children operating in this field first develop environmentally coupled motor-action coordinations. Next, we introduce into the field new artifacts. The children adopt the artifacts as frames of action and reference, yet in so doing they shift into disciplinary semiotic systems. We exemplify our thesis with two selected excerpts from our videography of Grade 4–6 volunteers participating in task-based clinical interviews centered on the Mathematical Imagery Trainer for Proportion. In particular, we present and analyze cases of either smooth or abrupt transformation in learners’ operatory schemes. We situate our design framework vis-à-vis seminal contributions to mathematics education research

Contours of Inclusion: Inclusive Arts Teaching and Learning

The purpose of this publication is to share models and case examples of the process of inclusive arts curriculum design and evaluation. The first section explains the conceptual and curriculum frameworks that were used in the analysis and generation of the featured case studies (i.e. Understanding by Design, Differentiated Instruction, and Universal Design for Learning). Data for the cases studies was collected from three urban sites (i.e. Los Angeles, San Francisco, and Boston) and included participant observations, student and teacher interviews, curriculum documentation, digital documentation of student learning, and transcripts from discussion forum and teleconference discussions from a professional learning community.The initial case studies by Glass and Barnum use the curricular frameworks to analyze and understand what inclusive practices look like in two case studies of arts-in-education programs that included students with disabilities. The second set of precedent case studies by Kronenberg and Blair, and Jenkins and Agois Hurel uses the frameworks to explain their process of including students by providing flexible arts learning options to support student learning of content standards. Both sets of case studies illuminate curricular design decisions and instructional strategies that supported the active engagement and learning of students with disabilities in educational settings shared with their peers. The second set of cases also illustrate the reflective process of using frameworks like Universal Design for Learning (UDL) to guide curricular design, responsive instructional differentiation, and the use of the arts as a rich, meaningful, and engaging option to support learning. Appended are curriculum design and evaluation tools. (Individual chapters contain references.

Messing up research: A dialogical account of gender, reflexivity, and governance in auto-ethnography

This paper aims to contribute to a growing critical and reflexive awareness of the implications of gendered assumptions about ontology, epistemology, and ethics in academic research governance and practice. It provides a retrospective account of the authors' shared experiences of an autoethnographic study of lap dancing clubs, focusing on critical or “sticky moments” encountered, and considering the implications of these for research more widely. It does so by highlighting the gendered power relations shaping academic research, showing how Judith Butler's critique of the heterosexual matrix can be applied to a critical, reflexive understanding of the impact of binary, hierarchical gender power relations. The analysis provides insight into some of the ways in which autoethnographic research on sexualized work may become messy, dirty, and sticky in ways that accentuate power inequalities but also open up moments of opportunity for gender binaries and hierarchies to be revealed, challenged, and resisted. Using a Butlerian lens to reflect on our experiences, we contribute to understanding how heteronormative assumptions shape perceptions of what makes “good,” “clean,” and ethically (formally) approved research that conforms to the governmental norms of the heterosexual matrix and, by implication, those contaminating forms of research that disrupt or resist its disciplinary effects. As ethnographic research is often messy by its very nature, and particularly so when situated within sex/sexualized work, we aim to show how gendered assumptions can inhibit reflexivity in academic knowledge production, resulting in research processes that are (paradoxically) unethical. In response, we suggest three ways in which gender reflexive research might be pursued, by: (i) identifying gendered assumptions reflexively and dialogically, (ii) adopting an anti-essentialist approach that foregrounds experiential, embodied knowledge, and (iii) developing an anti-hierarchical methodology. We do so in the hope of opening up ways that might enable others to avoid heteronormative assumptions having potentially detrimental consequences for their research and to offer a starting point for developing gender reflexive knowledge production in the future

Tangible user interfaces : past, present and future directions

In the last two decades, Tangible User Interfaces (TUIs) have emerged as a new interface type that interlinks the digital and physical worlds. Drawing upon users' knowledge and skills of interaction with the real non-digital world, TUIs show a potential to enhance the way in which people interact with and leverage digital information. However, TUI research is still in its infancy and extensive research is required in or- der to fully understand the implications of tangible user interfaces, to develop technologies that further bridge the digital and the physical, and to guide TUI design with empirical knowledge. This paper examines the existing body of work on Tangible User In- terfaces. We start by sketching the history of tangible user interfaces, examining the intellectual origins of this field. We then present TUIs in a broader context, survey application domains, and review frame- works and taxonomies. We also discuss conceptual foundations of TUIs including perspectives from cognitive sciences, phycology, and philoso- phy. Methods and technologies for designing, building, and evaluating TUIs are also addressed. Finally, we discuss the strengths and limita- tions of TUIs and chart directions for future research

How can we model subsurface stormflow at the catchment scale if we cannot measure it?

Subsurface stormflow (SSF) can be a dominant run‐off generation process in humid mountainous catchments (e.g., Bachmair & Weiler, 2011; Blume & van Meerveld, 2015; Chifflard, Didszun, & Zepp, 2008). Generally, SSF develops in structured soils where bedrock or a less permeable soil layer is overlaid by a more permeable soil layer and vertically percolating water is deflected, at least partially, in a lateral downslope direction due to the slope inclination. SSF can also occur when groundwater levels rise into more permeable soil layers and water flows laterally through the more permeable layers to the stream (“transmissivity feedback mechanism”; Bishop, Grip, & O'Neill, 1990). The different existing terms for SSF in the hydrological literature such as shallow subsurface run‐off, interflow, lateral flow, or soil water flow reflects the different underlying process concepts developed in various experimental studies in different environments by using different experimental approaches at different spatial and temporal scales (Weiler, McDonnell, Tromp‐van Meerveld, & Uchida, 2005). Intersite comparisons and the extraction of general rules for SSF generation and its controlling factors are still lacking, which hampers the development of appropriate approaches for modelling SSF. But appropriate prediction of SSF is essential due to its clear influence on run‐off generation at the catchment scale (e.g., Chifflard et al., 2010; Zillgens, Merz, Kirnbauer, & Tilch, 2005), on the formation of floods (e.g., Markart et al., 2013, 2015) and on the transport of nutrients or pollutants from the hillslopes into surface water bodies (Zhao, Tang, Zhao, Wang, & Tang, 2013). However, a precise simulation of SSF in models requires an accurate process understanding including, knowledge about water pathways, residence times, magnitude of water fluxes, or the spatial origin of SSF within a given catchment because such factors determine the transport of subsurface water and solutes to the stream. But due to its occurrence in the subsurface and its spatial and temporal variability, determining and quantifying the processes generating SSF is a challenging task as they cannot be observed directly. Therefore, it is logical to ask whether we can really model SSF correctly if we cannot measure it well enough on the scale of interest (Figure 1). This commentary reflects critically on whether current experimental concepts and modelling approaches are sufficient to predict the contribution of SSF to the run‐off at the catchment scale. This applies in particular to the underlying processes, controlling factors, modelling approaches, research gaps, and innovative strategies to trace SSF across different scales

Reinventing learning: a design-research odyssey

Design research is a broad, practice-based approach to investigating problems of education. This approach can catalyze the development of learning theory by fostering opportunities for transformational change in scholars’ interpretation of instructional interactions. Surveying a succession of design-research projects, I explain how challenges in understanding students’ behaviors promoted my own recapitulation of a historical evolution in educators’ conceptualizations of learning—Romantic, Progressivist, and Synthetic (Schön, Intuitive thinking? A metaphor underlying some ideas of educational reform (working paper 8). Division for Study and Research in Education, MIT, Cambridge, 1981)—and beyond to a proposed Systemic view. In reflection, I consider methodological adaptations to design-research practice that may enhance its contributions in accord with its objectives