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Positioned within Indigenous and ecological discourses, our paper reconsiders human-centered relationships with earth and activities such as STEM that view earth as commodity, resource, and platform. In doing so, we turn to the ways earth (e.g., rivers, forests, animals) teaches mathematics education for "STEM as place" and reveals intelligences that exceed those of humankind. Using examples of place and land, we illustrate how such a conception contrasts with current calls and goals for STEM and integrated STEM education. We contend that comprehending "STEM as place" renews potential for success to be defined "as the continuity of life"; that is, all that concerns the natural world, including human wellbeing in general, and in particular mathematics and mathematics education. To conclude, we propose research directions to study mathematical ways of being, mathematics, and mathematics education for "STEM as place." We include possible implications and pathways for such work which prompts (re)visioning and (re)enacting mathematics education to be for "STEM as place."

Spatial reasoning, recognised as playing a critical role across STEM disciplines, is gaining prominence in mathematics education, not only as fundamental to mathematics, but also as embodied mathematical activity. In this paper, we discuss spatial reasoning and its embodiment in mathematics. We then present a systematic review of the topics as researched and related to deaf and general education from 2010 to 2019. Publication trends during the ten years reveal similarities and differences across both fields. Based on the findings, we share insights, prospects, and provocations for promoting spatial reasoning in mathematics with an emphasis on research and pedagogy for deaf education.

Spatial reasoning is critical across the STEM disciplines. Examining deaf and hard of hearing (DHH) children's spatial reasoning in mathematics, particularly geometry, as an embodied phenomenon opens new possibilities for deaf education. The authors inquire into the embodied processes and forms of DHH learners' spatial reasoning, considering how such knowledge can expand access and conceptual opportunities for both DHH and hearing learners. The article focuses on the spatial reasoning of two grade 1 hard of hearing children as they complete a geometric task with a hearing peer in a mainstream classroom. Informed by research in cognitive science, mathematics, and the fields of deaf and general education, the authors explicate key spatial subcomponent processes of deconstructing and constructing as the children produce 2D and 3D figures. The findings of this qualitative study provide considerations for future research and pedagogy in both deaf and general education.

Coeditors of a special issue of the "American Annals of the Deaf" on mathematics instruction in deaf education, the authors provide a context for the five featured articles. First, the authors establish the importance of mathematics. They then give a historical account of previously related "stepping-stones." Beginning at 1990, the authors follow key events in the field that have led to the special issue. They summarize each article, highlighting three common themes: deaf and hard of hearing (DHH) persons as distinct and capable mathematics learners, the significance of conceptual understanding of mathematics concepts, and the role of language as a key component of mathematics instruction and learning. The authors conclude with a call for further research that recognizes the heterogeneity of DHH learners.

Current conceptions of STEM focus on the Western views of distinct academic disciplines--sciences, technologies, engineering, and mathematics. There are national and international initiatives aimed at increasing workforce and postsecondary participation in STEM-related fields, including individuals in under-represented groups. While the emphases of these initiatives are clear, further consideration regarding the meaning and purpose of STEM is necessary. From our indigenous and ecological perspectives, limited questioning around STEM not only marginalizes other cultural forms of knowing--especially those which are connected to the environment--but also denies the potential for other cultural forms of knowing to contribute to the development and advancement of STEM. We are particularly interested in how STEM might be re-imagined within indigenous and ecological perspectives; what alternative meanings of STEM are enabled; and in light of these, what other purposes are possible for STEM? In this paper, we consider other cultural forms of knowing, specifically those forms of knowing deeply connected to the environment, to explore how such practices enable a re-imagining of STEM. Focusing on living landscapes, topography, architecture, and algo-rhythms, we engage the reader to play with these ideas, question taken for granted meanings of STEM, and re-imagine STEM within ecological and indigenous perspectives.

Chet Bowers' contributions to education are numerous and provocatively persistent. Using the title "Ecological Revelations: Recovering the Unseen" to frame my examination, I explore four concepts central to Bowers' work: "oikos," "intelligence," "language," and "cultural maps." First, I reflect on the ways in which Bowers' conceptualization of the concepts created ecological meaning and discursive relevance in education over the course of his scholarship, which spanned more than four decades. I highlight how Bowers' development of the ideas, each on their own and collectively as a coherent whole, not only challenged assumed cultural ways of being for educators, but importantly, provided an alternative theoretical framework to make new sense of how education (re)produces culture. I examine these concepts in relation to Bowers' critique of STEM (science, technology, engineering, mathematics), the theoretical dilemmas they raise, and the ecological questions that emerge. Finally, I inquire into how the four featured ideas, STEM, and STEM education play out in the context of a community commons. Here, additional concepts such as collaboration, innovation, renewal, and relationality expand Bowers' theory, which, in turn, not only give rise to ecological alternatives for STEM and STEM education but for the cultural commons as well.

In mathematics education, as in other domains, drawing serves as means to access, assess, and attend to children's understanding. While theoretical accounts of drawings are often based on developmental stage theories, we examine insights gained by considering children's geometric thinking and reasoning from embodied cognitive perspectives. We ask, what if the act of drawing serves as a means by which children become aware of geometric concepts and relationships, rather than being viewed as a product of that awareness? In this paper, we examine three vignettes and inquire into the ways that children come to draw in geometric contexts. We suggest that the children's choice to draw as a mode of thinking, the different ways they draw, the manners in which they attend to the mathematics as they draw, and the conceptions that arise with their drawings, contribute in significant ways to their geometric understanding.

In response to a mandate to develop a more welcoming university for students, especially those of Aboriginal inheritance, we set out on a journey for ways of accommodating cultural differences in our university classrooms. Over the course of a year, we met regularly and audiotaped our conversations. By talking, transcribing, writing, and rewriting, we carried our understandings forth in a recursive manner. In our efforts to represent the ideas that arose in our conversations, the conceptual movements in our thinking, and the insights that evolved, a play took shape. In the play, three characters evolve their understandings over the course of four acts. In this article, we reflect on the conditions that produced the play; we comment on the process of writing the play; and we share the understandings, insights, and transformations that occurred in our desire to live well amidst differences.

This article presents a descriptive account of an after-school study. The participants--Allan (male, ten years), Veronique (female, nine years), and William (male, ten years)--all spoke English as their first language and were considered by their classroom teachers to be meeting the provincially set expectations for the fifth-grade curriculum standards in mathematics. Analyzing the three fifth graders' spatial, arithmetic, and algebraic reasoning as they worked on a three-dimensional task revealed a contrasting perspective to the suggestion that their physical actions and interactions come before their sophisticated reasoning. As one of the five Process Standards, reasoning (and proof) is an essential part of acquiring and using mathematics. More than a means by which to confirm whether a solution is correct, mathematical reasoning involves exploring the mathematics at hand; generating, implementing, and evaluating conjectures; as well as justifying thinking and actions as one engages in mathematics. This article concludes with four important considerations for teachers as they nurture their students' mathematical reasoning. (Contains 8 figures.)

Psychologists, philosophers, and educators have traditionally interpreted the phenomenon of insight learning as the result of the sudden comprehension of abstract/conceptual ideas. The present article shows that such phenomenon may also follow and emerge from the kinetic movements of the human body; that is, we conceptualize insight learning as a post-kinetic phenomenon. Further, it is suggested that kinetic movement constitutes the ground of all human knowing. To illustrate this innovative conceptualization of insight learning, we present the analysis of an exemplary classroom episode taken from a two-year longitudinal video-based ethnographic project. Our project is concerned with elementary students' mathematical knowing and learning. In the episode, which was selected among other structurally similar examples, three children are sorting geometrical objects. The evidence shown is interpreted as support for the theory of mathematics in the flesh, a radical approach to embodied cognition. In contrast to other embodiment/ enactivist theories in the field of mathematics education, we suggest that the kinetic movement of the human body constitutes a necessary condition for the emergence of abstract mathematical knowledge, and more specifically for the emergence of geometrical insight.

The idea that mathematical knowledge is embodied is increasingly taking hold in the mathematics education literature. Yet there are challenges to the existing conceptualizations: There tend to be breaks between (a) the living and experienced body (flesh) and linguistic forms of thought, (b) individual and collective forms of knowing, and (c) the material body and the source of intentionality. Grounded in material phenomenology, we theorize the living body as semiotic expression that not only grounds thought but also leads to its development. We provide a detailed case study that elucidates the three ways in which the living body serves as sign for the growth of a second-grade student's geometric understanding and the other bodies he interacts with.

Mathematical concepts and conceptions have been theorized as abstractions from--and therefore transcending--bodily and embodied experience. In this contribution, we re-theorize mathematical conceptions by building on recent philosophical work in dialectical phenomenology. Accordingly, a conception exists only in, through, and as of the experiences that the individual realizes it. To exemplify our reconceptualization of mathematical conceptions, we draw on an episode from a study in a second-grade classroom where the students learned about three-dimensional geometrical objects.

Geometry, classification, and the classification of geometrical objects are integral aspects of recent curriculum documents in mathematics education. Such curriculum documents, however, leave open how the "work" of classifying objects according to geometrical properties can be accomplished given that the knowledge of these properties is the planned outcome of the curriculum or lesson. The fundamental question of the present study therefore is this: How can a lesson in which children are asked to participate in a task of classifying regular 3-dimensional objects be a geometry lesson, given that the participating 2nd-grade children do not yet classify according to geometrical properties (predicates)? In our analyses, which are inspired by ethnomethodological studies of work, we focus on the embodied and collective work that leads to the "emergence" of the geometrical nature of this lesson. Thus, we report both the collective and the individual work by means of which the lesson outcomes--the complete classification of a set of "mystery" objects according to geometrical (shape) rather than other (color, size, "pointy-ness") properties--are achieved. In the process, our study shows how geometrical work is reproduced by 2nd-grade children who, in a division of labor with their teachers, produce a particular set of geometrical practices (sorting three-dimensional objects according to their geometrical properties) for the 1st time. (Contains 9 footnotes and 8 figures.)

Increasing the number of Aboriginal students graduating from university is a goal of many Canadian universities. Realizing this goal may present challenges to the orientation and methodology of university curricula that have been developed without consideration of the traditional epistemologies of Aboriginal peoples. In this article, three scholars in the Faculty of Education at the University of Victoria take up this issue by dialoguing with each other about the possibilities of incorporating Aboriginal perspectives into their courses. These conversations are woven together into the narrative form of a four-act play in which the authors caricature their personalities to highlight their initial resistances and eventual reconsiderations. As non-Aboriginal instructors from different cultural backgrounds, the authors confront issues of respect, responsibility, and (mis)representation as they struggle with the dilemmas involved in cross-cultural understanding. Through this journey they come to imagine a world where cultural differences, including the traditional epistemologies of Aboriginal peoples, present possibilities for greater understanding of each other and more authentic expressions of our humanity. (Contains 9 notes.)

This paper presents a qualitative study that investigated two third-grade students' understanding of number. The children were videotaped while they worked to record everything they knew about the number, 72. Their artifacts and conversations were then analyzed using the Pirie-Kieren dynamical theory for the growth of mathematical understanding as the theoretical framework. The results of the video analysis revealed the two students' understanding of natural numbers as being conceptually complex and existing in several different realms of the Pirie-Kieren model. Significant instances of "Primitive Knowing, Image Making, Image Having, Property Noticing, Formalizing, Observing", as well as how the children's understanding existed beyond "Don't Need" Boundaries are identified and examined in detail. Other features of the model--"Structuring, Inventising, Folding Back, and Connected Understanding"--are also explained and possible examples illustrating these kinds of mathematical thinking in relation to the two children's understanding of number are offered. (Contains 5 figures.)

Reports on a study in which three 3rd grade students were presented with the volume of cuboids. Examines the problem solving actions students demonstrate and analyzes students' strategies and solutions. Explores the connection between spatial structuring and the use of numerical operation. Considers perseverance and control emerging when solving problems. Discusses mathematical residue that results from developing understanding of volume. (Author/KHR)

Spatial reasoning, recognised as playing a critical role across STEM disciplines, is gaining prominence in mathematics education, not only as fundamental to mathematics, but also as embodied mathematical activity. In this paper, we discuss spatial reasoning and its embodiment in mathematics. We then present a systematic review of the topics as researched and related to deaf and general education from 2010 to 2019. Publication trends during the ten years reveal similarities and differences across both fields. Based on the findings, we share insights, prospects, and provocations for promoting spatial reasoning in mathematics with an emphasis on research and pedagogy for deaf education. [ABSTRACT FROM AUTHOR]