Spatial skills, while vital to STEM (Science, Technology, Engineering, and Mathematics) and STEAM (Science, Technology, Engineering, Arts, and Mathematics) fields, are fundamental to understanding all mathematics. Yet the absence of spatial development in elementary curricula, particularly geometry, where such skills can be deeply explored, is compounded by a lack of theoretical and empirical research, especially in deaf education, where little research addresses learners’ spatial-geometric understandings and the ways their bodies contribute to developing such understandings. We first review relevant literature to interrelate mathematics, spatial activity, and embodied cognition with aesthetics for STEAM (Science, Technology, Engineering, Arts, and Mathematics) in deaf education. We then present a case study in which we observed and assessed Evan, a deaf student, as he worked on three geometry tasks. This video-based research utilises the Pirie–Kieren Theory/Model to further consider the aesthetic, spatially dynamic, and embodied ways that Evan’s geometric understandings emerged and evolved into more formal mathematical activity. Finally, we discuss the ways the study findings focused on spatial-geometric development support future STEAM education research and classroom mathematics towards growth-oriented learning for deaf students.

Abstract The work of Japanese-Canadian teacher, administrator, educator, and theorist Ted Tetsuo Aoki (1919–2012) is both extraordinary and inextricably connected to who he was and who he became as curriculum theorist. Spanning more than four decades, his scholarship is nothing less than uniquely Aoki(an) in form, meaning, and effect. Aoki’s contributions, deeply intellectual but seriously playful and creatively performative, continue as vital to the advancement of curriculum studies in Canada and internationally as well as to education in general. At the heart of Aoki’s ideas, thinking, and modes of theorizing are radical concepts such as: curriculum as plan(ned), curriculum as live(d), bridge-not-bridge, lingering, inspiriting, metaphor, and metonymy. These Aokian concepts when examined more closely reveal as ontologically grounded in and epistemologically arising from his life as a Japanese-Canadian in Western Canada at the end of World War I, into the years of World War II, and through to the decade following the turn of the 21st century. Theoretically, the scholar’s work is often characterized as phenomenological and hermeneutic renderings of curriculum. Further study discloses Aoki’s scholarship as demonstrating greater intellectual breadth, also situated within critical, poststructural, postcolonial, postmodern, premodern, enactive, ecological, and cultural discourses including Zen Buddhism. Aoki’s studies expand notions of curriculum, but more fundamentally, they expose and bring into question entrenched ideologies and practices within education and its disciplinary areas. In these manners, Aokian theory prompts conceptual spaces for (re)new(ed) meanings of curriculum and ultimately what it means to be human. It is remarkable that Aoki’s decades-long theorizing has virtually gone without controversy or debate. While this attests to Aoki’s humility and brilliance as a scholar, it signals the need for continued engagement with Aokian concepts as well as deeper exploration into the scholar and his scholarship as a whole.

What begins as a search for a photograph of Japanese-Canadian curriculum scholar Ted Tetsuo Aoki ends up as a curriculum inquiry into a documentary film. Hayashi Studio focuses on the Japanese Canadians of Cumberland, British Columbia, Canada at the turn of the 20th century up to the evacuation of them during WWII, and today more than a century later. Through photographs taken at Hayashi Studio, together with the stories shared by a community member and Aoki’s eldest son, the scholar’s life and curriculum theorizing become dialectically part and whole of the curriculum inquiry. The author explores spaces of seeing and hearing, dis-covering, and recovering, all the while asking where there might be a place for the stories and narratives of the documentary in understanding curriculum amidst doing curriculum research.

Projective geometry is a prominent area in many fields including art, design, architecture, and mathematics, but how it can contribute to children’s spatial reasoning as well as a supplementary geometry to that of Euclid’s in school mathematics curricula raises the need for further consideration. With emphasis on the dynamic relationship between 2D and 3D objects, projective geometry not only offers important concepts but a meaningful context in which to develop spatial reasoning for STEM learning. In this article, we overview spatial reasoning as it relates to STEM and in particular, mathematics. Making a case for projective geometry, we present activities for the classroom, demonstrating how this mathematics topic connects to and opens new possibilities to promote spatial reasoning for STEM learning in the elementary grades.

Spatial thinking is an essential and uniting form of reasoning across science, technology, engineering, and mathematics (STEM). This paper explores projective geometry ideas accessible to elementary school-aged children, specifically focusing on understanding, exploring, and analyzing relationships between 3D objects and their 2D projections. We posit that projective geometry has the potential to elicit spatial reasoning actions, such as visualization, dimension-shifting, and perspective taking, and provides a unifying theme in which to explicitly attend to 2D representations of 3D objects. In the paper, we share three tasks rooted in projective geometry: Moving Shadows, Structured Perspective Drawings, and Design-Build-Draw. We piloted these tasks with children aged 5 to 11, illustrating the spatial actions elicited by the tasks through the children’s gestures, responses, drawings, and models.

Mathematics curricula continue to become more standardized worldwide, which makes researching topics not appearing in the explicit curriculum challenging. In this chapter, we describe four lessons learned while conducting classroom-based research in Canada on a topic in the null curriculum. Despite its potential to support geometric and spatial reasoning, research in projective geometry with children was abandoned decades ago. Through our project, we learned multiple lessons while resurrecting, updating, inventing, implementing, and conducting classroom-based research within the null space of projective geometry. These lessons include: (1) locating relevant curriculum resources for a non-existent topic in the elementary-grades curriculum; (2) inventing ways to create, pilot, and use unfamiliar tasks in a classroom-based setting; (3) rationalizing the value of the topic to school district personnel, teachers, parents, and students; and (4) generating reciprocal growth in understanding amongst teachers and researchers. The insights gained offer ways to explore and justify the research, teaching, and learning of topics outside of the explicit curriculum.

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.

We challenge current discourses of STEM which use place/land for economic prosperity by engaging with Indigenous and ecological worldviews of land. In doing so, we come to imagine, (re)member, and (re)cognize STEM with and as place. We examine how place/land, as culturally alive and living with situated experiences, supports imagining STEM in ways that (re)center responsibility for relationships with a more-than-human world. We share teachings from rivers, forests, and coral reefs, that illuminate courage, humility, truth, and wisdom to (re)generate and (re)actualize STEM among humans and more-than-humans.

Paul Lockhart is a former computer programmer, elementary teacher, research mathematician, university professor, and somewhat more recently a K-12 mathematics teacher and author. Lockhart's first written composition appeared two decades ago in 2002. All of 25 pages, his essay A Mathematician's Lament began like this:

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.

During the summer of 2016, Jennifer Thom introduces Chet Bowers to the works of scholar Ted T. Aoki. While Bowers is intrigued by Aoki's curriculum theorizing, his passing denies further conversation. In the spirit of authentic dialogue, Thom brings the two scholars into conversation with each other. Dynamically weaving key excerpts from each of their works, Thom creates three dialogues with which to illuminate the significance of Bowers' ecological literacy as it coheres with Aoki's curriculum writings. Focusing on Bowers' conceptual development of the non-neutrality of language, curriculum as cultural discourse, and linguistic forms of colonization through print, data, and technology, Thom examines his theory in relation to Aoki's. As a result, it is Aoki's concepts of tensionality, a bridge which is not a bridge, and the space between that facilitate deeper meaning, newfound relevance, and transformative possibilities for reconsidering emergent global challenges.

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.

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.

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.