Lynn McGarvey

The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes

Increasing globalization encourages assumptions of universalism in teaching and learning, in which cultural and contextual factors are perceived as nonessential. However, our teaching and learning are unavoidably embedded in history, language and culture, from which we draw to organize our educational systems. Such factors can remain hidden but can also provide us with opportunities to gain a deeper understanding of constraints that are taken for granted. This chapter provides a meta-level analysis and synthesis of the what and why of whole number arithmetic (WNA). The summary provides background for the whole volume, which identifies the historical, cultural and linguistic foundations upon which other aspects of learning, teaching and assessment are based. We begin with a historical survey of the development of pre-numeral and numeral systems. We then explore the epistemological and pedagogical insights and highlight the differences between linguistic practices and their links with the universal decimal features of WNA. We investigate inconsistencies between spoken and written numbers and the incompatibility of numeration and calculation and review a number of teaching interventions. Finally, we report the influence of economics and business, academic mathematics, science and technology and public and private stakeholders on WNA to understand how and why curriculum changes are made, with a focus on the fundamental losses and gains.

Spatial Skills Framework for Young Engineers

Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent research reveals that spatial ability is not innate, but that through experience, education, and intervention, people of all ages can improve their visualization skills—a key component of the engineering habits of mind. In this chapter, we examine the spatial skills that are predictive of success in engineering education and the types of intervention activities that have demonstrated improved performance in STEM subjects. In doing so, we identify parallel assessment measures, skills, and tasks in the development of a spatial skills framework for young engineers that includes physical and mental rotation, symmetry properties, paper folding and unfolding, and cross-cutting objects. These skills are developed through 3D modelling and 2D representational drawings. We illustrate the skills in the framework with samples of work from students in grades 2 and 3 in response to a series of linking-cube tasks in a cube-creature project.

Multidisciplinary perspectives on a video case of children designing and coding for robotics

Spatial reasoning plays a vital role in choice of and success in science, technology, engineering, and mathematics (STEM) careers, yet the topic is scarce in grade school curricula. We conjecture that this absence may be due to limited knowledge of how spatial reasoning is discussed and engaged across STEM professions. This study aimed to address that gap by asking 19 professionals to comment on a video that documented children’s progression through 5 days of building and programming robots. Their written opinions on the skills relevant to their careers demonstrated by the children revealed that spatial thinking and design thinking are central to what they see.RśuméLe raisonnement spatial joue un rôle essentiel dans la décision d’entreprendre une carrière STEM et de réussir dans les domaines concernés. Pourtant, ces matières sont peu représentées dans les curriculums à l’école primaire. Nous supposons que cette absence puisse être due à un manque de connaissances quant à la façon dont le raisonnement spatial est traité dans l’ensemble des professions STEM. Cette étude vise à combler ce manque en demandant à 19 professionnels de commenter une vidéo qui documente la progression d’enfants qui construisent et programment des robots pendant 5 jours. Les commentaires écrits des répondants sur les habiletés pertinentes illustrées par les élèves montrent que la pensée spatiale et la pensée conceptuelle sont fondamentales dans leur profession.