Our approach to geometry with young children begins with students’ informal knowledge about situations, followed by progressive mathematical reinterpretation of these experiences, an approach consistent with the Dutch approach to “realistic mathematics education�? (see Gravemeijer, chap. 2, this volume). Young children’s everyday activities-looking, walking, drawing, building, and manipulating objects-are a rich source of intuitions about spatial structure (Freudenthal, 1983; Piaget & Inhelder, 1948/1956; Streefland, 1991; van Hiele, 1986). By looking at pattern and form in the world, children develop informal knowledge about geometric constructs like perspective, symmetry, and similarity. For example, preschoolers pretend that miniatures are small-scale versions of familiar things, and even infants distinguish contour and symmetry (Fantz, 1958; Gravemeijer, chap. 2, this volume; Haith, 1980). By walking in their neighborhoods, children learn to reason about landmarks, routes, and other elements of large-scale space (Piaget, Inhelder, & Szeminska, 1960; Siegel & White, 1975). By drawing what they see, children represent form (Goodnow, 1977). By building structures with blocks, toothpicks, or Tinkertoys, children experience first-hand how shape and form play roles in function (e.g., objects that roll vs. those that do not) and structure (e.g., sturdiness; see Middleton & Corbett, chap. 10, this volume).
Lehrer, R., Jacobson, C., Thoyre, G., Kemeny, V., Strom, D., Horvath, J., … Koehler, M. (2012). Developing understanding of geometry and space in the primary grades. In Designing Learning Environments for Developing Understanding of Geometry and Space (pp. 169–200). Taylor and Francis. https://doi.org/10.4324/9780203053461-13