Students begin by recognizing shapes by their whole appearance, but not exact properties.

The levels are developmental – children of any age begin at level 0 and progress to the next level through experiences with geometric ideas (Van de Walle, Karp, Bay-Williams, 2019). Most elementary students are at levels 0 or 1 and some middle school students are at level 2. The van Hieles identified five levels of geometric thinking through which students pass. The development of geometric thinking comes from Pierre van Hiele and Dina van Hiele-Geldof. In the Kansas Mathematics Standards, geometry spans every grade level from kindergarten to grade eight it first begins with spatial sense, an intuition about shapes and the relationships between them including an ability to recognize, visualize, represent, and transform geometric shapes. Additionally, geometry “covers the skills and concepts of visualization, spatial reasoning and representation, and analyzing characteristics and properties of two- and three-dimensional shapes and their relationships” (Lappan, 1999). Michael Shaughnessy said, “If algebra is the language of mathematics, geometry is the glue that connects it” (Shaughnessy, 2011). The Standards describe particular aspects on which students at that grade level work systematically, deeply, and extensively, building on related experiences in previous years” (Progressions for the Common Core State Standards in Mathematics, 2013).įormer NCTM President J. From Kindergarten on, students experience all of the properties of shapes that they will study in Grades K–7, recognizing and working with these properties in increasingly sophisticated ways. In learning about shapes, it is important to vary the examples in many ways so that students do not learn limited concepts that they must later unlearn. “learning geometry cannot progress in the same way as learning number, where the size of the numbers is gradually increased and new kinds of numbers are considered later. The Progressions document goes on to say, “Geometric and spatial thinking are important in and of themselves, because they connect mathematics and the physical world… and because they support the development of number and arithmetic concepts and skills” (Progressions for the Common Core State Standards in Mathematics, 2013). Geometry is a branch of mathematics that studies the sizes, shapes, positions, and dimensions of things.

Decompose math geometry definition