# CA News

#### Montessori Monday 8 2013/14

The Constructive Triangles

Many of the goals of the Montessori materials are apparent at first glance: learning to pour water or identifying numerals or letters. But much of Montessori's genius lay in integrating concepts across the classroom in a way that allowed children to engage similar concepts in increasingly complex ways. Today, we call this technique "the spiral curriculum," as children revisit concepts from different perspectives and in more complicated ways as they advance through the materials.

The Constructive Triangles are a perfect example of this spiral at work. At home in the Sensorial area, the Constructive Triangle boxes appear at first to be simple, visual puzzles. The child lines up the pieces by their guide lines and is able to construct a same sized equilateral triangle from differing combinations of two, three, and four smaller triangles. But while the child is focused on creating those larger triangles, she is internalizing important foundational concepts of plane geometry. If you understand that all straight-lined shapes can be constructed by combinations of triangles, and you know particular qualities about triangles, you can apply those qualities to all straight-lined shapes. Advanced boxes will expand on the shapes the child can construct, while nomenclature lessons will help the child learn the language to describe isosceles, equilateral and scalene triangles. Equations for measuring triangles (and the shapes they construct!) will be made concrete as the child experiments with different combinations. Imagine, for example, that you made a mirror image of a triangle, then inverted it on the original. You could move its parts around to make a rectangle.

Now, imagine that you get to do that with real triangles in your hand. Suddenly, the equation we all memorized in high school, that the area of a triangle is 1/2 its base times its height, makes sense. You (and the child) can see why we take 1/2 of the base measurement. The equation isn't an abstract fact to memorize anymore... it's a representation of a concrete concept the child understands.

Our abstract minds are able to imagine those qualities, and to be interested in sorting out the problems from a purely intellectual perspective. For the child, though, having the concept made concrete means it has been made understandable. Watching smaller triangles slide along each other to become, seemingly by magic, a larger, square, rectangle, trapezoid, rhombus or parallellogram enchants the child's interest and engages them in the aesthetic attraction of the work.

As the child develops, these concrete concepts will be made more abstract, and revisited again and again through advanced materials in Sensorial and Math. Presented this way, the concepts of geometry that seemed so foreign to most students in traditional classrooms are just other, enticing puzzles to be solved for the Montessori child.

Catherine McTamaney, Ed.D.

Christopher Academy Alumna