WHAT “SHAPES” YOUR GARDEN?

WHAT “SHAPES” YOUR GARDEN?

This week, we turn our thoughts towards geometry.  Geometry is the study of points, lines, rays, segments, shapes.  The study of the geometry is divided into two distinct types of geometry, plane geometry and solid geometry.  Plane geometry contains everything that is not a three-dimensional shape.  Solid geometry contains only three-dimensional shapes.

It is important for a student’s first introduction to geometry be within the context of his or her environment.  The ability to observe the world around us is important in being able to categorize and classify the different types of shapes.  Most children are able to look at a window and recognize that it is shaped like a rectangle or square.  These initial categorizations allow students to build the necessary observation skills that allow students to piece together definitions of the shapes.  These early definitions are refined with each passing year, until the student’s definition of a square is regular rectangle.  The understanding of this definition will not come together without constant observation and refinement.  

In order to refine a definition, a student must be able to observe the shapes in different settings and sort the shapes based on his or her own interpretations of the defining attributes of the shape.  A squares defining attributes are many.  All squares are polygons, quadrilaterals, parallelograms, rhombuses, and rectangles.  However, as we all know, not all polygons, quadrilaterals, parallelograms, rhombuses and rectangles are squares.  Squares are a special 4 sided polygon that has alternate sides being parallel, all line segments form a 90° angle and are all sides are equal. Only by observation will a student be able to understand these relationships between the various classifications to which a square belongs and its special designation as a square.

It is sometimes difficult for children to make the connection between the shapes, as shown above.  They have been taught from an early age that there is a difference between squares and rectangles, that in fact, the two are distinctly different shapes. Only to discover later that the square is a special type of rectangle and not a distinctly different shape after all.  To further their confusion, we begin to introduce other types of shapes that contain the same attributes that squares and rectangles have.   These newer classifications of shapes are not exactly distinct, as their old friends are actually special subsets of the “new” shapes.

I am not advocating that polygon, quadrilateral and parallelogram be introduced prior to the introduction of square and rectangle.  However, I am advocating that these shapes be introduced sparingly in the earlier grades.  Being exposed to these shapes and their names will help assuage some of the confusion later.

The best way to discover the relationships between the shapes and refine the working definitions of the shapes is to sort the shapes.  It is important that the sorts be open with some guidance from the teacher.  These sorts allow the students to determine the rules and make observations of the similarities between the different shapes.  The teacher’s involvement is to direct each sort’s parameters.  The parameters contained on page 126 of Making Sense of Mathematics for Teaching Grades 3-5, by Juli K. Dixon, Edward C. Nolan, Thomasena M. Tobias, and Guy Barmoha are a great example of the teacher’s involvement in the sorting process.   These parameters allow the students to begin with a sort of curved and non curved shapes, so that each sorting loop has distinct and separate shapes contained within.  One of  the instructions asks the students to create 2 new rules, so that there are some shapes outside the loops, some inside one of the two loops and some that are in both loops. In order to succeed, a student will need to look at what makes each shape the same and what makes them different.  Finally, the students are tasked with creating another set of two new rules.  These rules are to sort the shapes  so that some shapes are outside of both loops, some shapes inside the larger loop and some shapes inside embedded the smaller loop. The rules must be such that the student is able to find shapes that while a bit different have the same attributes as another.  These sorts will allow the students to make the connections outlined above that squares, while the shape will always remain a square, it is also a polygon, quadrilateral, parallelogram, and rectangle, as well.

You might be surprised by the additional shapes you can find, while you wander around.  There are shapes everywhere, in tile floors, patio paving stones.  Each of these can make beautiful pictures.  I use many items such as these as inspiration for my quilts.

The Inspiration

The Quilt

Inspiration for future quilts.