Are We Teaching Geometry Backwards To Children?
Are Early Childhood Educators Teaching Geometry Backwards?
by Dennis Pierce
Summary: A recent webinar explains why it makes more sense to teach children about three-dimensional figures before they learn about two-dimensional shapes.
Traditionally, young children are taught about two-dimensional shapes such as circles, squares, and triangles before they learn about three-dimensional figures such as spheres, cubes, and pyramids.
But in a recent edWeb webinar, early childhood educator Jessica Bobo argued for a different sequence of learning.
“Helping students achieve success with the correct developmental approach will allow for better mathematical understanding later in life,” said Bobo, who is an early childhood math consultant for ORIGO Education.
Young children are active investigators of their world. They learn best by exploring and making connections to the world around them.
Following a proper progression of learning sets up young children for success, she noted—while also helping them to avoid misconceptions that could become barriers to their learning later on. Young children are active investigators of their world. They learn best by exploring and making connections to the world around them.
To learn about geometry, “students need to be able to feel, touch, sit on things, and go under things,” Bobo said. “We want them to explore their everyday surroundings, because that is what teaching geometry is to them.”
Whatever environment children are in, “they are looking around and seeing all sorts of three-dimensional objects,” she noted. “They are used to seeing depth in objects. This is the everyday world they are used to. (And this is why) we need to teach them 3D understanding before we move to 2D.”
In fact, laying the proper foundation for an understanding of geometry begins with teaching students about spatial awareness, Bobo said.
“We want children to have a full arsenal of language to describe spatial relationships,” she explained. “Children need to understand both positional and directional language to understand geometry: where things are (located) in relation to each other, and where they are heading in relation to each other.”
Learning Math Through Play
Early childhood educators should give students many opportunities to learn and practice this language through the day, she suggested. When they are lining up to leave the classroom, teachers can say: “We are heading toward the hallway. We are walking away from (or out of) the classroom.”
“Play is so crucial when it comes to learning geometry,” Bobo stated.
A great way for children to learn positional and directional language, she said, is to set up an obstacle course in the classroom, then have them describe what they are doing as they navigate the course: “I am crawling under the table. I am stepping over the chair.”
“Play is so crucial when it comes to learning geometry,” Bobo stated. If children are physically touching, moving, or acting out a concept as they hear the language that is used to describe it, then the learning tends to stick.
And this is where early childhood educators might be introducing misconceptions about 2D shapes versus 3D figures.
“So often, we give children misconceptions when we give them pattern blocks, because we say, ‘This block is a triangle.’ As a matter of fact, it’s not a triangle; it’s a triangular prism,” she noted. “When we (teach children about) 2D shapes, it always has to be in a very flat sense, where there is no depth or thickness at all. If you give them something they can physically hold in their hand, that is now a 3D object.”
Because our understanding of 2D shapes comes from 3D objects, it makes more sense to begin exploring these 3D objects first, Bobo argued.
“Let them get a sense for what we teaching geometry or it exists in their classroom: cubes, cylinders, cones, spheres, prisms, and pyramids,” she said. Because children won’t know these terms, it’s OK to use the language they are familiar with at first: a box, a ball, and so on.
Use party hats (cones), cereal boxes, soda cans (cylinders), and other trash you’ve collected to have students create things out of these figures, such as castles or robots. “This helps them construct their own ideas about 3D objects,” Bobo said. Talk about the attributes of various 3D objects. For instance: How many flat surfaces does a box have.
How many corners?
“You’re building a holistic approach to 3D objects, where they are discovering the attributes of these objects through exploration,” she said. “They are talking with each other about similarities: Which objects have six sides? Which have no sides? Which ones roll? Which ones stack? Which do both?”
As children are touching and exploring the attributes of various 3D figures, you can begin to introduce the language of geometry: A box whose sides are all the same length is a cube. A box whose sides are different lengths is a prism. A ball is a sphere. A cube has six flat surfaces and eight corners, while a sphere has one curved surface and no corners. A cone has a flat surface at one end and comes to a point (an “apex”) at the other end.
Once children have begun to understand 3D objects, you can introduce the idea of 2D shapes, Bobo said.
“If I’m looking at a cube, I can feel the flatness of each side,” she said. “Why is that important? Because when children think about 2D shapes, they need to understand the attributes of these: 2D has no thickness. It’s completely flat. The face of a cube is a square. It has corners and sides, but no depth. It’s not something you can pick up.”
To move from 3D to 2D understanding, give children 3D objects and have them paint or trace pictures using the flat surfaces of these objects, she recommended. The bottom of a cone makes a circle. The bottom of a cylinder makes a circle. The side of a box (prism) makes a rectangle. Then, you can discuss the various attributes of these shapes.
Starting with 3D understanding allows students to relate their learning more clearly to the world around them, while also avoiding misconceptions about the differences between 2D shapes and 3D figures.
For more insights about teaching geometry to young children in a way that builds a solid foundation for success, check out the full webinar here.