Many times I hear people say that they didn’t like and/or didn’t understand Geometry in high school. Many say they do not see the importance of Geometry. However, we use Geometry all the time. Geometry is involved when we:
- Use a map or GPS,
- Put groceries away in a cupboard,
- Rearrange a room,
- Complete a puzzle,
- Give directions or follow directions,
- Pack a suitcase,
- Park a car, and
- Put on make-up
Geometry is one of the five content areas in mathematics. The National Council of Teachers of Mathematics (NCTM) identifies these content standards for Pre-K through 12th grade.
- Number and Operations
- Data Analysis and Probability
Young children already have and utilize some geometric concepts when they enter Pre-K that can be extended and built upon. In Prekindergarten, children are NOT doing proofs and formulas as many of us remember doing in our school careers. Young children are involved in experiences and activities that help them understand shapes, spatial relationships and the properties of 2-dimensional and 3-dimensional objects.
NCTM points out in their Focus in Pre-K: Teaching with Curriculum Focal Points, “Geometry and measurement are two of the U.S. student’s weakest topics in mathematics. Even in the preschool years, children in the U.S. know less about shape than children in other countries.” As educators of young children, we need to recognize the importance of children’s knowledge and understanding of geometric concepts beyond circle, square, and triangle. This does NOT mean using flash cards or worksheets! It does mean giving children hands-on opportunities. As teachers of young children we need to be very intentional about planning opportunities, incorporating appropriate materials, and introducing and using math language and vocabulary for all of our students. Sally Moomaw states, “The more experiences children have with geometry in meaningful contexts, the more they can construct and solidify foundational concepts.”
The Early Math Collaborative at Erikson Institute states Shapes and Spatial Thinking are Big Ideas in their book, Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know. This is a guide to assist teachers in being more intentional and knowledgeable with their activities, questioning, and language regarding Geometry.
Defining and Classifying Shapes
Sometimes, people think that young children only need to know the names of the basic shapes – circle, square, triangle, and rectangle. The goal/outcome is deeper and more extensive. The goal is to help young children learn attributes of each basic shape. The Early Math Collaborative at Erikson Institute uses the activity, “Feel for Shapes” to assist Pre-K students in recognizing shapes by using their sense of touch instead of their sense of sight. The Early Math Collaborative points out:
Children need to go beyond the use of superficial shape labels to recognizing and specifying the defining attributes of shapes. As children sort and classify shapes with knowledgeable others, they become aware of rules about shapes, such as that a triangle has three sides and three angles. -“Feel for Shapes,“ Erikson Institute’s Early Math Collaborative website – www.earlymath.erikson.edu
2-Dimensional and 3-Dimensional Shapes
As teachers of young children, sometimes we focus a great deal on 2-D shapes. How often do we provide experiences and supportive math language with 3-D shapes? It is important to use the correct terms. We need to remember that a baseball is not a circle, it is a sphere.
As children are playing in the block area, we can point out how the flat faces of a solid cylinder are 2-D shapes which would be circles while pointing out that the entire solid 3-D block is called a cylinder. What other interest areas in the classroom can we focus on 2-D and 3-D shapes?
Combining Shapes and Decomposing Shapes
Children need time to explore shapes and discover that two triangles could make a square or six triangles can make a hexagon. Pattern blocks and unit blocks provide numerous opportunities for composing and decomposing shapes.
Children can also deconstruct a cereal box and see the different shapes and sizes of each side of the box. With assistance children can begin putting the box back together with tape.
As Creative Curriculum for Preschoolers from Teaching Strategies states in their Mathematics Volume that young children need “to recognize shapes, build with them, illustrate them in their own way, describe shape attributes, compare shapes, and sort them by their characteristics.” While doing this children are also working on other skills along with Geometry such as: fine motor as they draw, algebraic skills as they sort the shapes, measurement as they compare shapes, and language skills as they describe shapes during their play and in their conversations.
Along with recognizing shapes, young children also need to be exposed to and utilize spatial thinking. The children are developing their understanding of where objects are in relationship to other objects, people, and/or places. Many of us think of using descriptive words only as a language skill instead of geometric concepts. When teachers or parents give a direction or statement such as “Joey is standing in front of his brother,” they are giving a precise description of where Joey is in relationship to his brother.
When children play a game by following directions such as put the plastic egg behind their back, they demonstrate their knowledge or emerging knowledge of behind. With this knowledge a teacher will determine the next steps in their lesson planning for scaffolding children’s geometric concepts.
Children benefit from experiences that can help them visualize spatial relationships. Doing puzzles helps children develop this skill. Eventually children can begin to see mentally where pieces of the puzzle go without doing a trial and error approach.
Teachers also use geometric terms such as turn, flip, and slide as they assist or observe children working on puzzles. This spatial visualization helps children distinguish if a library book will fit in their bookbag/backpack.
As an educator or parent, research has shown that our attitude toward math will influence young children’s attitudes toward math. Even if we do not like Geometry, we do not want to state that to children. We need to become an actor and act as though we do. If we can’t answer a child’s question, let them know you will find out the answer or encourage the child to assist you in finding the answer. Geometry is all around our young children, and it is something that will be used throughout their lives.
Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know by The Early Math Collaborative-Erikson Institute
Focus in Pre-K: Teaching with Curriculum Focal Points from National Council of Teachers of Mathematics
Principles and Standards for School Mathematics from National Council of Teachers of Mathematics
Teaching Mathematics in Early Childhood by Sally Moomaw
Sherial McKinney, M.S. Ed., is an Early Childhood Resource Specialist for STARnet Regions I and III located at Western Illinois University, Macomb, IL. She has taught in a public school district and worked in the field of early childhood education for over 40 years. She is very interested in mathematics education for young children.