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Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.
Geometry is the mathematical study of shapes and patterns. When you're first introducing basic geometry to your students, you're introducing shapes, patterns, and analysis to very young minds, as well as setting the foundation for many years of growth and development in middle and high school.
At the basic level, your students need to know shapes at the visual level, which means they should be able to visualize a shape in their mind, recognize it when they see it, draw a reasonable representation, and know the name of the shape (circle, square, etc.). In addition, you want to introduce relational analysis, where students begin to understand how shapes can be related to and compared to one another. You want them to understand that shapes can be above, below, behind, in front, larger, smaller, etc., and how groups of them might look in relation to each other. For example, when introducing younger students to circles, you could provide them with the following scenario:
''Oh, no! Spot has stolen one of the circles that make up Ralph the Snowman! Hurry, someone go find me a circle that's just the right size to put Ralph back together!''
You also want to introduce patterns, or the ways that shapes, numbers, and other symbols can be meaningfully arranged, and fundamental reasoning, which means if one thing is true, what else must be true, and what things might be true, or will not be true? Finally, you want them to begin to understand problem solving, as it relates to shapes and patterns. For instance, the circle will not fit into the square hole in the block. What kinds of things might I change to make it fit?
All strategies for meeting these objectives should involve several areas of the students' minds because this reinforces their memory connections as they're learning. Lasting impressions are formed in the human mind, especially the young one, through the use of reinforcing sensory impressions. You want to appeal to as many learning styles, such as visual, auditory, or kinesthetic, and intelligence types, such as language, music, art, or mechanical knowledge, as possible.
Combining drama with visual (meaning picture-based), auditory (meaning based on language, sounds, or music), and kinesthetic (meaning based on movement and physical position) components can create a memorable experience for your students. For example, any popular children's story can be retold and enacted using shapes for the main characters. You can tell the tale of how Queen Circle captured the poor Princess Triangle and imprisoned her in the large square with a small star-shaped door that only a Star Prince can go through.
It can be pretty useful to have and use appropriate background music, active voices, and visual support by way of large drawn, labeled, and colored images for the set and for each of the actors and actresses to wear. At key moments in the story, you can ask for clarification from the audience: ''Watch what Queen Circle is doing. Is she above or below Prince Star? Does that mean she can drop things on him?''
Games played while sitting in a circle and bouncing a ball can be powerful memory aids for establishing and reinforcing patterns and sequences. It's actually pretty valuable to remember that loud, happy sounds are particularly memorable, as are vivid, large images, so props and loud singing or shouting can help in these exercises.
If you want to establish a pattern that's increasing by one, for instance, you can give each child a sign or hat to wear with a certain number of objects on it. The job for each child is to bounce the ball to the child with one more object on his or her sign than the bouncer has. If no child has more, then the ball is sent back to you. Children are sensitive to rhythm, so if you can get them bouncing to the beat of a song, the experience is so much the better.
Stories and puzzles are excellent visual supporting structures for teaching simple problem solving and basic analysis. For instance: ''The circle is behind the tree. What will the square have to do to catch the circle?'' Complexities can be increased as the children become used to analyzing and resolving situations, as shown in this scenario: ''King Square is at the front of the castle, but the only open gate is at the back. How can Prince Triangle reach the king?''
In every activity, there are small things that can be done to emphasize the meaning and reinforce the things you want the children to remember. For example, children can write down or draw a progression, based upon the progress of the ball game. When children answer questions for a story, you can have them draw the relationship, such as ''Draw Queen Diamond above Princess Heart.''
Remember, one powerful element to any learning exercise is emotional involvement. Asking how the shape feels about something engages more of the child's mind and tends to reinforce the symbols and relationships that you're trying to emphasize.
Let's take a few moments to review what we've learned about teaching strategies for basic geometry. Geometry is the mathematical study of shapes and patterns. At the basic level, it involves learning about shapes at the visual level, which means that the students can recognize, name, and create fundamental shapes, such as circles, squares, or triangles.
Relational analysis refers to a child's ability to understand how shapes can be related to each other, such as larger and smaller, in front or in back, etc. Patterns are the ways that shapes and other symbols can be arranged. Effective teaching utilizes visual (sight-based), auditory (sound-based), and kinesthetic (based on motion or physical position) components. Effective teaching also addresses a broad range of learning styles, which are the aforementioned visual, auditory, and kinesthetic styles, and intelligence types, such as language, music, art, etc. Fundamental reasoning involves being able to answer ''What if?'' questions about situations. Drama and emotion can emphasize the principles you're trying to teach.
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