Geometry: Understanding it! Rich experiences in guided math groups and whole class settings

Let no one ignorant of geometry enter my doors

Plato (inscription he carved above the entrance to his academy).

Geometry shapes our world.  It is important that educators understand the various levels and how to teach it so that our students come away with a deeper understanding of it.

The new Math Common Core has put a particular emphasis on the building of geometric understanding.  Much of the research shows that students walk away with a very shallow understanding of geometry and that they don’t really learn much more than they come to school knowing in the primary grades.  And thus, the problem becomes compounded because they are then not prepared for middle school and high school  geometry.

Now there is a change. Teachers have to understand the Big Ideas that students need to learn.  Van de Walle and Lovin (2006) talk about the need to understand the two major frameworks in geometry: spatial reasoning/spatial sense and the specific content.  The first has to do with how students think and reason about space and shape.  I will discuss that in this post.    The second has to do with the actual content, which I will discuss in the next post.

Spatial Sense:

an intituition about shapes and the relationships among shapes.” It includes the “ability to visualize mentally objects and spatial relationships- to turn things around in your mind.” It’s having a geometric state of mind.  It’s those folks who see the world in shapes – visualizing it in art, nature and architecture.  These are great ways to to teach spatial sense.  It is experienced through living in the world and experiencing it as a geometric space!  It involves talking about the world with geometry words – being able to describe and analyze the way our lives our shaped by geometry.

Think about your current curriculum. In what ways do you develop spatial reasoning? What types of rich experiences with nature, art and architecture do you provide for your students?  What might you add?  What can be “in live time” and what can be done “virtually?”  How does it look different across the grade levels?  Can everyone who teaches some aspect of geometry describe the big ideas and the differences between building content knowledge and building spatial sense?  What types of PD will help?  Just a few things to think about.

In the next few posts I will take a look at the teaching and learning of geometry and the critical areas named in the CCSS geometry domain across the grade levels.

Happy Mathing,

Dr. Nicki

References:

Van De Walle, J & Lovin,L (2006). Teaching students-centered mathematics. NY:Pearson.

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