Learning takes shape: Big Ideas of geometry & spatial relations

by Lisa Ginet

The EME Project’s May professional development workshop provided a first look at the Big Ideas of Geometry: Locations, Directions, and Movement. The day began with an obstacle course that required teachers to step over the line, between the chairs, around the table, and under the bridge, providing a fun framework for the rest of the day.

Next was a read-aloud of Rosie’s Walk by Pat Hutchins, done without showing the pictures so the listeners could draw their own maps. Teachers noticed that whether the representations of Rosie’s path looked circular or more rectangular, all of the paths were closed. That means they ended at the same point they began, creating a two-dimensional shape. This initiated what became a full day of observations concerning basic geometric understanding.

As they explored the Big Ideas of transformation, visualization, and spatial reasoning, a variety of manipulatives were used to construct Rosie’s chicken coop. Each group had a recorder to take notes on the kind of mathematical language the builders use, for example, longer, triangle, wedge, thin, pillar, cube, pyramid. When the chicken coop was complete, each group member made a “blueprint” on paper from whatever angle or perspective they chose. Some found that it was amazingly difficult to move back and forth from three dimensions to two dimensions.

Completing the same assignment with different materials allowed teachers to see the different opportunities and challenges presented by each type of material. For example, Magna-Tiles make the assignment relatively easy since each tile is essentially a large shape, or face, that connects magnetically to the edges of the others. This proves ideal for building things like floors and walls. TinkerToys, on the other hand, emphasized the vertices or edges of each shape and required more imagination (as well as dexterity!) to complete the task. While the Rosie’s Walk assignment is far too difficult for young children, it served to remind teachers about the space and shape learning that only blocks can provide, the language we use to describe shape and space, the difficulties of visualization in both two and three dimensions, and the distinct characteristics of different kinds of materials. It was very clear that everyone had to consider the geometric big ideas of visualization and spatial reasoning, as well as shape.

Finally, teachers learned how to play the Block-Stacking Game, in which a teacher facilitates children taking turns stacking blocks as high as they can, using language about spaces and shapes to talk about why some blocks stack more easily than others. When teachers take this game and others back to their classrooms, they will be applying the Big Ideas about Geometry & Spatial Relations that they explored at Erikson Institute.


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