It is important to create physical and social environments that promote mathematical thinking and authentic experiences that reflect a constructivist approach. This can be done through mathematical invitations consisting of a wide range of ‘loose parts’. In these images below, you can take a look at the mathematical invitation my group and I formed.
Although it was geared more towards number sense, it offered many extensions and opportunities that touched on geometry through the wide range of materials from our everyday lives. For instance, shapes can be formed through using popsicle sticks and can be drawn in the salt tray. The rectangular frames could be filled with nature objects, leading educators to prompt children through asking questions such as “how many pinecones did it take to fill the rectangle?”. Nature objects such as rocks can also be used to construct shapes, as we can see on the blog “Racheous”. Here we see the use of line art as well, making it more challenging to construct the shape as the placement of the corners must be acknowledged. This can be geared towards children who have mastered basic shape construction without the line art.
I highly suggest that all educators try forming mathematical invitations as all of these open-ended materials can result in fascinating and creative play experiences that trigger mathematical thought.