Polygon Properties: What is Possible? - Article

This article had a lot of information in it about all different types of polygons and geometric shapes. There are three levels of geometric thinking (visual, descriptive, and informal deduction) that are developed and strengthened over the grade school years. Level 0, visual level, the students are stating what a shape is and use nonverbal usage. Students make their discussion and thoughts heard aloud based on what they see and have seen in the past. Level 1, descriptive level, the students will expand on what a shape is and how it is categorized. The example in the article states, "a triangle is no longer a triangle because it looks like one, but because it is a closed figure that has three sides and three angles." This level shows how the students knowledge on the shape and knowledge from the class has helped them. Level 2, informal deduction, students are able to come up with a logical property for why a shape is in the category it is placed in. This was interesting to me, because I never knew that these levels existed. But I like how I they build on each other and promote higher thinking.

One activity that was presented in the article was, Shape Sorting. This activity gave each group of students a bag full of different shapes both regular and irregular. Then the students had to sort them, using any sorting technique they wanted. It gave the students the control in the sorting process. Once they were sorted in the first area, the students would sort them again from the groups they were originally in. I liked how the students each had a different view on what they thought the next sorting area should be. This activity shows so many opportunities to talk about and describe shapes of all kinds.

I liked how with the Shape Sorting activity the teacher made connections to the students about what was happening and what they needed to get done. The students would create their own shape, of any kind, and have to sort it into one of the groups that were created in the activity. They also had to explain why the shape was in this category. (Many process standards were being met in this activity!)

Another activity that was discussed was Riddle Activities which was something new to me, but I found that it was a good way to learn about shapes and shape types. The students were given riddles about a shape and had to determine which shape it could be. The students used Geoboards to show what the shape could be and to show "proof" of an answer. Riddles started out simple and sometimes obvious, but become generally harder and more difficult. The students would use trial and error to determine the shape, and in some cases an answer was not found. Students gradually found out that not every riddle could be solved. I like how this activity has the students working and thinking, even if the riddle is not solved.

Robichaux, R.R. & Rodrigue, P.R. (2010). Polygon properties: What is possible? Teaching children mathematics 16 (9), 524-531.