Example Turned Into Non-example

Recently for an assignment I had to find an activity that could be used while teaching about shapes and their attributes. I found these ideas and thought they were cute and fun, I fell into a trap that a lot of teachers do.

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After watching thisĀ Doug Clements video, I realized how big of a trap it really was. I understand the desire to present your students with cute and fun activities but they need to be accurate and beneficial for the students. In the first section of the picture above, if you are going to compare a shape with a real life object, the object MUST be a true representation of that shape. Comparing a triangle to a piece of pizza or pie would not be accurate as one side is curved, I’ve never seen a triangle with a curved side before. Just like it wouldn’t be wise to compare a circle to a ring or sucker; I’ve also never seen a circle that has a growth on it before. I think a good way to incorporate a sheet that has poor examples like the ones I’ve just mentioned would be to hand it out to your class and tell them that the objects that are on the sheet cannot be classified as shapes. Have the students use their knowledge of shape attributes and use critical thinking to determine why the objects aren’t shapes. At first this could be very challenging for students especially in lower grades, going through a couple as a whole class would be helpful for the students as well as doing this activity in groups. Group work in this would encourage them to communicate using math vocabulary, they can talk about the attributes a shape has versus the attributes of the object. If you search online for activities there a lot that would not be accurate or suitable to use as good examples to help reinforce an idea or objective, but that doesn’t mean they can’t be useful for teaching. You just have to be clear with your students that they are non-examples and have them use higher levels of thinking when they work through the non-example activity.

Examining the Van Hiele Theory

I never heard of the Van Hiele levels of geometric thought before it was brought up in class. I was intrigued by this theory and was researching it when I stumbled uponĀ this article. The theory makes a lot of sense to me and allows for students to smoothly transition through the stages as their knowledge and abilities grow. A key point made within the article is that the “theory does not explicitly tell teachers how to teach geometry, but can help teachers assess what level their students are working at”. Like many things in the world of education, this does not do the teaching, rather it is a tool that teachers can use to help with their teaching.
As this article was found on a learning disabilities website it was only appropriate that the author of the article showed the connection. The approach that is gone over in detail includes five phases that teachers should incorporate at each level to have more success in aiding the student’s progression through the levels. The phases break each step down and allow the teacher to build upon knowledge in a way that easier and more beneficial for the students while also allowing them to have the most possible success in terms to learning.
The article concluded with eleven strategies for instruction. This was wonderful for me, a “teacher in training” as it allowed me to take the ideas that were discussed and see how they could be brought into the classroom.
After reading the article I am left wondering if similar phases and levels to those of the Van Hiele Theory could be used in other subject areas. I’m sure they can be used in other math subcategories, but I wonder if science or history would follow a similar progression.
Examining the van Hiele Theory: Strategies to Develop Geometric Thought. (n.d.). Retrieved September 16, 2015.