4-1 The Van Hiele Model

August 2, 2010

Being unfamiliar with the Van Hiele model I spent a good amount of time looking for a media piece that I felt gave me a good description of what it was. I ended up going to Wikipedia (I usually don’t use Wikipedia for my information but I decided to give it a try) where I was finally let in on the secret of Van Hiele. The idea that Geometry is broken down into different levels of understanding makes it very clear why so many people have trouble with what seems to me to be an easy topic (Of course I say that as a math teacher, so take it with a grain of salt). It also made me think back to last weeks topic of Linearity and the ways in which we teach math in general. There was some discussion last week about the fact that math needs to be taught in a linear fashion, i.e. students must understand certain ideas before moving on to more complex problems. While it seems that some of our discussion harkened back to Dan Meyer’s piece on being less helpful, I find this weeks topic reiterating the thought that math needs to be taught in a very structured, straight forward way. The Van Hiele model exemplifies this mode of thinking by layingout a framework for the steps to follow in learning geometry, but I think the Phases of Learning could be applied, with a few tweaks, to just about every subject in math. ( just a friendly reminder of the Phases of Learning: Information acquisition, Guided orientation, Explication/Reflection, Free orientation, and Integration)

The piece that best helped me to understand the Van Hiele Model was a Mindmap I found online. While it still left me with a few questions, I really liked the way it laid things out and categorized the information. There was a very clear distinction between the levels, properties, and phases of learning. I know this might not be exactly what was asked for in terms of a media piece, but it was by far the most helpful to me.

Now, to address the questions in the task grid. The levels apply to individual students as a way of assessing where they stand in the continuum of understanding geometry. It also applies to the type of tasks being presented to the students. A student at a certain level in the Van Hiele model will be unable to answer a question based in a higher level of the Model. I think to try and apply the Model to a group of students would be irresponsible because each student will be in a different place in their understanding of each level.

Because of the linear way the Van Hiele model works a person can not be on two different levels at the same time. Since each level builds on the previous one, there is a need for a complete understanding of a level to move on and be successful at the next.


One comment

  1. Peter,

    I found the same Mindmap page! I thought it did a great job of putting more context into the rather dry and abstract levels of thinking required for each level of understanding. The Mindmap did a good job of placing the model within the structure of the way that learning occurs.

    I agree also that applying the van Hiele’s mode to a group of students would not be useful. Since every student may have a different level of understanding, finding a common ground for the group would require a lot of work. Using it when assessing and then modifying curricula for individual students can provide a good method for moving them along the levels.

    Finally, I don’t agree that a single person has to remain at the same level inside the model. I don’t have any evidence to support this. However, I trust my gut feeling that some students have a deeper understanding of some concepts than others. And as a result, they could be on different levels.

    Do you think that the levels apply directly to specific concepts in geomerty, like congruence, similarity, correspondence, symmetry and the like? Or do the levels generalize the overall understanding of all principles together? The model is very interesting and I think provides a great source of debate. And from this point of view, I think it is very useful.

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