A head start in the early grades is the only way to make sure students have a better van Hiele level when they enter high school geometry. ![]() Partners will need to be using the same level of vocabulary to work together effectively.Īs it goes with most learning, the earlier the better. They will not fully understand, and this can prevent them from ever achieving the next phase / level.Įven students of two different levels working together may have a hard time communicating about the geometric properties at play. Those who fall behind will only be able to memorize and scrape by. Always use correct terminology, but be aware that if you do not support your students with explicit vocabulary instruction to be sure you are all understanding the terms as you use them, you’ll lose some students. Adding a series of experiences that allows students to interact with geometric figures helps them to move on to the next level.Īnother thing to keep in mind is that all the language and vocabulary that you use has to match the particular student level. They realize that axioms are more arbitrary than concrete, and therefore can finally extend their thinking to accept non-Euclidean geometry.Ī student’s level is based on his/her experiences, not age. At the highest level, students are able to think like a mathematician. Students at the higher level know how axioms, theorems, and converses operate enough to extend the properties. Eventually, they then progress to the point of making deductions. They get to the point of analyzing a figure or shape. The levels are based around the idea that students can understand geometry visually at a young age, then from there develop the concepts behind the properties to the point that they can first just identify, then think more abstractly about the principles. Even though there isn’t much we can do about this, knowing that it is a factor is important. That means that if a student hasn’t reached that level of cognitive development, then it will be pretty hard for them to understand geometry. The problem with this is that some students haven’t reached that stage yet, since it can span from adolescence into early adulthood (ages 11-20). An individual needs to achieve the formal operational stage in order to understand, formally reason and build proofs. Jean Piaget and his theories on cognitive development help shed some light on this. Students without basic knowledge or the ability to back up statements with reason are easily set up to fail in class.Įven when notions of geometry are introduced early, some students just aren’t ready on a developmental level. ![]() Learning complex concepts like proofs require a much higher level (level 4 of 5) and most students enter the class at a level 2 or 3. It is based on the doctoral work of husband and wife, Dina van Hiele-Geldof and Pierre van Hiele.Īccording to their model and other research, students enter geometry with a low Van Hiele level of understanding. The Van Hiele Model is a theory which describes how students learn geometry. The Van Hiele levels help us get a better grasp on this lack of understanding that too many students experience. While some students can pick it up easily, others are left grasping at straws of understanding. ![]() More than that, because geometry concepts aren’t being introduced early, there are always some very confused students. Teachers aren’t able to spend the amount of time needed to truly cover all levels of understanding needed to be successful. Students need to know how to explain, prove, and show why long before they are in high school geometry. Of course the specific geometry concepts wouldn’t be on the same level, but introducing the pattern of thoughts earlier is better. If students were introduced to simple informal proofs and required to reasonably justify statements, they would be far more prepared for the formal proofs to come. This helps lay the groundwork for geometry as well as other subjects in high school. Students need to learn how to start proving and explaining why things occur before they hit high school level classes. It starts in elementary and middle school. The foundation for learning geometry doesn’t start in high school.
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