Learning about the Van Hiele levels in my grad class right at the start of the school year once again got me thinking about how I can assist my high school math students to perform at a higher level. With the implementation of Common Core and the looming SBAC assessments, math teachers are feeling the pressure now more than ever to ensure that our students are able to think critically, reason logically, and problem solve effectively. Basic comprehension and limited mathematical skills will in no way be enough when it comes time for mandated testing (nor should it!). I am realizing quickly that not only must we work harder, we also have to work smarter. This means understanding how our students learn.
The concept of Van Hiele levels follows the common educational theme of progressive levels of thinking. What makes it especially useful is that it is specific to geometry! Bloom’s Taxonomy, which seemed to be a hot topic during my undergraduate career, includes the following levels: Remembering, Understanding, Applying, Analyzing, Evaluating, and Creating. The more recent focus since our transition to the Common Core has been on Webb’s Depth of Knowledge (DOK), which includes Recall (level one), Skill/Concept (level two), Strategic Thinking (level three), and Extended Thinking (level four). Both models can be applied to all subject areas, and both mean basically the same thing. Now consider the Van Hiele levels: Visualization, Analysis, Abstraction, Deduction, and Rigor (as outlined in Marguerite Mason’s article). These levels can easily and directly be related to the Geometry Common Core State Standards.
Having Van Hiele in mind will help me to apply Webb’s DOK in my Geometry classes this year and to identify the levels at which my students are performing. I have only taught Geometry once prior to this year (as a sophomore-level course), and in my experience most students came in with Visualization and Analysis skills. Bright students picked up Abstraction, but Deduction was a struggle for almost all of my students. This year, my Geometry students will primarily be freshman. They will not have taken Algebra 1 yet, and I am interested to see if that impacts their capabilities or if my observations remain largely the same. I am hoping to develop strategies and activities that will push my students to use Abstraction and Deduction on a regular basis, so that eventually it comes naturally to them.
The concept of Van Hiele levels follows the common educational theme of progressive levels of thinking. What makes it especially useful is that it is specific to geometry! Bloom’s Taxonomy, which seemed to be a hot topic during my undergraduate career, includes the following levels: Remembering, Understanding, Applying, Analyzing, Evaluating, and Creating. The more recent focus since our transition to the Common Core has been on Webb’s Depth of Knowledge (DOK), which includes Recall (level one), Skill/Concept (level two), Strategic Thinking (level three), and Extended Thinking (level four). Both models can be applied to all subject areas, and both mean basically the same thing. Now consider the Van Hiele levels: Visualization, Analysis, Abstraction, Deduction, and Rigor (as outlined in Marguerite Mason’s article). These levels can easily and directly be related to the Geometry Common Core State Standards.
Having Van Hiele in mind will help me to apply Webb’s DOK in my Geometry classes this year and to identify the levels at which my students are performing. I have only taught Geometry once prior to this year (as a sophomore-level course), and in my experience most students came in with Visualization and Analysis skills. Bright students picked up Abstraction, but Deduction was a struggle for almost all of my students. This year, my Geometry students will primarily be freshman. They will not have taken Algebra 1 yet, and I am interested to see if that impacts their capabilities or if my observations remain largely the same. I am hoping to develop strategies and activities that will push my students to use Abstraction and Deduction on a regular basis, so that eventually it comes naturally to them.
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