6-C-2

What level(s) of Bloom’s Taxonomy most closely align with the level(s) of the Van Hiele Model? Justify your thinking.

Level 0 in the Van Hiele Model aligns with Bloom’s Knowledge and Comprehension category, because both levels require identifying, comparing and naming.  Students are merely required to recall  information.

Level 1 in the Van Hiele Model aligns with Bloom’s Application and Analysis categories, because both levels require students to analyze and differentiate to determine relationships amongst attributes.  Students are required to make discoveries.

Level 2 in the Van Hiele Model aligns with Bloom’s Analysis and Synthesis  categories, because both levels require students to analyze and research to formulate arguments.   Students are required to make predictions and formulate arguments, based on their previous discoveries.

Level 3 in the Van Hiele Model aligns with Bloom’s Synthesis category, because both levels require students to test proofs and formulate an understanding of geometric ideas.

Level 4 in the Van Hiele Model aligns with Bloom’s Evaluation category, because both levels require students to assess, argue and conclude.  Students are required to create and compare their own theorems, and implement a sophisticated level of thought.  

“How can you use the Van Hiele levels to help students learn mathematics?”

I can use the Van Hiele Model to help students learn mathematics, because the Van Hiele Model clearly indicates what students should master at each level; thus, I can implement the appropriate activities according to students level of development.  Since the model provides the opportunity for students to engage in discovery-based learning, students will gain a better understanding of geometric concepts, and a foundation is laid for the next level of learning and thinking.  The model can definitely be used to ensure that students progress beyond a basic, superficial understanding of geometric thinking.

Develop additional questions that you could ask students if you were to use this lesson in your classroom.

Knowledge: Define area & perimeter.

Comprehension: Predict what would happen to the perimeter if you were to place tiles in the corners.

Application: Is it always true that the corner tiles add no units to the perimeter?  Develop a rationale.

Analysis: Compare and contrast the area & perimeter when tiles are placed in the corner, as opposed to any other place.  What do you notice?

Synthesis: Construct a different design that has a perimeter of 16.  Does your design have fewer or more tiles?  Explain why.

Evaluation: Assess the discoveries you made as a result of engaging in this activity.  Were some more beneficial that other?  Decide which discover was the best.  Justify your answer.

 

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