What level(s) of Bloom’s Taxonomy most closely align with the level(s) of the van Hiele Model? Justify your thinking.
Van Hiele Level: Concrete– the student identifies, names, compares, and operates on geometric figures
Bloom’s Level: Knowledge/Comprehension– name, define, identify, compare, classify
Van Hiele Level: Analysis– analyzes figures in terms of their attributes and relationships among attributes and discovers properties and rules through observation
Bloom’s Level: Application/Analysis– apply, solve, relate, use, analyze, compare, categorize
Van Hiele Level: Informal deduction– discovers and formulates generalizations about previously learned properties and rules and develops informal arguments to show her or his generalizations to be true
Bloom’s Level: Analysis/Synthesis– analyze, classify, differentiate, develop, combine, predict, propose
Van Hiele Level: Deduction– proves theorems deductively and understands the structure of the geometric system
Bloom’s Level: Synthesis/Evaluation– solutions, solve, predict, formulate, measure, assess, deduct
Van Hiele Level: Rigor– establishes theorems in different postulational systems and compares and analyzes the systems
Bloom’s Level: Synthesis/Evaluation– discuss, formulate, assess, summarize/prioritize, evaluate
“How can you use the van Hiele levels to help students learn mathematics?”
The interaction aspect of the Van Hiele model is very important to student learning. Students develop greater understanding of the content at hand when using social and knowledge interaction. It is important for students to work together in math in order for them to see concepts from a different way of thinking. A deeper understanding of the subject matter turns students away from “parrot math” and helps them to draw their own conclusions about the geometric concepts.
Group Discussion for Pythagorean Theorem
· How does perimeter compare and contrast to area?
· What are the parts of the Pythagorean Triplet?
· How would you create a Pythagorean triplet of your own?
· Do you agree that a right triangle can have the measurements of 4 units, 5 units, and 6 units? Justify your answer.