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# Van Hiele Model of Geometric Thinking

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@CreativeNonagon

### What is the main focus of the van Hiele theory?

• The difficulties of learning geometry
• The importance of geometric thinking
• How to teach mathematics effectively
• How young people learn geometry (correct)
• ### What are the five levels of geometric thinking according to the van Hiele model?

• Basic, intermediate, advanced, complex, and expert
• Teaching, learning, understanding, applying, and analyzing
• Geometry, algebra, calculus, statistics, and trigonometry
• Visualization, analysis, abstraction, formal deduction, and rigor (correct)
• ### Why did Pierre van Hiele and his wife Dina van Hiele-Geldof develop the theory?

• Because they wanted to become famous
• Because they were interested in geometry
• Because they had personal experience with difficulties their students had in learning geometry (correct)
• Because they were good at mathematics
• ### Where was the research based on the van Hiele theory carried out in the 1960s?

<p>In the Soviet Union</p> Signup and view all the answers

### What was the outcome of the research based on the van Hiele theory in the Soviet Union?

<p>A new geometry curriculum was designed</p> Signup and view all the answers

### Who conducted large studies on the van Hiele theory in the late 1970s?

<p>American researchers</p> Signup and view all the answers

### What is the primary focus of the Van Hiele theory in geometry?

<p>Understanding geometric figures through visualization</p> Signup and view all the answers

### What is the characteristic of students at Level 0 of the Van Hiele theory?

<p>They recognize geometric figures by their shape</p> Signup and view all the answers

### At which level of the Van Hiele theory do students start analyzing properties of geometric figures?

<p>Level 1 Analysis</p> Signup and view all the answers

### How many levels of thinking or understanding in geometry are proposed by the Van Hiele theory?

<p>5 levels</p> Signup and view all the answers

### What is the characteristic of students at Level 1 of the Van Hiele theory?

<p>They analyze properties of geometric figures but do not see relationships between them</p> Signup and view all the answers

### What was the influence of the Van Hiele theory on American educational standards?

<p>It influenced the NCTM Standards and Common Core State Standards</p> Signup and view all the answers

### What is the primary goal of the Guided or directed orientation stage?

<p>To guide students to discover the properties of a concept</p> Signup and view all the answers

### What is unique about how teachers introduce terminology in the van Hiele model?

<p>Terminology is introduced after students have become familiar with the concept</p> Signup and view all the answers

### What is the main objective of the Explanation or Explication stage?

<p>To help students formulate their discoveries</p> Signup and view all the answers

### What do teachers use to guide students from one level to the next in the van Hiele model?

<p>Clear explanations</p> Signup and view all the answers

### What do students do during the Information or Inquiry stage?

<p>They start discovering the structure of the material</p> Signup and view all the answers

### How much time does the process of guiding students from one level to the next typically take?

<p>Tens of hours</p> Signup and view all the answers

### What is the primary goal of the 'integration' phase?

<p>To summarize what has already been learned</p> Signup and view all the answers

### What is the importance of definitions in understanding a concept, according to Pierre van Hiele?

<p>Definitions are only possible if one knows the thing that is to be defined</p> Signup and view all the answers

### What was the purpose of the American study based on the van Hiele theory?

<p>To describe and predict the performance of students in secondary school geometry</p> Signup and view all the answers

### How many students were involved in the American study?

<p>2699 students</p> Signup and view all the answers

### What is the role of the teacher during the integration phase?

<p>To give students an overview of what they have learned</p> Signup and view all the answers

### What is the reason why students often do not master the material in traditional teaching methods?

<p>Teachers only focus on the Integration phase.</p> Signup and view all the answers

### Who is the professor that the author thanks in the acknowledgment?

<p>František Kuřina</p> Signup and view all the answers

### What is the aim of the author's own thesis?

<p>To adapt Czech textbooks and exams to the van Hiele theory.</p> Signup and view all the answers

### What is the title of the yearbook that Crowley's work is published in?

<p>Learning and Teaching Geometry, K–12</p> Signup and view all the answers

### In which year was the work of De Villiers published?

<p>2010</p> Signup and view all the answers

### What is the name of the publisher of Mason's work?

<p>MacDougal Litteil Inc.</p> Signup and view all the answers

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