Van Hiele Model of Geometric Thinking
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Questions and Answers

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 main characteristic of a 'free orientation' activity?

    <p>Students solve complex tasks independently</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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