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An elementary school mathematics teacher decides to make a 'unit plan' on “Geometrical Shapes”. He writes the following expected learning outcomes.  (i) Recognize various shapes (ii) Differentiate between various shapes (iii) Identify sides, angles and vertices of shapes Which of the following levels of Van Hiele's geometric reasoning is he assessing his students on?

An elementary school mathematics teacher decides to make a 'unit plan' on “Geometrical Shapes”. He writes the following expected learning outcomes.  (i) Recognize various shapes (ii) Differentiate between various shapes (iii) Identify sides, angles and vertices of shapes Which of the following levels of Van Hiele's geometric reasoning is he assessing his students on? Correct Answer Analysis level

Mathematics is not just the study of numbers and statistical data but also studies the different types of shapes, figures, and patterns.

  • In early schooling, the learners began to learn about shapes and try to differentiate various shapes from each other.
  • The students learn according to their level of experience and their individual differences, the age can be different in each stage as they learn at their own pace. 
  • Van Heile's theory provides an insight to the teacher about how the students learn geometry at different levels. It was originated in 1957 given by Pierre Van Hiele and his wife from the Utrecht University in the Netherlands.
  • It helps in describing how the students learn at each level and pass to another level and shapes their learning of geometry at each level of learning.

Key Points 

Van Hiele levels: The Van Hiele levels are described below:

Level 0: Visualization
  • The students can recognize shapes by their whole appearance that should just like the exact shape.
  • They can also compare the figures with their prototypes (exemplar) or everyday things but can not identify the properties of geometric figures.
  • For example, they can compare the shape of a circle with bangles, coins, wheels, etc. but are unable to identify and describe the properties of a circle.
  • They will not be able to recognize the shapes if they are rotated upside down.
  • It belongs mostly to the elementary level of classes.

Level 1: Analysis 
  • Students will learn the functions and parts of a figure and will differentiate between various shapes.
  • They can describe the properties of a figure and recognize the figures with the same properties.
  • For example, they can identify the shapes and describe their properties such as a circle is a closed rounded figure with no corners.
  • It belongs to the upper level of elementary level classes.

Level 2: Abstraction or informal deduction
  • The students will be able to understand the relationships between the properties of a figure.
  • They can take part in informal deductive discussions and can discuss the different characteristics of figures.
  • For example, the opposite sides of a parallelogram are parallel. The opposite sides of a square and rectangle are also parallel which means square and rectangle is also a parallelogram.
  • It generally belongs to the upper elementary classes.

Level 3: Deduction or formal deduction
  • At this level, the students become aware of the more complex geometrical concepts.
  • They can prove an abstract statement on geometric properties to conclude.
  • For example, they can prove that the square is a rectangle but a rectangle can not be a square.
  • It belongs to the higher level of classes where students usually combine a certain set of elements to prove any theorem to draw conclusions or do the evaluation.

Level 4:Rigor 
  • The last level of geometrical learning belongs to the senior secondary and university level of classes.
  • The students are able to compare different geometrical results.
  • For example, the sum of all three angles of a triangle is 180 degrees is compared to the other properties or other results (to find exterior or interior angles of a triangle) related to the triangle to solve geometrical problems.


Hence, it is concluded that the teacher is assessing his students on the Analysis level of Van Hiele's geometric reasoning.

Related Questions

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