Developing geometric thinking van hiele levels
Sponsored Links
This presentation is the property of its rightful owner.
1 / 18

Developing Geometric Thinking: Van Hiele Levels PowerPoint PPT Presentation


  • 329 Views
  • Uploaded on
  • Presentation posted in: General

Developing Geometric Thinking: Van Hiele Levels. Mara Alagic. Van Hiele: Levels of Geometric Thinking. Precognition Level 0: Visualization/Recognition Level 1: Analysis/Descriptive Level 2: Informal Deduction Level 3:Deduction Level 4: Rigor. Van Hiele: Levels of Geometric Thinking.

Download Presentation

Developing Geometric Thinking: Van Hiele Levels

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Developing Geometric Thinking: Van Hiele Levels

Mara Alagic


Van Hiele: Levels of Geometric Thinking

  • Precognition

  • Level 0: Visualization/Recognition

  • Level 1: Analysis/Descriptive

  • Level 2: Informal Deduction

  • Level 3:Deduction

  • Level 4: Rigor

Mara Alagic


Van Hiele: Levels of Geometric Thinking

  • Precognition

  • Level 0: Visualization/Recognition

  • Level 1: Analysis/Descriptive

  • Level 2: Informal Deduction

  • Level 3:Deduction

  • Level 4: Rigor

Mara Alagic


Visualization or Recognition

  • The student identifies, names compares and operates on geometric figures according to their appearance

  • For example, the student recognizes rectangles by its form but, a rectangle seems different to her/him then a square.

  • At this level rhombus is not recognized as a parallelogram

Mara Alagic


Van Hiele: Levels of Geometric Thinking

  • Precognition

  • Level 0: Visualization/Recognition

  • Level 1: Analysis/Descriptive

  • Level 2: Informal Deduction

  • Level 3:Deduction

  • Level 4: Rigor

Mara Alagic


Analysis/Descriptive

  • The student analyzes figures in terms of their components and relationships between components and discovers properties/rules of a class of shapes empirically by

    • folding

    • measuring

    • using a grid or diagram, ...

  • He/she is not yet capable of differentiating these properties into definitions and propositions

  • Logical relations are not yet fit-study object

  • Mara Alagic


    Analysis/Descriptive: An Example

    If a student knows that the

    • diagonals of a rhomb are perpendicular,

      she must be able to conclude that,

    • if two equal circles have two points in common, the segment joining these two points is perpendicular to the segment joining centers of the circles.

    Mara Alagic


    Van Hiele: Levels of Geometric Thinking

    • Precognition

    • Level 0: Visualization/Recognition

    • Level 1: Analysis/Descriptive

    • Level 2: Informal Deduction

    • Level 3:Deduction

    • Level 4: Rigor

    Mara Alagic


    Informal Deduction

    • The student logically interrelates previously discovered properties/rules by giving or following informal arguments

    • The intrinsic meaning of deduction is not understood by the student

    • The properties are ordered - deduced from one another

    Mara Alagic


    Informal Deduction: Examples

    • A square is a rectangle because it has all the properties of a rectangle.

    • The student can conclude the equality of angles from the parallelism of lines: In a quadrilateral, opposite sides being parallel necessitates opposite angles being equal

    Mara Alagic


    Van Hiele: Levels of Geometric Thinking

    • Precognition

    • Level 0: Visualization/Recognition

    • Level 1: Analysis/Descriptive

    • Level 2: Informal Deduction

    • Level 3:Deduction

    • Level 4: Rigor

    Mara Alagic


    Deduction (1)

    • The student proves theorems deductively and establishes interrelationships among networks of theorems in the Euclidean geometry

    • Thinking is concerned with the meaning of deduction, with the converse of a theorem, with axioms, and with necessary and sufficient conditions

    Mara Alagic


    Deduction (2)

    • Student seeks to prove facts inductively

    • It would be possible to develop an axiomatic system of geometry, but the axiomatics themselves belong to the next (fourth) level

    Mara Alagic


    Van Hiele: Levels of Geometric Thinking

    • Precognition

    • Level 0: Visualization/Recognition

    • Level 1: Analysis/Descriptive

    • Level 2: Informal Deduction

    • Level 3:Deduction

    • Level 4: Rigor

    Mara Alagic


    Rigor

    • The student establishes theorems in different postulational systems and analyzes/compares these systems

    • Figures are defined only by symbols bound by relations

    • A comparative study of the various deductive systems can be accomplished

    • The student has acquired a scientific insight into geometry

    Mara Alagic


    The levels are “characterized by differences in objects of thought”:

    • geometric figures

    • classes of figures & properties of these classes

    • students act upon properties, yielding logical orderings of these properties

    • operating on these ordering relations

    • foundations (axiomatic) of ordering relations

    Mara Alagic


    Major Characteristics of the Levels

    • the levels are sequential

    • each level has its own language, set of symbols, and network of relations

    • what is implicit at one level becomes explicit at the next level

    • material taught to students above their level is subject to reduction of level

    • progress from one level to the next is more dependant on instructional experience than on age or maturation

    • one goes through various “phases” in proceeding from one level to the next

    Mara Alagic


    References

    • Van Hiele, P. M. (1959). Development and learning process. Acta Paedogogica Ultrajectina (pp. 1-31). Groningen: J. B. Wolters.Van Hiele, P. M. & Van Hiele-Geldof, D. (1958).

    • A method of initiation into geometry at secondary schools. In H. Freudenthal (Ed.). Report on methods of initiation into geometry (pp.67-80). Groningen: J. B. Wolters.

    • Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of Thinking in Geometry Among Adolescents. JRME Monograph Number 3.

    Mara Alagic


  • Login