Levels of Geometric Thinking (Pierre van Hiele)
Levels of Geometric Thinking (Pierre van Hiele) Level 1: Visual level
Students at this level recognize figures by their appearance. For example they may say that the shape on the left below is a square and the shape on the right is a diamond ...."because it looks like a...."
Level 2: Descriptive/Analytic
Students at this level recognize/analyze figures by their properties or components. For example, students will describe figures above as squares because they both have 4 sides, 4 right angles, opposite sides equal....and as many other properties as they know about squares.
Level 3: Abstract / Relational
Students at this level can distinguish between necessary and sufficient conditions for a concept; they can also form abstract definitions, and classify figures by elaborating on their interrelationships. For example, a student at this level may define a square as a rectangle with consecutive sides congruent. Or students at this level may argue that the sum of the measures of the interior angles of a pentagon is 3 times the sum of the measures of the angles in a triangle and 4 times the sum of the measures of a triangle for a hexagon by using a picture and reasoning why the angles of the triangles account for all the angles of both figures.
Level 4: Formal Deduction
Students establish theorems within an axiomatic system. They recognize the difference between undefined terms, definitions, axioms, and theorems. They are capable of constructing original proofs.
Level 5: Mathematical Rigor
Students understand the relationship between various systems of geometry. They are able to describe the effect of adding or deleting an axiom on a given geometric system. These students can compare, analyze, and create proofs under different geometric systems.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- revision 7 angle and circle properties
- levels of geometric thinking pierre van hiele
- geometry quick guide 1 angles
- sat math checklist facts and formulas ivy global
- name geometry polygons n 2 180 360
- two angles that are both complementary to a third angle
- geometry vocabulary word wall cards
- kumar online class
- lines and angles
- geometry postulates and theorems tutoring 101
Related searches
- benefits of positive thinking worksheet
- list of critical thinking questions
- power of positive thinking quote
- area of geometric shapes
- thinking of vs thinking about
- examples of strategic thinking competencies
- surface area of geometric shapes
- area of geometric shapes formulas
- causes of not thinking clearly
- the power of positive thinking book
- costa s levels of thinking and questioning
- finding area of geometric shapes