Presentation on the theorist Van Hiele. Done by Kenique Walker, Romaine Livingston, Jameilia Richards, Shawn Taylor and Rohan Lewis

2. Biography of Pierre Van Hiele
Van Hiele was famous for his theory that describes
how students learn geometry, he was born in 1909
and died November 1,2010. This theory came about
in 1957 when he got his doctoral at Utrecht
University in Netherlands. He was also a publisher,
he published a book titled Structure and Insight in
1986 which further describe his theory. The theory
came about by two Dutch educators, Diana Van
Hiele-Gelof and Pierre Van Hiele (wife and
husband).

3. Critical examination of how students
learn based on Van Hiele’s theory
Based on Diana Van Hiele-Gelof and Pierre Van
Hiele theory there are five levels to describe how
students learn or understand geometry. These are:
 -Level 0: Visual
 -Level 1: Description
 -Level 2: Relational
 -Level 3: Deductive
 -Level 4: Rigor

4. Level 0: Visual
 This level begins with 'nonverbal thinking'. Shapes
are judged by their appearance and generally
viewed as 'a whole', rather than by distinguishing
parts. For example; Student might just look at a
rectangle and identify it has a "door shape." They
would identify two shapes as congruent because
they look the same, not because they shared the
same properties.

5. Level 1: Descriptive/Analytic
This is where students develop the ability to recognize
shape by their characteristics. For example, the teacher
may asked the student what is a rectangle.
Spontaneously, they will reply by saying “it is a shape
with two pair of equal side and four right angles.”
Students at this level still do not see relationships
between the classes of shapes.

6. Level 2: Abstract/Relational
This is where Students are able to form theoretical
definitions, distinguish between necessary and sufficient
sets of conditions. At this stage student can group shapes
by properties. For example student may say a “square is a
rectangle, but a rectangle is not a square.”

7. Level 3: Deduction
At this stage students are able to prove theorems
formally within a logical structure. They are able to apply
what they already know to explain the relationships, and
to formulate definitions. For example, they could explain
why all squares are rectangles and why are rectangle not
classified as a square.

8. Level 4: Rigor
Students understand how different geometrical systems
relate and have the knowledge to create proof of why are
certain rules applicable in the geometrical system.
Example in sphere geometry lines are drawn on a sphere
rather than anything else. This is because it is sphere
geometry, so the lines must be drawn on a sphere.

9. Example of how to demonstrate the
thinking process that children use in
learning math base on his theory
Van Hiele strongly believed that using his theory in
Geometry it would improve the student learning. For
example in geometry at the visual level the teacher could
draw some triangles on the board, so the students would
know what a triangle looks like.

10. How Hiele ‘s theory contribute to
Mathematics education and it
application to the Jamaican classroom?
This theory contributes greatly to Mathematics Education since it
is a Geometry theory and most students find Geometry difficult.
This theory can be applied through five phases.
 Phase 1- (Information/ Inquiry): At this stage teacher introduce a
new idea and allow student to work with it. This new idea is
normally easier to understand than the original but it means the
same. So students get a better understanding. Example:
Alternate angles are equal but she could say ‘Z’ angles are equal.
So students will understand easier.

11.  Phase 2-(Guided or Direct Orientation): At this stage
teacher give lots of work to students for practice so
they get aquatinted with the concepts and learn it well.
 Phase 3-(Explication): At this stage teacher told
students to, in their own word describe what they
learn using mathematical terms. Example: Reflection
writing.
 Phase 4-(Free Orientation): This is where teacher
allow students to apply relationships they learn to
solve harder problems. Example: They learn from a cxc
and allow using the same principles learn to solve
questions from a cape book.

12.  Phase 5-(Integration): This is where students reflect on
what they learn and find easier way to do what they learn.
These phases when perform will build geometry students
understanding therefore build better students including
Jamaica.

13. Review Session
What year did Hiele’s theory come about?
a) 2010
b) 1940
c) 1957
d) 1909
How many stages are there in Hiele’s theory?
a) 4
b) 5
c) 6
d) 4.5

14. What level do you think we are in Hiele’s theory and
why?
a) Level 1
b) Level 2
c) Level 3
d) Level 4