Biography of Pierre Van HieleVan 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).

Critical examination of how students learn based on Van Hiele’s theoryBased 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

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 thesame properties.

Level 1: Descriptive/AnalyticThis 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.

Level 2: Abstract/RelationalThis 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.”

Level 3: DeductionAt 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.

Level 4: RigorStudents 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.

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.

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.

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.

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.

Review SessionWhat 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

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