Other
MAE102K Assignment 2
- Course
- MAE102K (MAE102K)
- Institution
- University Of South Africa (Unisa)
MAE102K Assignment 2 2020.
[Show more]
Content preview
Name: Rolize van TonderStudent number: 63238233
MAE102K Assignment 02
Unique number: 712516
Due date: 8 May 2020
, Question 1
1.1) According to Van Hiele’s theory, learners develop through levels of geometrical
thought. It begins with the most basic level where children display a Gestalt-like
visual approach and then progresses to increasingly advanced levels of description,
analysis, abstraction, and proof. It states that learning is a discontinuous process
and for learners to function sufficiently, they must have acquired most of the previous
level. Another characteristic of this theory is that each level has its own language.
This means that two people that function on different levels cannot understand each
other, even if they are uttering the same sentences.
1.2) Level 3: Formal deduction
The target of this level is the relationship between properties of geometrical objects.
Learners can establish theorems within an axiomatic structure. They can restructure
the differences among undefined terms, definitions, axioms, and theorems. This level
enables learners to construct original proofs. The result of their reasoning is the
establishment of second-order relationships.
Level 4: Rigour/mathematical
This is the highest level of Van Hiele’s theory. The target of this level is deductive
axiomatic systems for geometry. Learners reason about mathematical systems.
They are now capable of studying geometry in the absence of reference models, and
they can reason by manipulating geometric statements. The result of their reasoning
is the establishment, elaboration, and comparison of geometrical axiomatic systems.
1.3) 1.3.1) At level 0, learners will categorise shapes according to what they look
like. They will say something is a parallelogram because it looks like a parallelogram.
They will distinguish between different shapes, not by their properties, but by the way
they look.
1.3.2) At level 1, learners can recognise shapes according to their properties, for
example a parallelogram’s opposite sides are congruent. They will see the properties
of a shape in isolation and without any relationship with each other. For example,
they will say that all rectangles are parallelograms, but without reason.
1.3.3) At level 2, learners can see the relationships between shapes. They know the
requirements for a shape to be identified. Thus, they know that all rectangles are
parallelograms because they understand that all the same properties are included in
that definition. For example, that the diagonals of both a parallelogram and a
rectangle bisect each other.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller rolize3142. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R80,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
52355 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now