Geometry
Why?
Consecutive curriculum reforms have depreciated geometry over the past decade. Several geometry topics have given way to topics like data processing, statistics, and computational thinking. As a result, there are significant gaps in the construction of geometric knowledge. This leads to geometry lessons with a variety of disconnected lesson topics (such as sightlines, projections, naming figures).
What?
This part of the project was aimed at making geometry teaching meaningful again. After all, geometry is a rich subject with which students can practice building correct reasoning. And especially practicing this way of thinking would benefit the development of mathematical reasoning, including computational thinking.
With what?
The development of classroom materials was based on two pillars:
 Coherence in geometry concepts as visualized in the tree structure of the mathematical perspective. Geometry education can start from four major questions:
 Which figure is it?
 What kind of properties does it have?
 How does it transform?
 Where is it?
All different geometry topics covered, can be addressed from, and contribute to finding an answer to one or more of the above questions.
More information: https://www.universiteitleiden.nl/binaries/content/assets/iclon/onderzoek/watisechtdemoeitewaardomteonderwijzen.pdf
 Geometric thought levels as decribed by the Van Hiele theory, which postulates that students pass through different types of thinking when learning geometry. This theory was used as guideline for the consecutive levels of abstraction in the development of geometry in learners.
Level  Description  Students’ statements 
1. Visualisation  Students recognise mathematical figures visually by comparing them with a prototype. Properties of figures are not recognised at this level. A square tilted on one corner is often called a rhombus, even when the square is tilted before their eyes.  This figure is a rectangle because it resembles a door. 
2. Analysis  Students see figures as a collection of properties. They can recognise and name properties but see no relation between them. When students describe a figure, they will name all properties without distinguishing between necessary and nonnecessary properties. Students have no sense of what constitutes ‘sufficient’ properties to describe a figure. They also don’t see relations between different figures 
A square is not a rectangle.

3. Abstraction  Students see relations between properties and between figures themselves. They can give meaningful definitions and formulate informal arguments to support their opinion. They see relations between different classes of figures. They can hierarchically order figures. They can build simple ‘if… then…’ reasoning. The role and meaning of formal deduction is still unknown to them.  A square has all properties of a rectangle and is therefore a rectangle. 
4. Order  Students can construct proofs. They understand the role of undefined concepts, definitions, axioms, and theorems. They recognise that to check the correctness of a theorem, it is not enough to check very many examples, but you need to give a ‘proof’ by reasoning. They grasp the meaning of a more rigorous and logical system into which the properties of the figures fit. They can work with abstract statements and make decisions based on logical reasoning rather than intuition.  I can prove that if the diagonals of a quadrilateral intersect in the middle, the quadrilateral is a parallelogram. 
5. Mathematical system  Students understand the formal aspects of deduction such as the drawing and comparison of mathematical systems. They can handle indirect proofs and proofs by contraposition, and they are ready for nonEuclidean geometry.  ‘A square is a rectangle’ is equal to ‘a quadrilateral that is not a rectangle is also not a square’ 
How?
In the development of the material, we strove for richness of content and sobriety in form. Therefore, the teacher and students can both make use of the same learning materials. The structure of the material is as follows:
 Orientation: what are you leaning on, what are going to learn, where are you going to.
 Starting task: gaining insight into which knowledge is missing.
 Knowledge part: the insights explained.
 Practice part: many assignments to acquire, deepen and analyse the knowledge.
We chose to leave the approach (form of work, grouping, selection of assignments…) entirely up to the teacher. He determines what his pupils need to acquire this material. The material is suitable for a series of five to ten lessons.
More information: Het mooie wiskundige bouwwerk als springplank voor de leraar – Volgens Bartjens (volgensbartjens.nl)