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, significant gaps in the construction of geometric knowledge have come into existence, leading to geometry teaching with a variety of disconnected lesson topics (such as sightlines, projections, naming figures).
What?
In this part of the project we aimed to make geometry teaching meaningful again. After all, geometry is a rich subject that supports students practice building correct reasoning. And it’s especially the practice of these reasonings that benefit the development of mathematical reasoning, including computational thinking.
With what?
The development of classroom materials is 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 geometrical topics are related to the answers to these 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 a 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’ 
More information: Van basisonderwijs naar secundair onderwijs – Uitwiskeling
How?
In the development of the material, we have strived for richness of content and sobriety in form. Consequently, teacher and students can both work with the same learning materials. The materials are structured as follows:
 Orientation: preexistent knowledge, subject knowledge, future knowledge.
 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 have chosen 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 knowledge. 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)
Learning material: Geometric objects
Planar figures
The planar figures and their properties are being studied. This addresses the questions ‘which figure is it?’ and ‘what are the properties of this figure?’.
Situation
The material is suitable for students in the third grade of primary education/group 7 and 8 (about 11 or 12 years old). It can also be used in the first year of secondary education. At that time, students are in the process of acquiring level 3 of Van Hiele’s theory.
Insights

 formulating meaningful definitions
 classifying figures
 justifying properties of figures with informal arguments
 building simple if … then … reasonings
Practice
The assignments are arranged in three sequences. Series 1 is close to understanding and acquiring the basic insights. Series 2 contains indepth tasks. Series 3 contains challenging assignments for students who acquire the material quickly.