The methodology of this project has been based in:

Van Hiele levels of geometry reasoning

The work of two Dutch educators, Pierre van Hiele and Dina van Hiele-Geldof, has given us a vision around which to design geometry curriculum. Through their research they have identified five levels of understanding spatial concept through which children move sequentially on their way to geometric thinking:


Students can name and recognize shapes by their appearance, but cannot specifically identify properties of shapes. Although they may be able to recognize characteristics, they do not use them for cognition and sorting.


Students begin to identify properties of shapes and learn to use appropriate vocabulary related to properties, but do not make connections between different shapes and their properties. Irrelevant features, such as size or orientation, become less important, as students are able to focus on all shapes within a class. They are able to think about what properties make a rectangle. Students at this level are able to begin to talk about the relationship between shapes and their properties.


Students are able to recognize relationships between and among properties of shapes or classes of shapes and are able to follow logical arguments using such properties.


Students can go belong just identifying characteristics of shapes and are able to construct proofs using postulates or axioms and definitions.


This is the highest level of thought. Students at this level can work in different geometric or axiomatic.

In primary we should work in the three first levels.

Implications of van Hiele for instruction

Geometric taught in the elementary school should be informal and based in visualization, analysis and informal deduction.

Such informal geometry activities should be exploratory and hand-on in order to provide children with the opportunity to investigate, to build and take apart, to create and make drawings, and to make observations about shapes in the world around. This provides the basis for more formal activities at higher levels.

Exploration, analysis and communication

In each lesson three aspects are going to be worked: exploration, analysis and a

The first step, exploration, will focus on an attempt to bring the children in contact with their natural and built environment, in order to define and observe its particularities. This component will allow us to create a link between the knowledge the children possesses about their environment and the starting of a formalization process. We try to attend the children aware of the richness and variety of structures that make-up their living environment.

The second step, analysis, will bring a framework as reflection and critique, and secondly a framework of mathematization. Understanding geometric can’t be limited to the observation of similarities or differences. Therefore, understanding also includes a more structured means of reflection. Many themes can be addressed: establishing larger structures from smaller ones, using specific geometric transformations, properties,..

Finally, the communication component will focus on developing abilities that will allow the children to communicate through mathematical discourse and the various means associated with this discourse. Communication is an essential element mathematics and above all, when learning mathematics. Therefore, communicating in geometry is more than using the appropriate vocabulary; it also consist of using various means that allow us to describe the shapes in a space.

Learning Styles, thinking Styles, Multiple intelligences

Traditionally, approaches to teaching mathematics have focused in linguistics and logical teaching methods, with a limited range of teaching strategies. Some students learn best, however, when surrounded by movement and sound, others need to work with their peers, some need demonstration and applications that show connections of mathematic to other areas (music, sports, art, architecture), and others prefer to work alone, silently, while reading from a text.

The multiple intelligences approach does not require a teacher to design a lesson in nine different ways to that all students can access the material …In ideal multiple intelligences instructions, rich experiences and collaboration provide a context for students become aware of their own intelligence profiles, to develop self-regulation, and to participate more actively in their own learning.

Knowledge of students’ learning styles assists teachers in developing lessons that appeal to all learners. Visual learners appreciate lessons with graphics, illustrations, and demonstration. Auditory learners might learn best from lectures and discussions, Kinesthetic learners process new information best when it can be touched or manipulated; for this group of learners, written assignments, note taking, examination of objects, and participation in activities are valued strategies to consider.

We watch, we listen, we imitate, we adapt what we find to our own styles and interests, we build from there.

Visible thinking

The idea of visible thinking helps to make concrete what a thoughtful classroom might look like. At any moment ,we should ask “Is thinking visible here? Are students explaining things to one another? Are students offering creative ideas? Are they, and the teacher, using the language of thinking? Is there a brainstorm about alternative interpretation on the wall? A students debating a plan?

When the answers to all that questions are consistently yes, students are more likely to show interest and commitment as learning unfolds in the classroom. They find more meaning in the subject matters and more meaningful connections between school and everyday life.

When thinking is visible in class, students are in position to be more metacognitive, to think about their thinking. When thinking is visible, it becomes clear that school is not about memorizing contents but exploring ideas.


The programming is based on the Generalitat curriculum. The children are involved in a weekly geometry lesson, which lasts for one hour.
For the first 10 minutes of the lesson the class is involved in mental maths activities (reviewing).
During the next 40 minutes, the main focus of the lesson is introduced and again involves whole class teaching. Children study a range of topics about geometry: 2D, 3D, angles, coordinates, perimeters, areas, surfaces, symmetry, translation, rotation and problem solving. After the introduction, the children work individually or in groups, on follow up activities.
The final 10 minutes is called the plenary. Learning is reviewed and/or homework is discussed.