Geometry & Road Safety Education

During this Blog, we have seen that geometry is present in any area of our world. Today, we are going to talk about the importance of geometry in Road Safety Education. From my point of view, this topic should be more taught in our schools because it's really important for our students as future drivers, but also as current pedestrians. It is necessary for the citizen's security. Therefore, from this Blog, I would like to demand the teaching of Road Safety as another subject or, at least, as a part of any other common subject (Physical Education, Social Sciences or Citizenship Education, for instance). 

Our streets are full of geometric symbols that students need to interpret. First of all, we are going to focus on the road's pavement. Here, we can start teaching our children the concepts of different types of lines (straight, curved, continuous, discontinuous...) and their meaning related to Road Safety. In this way, we would teach at the same time geometry and Road Safety, so students will be able to learn two issues in a transversal way, as our curriculum suggests. 

In the case of the traffic signals, they are perfect examples to learn the geometric shapes in a visual way. They follow a kind of code to express different meanings (prohibition, obligation, warning...). In my opinion, the best way to teach them to our students is by showing and asking them questions about the polygons that they can see in each signal. Through visual thinking and their own experience, they will associate the geometric figures to their meaning regarding Road Safety. 

The following video will help you to teach the meaning of the different traffic signals to your students: 

Movements: the first step to learn geometry

Today, we are going to talk about learning geometry through movements. As we have said previously, students learn better through their own experience and using manipulative materials rather than listening to the teacher. 

However, there are some teachers who claim that the movement is what allows geometry to be learnt. They say that the first activities that bring us the spatial knowledge are those which implies movement: to walk, to touch things, to go up and down stairs or the typical game in which children follow different circuits drawn on the floor. That's why children have to realise that geometry is in their movements. 

The teacher Malena Martín establishes in her webpage Aprendiendo matemáticas, the golden rule for didactics of geometry. This rule has three different steps: 

1. Begin with the movement.  

2. Express verbally the discoveries.

3. Express in a plastic way what you have experienced.

Taking everything into account, we can see how movements and experiences have an impact on the following actions to acquire knowledge. Therefore, if we want that children make figures with spaghettis and gummies (according to the activity that I explained in a previous post), we cannot start with that. 

The first step should be that children experiment with their own bodies. In this case, they will make different types of lines and figures in order to internalise the concepts. After that, we can verbalise the shapes and figures we have made. It will help them to know the technical name of each figure. Finally, we will give them manipulative materials to work freely. In this way, the teaching and learning process will be more meaningful and enjoyable. 

Geometry and ICT tools

Nowadays, new methodologies and ways of teaching are being introduced in our classes because times are changing. Teachers have to be updated in every moment and implement all the resources that they consider interesting for the teaching-learning process. The implementation of ICT tools is undeniable. In fact, there is a methodology called BYOD, which means "Bring Your Own Device" that allows children to bring their laptops, mobile phones or tablets and work with them in the classroom. 

For this reason, I consider that every teacher has to be well-trained in the proper use of new technologies, in order to transmit this knowledge to their students. ICT tools give children the opportunity to do practical exercises in which they have to apply the theoretical aspects. However, these resources are fantastic to teach geometry in an interactive way, so our students will be more involved in the subject and the learning will be richer. I'm sure that they will enjoy the experience and the will want to repeat. 

Here, I'm going to give you some examples of different apps to use in class with your students. I hope you find them interesting and useful. 

-My Geometric Universe: as its name says, this app allows students to create their own universe. First of all, they have to draw the geometric figures with a pencil, a ruler and a compass. Then, they have to cut the plane shapes to make the three-dimensional objects that they need: a pyramid, a ball, etc. This is really useful because children can see how these figures are composed, starting from their plane development. The following video shows how this app works:

-Arloon Geometry: it's an app to learn geometry through different 3D models using augmented reality. With this app, students will improve their spatial vision because it allows them to interact directly with the figures. You can select the kind of figure you want to study and see its plane development. It also shows you the different formulas to work out the areas and volumes of the figure. Finally, there are a lot of exercises to practise. Here, you can find a video about it: 

-Doodle Math - Learning shapes: Doodle Math is an app to learn Maths for kids, but it has a specific section for drawing shapes. Students will learn the different polygons by drawing them. Then, they will make enjoyable characters and animals using these figures. In the following video, you can get a complete idea about this app: 

Polyhedrons

Until now, we have seen the construction of different flat figures with some materials. However, today we are going to see how to construct polyhedrons with our students. First of all, we have to know what are we talking about, don't you think?

Geometric bodies are any object that takes up a three-dimensional space. They include the polyhedrons and round bodies. These last ones have, at least, one of these faces curved. Nevertheless, the polyhedrons are formed by flat faces, vertexes and edges. 

In the following video, we can find a clear and easy explanation about polyhedrons to show to our students in class. 

But, how can we make polyhedrons with our kids? There are many ways and some of them are really simple. 

Last week, we attended a workshop about structure in the faculty and we were building some figures with gummies and spaghetti. I found these materials really useful for the construction of polyhedrons because they allow children to distinguish perfectly between vertexes and edges. Moreover, there is no danger because the spaghetti doesn't poke (as some sticks of wood do) and the gummies are suitable to join the spaghetti. The only challenge is that they don't break! Here, I have added some pictures of the experience: 

Apart from these materials, we can use whatever we want, like bars or rods and plasticine for the vertexes. There are also magnetic games that we can buy and allow children to build the figures easier and quicker, but it will depend on the availability of the game at school. 

Playing with TANGRAM!

In the previous posts, we were talking about some manipulative materials and the construction of figures with them. Today, we are going to learn about a special material to play with geometry, which is called tangram. 

The tangram is an old Chinese game which is composed of seven coloured pieces called "Tans" which are kept making a square:

-5 triangles (two big triangles, one medium-sized and two small ones) 

-1 square 

-1 rhomboid

According to some legends, the beginning of the game comes from different pieces of furniture that people wanted to place to save space. Another legend says that a servant of a Chinese emperor was carrying an expensive and fragile ceramic mosaic while he stumbled and fell down. The result was that the mosaic was broken in pieces. The servant tried to make the mosaic again but he couldn't. However, he realised that he could make other many figures with all the pieces.

Actually, the aim of the game is the same that the servant did: to make different figures with all the pieces without overlapping them. It is a fantastic material to use with our students because it allows them to manipulate, create, discover and use new shapes and figures playing in an enjoyable environment. In this way, they will learn through entertainment. The pieces are usually made of wood, although they can be also made of almost any material: cardboard, "goma-eva", paper... It will depend on the age of the students and the use that we give to it. The following video will show you how to create your own tangram:

In this other video, from the 2:00 minute, we will learn how to make different kinds of polygons (convex and concave) with the tangram. So, this resource can be used to teach any content related to geometric figures. 

Geometry and cities

As we have mentioned before, geometry is present everywhere and the city is the way in which students can understand reality through a geometric perspective. The city is the place where they live, so it is really close to them and we can use all its elements to teach geometry. The buildings, the roads, the signals, the streets... All of them are formed by geometric figures! And, what about the construction of the cities? Let's see it. 

Cities have grown according to different geometric shapes because geometry and civilization walk together. For this reason, there are three main kinds of cities. 

-The Roman city. The Roman Empire built fortified cities with rectangular shapes oriented by their two symmetry axes which were their two main streets: the cardo (North to South) and the decumanus (East to West). In the intersection of these axes were the foro, a kind of square where the public life was developed. The streets were distributed parallel to the two axes, creating a grid of blocks. 

-The Medieval city. The medieval cities were also fortified, but their drawing was irregular and sinuous. It was a kind of maze and there wasn't planning according to geometric patterns. The continuous wars are the main reason for this type of organization. In the centre, there was the market square with the most representative buildings and from this place, lots of narrow and winding streets arise making neighbourhoods where people from different trades were gathered. One of the best representative examples of a medieval city is Toledo. 

-Modern city. Cities change with time and the walls were no longer necessary. In Spain, the "Plaza Mayor" was created. From the Renaissance, the design of the cities follows geometric patterns. Straight and wide avenues and promenades are designed. The streets grow according to three types of geometric designs: "radiocéntrico", such as the starred city of Paris; orthogonal (Barcelona), and linear.

A good resource to teach geometry through the city to our students is Google Earth (https://www.google.com/intl/es/earth/) where they can see and compare the organization of the different cities. 

Furthermore, children can build their own city with geometric figures made by them in order to put into practice all the contents taught. Here, I leave you some wonderful examples. I hope you like them!

Mosaics

In relation to the previous section in which we talked about the construction of flat figures, now, we are going to learn about mosaics. As you know, we live surrounded by geometric constructions and the mosaic is one of the most common examples. 

The mosaic is the recovering of the plane through small pieces called tesserae which form different figures without leaving any space between them. There are lots of forms of getting a mosaic. The simpler ones are regular polygons of the same type (squares, regular hexagons, equilateral triangles, etc.). However, the construction of mosaics can also involve the combination of several kinds of polygons. 

Throughout history, several cultures have used the mosaic for different purposes: intellectual in Greece, decorative in Rome, religious in the Islamic world... In fact, the mosaic has been one of the most important representations in art. For instance, one of the most relevant periods of the mosaic was the Byzantine one. Through this video, our children will be able to see the application of the mosaic in the art and religious fields. 

Moreover, in the following video, different concepts related to geometry are explained through mosaics, making them really visual for children and using the Alhambra of Granada's monument as an example. In the video, lots of concepts are described, so the teacher should select the kind of concepts he or she wants to explain through it, according to the level of the group. Furthermore, it is important to highlight that using these resources we can teach different subjects such as Maths and History, so they allow us to interrelate contents and make the learning richer.  

Regarding the didactic application, we can build mosaics with our students to work the tesselation in an enjoyable way and using our creativity. One of the easiest activities to start working with mosaics is the repetition of a drawn pattern and its painting. We can give our students a sheet of paper with the pattern and they will become familiar with the mosaic by finishing it. 

Another activity to carry out with our students is the construction of mosaics with post-its, as we can see in the picture. In this case, the squares of different colours will be our main figures. Children can use their own design freely or follow some patterns offered by the teacher. Furthermore, if we want to increase the difficulty of the topic, we can build mosaics using the different flat figures of "goma-eva" that we created for our previous post. In this case, we will work with various figures, not just squares, and their combination could create really beautiful compositions. 

Finally, I have found a brief video which can be attractive to introduce our students on the topic of mosaics.

Flat figures construction

As we have said previously, children's learning become richer if they can see, touch and experiment with the different materials. In this section, we are going to talk about the construction of flat figures because we consider that it is better to practise with them firstly, before starting to learn the volume and the geometric bodies. 

In this activity that I'm going to suggest, students will learn independently or in groups, but it is a perfect way to encourage student's autonomy and creativity. The teacher can help each student in a more personal way, especially those who have more difficulties in the subject. The aim of this activity is that students learn the properties and geometric concepts through the construction and deconstruction of flat figures. But, how are we going to do that? It is really easy. 

We are going to prepare different geometric figures with any material (wood, plastic, etc.). In our case, we will use "goma-eva" because it is an easy material to use, cut and manipulate. So, we just need these figures (triangles, rhombuses, trapezoids, squares...). With this material, the teacher can suggest several proposals. 

Firstly, we can let our students manipulate freely the material in order to have the first contact with it and build some figures. Then, a good idea to continue using it can be trough different sheets with instructions that students will have to follow. For instance: "you have to build a triangle using 1 triangle and 1 trapezoid" (see the picture). In this example, the students will perceive the concepts of visual perception and increase because they will see that the new triangle is bigger than the first one. In other words, the first triangle is integrated into the new one. 

We can build lots of figures with these pieces, as we have found in other examples on the Internet: 

The next step with this material can be the composition of objects, animals, etc. using some templates, as it is represented in this picture. The end of the activity will depend on the creativity of our students and the teacher! 

Basic concepts: Point, Line and Plane.

Before starting to explain different issues related to geometry, it is important that our children have an idea of the basic concepts of geometry and what points, lines and planes are. 

Euclidean geometry is based on the definition of "ideal" geometric objects. The fundamental ones are the point, the line and the plane. None of these objects has volume.

- The point is an element without any dimension which takes up and describe a single position in the space. For example, when we let our pencil fall down on a piece of paper. 

- The straight line is a continue and indefinite succession of points in a unique dimension and direction. It does have no beginning or end, so it is infinite. 

- The plane is a two-dimensional element in the space. It has infinite points and straight lines.

To explain all these concepts, the use of videos can be a fantastic idea because they catch children's attention and make geometry more attractive and visual to them. Furthermore, another useful activity to learn the concepts can be by drawing the different elements in a piece of paper. 

This video explains perfectly all of them 

It shows the concepts and their application to real life

Another explanation in Spanish