“El Universo es un libro escrito en el lenguaje de las matemáticas, siendo sus caracteres triángulos, círculos y otras figuras geométricas, sin las cuales es humanamente imposible comprender una sola palabra; sin ellos solo se conseguirá vagar por un oscuro laberinto” Galileo Galilei.
These pictures show a short story very useful in order
to introduce it in the first day of a Mathematics class when you have to explain what it is
the meaning of geometry.
Through these pictures, teacher can start to talk
about the importance of the geometry and the close relation that exists between
this concept and our daily life.
On balance, I consider this activity very interesting to offer the
student the first connection with this term and, besides, it is a good
opportunity to show the students that the geometry is not a boring topic and
they can learn many new things.
In the following entry, I will make a review about
what the area and the perimeter are. Although I learnt this content in previous
years, I consider that I need to revise, since we are using it in some lessons and
maybe I will have to do exercise in the exam.
WHAT IS THE AREA?
The area is a geometric magnitude that expresses the extension of a plane in two dimensions: length and width.
WHAT IS THE PERIMETER?
The perimeter is the total distance around the outside of two
dimensions shapes.
Since this blog is a resource to acquiere learning, I have used
this entry to revise a basic aspect of the geometry due to the fact that there are always some formulas that I usually forget. Probably, this entry has not been
interesting for you, but it was necessary for me to create a direct link in
order that when I have to do exercises where this content is used, I have a
direct access across my blog.
Mathematics and art always have been narrowly related.
The symmetries, the proportions or the geometry are present elements in the
art. If we observe a picture or a sculpture we will see that the artist uses a
lot of mathematical aspects.
Many artists have been influenced in the creation of their
artistic works for the mathematics and, specially, for the geometric notions:
“Uno de los contextos
adecuados para la enseñanza y aprendizaje de nociones matemáticas es la
contemplación y creación de formas artísticas, ya que pueden ayudar al alumno a
intuir nociones geométricas al mismo tiempo que a desarrollar sentimientos y
emociones estéticas” (Edo, 2003).
This one is an aspect that many teachers do not bear
in mind, since they forget the close relation that exists between the
mathematics, the art and the context in which students lives. Do
you think that across these works of art we might teach mathematics in class?
Obviously, if we use these works of art, we will be able to explain a wide
range of mathematical concepts.
In one of the classes, the professor has
referred several times to the geoboard concept. I had never listened to this
term. In class, our teacher showed a brief information, nevertheless, in this
entry I want to dedicate to studying and analyzing with depth what a geoboard
is.
The geoboard is a didactic tool for the education of
the geometry.
The geoboard is a didactic element that helps to introduce
and guarantee great part of the concepts of the flat geometry, being a concrete
tool that allows students to obtain a major comprehension of diverse terms of
this matter.
Luis
The main aims that can be obtained by this type of
resources are:
Geometric
figures can be formed.
The
students could establish similarities and differences between parallelisms–
perpendicularity.
To identify the relation between surface -
volume and other concepts.
TYPES OF GEOBOARD
In the following video, we can see as a group of
pupils works the geoboard with a teacher. The motivation and concentration of
the activity are reflected in the video. It is a pity that I has not worked with this resource
previously, nevertheless, this will serve me to know that I have to work it with
my future students. It is a dynamic way of teaching geometry and contacting with
the reality. In addition, pupils amuses itself creating figures.
In this entry, I am going to speak about a blog called
“Mas
ideas, menos cuentas”. This blog deals with the mathematical education.
I consider it a useful resource because in every entry a professional education
gives his/her opinion about any mathematical topic.
In most entries is explained a topic that has been put into practice. Then, the same person exposes the strong points and the possible
improvements. Therefore, as a future teacher, I think that it is an essential tool that I can use in order that in particular moments I can glance it and
take some innovative and dynamic ideas and, at the same time, correct possible
failures.
Though in the first moment, it is possible to qualify
the blog as a difficult tool to analyse, as soon as you understand, it is a box
of surprise since you can find content and activities that previously you had
never practised.
From my point of view, I consider that it is a
material where the main aim is to share knowledge and, certainly, experiences
that in my case I will serve me to implement it in a future.
Here, you have the link of the blog “Más ideas, menos
cuentas”:
The music must be a very good resource at the moment
of acquiring a mathematical knowledge in ages of between 6 and 12 years.
As Jean Philippe Rameau said:
La
música es una ciencia que debe tener unas reglas establecidas; estas reglas
deben derivarse de un principio evidente, y este principio no puede revelarse
sin la ayuda de las matemáticas.
This aspect attracted the attention of the
mathematicians from the time of Pythagoras, nevertheless, always that we think
about a class of Mathematics we have in our mind a traditional class in which
the only used resources are the voice of the teacher and the textbook.
From my short experience, I believe that if teachers introduce
the music in class in order to explain any mathematical content, the motivation
of pupils will increase and, besides, the acquired learning will be more
significant, since it will relate the content to the pace of the music and it
will be more difficult to forget the content.
With this video, we can see a good example:
In this example, it is explained four geometric forms
(triangle, square, rectangle and circle). It is evident that this resource
would be in use in the first cycle of Primary Education. Though it seems to be useless
the small songs created for each figure, these are assimilated by the students
and, once learned; already they will not forget them. An important aspect of
this video is that each of the geometric figures is related to objects of the
daily life. This provokes that the pupil is aware of the importance of the
mathematics and they do not see it as anything isolated to their daily routine.
Many teachers consider the textbook as the
unique useful resource in order to teach Maths. From my point of view, it is true
that textbooks are an advantage for
teachers in order to plan and to give a lesson. Nevertheless, this advantage
must be correctly used and not to be the only material that teachers use.
Nowadays, we can find a large number of materials with whom students
acquire a more significant learning and enjoy learning. For example: Tangram,
geometric figures, flat figures, Geogebra or cardboard.
However, this idea is not carried out by every teacher. It might be
because it is easier to follow the planning of books without spending several
hours investigating and learning other ways of teaching the same content.
With this idea, I do not claim that textbook, as school material, disappears
of school but we must be aware of the help that provides us. That is to say, it
is essential to extract the maximum performance without considering textbook an
exclusive material.
The concept of geometry comes from the Greek
"geo"land and "metrein"to measure. It is a branch of the
mathematics that studies the properties of the space. The geometry deals with
problems metrically as the calculation of the area, the diameter of flat
figures or the surface and volume of solid bodies.
In this video, we can find a short introduction about the history of geometry:
According to the National Institute for
Education Assessment, it is relevant to teach this subject at school in order:
To know one of the most instructive
branch of Mathematics.
To cultivate a high level of
intelligence.
To develop strategies of thinking.
To discover the own creative
possibilities.
To learn an interesting and useful
matter.
To promote a sensibility towards the
beautiful thing.
To work Mathematics experimentally.
To observe the vision of the world
that surrounds us.
To enjoy the practical applications
of geometry.
To enjoy learning and teaching.
For all these points, we should consider that geometric
is totally related to every step we take in our life, even it is applied in our
everyday language. These are the main reasons of why geometric must be taught
in Primary Education.
However, when teachers are explaining this
topic, in some cases they are not able to transmit these ideas and they only
focus their attention on explaining geometric using theoretical concepts and
several mathematical formulas. In this way, students don’t see the close
connection that geometric has in our daily life.
In order to improve this behaviour, nowadays we
have a vast number of resources available such as manipulative figures,
geometric bodies or educational games. If we use these materials in class,
apart from transmitting the real significant of geometric using examples of our
ordinary life, we will get that our students change the meaning of the
geometric concept.
My name is Rubén Leiva. In this moment, I am studying to be a Primary Education teacher, that is why, this work has been carried out for the subject of Didactics of Geometry, which belongs to the third level the Primary Teaching Degree.
Throughout this work, I will develop different topics deal with in class related to Geometry and, besides, I will show different resources in order to teach these contents in a dynamic and manipulative way.
And why the name of my blog is Soy Geometría, amiga de Rubén? The main reason is because I have tried to establish a close relation between the subject and me. And, when I see this original title, I have a desire to work inside it and built a useful material, not only for this specific subject, also for my future as a teacher.
