**MATHEMATICAL ROUTES**

The routes have been organised in collaboration with the Mathematics Education Society of the Valencian Community Al-Khwârizmî. The aim of the activity is to use the environment as a didactic resource for science dissemination, teaching and learning mathematics so that secondary and high-school students can develop positive attitudes towards them and appreciate the implementation of mathematics in their surroundings. The routes that have been planned will turn both the old city centre and other modern facilities of the city into an important source of mathematical learning. The route will start with a presentation of the itinerary and the materials will be provided (tape measures, clinometers, calculators, didactic notebooks ...).

ROUTE 1: From Torres de Serrans to the Botanical Garden.

Meeting point: Torres de Serrans

ROUTE 4 - From Mercado de Colón to La Nau

Meeting point Mercado de Colón, Jorge Juan Street

**MATHEMATICAL WORKSHOP**

The workshop is divided in two main parts. In the first one, different types of surfaces, their sections (meaning which plain figures can appear on a surface that is cut by another plain) and the implementation of our knowledge about the sections of geometrical bodies will be explained.

In the second part, attendees will have the opportunity to build real models of the surfaces that they have seen in the first part, based on some sectional families of the surfaces. Using templates, paper and scissors, they will cut the sections and then rebuild the surface.

María García Monera, secondary school professor of mathematics, is the responsible of carrying out this workshop in the Faculty of Mathematics in Burjassot.

**GEOLOGY WORKSHOP**

Faculty of Biology of the Universitat de València (Burjassot Campus).

Anna García Forner. Curator of the scientific collections of the Geology Museum and responsible of the workshops.

Workshop of mineral identification. The workshop proposes to identify different types of minerals by analysing their physical traits: colour, brightness, hardness, magnetisms... In order to so, students will be provided a dossier, a simple single-access key and indicators. The workshop is divided into two parts. The first one is a theoretical introduction, while the second one will implement the previously acquired knowledge.

Workshop of micropaleontology. The objective of this workshop is to teach students an aspect of palaeontology that is unknown for the general public, but that has a great importance in terms of knowing our past. A guide will be given to the students. The guide will briefly explain the concepts that are going to be used. It includes illustrations that will help them identify the materials that they will find.

**ASTRONOMY WORKSHOP**

Place: Astronomy Workshop. Astronomy Room. Faculty of Physics of the Burjassot Campus)

Enric Marco, expert of the Astronomy Society, starts this workshop with a brief introductory talk (20 minutes) in order to detail the activities that are carried out by astronomers and explain the main celestial objects.

Then, the attendees will observe the Sun with a telescope. The main characteristics of the Sun will be explained. They will also teach students how to observe it with safety. In case of adverse atmospheric conditions, this activity will be substituted by another one of the Astronomy Society.

**CONFERENCES OF SECONDARY CENTRES**

IES BLASCO IBAÑEZ, Cullera. Conference in charge of Juan Monterde:

**02/12/2015
How do mathematics work?**

Summary

We will take advantage of typical examples to show what mathematicians really do: ask themselves questions using examples to reject them or prove that they are right. We will study the techniques to deduce facts from hypothesis and link the reasons that justify these statements.

The examples are typical because they are essential in the history of Mathematics. The first one is the tragic story of evidencing the vastness of the diagonal of a square, which is sided to the unit. The second one will be used to explain what inductive reasoning is.

**IES BENAGUASIL** Conference in charge of Juli Peretó

Date to be inserted

Darwin and the tree of life

Summary: About 150 years ago, Charles R. Darwin disseminated one of the most incredible and powerful ideas of biology: all living being have the same forebear. Therefore, they all have the same origin and they all are relatives. In this way, the relationships between all current organisms and its ancestors can be represented in a tree-like chart.

The tree of life, including the extinguished species buried in the ground and the living ones located in the foliage, is a very powerful Darwinist image. Soon, this idea was adopted to substitute the old and mistaken idea of the Great chain of beings: a hierarchical structure of all matter and life, from worms to humans and God. After the Darwinist tree of life, we were no longer beings about to become angels but evolved primates. The biochemical techniques and current computational methods have allowed us to rebuild the universal phylogenetical tree of life, making Darwin’s dream true, while we have found unexpected familiar relationships. This expands its value much more of what Darwin could have ever imagined. Apart from the obvious scientific interest provided by the tree of life and its phylogenetic relationships with modern biosphere, these type of research is useful and has practical implementations. Ultimately, in a more precise way, it allows us to ask ourselves who we are in scientific terms.

**IES Andreu Alfaro de Paiporta**, in charge of Vicent Martinez

Summary of the conference

When we look at the sky during the night and see all the stars, we ask ourselves how far they are from us. It is not easy to understand the size of the cosmos because of the enormous size of tails and galaxies and how far they are from us. They are so far that our daily experience is not clever enough to make us understand the hugeness of the universe.

Cosmic scales are explained in the conference by means of analogies, from the solar system to the furthest parts of the universe.

Ideas, keys, materials (books, documents, audio-visuals, webs, links, YouTube...)

http://metode.cat/Revistes/Seccions/Desvelant-l-univers/Les-escales-cosmiques http://sociedad.elpais.com/sociedad/2009/01/19/actualidad/1232319606_850215.html

Innovative elements of the conference. This year a 1-minute amateur video on the size of the Solar System has been carried out by students of the 3^{rd} year of Secondary School.