In this work it is detailed a proposal that a group of lecturers belonging to the investigation group of the  Universidad Politécnica de Madrid (UPM) “Mathematics applied to Civil Engineering: MAIC” is  accomplishing through a project of educative innovation financed by the UPM. It is proposed a  “Mathematic Thinking Lecture Room” to be incorporated in the web pages of the universities. It is  offered in it a series of activities which permit  the training of the students in several transversal  competences, most of them related to the mathematical thinking, and others that, although can seem  far from it, it is possible to develop them together. The list of activities proposed for this `lecture roomweb´ that can be increased with others along the beginning of it is:  • Games, pastimes and mathematical puzzles.  • The mathematical language: prove and solve.  • Training for the mathematical Olympiads.  • Activities related to the mathematical thinking: readings with mathematical content,  mathematical cinema...  • Convocation of competitions: mathematical short stories, mathematical photography,  mathematical short films...  • Forums and open discussions

Lantarón Sánchez, Sagrario

López González, M. Dolores

Rodrigo Hitos, Javier

Archivo Digital UPM

Lecture room web for the improvement of mathematic knowedge

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

LECTURE ROOM WEB FOR THE IMPROVEMENT OF MATHEMATIC 
KNOWLEDGE 
Mª Dolores López1, Javier Rodrigo2, Sagrario Lantarón1 
1Universidad Politécnica de Madrid (España) 
2Universidad Pontificia Comillas (España) 
marilo.lopez@upm.es, jrodrigo@upcomillas.es, sagrario.lantaron@upm.es   
Abstract  
In this work it is detailed a proposal that a group of lecturers belonging to the investigation group of the 
Universidad Politécnica de Madrid (UPM) “Mathematics applied to Civil Engineering: MAIC” is 
accomplishing through a project of educative innovation financed by the UPM. It is proposed a 
“Mathematic Thinking Lecture Room” to be incorporated in the web pages of the universities. It is 
offered in it a series of activities which permit the training of the students in several transversal 
competences, most of them related to the mathematical thinking, and others that, although can seem 
far from it, it is possible to develop them together. The list of activities proposed for this `lecture room-
web´ that can be increased with others along the beginning of it is: 
• Games, pastimes and mathematical puzzles. 
• The mathematical language: prove and solve. 
• Training for the mathematical Olympiads. 
• Activities related to the mathematical thinking: readings with mathematical content, 
mathematical cinema... 
• Convocation of competitions: mathematical short stories, mathematical photography, 
mathematical short films... 
• Forums and open discussions.  
1 INTRODUCTION: THE NEED FOR COMPLEMENTARY ACTIVITIES  
The changes that are being implemented in universities within Europe show that the aim of centres is 
not to teach. The aim is rather for the student to learn, and to learn not only knowledge but 
professional skills too. It is worth highlighting that, as with other subjects, although perhaps in a more 
pronounced manner, mathematics subjects’ credits have been reduced dramatically in the new study 
plans. Consequently, offering actions that make it possible to obtain skills related to it and other 
sciences is very useful. With this aim, we propose to offer students a “Mathematical thought class”, the 
activities involved in which focus on motivating students towards subjects relating to mathematics. Its 
purpose is to support university students, above all in their initial stages, and promote a better 
environment of work and cooperation, as well as greater interest in Mathematics.  
The activities incorporated in the class, for which extensive knowledge of mathematics is not required, 
aim, on the one hand, to show that this science is astonishing, interesting and useful, accessible to 
almost everyone and plays an important role in professional as well as daily life, that it has great 
importance in culture, development and progress and, on the other hand, to complement and show 
students certain elements of this science that will help them in their education. It focuses on play, 
experimentation and participation making it an important teaching resource.  
1.1 Objectives 
The work to be carried out focuses on the creation of a Mathematical Thought Class to be 
incorporated into the website, where interested students are provided with, amongst others, the 
following possibilities: 
• To learn mathematical concepts they do not know about and that are necessary to cope with 
their university studies 
• To handle mathematical language and its symbols 
• To train their brains towards scientific problems 
• To learn to appreciate maths and its usefulness in all fields  
• To link the scientific world to leisure 
2 DESCRIPTION OF THE LECTURE ROOM WEBSITE 
The activities proposed will be implemented via a website in order to reach all university students or 
students from interested centres. They shall be simultaneously accessible and interrelate with one 
another. They shall be complemented with contests and competitions that shall be announced on 
various dates.  
A forum will be available at all times that will enable interaction between the students and between 
students and professors.  
The structure of the website is shown in figures 1 and 2: 
 
 
Figure 1: Website introduction screen 
 
 
Figure 2: Website contents screen 
 
Each of the activities are briefly detailed below: 
2.1.1 Mathematical games, puzzles and problems 
The mathematical challenges presented as games or puzzles can be recreational and entertaining for 
students and exercise their intelligence and equip them to resolve the problems that will undoubtedly 
arise throughout their studies and occupation more easily. It acts as complementary material that can 
be incorporated successfully into the basic subjects.   
It aims to stimulate the capacity for reasoning, analysis and synthesis as well as that of mathematical 
thought in general.  
The material to be included shall be selected in such a way that students encounter unusual and fun 
riddles that, although they will need a basic knowledge of mathematics, will provide them with a 
stimulating perspective at the highest levels of mathematical thought. They will be grouped in sections 
concerning the different areas of mathematics (see figure 3) and each of these sections will refer to 
other activities that contain complementary material (interesting lectures about the topics being dealt 
with, recommendation of a particular film with related content). 
 
 
Figure 3. Structure of the mathematical problems, puzzles and games module 
 
The existence of the open forum between students taking the module and between the participants 
and professors enables interaction and the discussion of queries, clues, proposals, etc.  
It is very probable that playing with mathematical problems and puzzles will make students discover 
that mathematics is fun and interesting, therefore motivating their desire to study it in more depth.  
2.1.2 Mathematical language, demonstrate and resolve 
The manner of thinking, developing and expressing oneself in mathematics is, in many aspects, 
different to the manner of doing so in daily life. When a student attempts to delve into a more in-depth 
study of this science, there are various essential points they must take into account:  
• Use the language of mathematics correctly, with its expressions and symbols that, on many 
occasions, are used with other meanings in daily life.  
• Understand and be able to correctly prepare a demonstration. It is important to endeavour to 
be able to recognise which method is the most adequate to demonstrate a statement.  
• Familiarise yourself with the idea of a mathematical problem and the various points of view for 
the resolution of such. Learn to apply the usual strategies for the resolution of problems.  
This activity will help to clarify all of these matters in order to guide those who wish to delve into 
mathematics at university level. It aims to provide students with useful material to begin their technical 
studies in cases where students find themselves involved in serious difficulties regarding the 
professors’ proposals (Figure 4).  
Topics such as the following will be covered:  
• Differences between daily and mathematical languages: Towards scientific language. 
• What is a demonstration? 
• Strategies for the resolution of problems. 
 
 
Figure 4: Screen relating to the Mathematical language activity  
 
2.1.3 Preparation for the mathematical olympics 
Preparation for the Mathematical Olympics and the participation in such represent a challenge for the 
highest achieving university students in the scientific disciplines. Consequently, this activity aims to 
include a university mathematics competition preparation manual, which will provide the student with 
the theoretical knowledge necessary for resolving the problems proposed in these types of tests, 
which tend to be more difficult than those that the student deals with in the degree subjects.  The 
manual also includes a list of the main problems that, in recent years, formed part of exams for certain 
distinguished international mathematical contests and original solutions to these problems are 
provided. Attempts to resolve the problems proposed in the manual improves the students’ deductive 
skills, it encourages their creativity and develops their mathematical thought, which can help them in 
the maths subjects of their studies. The mathematical theory dealt with in the manual is divided into 
topics (Figure 5).     
This activity is closely related to the two previous ones as the mathematical puzzles and games are 
excellent preparation for dealing with more complicated problems, such as those proposed in the 
Mathematical Olympics, and the mathematical demonstration techniques are a useful tool for solving 
these types of problems.   
 
 Figure 5: Structure of the mathematical Olympics preparation module  
 
2.1.4 Activities related to mathematical thought: Lectures with mathematical content, 
mathematical films  
The idea behind this module is to propose daily activities to students in which mathematics can easily 
be found which motivate them to study it and take an in-depth look at it. It aims to offer students 
information about films and books geared towards the general public but with certain scientific content, 
as well as comprehensive information about the mathematics dealt with therein. Through the forum, 
we hope to encourage debate and an exchange of opinions on these works, which is not only 
interesting from an artistic perspective but also in terms of scientific popularisation. 
It is frequently found that adequate motivation and the proposal of activities that capture the students’ 
interest can switch a light on in the class, and encourage the students to continue researching and 
forget about their predisposition to reject mathematical content. This is when it becomes possible to 
teach them how to formalise and describe scientific concepts with precision. 
2.1.5 Geometric chip 
The aim of this part of the class is to propose certain activities that cover various topics from a 
geometric point of view such as, amongst others: symmetry, proportions, fractal dimension, curves, 
surfaces, brain-teasers, puzzles, etc. (Figures 6 and 7).  
Geometry has for many centuries been one of the pillars of academic education from the early ages. 
During the last century, it has gradually become less prevalent in curricula. Fortunately, current 
mathematical curricula at all levels are placing due importance on geometry.   
The general objectives of this part of the class is to offer students activities, which in the majority are 
interactive, that will broaden their geometric capacity and motivate them towards this aspect of 
mathematics.  
 
 
Figure 6: Geometric chip module front page 
 
 
Figure 7: Geometric chip module contents 
 
2.1.6 Competitions and contests 
This part of the website will contain an up-to-date list of all of the contests and competitions related to 
mathematics that we have found out about (mathematical photography, mathematical short stories, 
problem solving, programming, etc.). This aims to encourage the students’ participation in the 
competitions and contests.  
3 CONCLUSIONS 
The text presented aims to detail a project that a group of professors from UPM are carrying out in 
order to improve teaching and the performance of the students in subjects related to mathematics.  
The aim is to present it as an appropriate and innovative tool in the educational system that is useful 
for other groups to adapt to their needs and to their students, therefore providing them with better 
results.  
Moreover, the activities presented in the project are of an open nature which facilitates the connection 
amongst the university students and brings secondary school students closer to the university world.  
REFERENCES 
[1] R. Criado, A. Moreno, “Una propuesta de enseñanza virtual y su aplicación a la asignatura 
Matemáticas e Imaginación”, Relada 1 (1), 54-58. (2007). 
[2] M. de Guzmán. “Iniciación al método matemático: Como hablar, demostrar y resolver en 
matemáticas”. Anaya. (2003). 
[3] S. Lantarón, M. D. López, “Metodologías activas de innovación educativa para el acercamiento de 
los estudiantes a las matemáticas”. Segundo congreso internacional de matemática aplicada a la 
ingeniería y la arquitectura. ETSI Caminos. UPM. (2008). 
[4] M. D. López, J. Rodrigo, A. Salvador. “Actividades de acercamiento a las matemáticas del 
alumnado de las escuelas técnicas”. V Congreso Iberoamericano de Docencia Universitaria. 
Valencia. (2008). 
[5] M. D. López, J. Rodrigo, A. Salvador. Teaching mathematics with the help of the TV. International 
Conference on Education and New Learning Technologies (EDULEARN09). Barcelona del 6 al 8 
de Julio de 2009.  
[6] M. D. López, J. Rodrigo, A. Salvador, A. Garmendia. Computer science and mathematical e-
learning materials in the web. International Conference on Education and New Learning 
Technologies (EDULEARN09). Barcelona del 6 al 8 de Julio de 2009.  
[7] M. D. López, A. Salvador, S. Lantarón: Actividades de apoyo al desarrollo de la competencia  
“pensamiento matemático”. III Jornadas Internacionales UPM sobre Innovación Educativa y 
Convergencia Europea (INECE’09). Madrid del 24 al 26 de Noviembre de 2009. 
[8] V. Melvilla. “Las matemáticas del arte”. Almazana. (2007). 
[9] A. J. Población. “Las matemáticas en el cine”. Proyecto sur. (2006). 
[10]  V. Pollán. “Selección comentada de lecturas matemáticas”. Rev. Galega de Educ.Matemat, 4. 
(2004). 
[11]  M. A. Queiruga, M. Gutiérrez, E. Gutiérrez. Una mirada diferente. Editorial Q. (2008). 
[12]  Webs: http://innovacioneducativa.upm.es/sandbox/pensamiento/index.htm 
http://www.caminos.upm.es/matematicas/PORTADA.htm, http://www.divulgamat.net/, 
http://www.aulamatematica.com/ 
http://www.catedu.es/matematicas_mundo/PROBLEMAS/problemas.htm, 
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Lecture room web for the improvement of mathematic knowedge

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