Salvador Rodriguez-Lopez

In my opinion, the learning of Mathematics is a complex process that involves developing new ideas while transforming one's ways of doing, thinking, and also becoming a certain type of person, aligned with the practices of a community of Mathematics-practitioners, where learning occurs through social participation.

When I teach, my aim is to create an atmosphere where the
students can develop their learning and to give support for
it, both in and outside the classroom, providing the
necessary scaffolding for the students to develop their
mathematical *discursive identity*. More
specifically, my teaching philosophy is to *help*
the students to:

- understand basic mathematical concepts and tools
- see the connections between these and those that they have previously learned
- use these concepts, methods and techniques to solve mathematical problems
- develop constructive critical thinking
- create their own methods and ways of solving problems
- present mathematical ideas, concepts and arguments to others

*I maintain a positive attitude towards teaching*: In my experience, students perceive and welcome this positive attitude, aligning their own attitude to it, which helps in creating a positive learning atmosphere.*I maintain a personal approach*: I make an effort to maintain an empathic attitude with the students' needs, understanding difficulties they may be having with their work. I believe that students who are*active*participants in their education, learn much more than those whose participation is mainly passive. So I try to apply teaching strategies that match their needs and interests, to boost their participation.*I give positive reinforcements*: I praise students when they participate actively in the classroom, which triggers students' motivation. I strongly encourage interventions from the students, as I consider that the classroom should be a space for two-way communication.*I am aware of diversity*: In all my scholarly activities, I promote respect, equality of opportunity and non-discrimination, as well as gender and ethnic-sensitive teaching.

In my aim to support the development of students' discursive
identity and to facilitate the naturalisation of the
discourse into the students' everyday practice, I find the
following facts especially important:

*To act as a model of Mathematics-practitioner*: I consider that the teacher plays a key role acting as a model for the students in the use and development of mathematics, as a vehicle for active*imitation learning*. For instance, whenever I explain the solution of a problem I emphasise*how to solve it*more than focusing on the solution itself. Sometimes I use a*role-playing dynamic*, in which I involve all the students in the classroom, to solve a certain problem, where I act as a facilitator towards the solution, trying to encourage intuitive reasoning in the students.*To act as a facilitator*: I aim to create the space for the students to develop a pro-active role in their learning process, and to facilitate that development. I consider that individual work is fundamental in Mathematics, but I also believe that learning how to work in groups and how to effectively present rigorous mathematical arguments to others, are critical parts of the students' mathematical education, which deserve special attention. So I try to facilitate the social learning facet of Mathematics.*Cooperative learning*benefits students not only in terms of developing communication skills and problem-solving skills, but also when it comes to achieving*deep & lifelong learning*.*To make the material relevant for the student*: I always try to make the course material interesting and relevant to the target students. To this end, I adapt course material to suit the scientific background of the students. I emphasise topics relevant to each discipline by giving examples of applications of the mathematical concepts, always aiming to obtain a solid contextualised working knowledge of the course topics.*To use all channels of communication*: Whenever it is suitable, I use electronic resources, such as videos and applets in my classes. I find that this encourages students in their autonomous learning.

*To have a flexible, dynamic approach*: I strive for excellence. I am open to change, and constantly evaluate the courses that I teach with the goal of improving the teaching environment. In this sense, I consider the feedback from students to be an important factor, as it helps to regulate the quality and the quantity of the course material, adapting the teaching content to the students' individual academic needs. After each session, I take some time to reflect on both the positive and improvable aspects of my performance.*To present Mathematics as a science in development*: I incorporate parts of my own and others research results in the lectures (when applicable) in order to illustrate current activities in the field. This brings the students to the forefront of research and tells them about the current state of play. In my experience, this also helps students to see mathematics as a science in development. In some higher level courses, I illustrate how research in mathematics can be conducted by giving specific examples and/or projects.

Teaching mathematics is one of my abiding passions. I am
developing my identity as a maths teacher moved by that
passion, both through my daily scholarly activities and my
pedagogical education.

Among the scholarly activities, many institutional factors
have positively influenced my development. It has been
relevant, for instance, the fact of working shoulder to
shoulder with good pedagogical and experienced fellow
teachers and mathematicians, whose advise has been always
welcomed. Another important factor has been the fact that I
have had always the confidence from directors of studies and
coordinators, who have delegated full teaching
responsibilities to me (organising material, grading,
preparing and marking exams,...). In this way, I have always
seen the fact of taking those responsibilities as a natural
part of my teaching activities, which I carry out with
confidence.

A definitively vital part of my development as a teacher,
has been the fact of having direct contact with the
students. This has allowed me, not only to have immediate
feedback on the teaching performance, but also to learn,
from practice, about the learning and creation processes of
mathematics. The latter has had an impact not only on my
identity as a teacher, but also as a researcher. In this
connection, I try to explain mathematics in the classroom as
I would do research with one of my collaborators:
discussing, experimenting, creating...

In light of my interest on the teaching of mathematics, I
consider that taking pedagogical courses regarding higher
education is an important factor whenever one strives for
excellence in teaching. These courses allow one to have
contact with pedagogical ideas, trends, strategies and
tools, which can be used in the classroom. This has
motivated me to participate in several of these courses,
that have influenced my professional development.

I am always endeavour to enhance my teaching performance and
skills. With this aim, I emphasise my efforts in the
following factors:

*Build on my pedagogical education.*For myself teaching provides a chance for continual learning and development. This is why I opine that in-service training is an important tool for continuing to improve my teaching skills and build a solid pedagogical background.*Maintain an alert attitude towards the students' needs.*I consider the feedback from students to be an essential factor for my teaching activities. During the course, I perform continuous course evaluations to regulate the quality and the quantity of the course material, adapting the teaching content to the students' individual academic needs. In addition, I use the summaries from previous students' evaluations for adjusting my teaching performance and contents.*Be open to comments and new pedagogical ideas from colleagues.*Great part of my experience comes from practising the trade and listening to the advise of other colleagues, specially from those more experienced. In this sense, I praise any constructive feedback and suggestion, as well as new pedagogical ideas to be implemented in the classroom (use of online resources, videos, applets,...).*Reflect on my own performance.*After each teaching session, I spend some time reflecting upon it, thinking about the positive and improvable aspects, for future adjustments. For instance, if there is an important concept that I have perceived the students to have difficulties to assimilate, I spend some time for adjusting the contents of the next tutorial or lecture, preparing examples or relevant exercises, for clarifying this concept. I use also this information for improving the teaching for the next year.