A Case Study of a Training Program for Teachers of Mathematics
María Isabel Ramírez, Center for Research and Development in Education (CIFE) at Universidad de Los Andes,
Bogotá, Colombia.
Abstract: This document is part of a case study for the professional contexts axis of the Bachelor’s
program in Elementary Education with emphasis on Mathematics. This program was established
in 1999, in order to train mathematics teachers to respond for the high demands of the Colombian
context in this field. Today, more than 243 professionals have been graduated from this program
and it is considered a curricular innovation in Colombia.
The goal of qualitative study was to better understand the educative experience denominated ‘professional contexts
axis’. This experience is the articulating factor on which the entire curriculum actually depends. In this sense, the
skills, abilities and knowledge acquired by students in other axis’ program make sense for them in the professional
contexts axis. Doing so, I used as data collection techniques interviews and surveys. The main sources of
information were students, teachers, administrative stuff, graduated and employers. The results show how important
this experience is and how valuable it is as a pedagogical educative experience. In conclusion, these results are
relevant in the comprehensive training for teachers of mathematics in High Education.
Background and Literature Review
The Bachelor’s program in Elementary Education with emphasis on Mathematics was designed to address the
difficulties presented by the training of mathematics teachers in Colombia. [1] The separation of the three
components in the formation of a teacher: mathematics, pedagogy and humanities, [2] the belief that to teach math it
is enough to know math, and [3] to recognize that school mathematics is different from mathematics itself
(Vergnaud, 1995; Chevallard, 1995 quoted in Romero, 2002).
Lurduy (2009) presents The Bachelor’s program in Elementary Education with emphasis on Mathematics as a
training program for teachers of mathematics that has taken one perspective from the pedagogy as a reconstructive,
critical and complex discipline. Also, it was based in a systemic perspective of the didactics of mathematics and
mathematics education as a scientific discipline. It means, it is conceived as a research project from a viewpoint
supported interdisciplinary research conceptions and beliefs from the teacher and math teacher, curriculum
innovations and curriculum as a research project, research and conceptualization in teacher training mathematics, the
construction of professional knowledge of mathematics teachers, reflective professor and research professor, and
problem solving as teaching methodology. Since the program's inception in 2000, the curriculum is divided into four
axis of training: school mathematics, advanced mathematical thinking, practice in the classroom and professional
contexts, which is the focus of this research study.
However, research regarding the training of mathematics teachers in last generation programs (2000-2009) is recent.
The information like research, articles in recognized journals, academic production plus the skills developed and
learning acquired in these programs is nonexistent (Lurduy, 2009). Also there are few evaluation programs
concerning specific aspects such as the role of the pedagogy, social and human in the training of teachers of
mathematics. In this respect Wood (2008) relates the specific aspects of the training of mathematics teachers as
issues that deserve further investigation. To bridge the gap in research its study was designed to take a closer look at:
[1] perspective with stakeholders on how to address the teaching and learning of pedagogy in the program, and [2]
the contribution of this axis to the formation of mathematics teachers in Colombia.
Methodology
The case study was conducted at public university in Bogotá, Colombia. A total of 293 students (75%), the
coordinator of program, 10 teachers, 37 graduates and 12 employers made the stakeholders groups. They gave their
perceptions from their experiences about the professional contexts axis and they talked about how this experience
has affected their practice or their career path. The approach to the stakeholders was made through surveys and/or
semi-structured interviews during twelve weeks of the second semester of 2011.
Data Analysis and Results
The data was analyzed using qualitative techniques established by Robert Stake (2010). This qualitative design
assisted in defining codes and developing a way perspective on the perceptions of the stakeholders.
The stakeholders identify some important factors of axis. They agreed that the execution of the program corresponds
to a solid design that is evident in [1] the theoretical basis of complex thinking, [2] the value added, offering teacher
training: the knowledge across of mathematics, [3] which encourages reflection on the student-teacher: the
complexity of human beings and the reality of the profession "math teacher". Consequently, stakeholders consider
that the professional contexts axis brings from three large fields to mathematics teacher training:
Pedagogical training. By transforming traditional teaching and encyclopedic pedagogy, this axis links the whole
human component to teacher training.
Development of five skills. (a) Critical thinking, to give items for students to have understanding about education in
relation to the condition of the world. (b) Communicative skills, the professional context axis maintains a high level
of requirement from all activities that promote processes regarding reading, oral and writing skills. (c) Teamwork as
one of the skills that today’s professional must manage. (d) The ability to solve problems. The professional contexts
axis gives analysis elements that allow student to think and solve problems of their profession. (e) It contributes to
develop research skills in their practices.
Teacher’s Projection The professional context axis encourages students to make teaching their option for life. It
works for the construction and establishment of the identity of the teacher. It invites students to think themselves as
future teachers of mathematics and to be aware of the implications of this for their professional lives. Finally, it
remarks the social, political, ethical and moral responsibilities they will have with their future students’ lives.
Discussion / Conclusion
This work contributes to close the gap between research on mathematics teacher training, both in the national and
international field (Wood, 2008). This identifies the important elements of a successful practice of pedagogy
teaching in a training program for mathematics teachers, who have accepted the challenge of innovation in higher
education. It is presented a discussion on some aspects that are generally not considered relevant in higher education
curriculum related to the training of mathematics teachers.
References
Lurduy, J. O. (2009). El profesor investigador de su práctica. Formación y competencias. En Revista Uno: Revista
de Didáctica de las Matemáticas. No. 51. p. 19 - 29.
Lurduy, J. O. (2009). Investigación en la formación de profesores de matemáticas. Agendas y perspectivas. En
Revista Científica No.11. p. 165 - 178. Bogotá, Colombia: Universidad Distrital Francisco José de Caldas.
Romero, J y otros (2002). Matemáticas para todos. El sentido de la profesión profesor(a) de Matemáticas. Bogotá:
Universidad Distrital.
Stake, R. (2010). Qualitative Research: Studying how things work. The Gildford Press, USA.
Wood, T. (2008). The International Handbook of Mathematics Teacher Education. Purdue University, West
Lafayette,USA (eds.)