# Initial Teacher Preparation

In this work the types of institutions where teachers are prepared, the degrees that are given, the extent to which teacher preparation is related to the national school curriculum, as well as the curricular components of teacher education, are of interest. Identifying the specific pedagogy of mathematics (mathematics teaching methods courses) is of particular relevance, as it is an indication of the extent to which mathematic education in the country has developed as an independent discipline.

In some of the cases presented here, teacher preparation is designed for secondary teaching, but also serves for teaching mathematics in institutions of higher education (in programs that require mathematics), but not for doing research in mathematics.

In these countries initial teacher preparation is provided in universities and other higher education institutions (such as “normal schools” in the Dominican Republic). In each country the names of the undergraduate degrees are different (or the same names may refer to different degrees).

In Colombia, initial teacher preparation was in normal schools, then in higher normal schools, and eventually the “normal” programs were passed to schools of education in the universities. Since the middle of the first decade of the 21st century, teacher preparation has been considered to be “technical” rather than “professional”. With respect to secondary education, since the 1990s individuals with undergraduate degrees (“licenciados”) have taught mathematics in secondary schools. By the end of the last century, a basic undergraduate degree with a major in Mathematics *(Licenciatura Basica con Enfasis en Matematicas)* has been offered for lower secondary teachers and an undergraduate degree in Mathematics (*Licenciatura en Matematicas*) for teachers in upper secondary schools. However, in practice those with the degree in Mathematics work at all levels of secondary schools, as do those with degrees in other fields. Elementary school teachers have either received a very general teaching degree or a degree in some other field.

In the last 15 years, the initial teacher preparation programs in Colombia have moved from an emphasis on mathematics to an emphasis on pedagogy, which has led to the expansion of mathematics education as a field. The main emphasis to date has been to follow a curricular model based on competencies.

In general, initial teacher preparation programs in Colombia include mathematics, curriculum, mathematics pedagogy, general pedagogy, and elements of communication to support actions in the classroom. There is also a course in either physics or computer science. The mathematics courses include Arithmetic and Algebra, Calculus, Geometry, Probability and Statistics. With respect to curriculum and pedagogy, the courses are related to the national *Curriculum Guidelines for Mathematics* or to research results in mathematics education.

Since 1996, in the case of Venezuela, initial teacher preparation from elementary through secondary has been structured with four dimensions: general, pedagogical, specialized and professional practice. For secondary schools the initial preparation is in public universities. For elementary schools, both public and private universities provide programs. There are a variety of degrees offered to future secondary teachers: Mathematics Teacher; and Bachelor’s Degrees in Education with a major in Mathematics, in Mathematics, in Mathematics and Physics, in Mathematics Teaching or in Mathematics and Computer Science. The programs are for four or five years. The mathematics courses include Geometry, Calculus and Analysis, Algebra, Probability and Statistics. Except for one institution there are no courses specifically on mathematics pedagogy. Student teaching experiences vary widely across the country.

Elementary teachers that teach mathematics in Venezuela are prepared as generalists. They usually have three mathematics courses. Two of them attempt to relate to work in the classroom and the other (Geometry) emphasizes strengthening the logical, deductive and spatial reasoning of teachers.

In Venezuela there is a deep divide between the state educational agencies and the institutions that prepare teachers. In particular, there is not a close and consistent correlation between the official national curriculum and the programs for initial preparation (there is almost no mention of the school curriculum in the courses). The majority of the characteristics of the programs for initial preparation were set in the 1990s and have not been changed very much. A relevant detail is that there is a shortage of secondary mathematics teachers.

In the Dominican Republic most of the initial teacher preparation programs for grade 1-8 are in normal schools and universities under the coordination of the National Teacher Institute for Preparation and Professional Development *(Instituto Nacional de Formation y Capacitacion del Magisterio).* Recently there has been a great demand for teachers particularly for grade 1-8. The teacher education programs were divided into grades 1-4 and grades 5-8. In those programs mathematics courses were no more than 10 % of the total and mathematics teaching methods courses were almost non-existent. For upper secondary education (grades 9-12) initial teacher preparation which is called “Secondary Education with a major in Physics and Mathematics” is structured with the usual dimensions: mathematics, general pedagogy, mathematical pedagogy, general education, etc. There are also courses in physics given the double major. The mathematics courses that are usually present are Algebra, Trigonometry, Higher Algebra, Statistics and Calculus. Mathematics teaching methods are usually confined to one course associated with student teaching. In the Dominican Republic the student teaching experience varies greatly from institution to institution.

In Costa Rica the public and private universities are charged with providing initial teacher preparation for both elementary and secondary teachers. Elementary teachers receive a bachelor’s degree (four years in the public universities) or a licentiate’s degree (5 or more years in the public universities). The program prepares generalists with at most two or three mathematics courses; in some private universities courses from other disciplines replace the mathematics courses. For secondary teaching the initial preparation can be a three-year Teaching degree often called a “profesorado”. This degree is considered to be a lateral exit from the bachelor’s or licentiate degrees. These three-year programs for preparing secondary mathematics teachers have courses in mathematics, general teaching methods, mathematics pedagogy, general education and student teaching. Beginning near the end of the first decade of the 21st century the public universities have made efforts to increase the time dedicated to mathematics pedagogy. As of 2016 this process is still being developed with different levels of success. The mathematics courses include abstract algebra, linear algebra, calculus and analysis, geometry and topology, probability and statistics, and number theory. Various private universities offer initial teacher preparation programs. Although their programs are fairly similar to those in the public universities, they usually require one or two years less. In Costa Rica the programs for initial teacher preparation, particularly at the secondary level, have had to make changes related to the new school mathematics curriculum adopted in 2012.

In these countries, most initial preparation of teachers is done in a face-to-face format.

With respect to initial preparation for elementary schools a “generalism” predominates, that is, a preparation for teaching all subjects. However, in Costa Rica there is some subject matter specialization, in Colombia the title of the degree indicates the specialization, and in the Dominican Republic there are plans for such specialization.

For secondary education (grades 6 or 7 to 12) there are initial teacher preparation programs that focus on mathematics teaching. In all four countries the programs are similar, although with some differences in the proportion dedicated to various aspects of the programs. For example, in Venezuela and the Dominican Republic there is less emphasis on mathematics pedagogy than in the other two countries.

The degree to which teacher education is aligned with the national school curriculum various from country to country. In Venezuela there is very little alignment. There is somewhat more in the Dominican Republic. In Colombia there is supposed alignment, but regional autonomy in program implementation makes it difficult to confirm. In Costa Rica the universities that provide teacher education programs have made an effort to align their programs with the new national curriculum, but they have not completed the process.

The teacher education programs in these four countries do not require previous university studies (such as, for example, a bachelor’s degree in mathematics). A student decides upon entering the university that they will become a mathematics teacher. However, the students are not recruited from among those with the strongest academic backgrounds.

There is use of technology in all of the initial teacher preparation programs in these countries, although each one has weaknesses and challenges. Despite requiring the use of technology in teacher education programs in Colombia, it is not clear how that leads to classroom implementation and what the impact might be. In Venezuela there is also a requirement to use information and communication technologies, but until recently they had not been incorporated into the teacher preparation at either the elementary or secondary level. There are now plans to introduce them across all disciplines. In the Dominican Republic there is some minimal use of technology but not specifically in mathematics. The new national curriculum in Costa Rica includes a relatively strong use of technology in the classroom; also the on-going curricular implementation has had a vigorous use of online communication technologies for in-service teacher development. This process is leading to new technology uses and perspectives in pre-service teacher education.