Historically, the way of teaching mathematics adopted an expository and deductive approach in which the role of the teacher was predominant. The development of communication and information technologies, the curricular reforms in response to the demands of teachers and students and the need to achieve a mathematically competent society triggered the introduction of approaches in which the student body begins to have a leading role.

The foregoing seems to reflect the existence of two types of teaching practices: those in charge of those who remain anchored in a traditional teaching of mathematics compared to those who opted for a change. However, reality is not dichotomous. Most mathematics teachers do not respond to one of these two archetypal profiles, but to a combination of four tendencies.

Conceptions and beliefs

Although the profile of a teacher is determined by multiple factors (for example, the context, behavior, skills, identity, or mission), teachers’ conceptions and beliefs about teaching and learning mathematics play an important role. determining role in their teaching practice. In turn, these conceptions and beliefs influence other aspects related to the teacher, such as knowledge of it.

The conceptions and beliefs about the teaching and learning of mathematics refer to the premises or propositions held psychologically by the teacher about the learning objectives, their own role in teaching, the role of the students, the activities, the didactic approaches, mathematical procedures, or learning outcomes.

For a teacher, describing their conceptions and beliefs about the teaching and learning of mathematics is a complex task. On the other hand, identifying with a didactic trend is easier.

Four types of approaches

From this perspective, we consider four didactic tendencies : the traditional, the technological, the spontaneous, and the investigative.

The traditional trend is characterized by the adoption of an expository style as the only teaching method and the textbook as the only resource. Understands that learning is achieved using only memory, and conceives evaluation as a final activity.

In this trend, the repetition of type exercises is the protagonist of the activity in the classroom. The students listen to the teacher’s explanation (based on a literal transmission of what appears in the textbook) to be able to repeat the explained process later.

In the technological trend , teachers carry out a simulation of the knowledge construction process from an informative, practical and organized perspective. Assessment is done throughout the learning process.

A characteristic practice of this trend would be the repetition of exercises that try to reproduce the logical processes and the mistakes made on a regular basis by the students. The teacher exposes the content in an organized and attractive way, and the students reproduce this content, thus imitating their cognitive style.

The spontaneous tendency is characterized by proposals in which the student understands the learning objectives through context and manipulation. With it, the acquisition of unorganized knowledge is produced, which is channeled through evaluation.

In this trend, the student performs non-reflective activities created by the teacher, actively participating in each of them, and the teacher analyzes their reactions and responds to their proposals.

Finally, in the investigative trend , teachers organize the teaching process to ensure the acquisition of knowledge through research. In other words, they are committed to a more autonomous learning by the students.

Typical practices of this trend would be the confrontation of the students with situations for which they do not have known resolution processes, where the teacher provokes the search for answers to new questions and arouses the curiosity of the students.

Types of math teachers

Based on the responses of 247 future teachers, both in Primary and Secondary Education, on the degree of agreement with certain statements about mathematics, teaching methodology, learning processes, the role of students, and the role of the teacher, Four factors emerge that explain the conceptions and beliefs of the teaching staff (investigative aspects, the role of the teacher, the role of the textbook, and teaching planning) and four groups of teaching profiles .

What is significant is that each of these profiles does not respond to a single didactic tendency, but to a combination of the four previously described, distinguishing themselves in the weight with which they conceive each one of them.

For example, the group of teachers that shows a greater degree of agreement with typical affirmations of the investigative tendency, also prioritizes the role of the teacher in the classroom (this belief being characteristic of a tendency such as the traditional one).

Primary – secondary differences

One aspect to take into account is the differentiated behavior that is observed according to the academic training of the future teachers, that is, between those with a degree in Primary Education (who will carry out their teaching work in this educational stage) and those with a degree in mathematics. (candidates to teach in Secondary).

It is possible to assume that the way in which mathematics has been taught to one and the other is different. The training of future teachers has a more constructivist nature than that of mathematics students, completely outside the field of mathematics didactics.

In turn, it is known that the type of teaching received by those who plan to be teachers exerts a certain influence on their own beliefs and conceptions about the teaching and learning of mathematics, to the point that future teachers tend to inherit the models with which he has been trained, especially at the beginning of his teaching career.

This helps to explain that the way of teaching mathematics known to those with specific training in this field comes from what they have observed in their teaching staff in Secondary and University Education, which is still highly influenced by formalism.

However, it is also possible to distinguish in this future teacher traits of spontaneous and investigative tendencies in their conceptions and beliefs about the teaching and learning of mathematics.

Has anything changed in the last 30 years?

The results of similar research carried out 30 years ago indicate a predominance of traditional and technological trends. Even though there are reminiscences of both, in the current reality the investigative and the spontaneous are the two most represented didactic tendencies. One possible explanation is the curricular changes that have taken place in recent years, characterized by teaching and learning mathematics with a more constructivist approach.

The X-ray of the current teaching profile does not obey the old dichotomy between constructivism versus transmission, it even makes it impossible to encapsulate the conceptions and beliefs about the teaching and learning of mathematics in rigid and well-defined profiles, but advocates a combination of different characteristics.

Author Bio: Laura Muniz Rodriguez is Assistant Professor Doctor at the University of Oviedo