Abstract:

In the field of education, the formulation of new paradigms is an evolution for enhancing the learning process and its outcomes. Based on that understanding within education, several types of paradigms are recognized – behaviorism, constructivism, cognitivism, and historical-social paradigm. In particular, the cognitive paradigm is oriented not only to the teaching knowledge but also to the development of the learning skills; not only to memorization but also to building of thinking skills; not only to reproduction of knowledge but also to applying it in practical situations. The cognitive constructs that this paradigm addresses are attention, memory, intelligence, language, thinking, decision making, problem solving, responsibility, etc. In that context the authors consider the competence approach in education as an instrument of the cognitive paradigm.
The paper is structured as:
• The aim of the paper is to research the establishing of the educational competencies and in particularly the competencies of the mathematics teachers. The paper is based on the pragmatic understanding that educators’ competencies consist of acquiring of complex knowledge and skills at an expert level, which is high enough to be a specialist who can perform a specific task in or outside the academia.
• In priority is to apply the methodology of the qualitative pedagogical research, as it gives opportunity for an in-depth study of the relevant processes and trends. The used methods are content analysis, expert evaluation, case study, behavior diagnostic. Each one of the stated methods has a certain cognitive value and a specific of application. The goal is to combine these methods in such way as to reach to objective interpretation of the results and generalizations with a prognostic focus.
• The subject of analysis is a wide range of issues, related to the key problem - the competencies of the mathematics teachers. The goal of the study is to trace the origin of the concept, its use in a purely professional aspect, its acquisition, stages of development, and evaluation.
The attributes of these competencies are:
- The ability to transform acquired knowledge and skill for a new situation.
- Planning and organizing the professional activities.
- Using the innovations
- Dealing with non-routine situations, etc.
The nature of competencies is studied through a hierarchical scheme of transforming knowledge and skills into competencies. The scheme is consisting of three stages:
- Proceduralization - the process of transition from explicit, directly used declarative knowledge to directly applicable procedural knowledge.
- Tactical learning - the process of learning how to determine the procedures for solving a given task.
- Strategic learning - the process of assimilation of ways of organizing the optimal solution of a problem.
The process of building the competencies of the mathematics teacher is based on several developed examples based on building the concepts of mathematical language, algebra, geometry, heuristics.
• The main goal of the authors is to understand whether and how this hierarchical scheme works at the classroom level. The conclusions from that analysis will allow for planning and realization of the final stage – validation in practice as a part of academic training of professional development of pre-service and in-service mathematics teachers.

Keywords:

Competencies, mathematics teacher training, examples based on concepts, problem solving, content analysis, case study.