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Top2. Mathematical And Didactic Content Of Mathematics
The lack of skills of teachers in knowing and teaching mathematics is a concern among the teacher training community, so the academic field seeks to establish what are the knowledge and professional competences of the prospective teachers of mathematics. Determining these requirements remains a goal of didactic research, especially since the 1980s. These researches are based on the conjecture “the knowledge and professional competences of the professor of Mathematics must be acquired through different scientific domains: Mathematics, Didactics of Mathematics and Educational Sciences “(Socas, 2011). In recent years, several international studies (TIMSS 2015, PISA 2012, etc.) have shown differences in mathematical performance between countries due to a many different factors. Among the important factors of the mathematical performance of students are teachers and their mathematical training, the curricula and the assessment that different countries give to mathematics (Thaqi, 2009). In these studies, it has been shown that the differences between countries are greater than expected, although similar curricula are developed.
On teachers and their mathematical training, Shulman (Shulman,1986) points out for the first time the importance of teaching the specific subject in teacher training. He determined three categories of professional knowledge: Knowledge of the specific subject matter; Knowledge of pedagogical content knowledge and didactic knowledge of the content; and curriculum knowledge. Subsequently, Bromme (Bromme 1988, 1994), describes the qualitative characteristics of the five major areas of professional knowledge, which he calls Knowledge of Mathematics as discipline, Knowledge of Mathematics as a school subject, Philosophy of School Mathematics, Pedagogical Knowledge and Specific Pedagogical Knowledge of Mathematics. These and other studies propose that the professional knowledge of future teachers is not simply a conglomerate of these domains of knowledge, but an integration of them. Considering the Primary teacher also as a math teacher (we know that Primary teachers in addition to Mathematics teach other subjects in their professional practice), and from the perspective of the work that a math teacher must develop, Llinares (Llinares et al. (2000) have identified different components, from which the domains of base knowledge derive, which are necessary to teach Mathematics and which must be taken into account in the training programs: Knowledge of Mathematics, Knowledge on learning mathematical notions and Knowledge of the instructional process. Subsequently, Llinares (2004 and 2009) proposes the articulation of three systems of activities or tasks to develop the knowledge and professional competences of the future math teacher: (i) analyze, diagnose and give meaning to the mathematical productions of his students; (ii) plan and organize mathematical content to teach; and (iii) manage mathematical communication in the classroom.