Academic journal article The Mathematics Enthusiast

Mathematical Problem Solving in Training Elementary Teachers from a Semiotic Logical Approach

Academic journal article The Mathematics Enthusiast

Mathematical Problem Solving in Training Elementary Teachers from a Semiotic Logical Approach

Article excerpt

Abstract: The aim of this article is to consider the professional knowledge and competences of mathematics teachers in compulsory education, and to propose basic tasks and activities in an initial training programme in the framework of a global proposal for "Immersion" in the curriculum of the educational phase which the trainee teacher would go on to work in. Problem-solving, in this context, is considered as being an inherent part of mathematics and this is described in terms of problem-solving, establishing connections between concepts, operations and implicit processes in the mathematical activity (conceptual field) and their relationships problem-solving; and it is assumed that the learning of problem-solving is an integrated part of learning in mathematics.

Keywords: Problem Solving, Teacher Training, Didactical Analysis, Semiotic Logical Approach (SLA).


The analysis of the results obtained, in recent years, in different national (in Spain) and international assessments shows that the knowledge of mathematics (Problem Solving) of students in compulsory education (K-9 Grades) is insufficient in terms of the desired curriculum. What needs to be done to improve the learning and teaching of mathematics and, in particular problem solving in this educational stage? This question is addressed here by reflecting on the role played by teachers in primary and secondary education in the pursuit of an effective learning of mathematics and problem solving. At present, the initial training of teachers in primary and secondary education takes place within the European Higher Education Area, where primary school teachers need four years training and secondary school teachers are required to have completed a mandatory Professional Masters degree. This initial teacher training has a great opportunity for improvement.

Problem solving in mathematics education

Problem solving has always been regarded as a basic component in the construction of mathematical culture. However, when mathematical knowledge is presented in its final state, what prevails is the conceptual organization of the objects of such knowledge in which problem solving appears again as a core of relevant mathematical knowledge. In the early eighties, in view of the primacy of the concepts and their properties as well as their algorithmic use, problem solving was vindicated as a key activity in the learning of mathematics, which has led to the development of an emerging theoretical and practical body of research in mathematical education, and a notable increase of its presence in the curriculum, either as a further block of contents or as cross content but specific to mathematics at the corresponding level (Santos-Trigo, 2007, Castro, 2008). The follow-up research on problem solving clearly shows that, despite all amount of effort, there are no significant data on the improvement in this on the part of the students and different questions arise ranging from the need to establish relationships and existing connections between the development of the understanding of mathematical contents and problem solving skills, to the need of having theoretical bases to guide problem solving (Lester and Kehle, 2003).

Some authors such as Lesh and Zawojewski (2007), suggest that the rise of research in problem solving was very important between 1980 and 1990, and that some trends are presently aimed at putting an emphasis on critical thinking, technology and mathematical problem solving, and analysis of how mathematics is used in other sciences and professions that does not match the way mathematics is taught in school, or the development of problem solving in other settings or contexts such as situated cognition, communities of practice or representational fluency. These directions and perspectives in solving mathematical problems are, at the present, promising lines of research.

The knowledge and professional skills of a mathematics teacher

The concern, from the point of view of mathematics education, regarding teacher's knowledge and professional skills has been and is, a constant research topic, and is based on the following conjecture: The knowledge and professional skills of the mathematics teacher must be acquired through different scientific domains: mathematics, mathematical didactics and educational sciences. …

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