The PhD dissertation “An approach to the relationship between teacher’s knowledge and the making of connections in the classroom” constitutes a contribution to the field of Mathematics Education, particularly to the study of teacher knowledge. The implicit relation between teacher knowledge and connections is identified from a theoretical analysis of different models for teacher knowledge. This relation generated the key research question: ¿How does teacher’s knowledge influence the making of connections in the classroom? To tackle this question, four goals have been posed: 1) To identify connections in a real classroom setting and characterize them; 2) To create a definition of connection from a practical perspective and to establish criteria to classify them; 3) To identify what kinds of teacher’s knowledge are related with each kind of connection; 4) To analyze the links between different kinds of teacher knowledge for the making of connections in the classroom. To achieve these goals eight consecutive sessions from a real class have been analyzed in a public secondary school in Barcelona, with 12 and 13-year-old students. The theoretical framework has two main parts. Firstly, the making of connections is analyzed from three different perspectives considering a classroom context: the mathematical content, the students and the teacher. Secondly, a deep revision of the reference models for teacher knowledge is carried out. As a result of this analysis, a reinterpretation of Shulman’s model (1986) is proposed. The reinterpretation is based on the three original dimensions of teacher knowledge: mathematical content knowledge, pedagogical content knowledge and curriculum knowledge. A case study is conducted. The intensive analysis of the same group during one teaching unit gave homogeneous data. The analysis of the data showed explicit links between knowledge and the making of connections. For the first two goals, the analysis design was inspired by the grounded theory paradigm. The constant and meticulous comparison between partial results and data resulted in the construction of a classification for connections in a classroom environment. Next, indicators of teacher knowledge are identified for each kind of connection. Results showed that there is a strong relationship between the explicit discussion of student’s mistakes in the classroom and the emergence of connections. Thus, connections are considered as a web of links, and it’s incomplete or wrong interpretation produce common misconceptions. Four kinds of connections are identified: extramathematical connections; intramathematical connections related with cross processes; intramathematical connections with conversion; and intramathematical connections with treatment. An explicit relation between each kind of connection and kinds of teacher knowledge is identified, described and discussed. This relation permitted the identification of the kind of knowledge that is related with the enrichment of connections in terms of taking advantage from the learning opportunities. Conclusions suggest that there are different levels in teacher knowledge that can be described in terms of the different kinds of connections and the depth of the mathematical knowledge that is constructed. The progression in these levels is related to the teacher’s capacity to make sophisticated connections and to use the opportunities that emerge from the classroom activity.
Aproximación a la relación entre el conocimiento del profesor y el establecimiento de conexiones en el aula
Gamboa Rojas, G. D. (Author). 17 Dec 2015
Student thesis: Doctoral thesis
Student thesis: Doctoral thesis