Comparing the Didactic-Mathematical Knowledge of Derivative of In-Service and Pre-service Teachers

Walter Fernando Castro Gordillo,Luis Roberto Pino-Fan

doi:10.17648/acta.scientiae.5842

Abstract

Background : The knowledge that a mathematics teacher should master has taken an increasing interest in recent years. Very few studies focused on comparing didactic-mathematic knowledge of in-service and pre-service teachers aimed at identifying features of the teachers’ didactic-mathematical knowledge on specific topics that can establish a line between pre-service and in-service teachers’ knowledge for teaching. Objective : The research aims to compare derivative knowledge of pre-service and in-service teachers to identify similarities and differences between teachers’ knowledge. Design : This research is a mixed and interpretative study. Settings and Participants : The participants were 22 pre-service teachers, and 11 in-service teachers enrolled in a pre-service teacher education programme and a master’s programme, respectively. Data collection and participants : Data were collected based on a questionnaire designed purposefully for the study. Results : The results show that pre-service teachers lack both epistemic derivative knowledge, while in-service teachers not only have this knowledge but relates it to its use in teaching. Pre-service teachers may not be making sense of the concept of derivative means, much less related to teaching. Conclusions : The insufficiencies found in pre-service teachers’ knowledge justify the pertinence to design specific formative cycles to develop prospective teachers’ epistemic facet of didactic-mathematical knowledge. It is recommended that both in-service and pre-service teachers discuss activities in which they can identify and reflect on possible mistakes and errors made by students. The development of these formative cycles should consider the complexity of the global meaning of the derivative.

Highlights

Teacher education is experiencing unprecedented attention by the mathematics education research community and the government
The analysis of data concerning the cognitive configuration is carried out by the technique known as semiotic analysis (e.g., Malaspina & Font, 2010; Godino, Font, Wilhelmi, & Lurduy, 2011), which allows describing systematically both the mathematical activity performed by teachers while the primary mathematical objects are put in place to solve the problems
The type of didactic-mathematical knowledge is closely related to the feature type of cognitive configuration associated with students’ answers, because the epistemic facet of didactic-mathematical knowledge depends on the presence or absence of the mathematical objects, their meanings, and relations among them

Summary

Introduction

Teacher education is experiencing unprecedented attention by the mathematics education research community and the government. Objective: The research aims to compare derivative knowledge of preservice and in-service teachers to identify similarities and differences between teachers’ knowledge. Pre-service teachers may not be making sense of the concept of derivative means, much less related to teaching. Conclusions: The insufficiencies found in pre-service teachers’ knowledge justify the pertinence to design specific formative cycles to develop prospective teachers’ epistemic facet of didactic-mathematical knowledge. It is recommended that both in-service and pre-service teachers discuss activities in which they can identify and reflect on possible mistakes and errors made by students. The development of these formative cycles should consider the complexity of the global meaning of the derivative

Objectives

Methods

Results