Δημιουργία και υλοποίηση ενός ηλεκτρονικού περιβάλλοντος για τη διδασκαλία στρατηγικών πρόσθεσης νοερού λογισμού, βασισμένο στα στάδια γνωστικής ανάπτυξης του Jerome Bruner

Abstract

This thesis is based on the design and implementation of a digital environment, which deals with mental computation strategies at First (1st) Grade of Primary School for adding by exceeding ten. At First Grade, students are asked to learn the mechanism of addition and thus, they are taught strategies in order to perform additions easily and correctly. The aim is the students to learn to add fluently until number 20, slowly overcoming the supervisory materials and performing mental additions either by recalling sums (from their memory) directly (recalling mental addition strategies) or by using memorized sums for computing other sums (constructing mental addition strategies). However, the strategies that the students are taught are not always easy to be understood and used, because, at this age, many children need immediate sensing and visualization of quantities with the aid of supervisory materials or even with the use of their fingers. In this thesis, the theoretical model of Jerome Bruner regarding the three stages of cognitive development is applied, so students can start from familiar cognitive techniques and gradually move forward and acquire abstract mathematical concepts. According to this theoretical model, students go through multiple stages of representation of mathematical concepts until they understand and are able to apply the taught mathematical concepts. More particularly, at the first stage of cognitive development, the enactive representation (action-based stage), the young students learn to calculate with the aid of objects, at the iconic representation (image-based stage), they calculate with the help of images and at the symbolic representation (language-based stage), they learn to calculate with symbols, numbers and letters. The importance of multiple mathematical representations lies in the fact that young students are greatly enhanced in normal transition from the one cognitive development stage to the other, understanding in depth and conceptually each strategy and discovering the relations of numbers, which will prove to be very helpful for performing mathematical operations with the following ten, up to number 100. In this study, the following research questions arise: a) Whether the performance of the students in exercises following the attendance of e-course improved and b) To what extent the young students could understand and use the mental computation strategies that they were taught at e-course. E-course is structured in three sections, each one of them represents each stage of cognitive development and at the same time, each strategy goes through all three stages of enactive, iconic and symbolic representation.