Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions

Vicenç Font,Karen Gisel Campo-Meneses,Javier García-García,Alicia Sánchez

doi:10.29333/ejmste/11126

Abstract

The current paper aims to identify the mathematical connections activated by 10 Mexican high school students while solving mathematical tasks that involve the exponential and logarithmic function. We used the Expanded Mathematical Connections Model (EMCM) and the Onto-Semiotic Approach of Cognition and Mathematical Instruction (OSA) as theoretical frameworks. Task-based interviews were used to collect data that was analyzed using thematic and onto-semiotic analyses. It was found that the connection of reversibility is essential for achieving students’ full understanding of the existent relationship between the exponential and logarithmic function; however, this requires a network of connections.

Highlights

Mathematical connections activated by Math students and teachers represent a scope of action that claims more and more attention by the international community of researchers specialized in Didactics of Mathematics and the educational administrations at a global scale (e.g., Jaijan & Loipha, 2012; Koestle et al, 2013; Mhlolo, 2012)
The current paper aims to identify the mathematical connections activated by 10 Mexican high school students while solving mathematical tasks that involve the exponential and logarithmic function
The following reasons have led us to set out our aim: 1) By consulting literature, we found no previous research focused on the particular study of mathematical connections related to the exponential and logarithmic function (only studies related to the co-variational reasoning such as the one from Gruver (2018), and Ferrari-Escolá et al (2016)), and 2) the study of functions is a key subject in Senior high-school curriculum

Summary

Introduction

Mathematical connections activated by Math students and teachers represent a scope of action that claims more and more attention by the international community of researchers specialized in Didactics of Mathematics and the educational administrations at a global scale (e.g., Jaijan & Loipha, 2012; Koestle et al, 2013; Mhlolo, 2012). The NCTM (2000) declares, among its principles and standards, that students must be capable of reorganizing and establishing connections among mathematical ideas. According to this curriculum, making mathematical connections enhances students’ possibility to develop a better understanding of a given problem, as well as a better understanding of mathematics as a body that comprises interrelated objects (NTCM, 2013). The current research is settled in this research agenda and aims to study the mathematical connections activated in Mexican high school students’ practice when solving tasks regarding the exponential and logarithmic functions

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