Date of Award

Spring 5-8-2018

Degree Type


Degree Name

Doctor of Education in Secondary Education



Committee Chair

Dr. David Glassmeyer

First Committee Member

Dr. Kimberly Cortes

Second Committee Member

Dr. Kimberly Gardner


The purpose of this research study was to examine both qualitatively and quantitatively the difference in conceptual understanding of logarithms of students participating in a traditional classroom setting in which a correspondence approach (Confrey & Smith, 1995) was used and students participating in an integrated STEM unit of logarithms and pH in which a covariational approach (Ferrari-Escolá, Martínez-Sierra, & Méndez-Guevara, 2016) was used. In addition, the researcher investigated how students make connections among different representations of logarithms and transferring knowledge between mathematics and science.

A quasi-experimental design was used in which qualitative data were collected using an Observation Protocol and quantitative data were collected using the Logarithms and pH Assessment (LPA). The qualitative data showed that students in the treatment group were thinking of logarithms in a mathematics and science context at a deeper level of conceptual understanding according to Weber’s (2002) levels of understanding exponential and logarithmic functions and Park and Choi’s (2012) levels of understanding pH. In addition, the qualitative data showed that students in the integrated STEM classroom were better able to transfer their knowledge of logarithms to pH and make deeper connections among different representations of logarithms (numerical, algebraic, and graphical). However, the quantitative data from the LPA, which defines conceptual understanding as the ability to represent concept in multiple forms: written, numerical, algebraic, and graphical (Panasuk, 2010; Rittle-Johnson, Siegler, & Alibali, 2001), indicated that the traditional classroom developed students’ conceptual understanding more than the integrated STEM classroom.

This study provides mathematics and science educators with relevant information about incorporating integrated STEM lessons and covariational reasoning to teach logarithms conceptually, to improve a student’s conceptual understanding of logarithms and pH, and their ability to apply mathematical knowledge to settings other than the mathematics classroom.