Helping Students Make Sense of Logarithms and Logarithmic Relationships

Abstract

This paper summarizes difficulties that chemistry students at all levels commonly exhibit when translating, manipulating, and interpreting mathematical expressions that contain logarithms, and offers approaches that the authors have found useful to help students overcome such difficulties. The online supplement provides problem sets created by the authors, based on student–instructor interactions that have taken place during many classes, help sessions, and laboratories. They range in level of difficulty from those appropriate for high school and first-year college students, to those appropriate for more advanced students.

Development of a Biological Science Quantitative Reasoning Exam (BioSQuaRE)

“…Some of these difficulties have been previously documented in the STEM literature. For example, students’ difficulty with logarithms, primarily in the context of pH, has been described ( DePierro et al , 2008 ; Watters and Watters, 2006 ), and misconceptions about hypothesis testing are known to be a challenge in statistics education (e.g., Castro Soto et al , 2009 ).…”

Exploring Exponential Decay Using Limited Resources

“…For many years we have relied on an action research model, in which feedback obtained by observing students and interacting with them in the laboratory, classroom, and help sessions has guided improvement of classroom presentations and laboratory activities. ,− The evolution undergone by this experiment over several years is a case in point. Although estimation of the excess thermal energy in the stainless steel shell of the thermometer is crude at best, we found that it was easier for students to think about an extensive property, energy, leaving the system as time passes (TE = TE 0 e – kt ) rather than thinking about how the difference in temperature between the room and the warm system decreases as time passes (Δ T = Δ T 0 e – kt ).…”

“…The responses of some students to the graph interpretation activity in Part A of the experiment indicated that they were still struggling with simple ratio interpretation. In addition, logarithms have always been a challenge to many students, so it was deemed best to avoid confronting them with expressions like ln (Δ T /Δ T 0 ), as was done in earlier versions of the experiment. The logarithm of a ratio of two quantities that are each in turn the difference of two quantities is not easily interpreted by most students.…”

¿Interpretan los alumnos de ingeniería química los gráficos logarítmicos correctamente? Desarrollo de una herramienta para mejorar su precisión

“…A continuación se enumeran algunos ejemplos de los diagramas logarítmicos más utilizados en el campo de la ingeniería química: Pese a que existe una predisposición natural en los humanos a interpretar cambios de variables en escalas lineales, multitud de procesos naturales también tienen lugar en forma de caídas o incrementos exponenciales. En el campo de las ciencias naturales, existen diversas propuestas docentes basadas en laboratorios de química o de física para inculcar la comprensión de dichos procesos y familiarizar a los alumnos con el uso de representaciones logarítmicas (DePierro, Garafalo, & Toomey, 2008;Di Capua, Offi, & Fontana, 2014;Park & Choi, 2013). En los estudios de Ingeniería Química, la lectura de diagramas con escala logarítmica se suele tratar de forma accesoria en la resolución de algunos problemas muy específicos de diferentes asignaturas.…”