## Reflection: Developing a Conceptual Understanding Exponential Functions and Logarithms - Connecting the Dots - Section 2: Lesson Middle

When I first started teaching logarithms, I quickly discovered that I was having a difficult time explaining to the students why we could not have a negative base.  Although it sounds like a sufficient explanation to a math teacher, when I would say "A negative base with an exponent will oscillate signs," the students just weren't following.  Early on in my teaching of the course, I remember saying this 2-3 times per class period.  A similar (even uglier) explanation followed each time that my students would ask why we couldn't take the logarithm of a negative number.

Rather than explaining these concepts in the context of a logarithm, I discovered that I could have greater success with my students if I translated what I was saying to exponential form.  I found the attached article to be extremely helpful in my explanation to the students.  Creating 2-3 problems on the board with the "boxes" helped my students visualize what I was saying about the negatives, and then I was able to connect the examples to the definition of a logarithm.  This worked out much better for everyone involved!  Trying to grasp what a logarithm is and break down the issue of negatives proved to be too much.  However, I found success in teaching the issues of negatives in exponential form first, and using what we showed to supplement our definition of a logarithm.

Developing a Conceptual Understanding: Addressing the Issue of Negatives

# Exponential Functions and Logarithms - Connecting the Dots

Unit 2: Exponential and Logarithmic Functions
Lesson 8 of 21

## Big Idea: This lesson builds nicely on the students’ knowledge of inverse functions and introduces them to the world of logarithms. Rather than trying to memorize mathematical notation, the students are guided through an in-depth study under the umbrella of exponen

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45 minutes

### Jarod Hammel

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