This learning activity allows the student to explore the graphs of exponential functions and logarithms.
Type of Material:
Classroom demo; student exploration
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Identify Major Learning Goals:
The successful student will learn what the shape of the exponential graph is and what the number e is. The identity b^(x+1) = b*b^x is also explored. An introduction into the graphical definition of logarithms is also explored.
Target Student Population:
Prerequisite Knowledge or Skills:
Graphing functions and the horizontal line test.
This learning object consists of a graphing tool accompanied by three activities. On the left is a frame containing well written instructions that guide the student through the activities. The frames width can easily be resized. On the right is the graphing tool. In the activities, the student is asked to enter the equation of the function y = b^x and then explore the graph for various values of b. The parameter can be inputted, incremented manually, or automatically so that the student can explore the effect on the graph when the parameters change. Instead of telling the student what to do, the activities ask to students to explore on their own. The student is then asked to compare y = x + 1 with y = b^x and find a value of b such that they have the same tangent line. This is a nice visual introduction to the number e. The third activity asks the student to compare b^x with log x in base b.
Reformatting the left activity frame to use bulleting, numbering, or some other organizational technique would make the instructions easier to follow.
Potential Effectiveness as a Teaching Tool
The object is can be used by students learning on their own without the assistance of an instructor. The student using this activity will have the opportunity to explore the graphs of exponential and logarithmic functions without getting frustrated. They will develop a visual understanding of the relationship between the exponential and logarithmic functions. This is especially effective for the student who learns well visually and kinesthetically. For the user who may be unsure of the expected results, summaries are provided at various intervals to keep the user on track.
The animation can be extremely quick, depending on the users computer. An additional comment that using a value of E that is negative will produce a slower graph would be helpful to the student who does not realize this in advance
Ease of Use for Both Students and Faculty
The instructions for each of the activities are easy to follow. If the student follows the directions then there should be no difficulties in using this learning object. A help link that gives explanations on how to use the graphing tool is provided.
The parameter controls could be enlarged and separated so that they do not overlap. It would be helpful to have the Stop button present whenever the animation feature is used.
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