Logarithms
Lurking in the Shadows
(A WebQuest)
(A WebQuest)
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Logarithms
Lurking in the Shadows (A WebQuest) |
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This Webquest is designed to bring the logrithms out of the dark and into the light. Logarithms are an important concept introduced in College Algebra. At this point, logarithms may just be a name for another set of steps (algorithms) your teacher wants you to follow. Upon completion, you will know the importance of logarithms, the history behind them and some places where logarithms appear.
You probably know the definition of logarithms in terms of exponential expressions, but what you may not know is that their relationship with exponents wasn't even realized until years after their invention. Indeed, there was another reason that led mathematicians to develop the idea of a logarithm, and part of your task is to identify those mathematicians and the reasons behind their work.
There are many contexts in which logarithms are used today. Most commonly, they are used to design certain measurement scales. Other uses of logarithms that were very common in the past have now been programmed into machines, so that we do not actually see the logarithms on the surface. In this day and age, one encounters many logarithms without even realizing it, because they do most of their work behind the scenes. The other part of your task is to find some of these logarithms lurking in the shadows.
Your assignment consists of writing a report that contains three parts. Each group will turn in one report. For your research, you may use the links to the websites that I have provided as well as any books or other outside sources. A list of references must be included at the end of your project.
1. First, research the history of the logarithm. Write 1-2 pages about the following topics:
Who were the mathematicians responsible for inventing logarithms?
What reason led them to invent logarithms?
Who was(were) the mathematician(s) responsible for adapting logarithms into the system that we recognize today?
Though not required, you may also write about any other historical topic relating to logarithms that you find interesting. (The discovery and uses of the natural base "e" is one such possibility.)2. Find three applications of logarithms in real-life situations that you find interesting. For each of the three applications, include the following:
Description of the application
Your reason for choosing the application
Explain exactly where the logarithm appears in the application and how it works mathematically. You will need to use all the knowledge you have about logarithmic functions and possibly exponential functions here. This section must include a mathematical equation describing the process, with all variables clearly identified.
Though not required, you can discuss any other aspects of the situation that you find interesting. For example, explain why the use of a logarithm is convenient in your particular context or if the use of logarithms could lead to misconceptions by those who are not aware of its role.3. Finally, write a one page reflection about the experience you had working on this project.
Did you enjoy learning about some of the history of mathematics?
Do you have a better knowledge of and appreciation for logarithms now that you know why they were invented and some places where they appear in
nature? You may answer these questions and/or talk about anything else relating to your project experience.
* Arranging - Meet as a group and choose the most interesting sites. Do not include every site found - only those that capture your interest and would therefore capture the interest of your classmates and teacher.
* Presenting - Present your information in a report (preferably illustrated). Each individual must write a one page reflection about the experience you had working on this project to be turned in with the report.
Resources
These resources are just examples
of the types of sites available on the internet. You will be able to find
other websites by performing searches.
Blinn College Library
College Algebra, 3rd Edition by Stewart, Redlin, and Watson - Real world
uses can be gathered from several sources. A starting place is your text where
you can gather occupations that use logarithms by looking at the application
problems.
History of Logarithms:
http://www.ualr.edu/~lasmoller/napier.html
http://pages.cpsc.ucalgary.ca/~williams/History_web_site/time%201500_1800/logarithms%20and%20slide%20rules.htm
http://michaelshepperd.tripod.com/algloghist/
http://www.csc.liv.ac.uk/~ped/teachadmin/histsci/htmlform/lect3.html
http://home.att.net/~numericana/answer/culture.htm#napier
http://www.rit.edu/~bpbsma/Slide%20Rule.htm
Applications of Logarithms:
http://www.dxarts.washington.edu/music/courses/401-3/mathbasics/#logpitch
http://asms.k12.ar.us/asms_teaching_units/Teaching_Units/Mathematics/Applications_of_the_Logarithm.htm
http://library.thinkquest.org/C0110248/algebra/isllog.htm?tqskip1=1&tqtime=1130
http://members.aol.com/hostaacpae/private/topics/loginfo.html
http://www.tpub.com/photographyadv/14.htm
Evaluation
This WebQuest will be evaluated
based on the following rubric:
Final Grade = 4 times Group score (max 64) + 3 times Individual score (max 36)
Total points possible = 100
Individual Score
| Category | Outstanding 4 |
Accomplished 3 |
Developing 2 |
Minimal 1 |
| Initial research | 2(or more) exceptional uses of logarithms found | 2 interesting uses of logarithms found | 1 interesting use of logarithms found | 1 uses of logarithms found |
| Evidence of group participation | Taking a leadership role in the group and actively participating | Actively participating in the group | Participating in group but only with minimal input | Providing little input into the group project |
| Report | Providing input into the report Report outstanding |
Providing input into the report | Providing input into the report | Providing little input into the report |
Group Score
| Category | Outstanding 4 |
Accomplished 3 |
Developing 2 |
Minimal 1 |
| Evidence of Group Collaboration | More than 3 interesting uses of logarithms - at least one from a website not provided | More than 3 interesting uses of logarithms | 3 interesting uses of logarithms | less than 3 interesting uses of logarithms |
| Accuracy | Exceptional information | Useful information | Little information gained | No information gained |
| Report | Group worked well together. Every individual providing input into the report Report outstanding |
Group worked together. Every individual providing input into the report Good report |
Group had some difficulties working together.
Some individuals providing little input into the report |
Group depended on one individual to do all the
work. Other individuals providing little input into the report. |
| Creativity | Report well organized, illustrated, and documented | Report well organized, illustrated, and documented (2 of 3) | Report well organized, illustrated, and documented (1 of 3) | Minimal effort to prepare report |
Thank you all for participating in this project. Hopefully, you have enjoyed your experience and now have a better understanding of the concept of logarithms. You now have two different ways of looking at logarithms and have seen a relationship between mathematics and history as well.
The WebQuest concept was originally developed by Bernie Dodge at San Diego State University.
Thank you to Dr. Cindy Peterson for introducing me to so many uses of hypermedia in the classroom.
Thank you to Matt Kurser for allowing me to modify his WebQuest for Blinn College students.
Freeware clipart courtesy http://www.clipart-graphics.net
A College Algebra
WebQuest Designed by Karen Anglin Mathematics Instructor Blinn College Last Updated April 7, 2003  Top |