Time Traveling to Mathematics’ Past

Time Traveling to Mathematics’ Past

Student Page

A WebQuest for 12th Grade (Calculus)

rileybl@nsuok.edu

Who were the ones that set us on this journey into the mathematical concept of Calculus and what was the purpose of them to develop Calculus?

As you know Calculus has only been used for the last 300 years. But did you know that there were mathematicians that were formulating the ideas and concepts behind the subject in Ancient Greece?

This lesson will let you discover who these famous men (and women) were. You will be introduced to the founding fathers and will discover what they were thinking to come up with the concepts of Calculus.

So get ready to roll your sleeves up and start to discover math’s past.

The Task

You will be using the internet, the library, and history videos to write a 1-2 page paper and give a 5-10 minute presentation over the History of Calculus.

*THIS IS INDEPENDENT RESEARCH OUTSIDE OF CLASS. YOU WILL HAVE TWO WEEKS FROM NOW TO COMPLETE THIS ASSIGNMENT.*

Your paper will be double spaced, in 12 point font, and in 1inch margins. Make sure you list references!

*Note: if you do not want to write a paper, you can make a 10 slide PowerPoint instead with at least 3 sentences per slide.*

For the oral presentation, You can either: Give a talk about the information you were assigned, write a musical composition, construct a play set in ancient Greece with up to 3 of your classmates, or anything else to display your knowledge of the History of Calculus.

Papers and presentations that are late will be given one letter grade lower than there original score.

The Process

The first thing you should do is to go to a search engine and locate a few websites with information about an overview of the History of Calculus.
From here search for any names you might have found. (Such as Archimedes, Aristotle, Isaac Newton, Leibniz, etc.) Maybe search the library for an autobiography on these individuals.
Explain what the culture was like during these individuals’ lives. For example: Was math being used for practical purposes? Were women allowed to study the subject? Who were their peers? Were there any rivalries between the mathematicians? Were people racing to discover new ideas?
After you have gathered this data, organize your paper (or PowerPoint) in this way:

Paragraph 1: Introduction- Introduce your reader to the stage of Calculus and discuss the main players. This should entice your readers to want to read more.
Paragraph 2-4: Introduce three of the mathematicians you discovered in separate paragraphs and give details on who they were, what they were famous for, what their childhood was like, and/or what their goals and dreams were
Paragraph 5? : Introduce the environment of the mathematicians. Describe in detail what the government and the economy of their day were. Try and relate to the reader what it must have been like to live in those conditions and try and discover new mathematical ideas. Describe any hostility they might have received from other mathematicians.
Paragraph 6? : Opinion/Discussion: Would you have liked to live in these times? If so, why? If not, why not? Do you think it would have been easy for these people to have done the things they did knowing some of there circumstances? What impresses you the most about these individuals? How can you use them as motivation to accomplish your goals?
Your presentation should be around the 5-7 minute mark and should display what you have gleaned from your research. Make it entertaining (if you can). Try and ask yourself, “If I was listening to this, would I pay attention and learn anything?”

Their presentation should be around the 5-7 minute mark and should display what they have gleaned from your research. It should be interesting to the listener.

Evaluation

You will be evaluated in two categories: 1. Your paper and 2. Your Presentation. There is a total of 200 points on this assignment (120 for your paper, 80 for your presentation).

	Unacceptable 0-10	Acceptable 11-20	Above Average 21-30	Exemplary 31-40	Score
Paper: Was the main question or research fulfilled?	The question was not answered or was lacking in depth.	The question was answered with little or no research.	The question was answered with sufficient research but with limited discussion or description	The question was answered with superior research and was concise and to the point.
Paper: Was the paper well organized and in correct grammatical structure?	The paper was unorganized, not proof-read, and unclear.	The paper had many mistakes and was unorganized in places.	The paper had few or little grammatical mistakes and had a clear message.	The paper had no grammatical mistakes and was clearly put together.
Paper: Is there sufficient research?	There was little or no research.	The paper had 2 or more sources and lacked any credible sources	The paper had 3 or more sources listed as references.	The paper was backed up with 4 or more sources. It also had citations in the paper.
Presentation: Was the topic addressed?	The topic was not presented or was unclear.	The topic was vaguely known.	The topic was clearly known.	The topic was clearly known and was restated in different ways.
Presentation: Was the presentation geared so the audience would be involved and learning?	The presentation had no audience involvement and/or was not interesting.	The audience was entertained but the presentation didn’t stay on topic.	The presentation grabbed the audience’s attention but the topic was a little unclear.	The presentation gave the audience a better understanding of topic.

Conclusion

As you complete this assignment, you should have a better understanding about the life and times of some of the brightest mathematicians that have ever lived. You should have gained a greater appreciation for these mathematicians. Also, you should have gained confidence in yourselves as you start your Calculus careers.

Credits & References
Thanks to: http://www.goodthinkingworks.com/images/Aristotle.jpg for providing pictures of Aristotle.

Also, thanks to http://www.myclassiclyrics.com/artist_biographies/Isaac_Newton_Biography.htm for the picture of Sir Isaac Newton.

Time Traveling to Mathematics’ Past

Teacher Page

A WebQuest for 12th Grade (Calculus)

rileybl@nsuok.edu

Introduction
This lesson was developed as a kick start of the semester for introducing the origins and the reasons for the development of Calculus. It is designed for student interaction and independent study.

The objectives of this lesson is:

· To introduce the founders of Calculus

· To introduce the topics and ideas of Calculus

· To get the student’s interested in the subject

· To let the student’s interact with each other (presentation) and become comfortable with each other

· To encourage independent study (the desire to learn information on your own).

This lesson is about the History of Calculus. The student’s will get an idea of some of the topics of Calculus (such as area under a curve, limits, point continuity, etc.). Students will gain appreciation for the subject and will become comfortable with research materials.

Learners
This lesson is designed for 12^th grade Calculus and involves writing skills from the student’s English classes and research skills from there History classes.

Learners will need to have basic research and grammar skills in order to complete the lesson. The students will also need to be familiar with giving oral presentations.

Students will learn:

· Who the founders of Calculus were and what their lives were like

· Some of the topics and ideas of Calculus

· About each other and give them an opportunity to have classroom critical reaction

· How to conduct an independent study

Students should start to think critically about why these people had accomplished what they did. Students should also be influenced to think in away similar to these mathematicians.

Students will have to use organizational skills to formulate a picture of who each of the famous mathematicians were. Students should compare methods of one mathematician to another and should compare situations and trials the mathematicians had to overcome.

Also by giving the students a choice as to how to do there presentation, will give them a creative outlet about what they just learned. It will be okay if the student’s came back and expressed their disinterest in the subject; but, it is not the desired result of this lesson.

Curriculum Standards
This Web lesson meets the following Oklahoma State Department of Education PASS objective:

High School Mathematics:

Process Standard 2: Communication

1. Use mathematical language and symbols to read and write mathematics and to converse with others.

2. Demonstrate mathematical ideas orally and in writing.

Process
Here are the steps the students will need to do to accomplish the lesson’s goals:

The first thing the student’s should do is to go to a search engine and locate a few websites with information about an overview of the History of Calculus.
From here, they should search for any names they might have found. (Such as Archimedes, Aristotle, Isaac Newton, Leibniz, etc.) they could then search the library for an autobiography on these individuals.
Next, they can explain what the culture was like during these individuals’ lives. For example: Was math being used for practical purposes? Were women allowed to study the subject? Who were their peers? Were there any rivalries between the mathematicians? Were people racing to discover new ideas?
After the students have gathered this data, they will organize their paper (or PowerPoint) in this way:

Paragraph 1: Introduction- Introduce your reader to the stage of Calculus and discuss the main players. This should entice your readers to want to read more.
Paragraph 2-4: Introduce three of the mathematicians you discovered in separate paragraphs and give details on who they were, what they were famous for, what their childhood was like, and/or what their goals and dreams were
Paragraph 5? : Introduce the environment of the mathematicians. Describe in detail what the government and the economy of their day were. Try and relate to the reader what it must have been like to live in those conditions and try and discover new mathematical ideas. Describe any hostility they might have received from other mathematicians.
Paragraph 6? : Opinion/Discussion: Would you have liked to live in these times? If so, why? If not, why not? Do you think it would have been easy for these people to have done the things they did knowing some of there circumstances? What impresses you the most about these individuals? How can you use them as motivation to accomplish your goals?

Their presentation should be around the 5-7 minute mark and should display what they have gleaned from your research. It should be interesting to the listener.

This lesson is designed as an independent research assignment. It should take at least 6 to 7 hours outside of class to accomplish this assignment. Students are encouraged to help each other with oral presentations and determining credible places to research. This lesson is interdisciplinary because it involves research skills, English skills, and mathematical history.

A couple of the stumbling blocks that I feel will be the most hurtful to the student’s learning is the lack of internal motivation. Also, If this assignment is given during a busy period the student may be overwhelmed (though this lesson is designed for the beginning of the semester).

If these are problems a teacher could extended the due date from the current 2 week deadline. Also, a teacher can provide constant external motivation to spark the desire to learn more about the subject’s past.

Younger teachers should be okay in handling the outside project. The disciplinary problems that might arise during the actual presentation might be a problem for a teacher who has poor classroom management skills. This type of teacher may opt out of the presentation portion of the assignment if he or she desires.

Again most of this lesson can be reworked to a specific need of the teacher or the class itself. However, this lesson should be used for self-learning and a retooling of mathematical conversation and research.

Resources Needed
Students might need the following during this lesson:

Student access to computers
Student access to a library or research materials
Specific student requests for oral presentations
Textbooks (high school or collegiate)

Here are a few suggestion of books that the student’s might want to try and access:

· The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time by Jason Socrates Bardi

· The History of the Calculus and Its Conceptual Development
by Carl B. Boyer

· The Calculus Gallery: Masterpieces from Newton to Lebesgue
by William Dunham

Also, you might want to schedule some time in the library maybe once a week so the students with limited internet access can get some research done. This will require making an appointment with the high school librarian.

Adaptations and Variations
Since this is the introduction to the course, the student’s should have little or no pre-knowledge about the history of calculus let alone calculus itself. If you would like to pre-asses your students, you can make a quick quiz to give them some participation points. Make sure that you don’t penalize your students for not knowing the information.

This lesson should help the tactile and kinesthetic learners in the class by giving them a hands on activity. Auditory and visual learners could find history videos and learn form them. Analytic people will have a detailed outline of instructions. Global people will have the freedom to create what they want to express there knowledge base.

This assignment is designed for an advanced mathematics course, so special needs children will be rare. However if a child has a special need (such as visually impaired or physically impaired), special arrangements will be made so that they can have as much access to research materials as possible.

Evaluation

Students will be evaluated in two categories: 1. the paper and 2. the Presentation. There is a total of 200 points on this assignment (120 for the paper, 80 for the presentation).

	Unacceptable 0-10	Acceptable 11-20	Above Average 21-30	Exemplary 31-40	Score
Paper: Was the main question or research fulfilled?	The question was not answered or was lacking in depth.	The question was answered with little or no research.	The question was answered with sufficient research but with limited discussion or description	The question was answered with superior research and was concise and to the point.
Paper: Was the paper well organized and in correct grammatical structure?	The paper was unorganized, not proof-read, and unclear.	The paper had many mistakes and was unorganized in places.	The paper had few or little grammatical mistakes and had a clear message.	The paper had no grammatical mistakes and was clearly put together.
Paper: Is there sufficient research?	There was little or no research.	The paper had 2 or more sources and lacked any credible sources	The paper had 3 or more sources listed as references.	The paper was backed up with 4 or more sources. It also had citations in the paper.
Presentation: Was the topic addressed?	The topic was not presented or was unclear.	The topic was vaguely known.	The topic was clearly known.	The topic was clearly known and was restated in different ways.
Presentation: Was the presentation geared so the audience would be involved and learning?	The presentation had no audience involvement and/or was not interesting.	The audience was entertained but the presentation didn’t stay on topic.	The presentation grabbed the audience’s attention but the topic was a little unclear.	The presentation gave the audience a better understanding of topic.

Credits & References
Thanks for Mrs. Barbara Fuller for the help in developing this Web Quest. You are truly a great resource of knowledge and compassion.

The following web links provided images and materials for the development of this Web Quest:

http://www.amazon.com/Calculus-Gallery-Masterpieces-Newton-Lebesgue/dp/0691095655/ref=sr_1_10?ie=UTF8&s=books&qid=1209497222&sr=8-10

http://www.amazon.com/History-Calculus-Its-Conceptual-Development/dp/0486605094/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1209496952&sr=8-1

http://www.amazon.com/Calculus-Wars-Leibniz-Greatest-Mathematical/dp/1560257067/ref=pd_bbs_sr_2?ie=UTF8&s=books&qid=1209496952&sr=8-2

http://sde.state.ok.us/acrob/pass/PASSGrade/m-HiSc-Math.htm#LinkTarget_716

http://en.wikipedia.org/wiki/Image:Gottfried_Wilhelm_von_Leibniz.jpg

http://www.goodthinkingworks.com/images/Aristotle.jpg

http://www.myclassiclyrics.com/artist_biographies/Isaac_Newton_Biography.htm

Last updated on June 18, 2007.. Based on a template from The WebQuest Page