Thursday, December 10, 2009
Monday, November 23, 2009
Assignment 3
MAED 314 – Assignment 3
•Vincent Collins
•Gregory Thiessen
•Rosemary Qi
November 23, 2009
Part 1 – (8) Develop a project of own choice based on the in-class library. Topics include Goldbach’s Conjecture (from novel), infinities, fractals, paradoxes, etc.
Grade: 11
Purpose:
This activity is both a history project as well as an activity to have the students think mathematically. These mathematical concepts can be very difficult to grasp and by doing this project, students will have to go beyond instrumental comprehension to fully understand the given topics and produce the desired results. Students will get the opportunity to work in small groups and present their findings to the rest of the class in a short presentation.
Description of Activity:
Project
In groups of 2 or 3 you will choose a topic from the provided list. Feel free to research and choose your own, however, please confirm your decision with me before proceeding.
• Goldbach’s Conjecture
• Infinities
• Fractals
• Paradoxes (Choose only one to work with)
A paradox is a statement that goes against our intuition but may be true, or a statement that is self-contradictory. Examples of some mathematical paradoxes are:
• Zeno’s paradoxes of motion (the dichotomy paradox, Achilles and the tortoise paradox, arrow paradox or the stadium paradox
• Russell paradox (Barbershop paradox)
• Greeling paradox
• Petersburg paradox
• Galileo’s paradox
• Etc.
Once you have made your decision, the following tasks must be completed:
1. Research your topic through the internet or by using books from the school library. I will provide a list of books that are available in the library.
2. Produce a visual representation of your topic. This can be in the form of a poster, tables, comic, performance, etc. Include a brief history of the topic including the person who developed the concept.
3. Present your work to the class in a short presentation of no more than 5 minutes.
Marking Criteria:
Your grade will be dependent on your understanding of the mathematical paradox which will be conveyed through your final product and presentation. Effort and contribution to the team will affect your final mark. There will be a peer evaluation at the end.
Due Date: 2 weeks from day assigned.
This project is expected to be completed primarily outside of class.
Sources:
http://www.stormloader.com/ajy/paradoxes.html
http://www.suitcaseofdreams.net/Content_Paradox.htm
Mazur, Joseph. Zeno’s Paradox: Unravelling the Ancient Mystery Behind the Science of Space and Time.
Part 2 – Evaluation of the project
This project is an enrichment project designed to make students think mathematically about concepts not ordinarily encountered throughout life. Benefits and weaknesses of this project are listed below.
Benefits:
Students will learn of various mathematicians who have contributed to mathematical knowledge over the centuries.
Students will have to critically think about concepts of math outside of what they usually experience.
Students will have to work in groups to accomplish tasks.
Students will have to present their findings in a clear manner such that peers will understand.
Weaknesses:
Not all of the topics are connected to the grade 11 IRP’s. Some of the mathematical concepts may be more suited for grade 12.
Students may have a difficult time comprehending some of the paradoxes.
Students may not comprehend the purpose or necessity of this project and may view is as another mundane task they must work through.
Trying out the project as a sketch
Our group has decided to tackle this project by focusing on Zeno’s paradoxes of motion.
History of Zeno of Elea
The Greek philosopher Zeno of Elea, born around 490 B.C., proposed four paradoxes that are still discussed 2500 years later. He wanted to challenge the accepted notions of space and time that he encountered in various philosophical circles. His paradoxes confounded mathematicians for centuries, and it wasn't until Cantor's development (in the 1860's and 1870's) of the theory of infinite sets that the paradoxes could be fully resolved.
Zeno's paradoxes focus on the relation of the discrete to the continuous, an issue that is at the very heart of mathematics. His four famous paradoxes include the dichotomy paradox, Achilles and the tortoise paradox, arrow paradox and the stadium paradox.
http://mathforum.org/isaac/problems/zeno1.html
Part 3 – New Math Project Design
Grade: 11
Purpose:
The goal of this math project is for students to examine cyclical patterns in an artistic, fun and unique way. The students are presented with a classic problem that has been posed in an abstract way, to see if they can discover the numerical relationship. The students will be challenged to recreate and experiment with the ‘celtic knot’ pattern and hopefully they will begin to see that math exists is science and in art too. This is an enrichment project that promote deeper thinking in the students.
Description of activities:
1. Follow the guide (see below) for producing a ‘celtic knot’ and produce a 4 by 3 knot. Decorate it as necessary to show how the pattern loops.
2. If the knot has m vertices along the left side and n vertices along the top side, determine the formula/algorithm for determining the number of loops present in an m by n knot.
3. What other patterns of loops can be made by combining loops of various sizes. What are the limitations of this pattern, if any?
Guide:
The (1) blocks are placed at the four corners of the pattern (see below), each rotated 90 degrees from each other. The (2) blocks are placed next to them, cascading along the edge of the knot pattern to form a perimeter. The (3) blocks are placed in the middle to fill the space and complete the knot design. The picture below illustrates how this works. Under ‘Graphic’, there is a drawing of a completed knot for reference.
Sources:
There is no source for the creation of this knot pattern. This is original artwork that shall now be examined for mathematical inquisition.
Length of time that project will take:
Students are given 1 week from the date assigned to complete this project. If time permits, a small section of class time may be devoted to beginning the project. Otherwise, it is to be work upon outside of class in groups of 2-3.
What students are required to produce:
1. The students must draw a 4 by 3 ‘celtic knot’ and decorate it to make it easy to see.
2. The students must derive a formula for determining the number of loops in an m by n knot.
3. The students must create a new knot pattern by opening & closing loops to create their own knot pattern.
Graphic:
m=4, n=4, # of loops: 4 (highlighted as purple, red, green & blue)
Marking Criteria:
1. /4 - Completed drawing of 4 by 3 ‘celtic knot’.
2. /4 - Formula for the # of loops.
3. /2 - Originality of design.
•Vincent Collins
•Gregory Thiessen
•Rosemary Qi
November 23, 2009
Part 1 – (8) Develop a project of own choice based on the in-class library. Topics include Goldbach’s Conjecture (from novel), infinities, fractals, paradoxes, etc.
Grade: 11
Purpose:
This activity is both a history project as well as an activity to have the students think mathematically. These mathematical concepts can be very difficult to grasp and by doing this project, students will have to go beyond instrumental comprehension to fully understand the given topics and produce the desired results. Students will get the opportunity to work in small groups and present their findings to the rest of the class in a short presentation.
Description of Activity:
Project
In groups of 2 or 3 you will choose a topic from the provided list. Feel free to research and choose your own, however, please confirm your decision with me before proceeding.
• Goldbach’s Conjecture
• Infinities
• Fractals
• Paradoxes (Choose only one to work with)
A paradox is a statement that goes against our intuition but may be true, or a statement that is self-contradictory. Examples of some mathematical paradoxes are:
• Zeno’s paradoxes of motion (the dichotomy paradox, Achilles and the tortoise paradox, arrow paradox or the stadium paradox
• Russell paradox (Barbershop paradox)
• Greeling paradox
• Petersburg paradox
• Galileo’s paradox
• Etc.
Once you have made your decision, the following tasks must be completed:
1. Research your topic through the internet or by using books from the school library. I will provide a list of books that are available in the library.
2. Produce a visual representation of your topic. This can be in the form of a poster, tables, comic, performance, etc. Include a brief history of the topic including the person who developed the concept.
3. Present your work to the class in a short presentation of no more than 5 minutes.
Marking Criteria:
Your grade will be dependent on your understanding of the mathematical paradox which will be conveyed through your final product and presentation. Effort and contribution to the team will affect your final mark. There will be a peer evaluation at the end.
Due Date: 2 weeks from day assigned.
This project is expected to be completed primarily outside of class.
Sources:
http://www.stormloader.com/ajy/paradoxes.html
http://www.suitcaseofdreams.net/Content_Paradox.htm
Mazur, Joseph. Zeno’s Paradox: Unravelling the Ancient Mystery Behind the Science of Space and Time.
Part 2 – Evaluation of the project
This project is an enrichment project designed to make students think mathematically about concepts not ordinarily encountered throughout life. Benefits and weaknesses of this project are listed below.
Benefits:
Students will learn of various mathematicians who have contributed to mathematical knowledge over the centuries.
Students will have to critically think about concepts of math outside of what they usually experience.
Students will have to work in groups to accomplish tasks.
Students will have to present their findings in a clear manner such that peers will understand.
Weaknesses:
Not all of the topics are connected to the grade 11 IRP’s. Some of the mathematical concepts may be more suited for grade 12.
Students may have a difficult time comprehending some of the paradoxes.
Students may not comprehend the purpose or necessity of this project and may view is as another mundane task they must work through.
Trying out the project as a sketch
Our group has decided to tackle this project by focusing on Zeno’s paradoxes of motion.
History of Zeno of Elea
The Greek philosopher Zeno of Elea, born around 490 B.C., proposed four paradoxes that are still discussed 2500 years later. He wanted to challenge the accepted notions of space and time that he encountered in various philosophical circles. His paradoxes confounded mathematicians for centuries, and it wasn't until Cantor's development (in the 1860's and 1870's) of the theory of infinite sets that the paradoxes could be fully resolved.
Zeno's paradoxes focus on the relation of the discrete to the continuous, an issue that is at the very heart of mathematics. His four famous paradoxes include the dichotomy paradox, Achilles and the tortoise paradox, arrow paradox and the stadium paradox.
http://mathforum.org/isaac/problems/zeno1.html
Part 3 – New Math Project Design
Grade: 11
Purpose:
The goal of this math project is for students to examine cyclical patterns in an artistic, fun and unique way. The students are presented with a classic problem that has been posed in an abstract way, to see if they can discover the numerical relationship. The students will be challenged to recreate and experiment with the ‘celtic knot’ pattern and hopefully they will begin to see that math exists is science and in art too. This is an enrichment project that promote deeper thinking in the students.
Description of activities:
1. Follow the guide (see below) for producing a ‘celtic knot’ and produce a 4 by 3 knot. Decorate it as necessary to show how the pattern loops.
2. If the knot has m vertices along the left side and n vertices along the top side, determine the formula/algorithm for determining the number of loops present in an m by n knot.
3. What other patterns of loops can be made by combining loops of various sizes. What are the limitations of this pattern, if any?
Guide:
The (1) blocks are placed at the four corners of the pattern (see below), each rotated 90 degrees from each other. The (2) blocks are placed next to them, cascading along the edge of the knot pattern to form a perimeter. The (3) blocks are placed in the middle to fill the space and complete the knot design. The picture below illustrates how this works. Under ‘Graphic’, there is a drawing of a completed knot for reference.
Sources:
There is no source for the creation of this knot pattern. This is original artwork that shall now be examined for mathematical inquisition.
Length of time that project will take:
Students are given 1 week from the date assigned to complete this project. If time permits, a small section of class time may be devoted to beginning the project. Otherwise, it is to be work upon outside of class in groups of 2-3.
What students are required to produce:
1. The students must draw a 4 by 3 ‘celtic knot’ and decorate it to make it easy to see.
2. The students must derive a formula for determining the number of loops in an m by n knot.
3. The students must create a new knot pattern by opening & closing loops to create their own knot pattern.
Graphic:
m=4, n=4, # of loops: 4 (highlighted as purple, red, green & blue)
Marking Criteria:
1. /4 - Completed drawing of 4 by 3 ‘celtic knot’.
2. /4 - Formula for the # of loops.
3. /2 - Originality of design.
Wednesday, November 18, 2009
Tuesday, November 17, 2009
Problem Solving
I scanned my problem-solving worksheet, but I could not put the image in my poster.
My conclusion for the problem sequence on page 192 is that no matter how many digits there are in a sequence of 0s and 1s, if there is no “1” or there are even numbers of 1s, the final digit will be “0”. Otherwise, the final digit will be “1”.
This conclusion is similar to my team workers'.
My conclusion for the problem sequence on page 192 is that no matter how many digits there are in a sequence of 0s and 1s, if there is no “1” or there are even numbers of 1s, the final digit will be “0”. Otherwise, the final digit will be “1”.
This conclusion is similar to my team workers'.
Monday, November 2, 2009
Two stories in my short practicum
One of the exciting things is about the Tablet PC. In the first day, both my sponsor teachers were using Tablet PC in their classes, and I really liked it. They told me that I could use their Tablets in my lesson. However, when I figured out what software they used, I found that I had the software and hardware in my computer. In the other word, my computer is a Tablet PC, and I had never used these functions. Then, I was so excited and started to learn how to use it for my teaching. Finally, I used my Tablet PC in my four lessons, and my sponsor teacher was very pleased to see that.
Another story is about the school. The Prince of Wales Secondary School is a good school, and we, student teachers, were welcomed in the first day in our short practicum. The principal and vice principals showed up, gave the orientation,and offered breakfast and lunch for all student teachers. They also made a list of all classes where we were welcomed to go and observe the teaching, which made us much easier.
Another story is about the school. The Prince of Wales Secondary School is a good school, and we, student teachers, were welcomed in the first day in our short practicum. The principal and vice principals showed up, gave the orientation,and offered breakfast and lunch for all student teachers. They also made a list of all classes where we were welcomed to go and observe the teaching, which made us much easier.
Friday, October 30, 2009
Reflection on Timed Writing
I don't think that I am good at timed writing, and I also don't like it. However, as a teaching skill, it is useful.
Strengths:
Timed writing exercise:
• Makes students concentrate to their work.
• Contributes to classroom management, and it can make students calm down.
• Improves the students’ communication skills.
Weaknesses:
Timed writing exercise:
• Isn’t exactly related to Math teaching.
• Causes unnecessary pressure on students’ study because getting ideas in very short time sometimes makes people frustrated.
• Students might feel boring about this exercise, and it is not an active activity which is really needed in math class.
Strengths:
Timed writing exercise:
• Makes students concentrate to their work.
• Contributes to classroom management, and it can make students calm down.
• Improves the students’ communication skills.
Weaknesses:
Timed writing exercise:
• Isn’t exactly related to Math teaching.
• Causes unnecessary pressure on students’ study because getting ideas in very short time sometimes makes people frustrated.
• Students might feel boring about this exercise, and it is not an active activity which is really needed in math class.
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