# Month: November 2016(Page 2 of 3)

The last significant group assignment for your semester project is a group presentation (there will be one more individual assignment, a reflection on the process).  I’ll put the details here, followed by an outline of the grading criteria (the presentation is worth 20 points total).

Semester Project – Group Presentation

This is your chance to share your group’s work with the rest of the class.  Each group will give a 5-8 minute presentation, including the following items:

• State your conjecture (this should be written down, either on a slide or on the board).  Give an explanation, and an example to demonstrate your conjecture.
• If you were able to prove your conjecture, give a proof.  If not, describe briefly some of the ideas you had and strategies you tried while trying to prove it.
• Give the class at least one puzzle to work on on their own – a challenge!
• Give the audience a chance to ask questions (either during the presentation, or after).

Keep in mind the following:

• You must include some kind of slides (you may also put work on the board):  PowerPoint, Google Slides, Prezi.com, LaTeX Beamer, or other.
• You may decide as a group how to divide up the work, but each group member must present something to class.
• Be aware that you will be asked at a later time to describe your own specific contributions as well as those of each group member.
• Presentations will be given at the beginning of class on Thursday, 12/1 and Tuesday, 12/6.  Your group must sign up for a presentation time before leaving class on 11/20.

_____ points (4 possible).  Basics.  Stay within time limits (5-8 minutes). All group members participate.

_____ points (6 possible).  Conjecture.  Conjecture is written down.  Explanation and example are provided.

_____ points (7 possible).  Proof of conjecture or proof process description.

_____ points (3 possible).  Challenge the class.  At least one puzzle is given for the class to work on on their own.

____ points TOTAL (20 possible)

Part 1:

From watching this video I’m amazed that you can make 90 and 180 degrees from make of any size or folded. When I’m in school I would always be using a ruler or a protractor in middle school and high school. I feel so amazed from learning how much a small of piece of paper can accomplished when folded. If I ever need to draw a 90 or 45 degree angle I would know a good way to create one know. I would really recommend that others should watch this video also on how informative it is.

This video is interesting and also I enjoyed how the person was rhyming like if they were actually there during that time. The video was like a code book because the person was using the numbers from pi. This is making me think about the books that I read from high school from William Shakespeare. I think now that could there way of speaking be some kind of language from using the numbers from pi. The video was also informative for me learning about champernowne’s number and also copelano-erdos number.

I know that singing was a good way to help memorize things for class or was a good educational way to learn new things. I didn’t realize that you can memorize pi from singing it by changing your pitch while singing each of the numbers. The video helped me remember some of the numbers of pi that I forgot. This video is a good way of helping us remember the numbers of pi. Singing the number in a higher pitch for the bigger numbers while a lower pitch for the lower numbers in pi. This is a good method for helping others to remember the digits of pi other than 3.14.

Part 2:

From watching the three videos I really enjoy watching them and the information they talked about. I now know resourceful ways in creating 90, 60, 45, 22.5 degrees with folding a piece of paper 3 to 4 times in have depending on what angle you want to draw. Another video helps helps we with remembering the digits of pi with a way that everyone enjoys doing and listening in this kind of day and age. Singing can be a good way to help anyone to remember information for class or for teachers to help students learn a new topic that they are having trouble with. I didn’t realize that when the characters in William shakespeare books could be speaking in code from using the digits of pi. I knew that numbers can be used as codes for letters but I didn’t know that numbers from pi. The one question that I have is was the characters from William shakespeare plays actually speaking in pi when you decode the words that they are saying into numbers? Another question that I have is if you can sing about the digits in pi can you sing with some of the digits in pi but can you do it for all the digits in pi?

Part 3:

The videos could mean in my own teaching is that I can teach students to be resourceful for things that aren’t enough supply of in the classroom like protractors. I believe that the videos can be both math and teaching because when watching the videos you are learning a concept form math and also teaching you new information that you didn’t know until you watched the videos. I believe that the video about William Shakespeare and connecting to pi could be a prove and is still trying to prove it now currently. I can connect this to Lockhart’s Lament because students can learn from watching videos or find creative ways to help them to remember information for a new topic or information for a test.

Part 1:

Vi Hart’s “How to Draw a Perfect Circle” had similar traits to Lockhart’s Lament. While Lockhart emphasised trial and error and exploration into concepts, the pen’s character and voyage for adventure hearkened to that same concept. While some may have thought it was frustrating to see the pen constantly fail or go against Vi Hart’s instructions, the end result sparked a eureka moment. I think I’ll remember how to draw a perfect circle because of the zaniness of the pen’s quirky deviancy.

I thought this video was clever in explaining a paradox. The supposed pi=4 illusion is easily explained by asking “what’s a circle?” That alone was simple enough to disprove this sophistry. I can’t help but make a connection to our course in making sure our arguments while (dis)proving something must be logical and not fall into fallacies.

I found this video to be creative and amusing. Our standard way of proving something is chalk on blackboard, this is just another engaging way in learning the Pythagoras Theorem in a more hands on approach. We’re not simply told this is true but shown; that and asked to try it ourselves!

Part 2: How to Draw a Perfect Circle

Initially I felt intrigued by the video, who wouldn’t like to know how to draw a perfect circle? Then I see this weird conversation between Vi Hart and a super determined pen. After various struggles from the pen I did feel a little bored, wondering “why am I watching this again?”

Vi Hart then interrupts the pen’s crazed state and simply shows us how to draw the circle in the end. While it was funny, the actual answer kind of came about at a halt. The video still did achieve that “aha!” moment, so that actual lesson in drawing a circle did click and stick in my head.

I learned to draw a perfect circle, although it’s not too different from most techniques out there (the idea of rotating paper isn’t new). I also frowned slightly when she drew against the natural curvature of her hand to draw said circle. Coming from a slight architectural background; it’s much better to draw with the natural curve of your wrist than go against it.

I don’t have any particular questions, it was a simple how to video. I would initially ask why the quirky beginning but that adds to the charm of the lesson.

Part 3: Lockhart

This video actually taught me something important about teaching; make it fun! Despite the dorky dialogue and zany frenzy of the pen; I bet kids would love a video like this. Imagine teaching a child a simple technique for drawing (whether it be for arts or graphs) and have it click in their heads in an engaging and humorous manner. It’s definitely teaching, but is it maths? Probably not. I can’t imagine it being super relevant to the work we’ll be doing in class other than working through our proofs and concepts.

As I talked about in Part 2; this reminded me of Lockhart’s Lament where he talked about trusting our youth to make mistakes through trial, error and exploration. The pen reflects that sentiment.

Wau: The Most Amazing, Ancient, and Singular Number
In this video Vi Hart talks about a number that was discovered in East Asia and in many other ancient societies. She describes the different mathematical relationships, usually infinite fractions, that included Wau (some that just included Wau and others were equal to Wau). She related the special number to nature and other fields of study like physics.
Why Every Proof that .999… = 1 is Wrong
In this video Vi Hart goes through some of the many proofs that are used to show that .9 repeating is equal to one. She goes on to prove or attempt to prove these wrong to say that the two are different numbers that are independent of each other. She invalidates these proofs and then briefly talks about why mathematicians believe it is so.
Doodling in Math Class: Stars
In this video Vi Hart talks about drawing stars and connects this activity to math. She talks about stars with different numbers of points and how the number of points relates to the number of sides in each of the polygons that make up the star. She then makes this star drawing into a “game”.
I was a little confused, especially during Hart’s “Doodling in Math Class: Stars” video not because I did not understand what she was saying just because I felt that she was going a little to quick while speaking and the video recording was also sped up so while trying to process what she had just said she was already on to the next part of her speaking and all throughout her hand was moving very quickly on the paper. She did show what she was saying at the same time that she was saying it. For this reason I had to pause the video multiple times to reassess what she said.   There was not anything in the video that particularly bewildered me or made me say wow except for when Hart started drawing the much larger stars with many points (when she began using the protractor): I thought that the stars that she made were beautiful and they also require a lot of talent to make. I learned that a star with p points can be drawn with 2 p/2- gons; this was a mathematical relationship that I had not been aware of. In fact I have not ever looked into the math behind stars before. I also learned that even with a set number of points in the star and a set number of polygons formed within the star, there are still multiple ways of drawing the star even with the restrictions. Although I did have to pause the video ever so often so that I did not fall behind on what Hart was saying, I for the most part understand everything that she said. So the only question I have after watching the video, is not directly about the math or the drawing in the video, it is: how does Hart discover the relationships between things like the sides of the stars and the number of polygons in the star; or rather: how is she so successful at finding things like the “game” in this video, that still relate to math, but that a majority other people would not be able to discover?
I think the video could really help me with my own math teaching, even though I did not really enjoy the fast pace of it.  What I can learn from Hart is that I need to implement creativity in the classroom at least every once in a while especially in order to keep the students engaged. As Hart emphasizes in the beginning of the video while talking about how she was bored during her math class while learning about factoring, classes that are only lecture can get boring and can cause students to become distracted. So rather than have my students lose focus like Hart did from what the class was actually about: I will give my students an activity to do in class that directly relates to the topic of the day. This way they have something fun to look forward to and are then more inclined to pay attention during class so that they can preform well during the activity. This way they get the fun that they want in class, without losing focus from the actual class and making fun for themselves. Hart’s video really helped me come up with this idea for my own classroom because she expresses that class can get boring, which is true for any student at one point or another and that there are fun and thought-provoking activities to do during class that can still be mathematical and related to class. Kids have a hard time focusing on school work especially for note-taking and problem solving but they are often all for interactive activities, and so I have come to realize after watching this video that combining the two ways of learning can help to take away some of this lack of focus.

Hi everyone,

The group process paper will be worth 35 points towards your Project grade.  I will be filling out the sheet below for each paper submitted.  Please let me know if you have any questions.

Best,
Prof. Reitz

Semester Project – Puzzle Process Paper

_____ points (3 possible).  Basics/formatting.  Length (1500 words required).  Group members names.  Semester/Date/Course.

_____ points (2 possible).  Puzzle description. Description given in own words, demonstrates understanding of puzzle mechanics.

_____ points (16 possible).  Proof process narrative.

_____ points (4 possible).  Shows progress across various stages of the project.

_____ points (4 possible).  Includes all participating members of the group.

_____ points (4 possible).  Includes objective facts (“what we did”) as well as experience (“how it felt, what it was like”).

_____ points (4 possible).  Tells a story.

_____ points (5 possible).  Conjecture.

_____ points (3 possible).  State your group’s conjecture.

_____ points (2 possible).  Proof or disproof of conjecture. If no proof or disproof was obtained, these points can be earned by clear explanation of proof process in the preceding account.

_____ points (9 possible).  Images (3 points each).  Original or clearly attributed.  Includes caption.  Connection to puzzle/process is evident.

____ points TOTAL (35 possible)

Written work – Due Tuesday, November 15, in class:
Chapter 10 p167: 1, 2, 5, 10, 15
Chapter 10 p167: 25, 28, 30
WeBWorK – none
OpenLab – none

Project – First draft of your group paper is due in class on Thursday, 11/17.

Part 1)

a) How to Draw a Perfect Circle- This video reminds us what is the definition of a circle and how to perfeclty draw one each time.

b) The Calculus of Bad Driving- This video goes into detail of the math behind the situation a a car approaching an intersection.

c) Visual Multiplication and 48/2(9+3)- This video show us the meaning (or another representation) of a commonly used algorithm.

Part 2)

Response to video three.

This video had me in a state of amazement. I had no clue that the algorithm multiplication can also be represented by intersection points. I am such a visual person when I learn, so seeing that this works before my very eyes was beautiful. I totally learned a new way to multiply, but one question I do have is, does this only work for two numbers that are both in the tens place.

Part 3)

My definition of teaching is the sharing of information where you understand and express in some way or another the information you just got. Since I can successfully understand and repeat what she did in this video, I say, this is teaching. I feel a lot of people think math is all about algorithms, but math also has diagrams, ideas and expressions that then get transformed into algorithms, so I do believe this is math. One thing that always stays in my head from Lockhart’s article, is that any little thing can be beautiful in math, and geez, this sure was. I also recall the article saying that math is so much more than algorithms, which is why I wonder, why this wasn’t shown to me in one form or another in school.

Assignment.  Your goal for today is to refine the conjecture you decided on during your last class meeting.  Some things to consider:

• Specificity: The conjecture should be stated clearly.  It should include all information necessary to be understood by someone who is familiar with graph theory terms (vertex, edges, paths) and familiar with the assignment (walking tours).  A reader should be able to tell from the statement whether a conjecture applies to a given drawing or not.
• Generality: Your conjecture should apply to more than just a single specific graph (it can apply to a collection of similar graphs, for example, as long as you describe exactly what types of graphs you are considering).
• Drawing: You can create a drawing to accompany your conjecture, but your conjecture should be understandable without the picture.
• You can revise your conjecture as a group if you wish – but try to come up with something similar.
• You can extend your conjecture to include more types of graphs.

GROUP CONJECTURES SUBMITTED AT END OF CLASS TODAY:

Vi Hart describes herself as a “recreational mathemusician” – she has a unique approach to mathematics and its connections to the world.  In this assignment you’ll be exploring some of her videos (she has a YouTube channel here), and using them as a basis for creating a new blog post.

Assignment (Due November 10, 2016).  Create a new blog post responding to the instructions below. Creating a new blog post allows you more flexibility than simply leaving a comment. You have the ability to edit your work after you submit it, and to include photos, videos and other media. It also allows you to contribute to the public content of our course website.

You can get started by clicking the plus sign at the very top of our site (if you don’t see it, make sure you are logged in to the OpenLab). Detailed instructions on creating a new blog post can be found here (see “Writing a Post” in the middle of the page). You should create a new post including the following:

• The title should include the word “Videos” and also your name.
• Your post should include responses to all three parts of the assignment described below.
• Under “Category,” select “OpenLab Assignments” (you will see this on the right side of the screen)
• Under tags, enter “OpenLab 8”, “Vi Hart”, and any other tags you think describe the videos you watched (for example, you might choose “pi” if it’s a video about pi).  Don’t forget to click “Add” after entering your tags in the box.
• When you’re done, click “Publish” (the blue button towards the top right on the screen).

Instructions:

Watch at least three different videos by Vi Hart from  https://www.youtube.com/user/Vihart/ .  You should:

• choose videos at least 2 minutes in length
• choose videos that are related to math in some way
• choose three videos, at least two of which should not appear on her front page (older or less popular videos).  For a full list of her videos, click the “Videos” button near the top of her page – or click here.  Scroll to the bottom and click “Load more” to see older videos.

In your post, include a response to each of the following three Parts:

Part 1. Include a link to each video you watched (3 minimum), the title, and a one or two sentence description of what the video was about.

Now choose one video to focus on.  You MUST watch it 3 times. Use it as the basis for parts 2 and 3.

Part 2.  Write one paragraph discussing the contents of the video:

• How did you feel watching it? Did you like it, or not? Were you confused? Inspired? Bored? Excited? Bewildered?  Why?
• What is one thing you learned from the video?
• What is one question you have after watching it?

Part 3.  Write a one-paragraph reflection discussing what the video could mean to your own math teaching.  Is it math? Is it teaching? Is it relevant to the work you will be doing in the classroom? Is there any connection to the earlier reading assignment Lockhart’s Lament?  Any other thoughts?

Extra Credit.  You can earn extra credit by responding to one of your classmates’ posts.  As always, be kind, be respectful, be honest.

In his essay A Mathematician’s Lament, Paul Lockhart says “A good problem is something you don’t know how to solve.” This is quite different from most of the “problems” that appear in our mathematics education.  In the past weeks, you’ve all spent some time individually and in groups working on such problems, in the context of graph theory (“Bridges and Walking Tours”).

As a group, write an account of your experiences working on your puzzle/problem.  You should include the following elements:

• Description of the Bridges and Walking Tours problem, in your own words.
• An account of working on your problem as a group, from playing with the problem to formulating and perhaps proving a conjecture.  What did your group do/think/feel?  You can include examples of puzzles and solutions if you wish, as well as work by individual group members completed outside the group (both optional).  Your goal is not to go over every detail, but to tell a story that your readers will enjoy – “what was it like”?.
• A statement of your group’s chosen conjecture, and a proof (or disproof) of the conjecture.
• At least three images (more if you wish).  They can include images of puzzles you’ve created or solutions, but you can also be creative with images or photos related to your puzzle, your group or your story in some way.  Each image should have a caption describing.  NOTE: You may freely use your own drawings, images or photos.  If you wish to use photos from another source, they must be from a legal source (for example, Creative Commons licensed, with proper attribution – the library or your professor can help with this).
• Basic details: the names of all group members, the date, course and section numbers, and your professor’s name.

I will be meeting with each group next Thursday, November 10th, in class.  Please be in touch with your other group members before then!  Be prepared to discuss your progress so far – at the very least, you should be able to describe how you are dividing up the work of the paper among your group.

The first draft of this assignment is due in class on Thursday, November 17.  Each group should submit one paper, of no less than 1500 words.  You may decide as a group how to divide up the work.  Be aware that you will be asked at a later time to describe your own specific contributions as well as those of each group member.

The final draft of this assignment is due in class on Thursday, December 1.

REGARDING SEMESTER PROJECT:  As you may recall from the Course Description, the semester project is worth 10% of your overall grade.  The project consists of a number of interrelated activities (many of which have already been completed) – complete details can be found on the Project Overview & Deliverables page.  The group paper assigned here forms a significant portion of the project.

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