Videos- Victor Lee

OpenLab Assignments

Doodling in Math: Spirals, Fibonacci, and Being a Plant (Three Part Series)

I chose this video because it seemed pretty relevant with our recent introduction to Strong Induction and Fibonacci Numbers. It serves as an introduction to Fibonacci Numbers and the Fibonacci Spiral and their appearances in various organisms, with particular focus on plants whose names start with “pine-“. It was interesting seeing how the number of spirals in certain plants exist in more than one direction (and in Fibonacci numbers no less). So are there any plants that violate the sanctity of this pattern?

Phi is the most irrational number? An interesting correlation between ratios of the larger over the smaller of two consecutive Fibonacci numbers exists. But, wait a contradiction arises?

Something wrong happened at the start and now we have a new type of sequence. It’s not quite a Fibonacci Sequence but very close; introducing Lucas Numbers. Also, here are instances where plants break apart from Fibonacci sequences. Okay, that answered my question.

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Are these videos relevant to the teaching I will be doing? While it is interesting to learn on our own, there is an issue where the students will not likely come across these sequences within the curriculum unless I choose to assign them some sort of project. That being said, my attention was kept, and I was borderline captivated with the presentation. There was visual evidence to prove the concepts scientifically and and additional artistic diagrams to better represent these observations. These videos are also demonstrations into how math exists outside of the textbooks, notebooks, and chalkboards as well as how we can discover and apply new knowledge. This is most certainly teaching math and I’d like to believe I have a greater understanding of Fibonacci numbers through these demonstrations.

Is there a connection between these videos and Paul Lockhart’s Lament? I could imagine so. If Lockhart wishes to expose the soul of math to students, I would go so far as to say that Vi Hart does so with these videos.  She most certainly presents math in an artistic method that is seemingly fun and engaging and it’s pretty clear she’s enjoying making these videos. The only issue I might have is how would students react to seeing such a demonstration in their classrooms? Feedback is a pretty important assessment tool and I know firsthand that a comments section on the Internet is not the best place to garner such information.

Videos- Rushdha Rafeek

OpenLab Assignments, , , , ,

1.

The title of this video is “Hexaflexagons.” In this video Vi-hart talks about how a student named Arthur.H.Stone discovered and invented hexaflexagons with strips of papers. She cuts-off ends of the paper that could not fit in her English binder and then folds those strips of papers to create different shapes such as hexagons. Each time they were folded in a certain way it revealed more than two faces or sides creating a flexagon.

Title- “Doodling in Math: Sick Number Games” In this video Vi-hart she writes down numbers in order and arranges them in spirals known as ulam spiral to find out patterns prime numbers can make. She also doodles around to find patterns in pascals triangle by using this number game and highlighting prime numbers to create a picture with different sizes of triangles.

Title- “Doodling in Math: Stars” This is a great video to learn to draw many pointed stars in many different ways. She basically shows how factoring numbers are found in real world such as in stars.

Title- “Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]”  This video is about how Fibonacci numbers are found in living things such as plants and other things. She practically experiments on plants to show how Fibonacci numbers exists in spirals and many other geometric drawings.

2. These videos are simply amazing! I am definitely inspired how Vi-hart makes great connections to math with her “doodle stuff” She was very creative in her drawings in the videos that made me wonder how artistic and yet clever enough to relate every single thing to math in some way. One thing I learnt is that she appreciated math more than I did and in some sense she made great attempts to prove the math facts herself by experimenting on real world materials instead of simply relying to the things she is taught in class. For example discovering the Fibonacci sequence in spirals of pine cones, pineapples, flowers and many others. And one question I like to know is if she came up with a math story every time she doodled in a math class?

3. I really enjoyed watching these videos. Vi-hart has a unique approach to math by making connections to real word applications. I also learnt a lot from “Spirals, Fibonacci and being a plant” video. I think the way she demonstrated on the flowers and other things to describe the Fibonacci numbers were very beneficial. And not only that she made math seem very unique and an enjoyable subject, and quite often math is not observed this way in a classroom because it’s mostly taught in a very boring way by spoon feeding facts to students where they don’t have the opportunity to be inspired with the mathematical concepts. I found this video also relevant to what is being taught in class especially with the Fibonacci numbers and its unique properties. She also shows how math is an art as described in the reading “Lock hart’s Lament” and uses her creative imaginations in her explorations. I honestly wish I was taught this way back in school.

Videos–> Sidney Sao

OpenLab Assignments,

Part 1

1)Title: Scary Sirepinski Skull Time

Description: Vi Hart was showing us how you can make triangles out of triangle candy corns. She basically Showed that there where infinite number of triangles in a triangle.

Link: https://www.youtube.com/watch?v=z8ZWlUamNPI&list=UUOGeU-1Fig3rrDjhm9Zs_wg

2)Title: Doodling in Math: Sick Number Games

Descriptions: In this video, she talks about prime numbers, Pascal’s Triangle, and Floyd’s Triangle.

Link: https://www.youtube.com/watch?v=Yhlv5Aeuo_k&list=UUOGeU-1Fig3rrDjhm9Zs_wg&spfreload=1

3)Title: Doodling in Math: Spirals, Fibonacci, and being a plant [1 of 3]

Descriptions: She discusses the Fibonacci series and show us how to find the numbers in the series (starting with 1 add 1 and than add the previous number number to the first number to get the next number). After than she show us how the Fibonacci numbers are in everything with spikes, such as, flowers, pineapples, acorns, and etc.

Link: https://www.youtube.com/watch?v=ahXIMUkSXX0&list=UUOGeU-1Fig3rrDjhm9Zs_wgPart 2

Part 2

Chosen Video: Doodling in Math: Sick Number Games

I watched some of her other videos, and I found them them to be pretty annoying because she talks really fast and make a bunch of weird/annoying sounds. Despite that, this was the only video I liked. I found it really interesting because she talked about prime number. To be honest, I don’t really know what’s the point of knowing that a number is prime. What’s the purpose of prime numbers? She also talked about the largest prime number, (2^43,112,609)-1, and how the guy who came up with this number was rewarded $100,000. One thing that I found funny and interesting was that scientist sent the largest prime number to space in an attempt to communicate with aliens. Also I liked the statement, “mathematics is one of the only thing all life have in common.” I also liked how she showed a different way of viewing the Fibonacci’s Triangle. When you circle all the odd numbers in Fibonacci’s Triangle, you get sierpinski’s triangle. After that, she divides all the numbers in Fibonacci’s Triangle by three, and colors in all the numbers with remainder 0, 1, and 2 with different colors (R0[red], R1[black] and R3[Green]); she comes up with a set of rules (ex: black+black= Green). One thing I learned from this video, is that when you draw the Ulam’s spiral all the prime numbers connect in a diagonal. One question I have, If I find a prime number greater than the largest prime number do I too get a reward? 🙂

Part 3 

I think this video teaches us about some things in math because she’s show you steps to find certain numbers through the use of Fibonacci’s Triangle and etc. This video is telling me that when I teach I should encourage my students to do what Mr. Reitz does, think about the process of solving problems because it can open up to new math ideas. theorems, and etc. I believe this work is relevant to the work we are doing in class because we use the Triangles mentioned earlier and discussed a little bit about prime numbers and how there’s no formula for a prime number, yet. I don’t think it relates to Lockheart’s lament. Overall, I like how this video shows you how you can view things in different ways.

Videos- Leonardo Perez

OpenLab Assignments,

part 1)

this video talked about arranging  snake fragments into desired shape or length.

this video was interesting it talked about the Pythagorean theorem and the life of  Pythagoras.

 

this was a funny video but it talked it about how kids are given the wrong information about some mathematical concepts, like the Fibonacci sequence she says that spongebob’s pineapple house is not really a pineapple because  it doesn’t follow the Fibonacci sequence.

part 2)

the video on “How to snakes” was a very interesting video. I saw the video at least five times just understand what she was trying to prove. The reason I like this video is because I feel that it is somehow related to Pascal’s triangle, when she showed one can arrange the snake so it can have two or more heads it look a lot like Pascal’s triangle which was very interesting because her explanation can be a good way to introduce Pascal’s triangle in a fun way. This was inspiring to me because it made me look at math in a fun way meaning that I don’t have to see it as just as numbers and formulas.

part 3)

I think that this video has a lot to do with math because it shows a relationship between the snakes fragments and Pascal’s triangle. I believe that this is a way of teaching math in a more calm and easy approach rather than giving students formulas or rules to follow which will cause them (like me ) to forget or not memorize it. I think that this relevant to the work that we are doing in the classroom because we are trying to prove conjectures and state whether it is true or false. I think that Vi Hart idea is to try and prove these conjectures in a more straight forward approach with representation that allows the audience to stay focus.

Videos (Julia Rivera)

OpenLab Assignments

Doodling in Math class snakes and graphs ( https://www.youtube.com/watch?v=heKK95DAKms&list=UUOGeU-1Fig3rrDjhm9Zs_wg)

This video was about doodling snakes and how it relates to graphs. Vi Hart showed us that when you draw and snake and you put the snakes head and the tail touching then you can create cool designs which deals with graphs.

9.999… reasons that .999…. = 1 (https://www.youtube.com/watch?v=TINfzxSnnIE&list=UUOGeU-1Fig3rrDjhm9Zs_wg&index=41)

This video was about how .999… = 1 is the same as saying 1/2 =0.5 because it has the same value. This reason is not a proof but it is to stay open minded where numbers that are different can have the same value. Vi Hart shows a equation in when you multiply by 10 and subtract x or .999… then divide by 9 you get .999….. She also shows us 9.999 rules of why .999….. equals 1.

How I feel about Logarithms (https://www.youtube.com/watch?v=N-7tcTIrers&index=8&list=UUOGeU-1Fig3rrDjhm9Zs_wg)

Vi Hart talks about how algebra is just fancy counting where you are only counting +1 +1 +1 +1. Hart states that numbers are just symbols of +1. She says that when you subtract or have negative numbers they are +1’s that is going back in time. She says division, multiplication, addition, and subtraction is only counting in a fancy way. To in log you use a system time count, where you have a system that counts in a time sort o way.

 

The video I watched more then 3 times was: Doodling in Math class snakes and graphs. When watching the video I was a bit confused because Vi Hart was talking way too fast and she kept drawing many different pictures. I liked her theories and what she believes in and I like that she was creative. Her creativity and her drawings made me more intrigued to watch more videos because it was interesting to see her perspective of certain math topics.  I really enjoyed watching this video because it made me think about the designs snakes can make which I have never thought about before, it made me more open minded. I learned that when you draw squiggles is the same as making snakes where the two sides are closed, where you can weave and put on the finishing touches, weaving works out perfectly. Where it works for any number closed curved on the plane. I learned that drawing integrals gives you a picture of a rope which is part of knot theory. I also learned that when you draw a squiggle and you close the squiggle up and you color every alternate part, there will be no two colors touching in your shape and this will always happen with any squiggle you draw which is pretty cool. You can also draw squiggle and make interesting surfaces when you shade them in where you will have one edge and one side. I wonder if there was other shapes or drawings that you can draw other then a snake that give you a function on a graph?

I believe that as a teacher I need to get students to be more open minded and not bored by teaching them just facts and formulas and what to memorize. I would have to come up with ways to get students to think creativity so that they are able to come up with ideas. I will guide them to do this. I believe that this is math because the drawings relates to graphs and how graphs are, but it deals with math in a creative way. I don’t believe its teaching I think its something a person can think about when they see a graph or when they are drawing. This wont be work I will be doing in a classroom however if I were to teach students about graphs I will mention this to them so that they can find it interesting and so that they can discover for themselves the way graphs behaves.  This relates to Lockhart’s theory when he stated that math is an art, because in fact I believe it is an art, and Vi Hart uses her creativity and art work to prove it. She uses her imagination of doodling in class which you cant get when you are given a formula to memorize. She is using her ideas in a creative way and it relates to math. Lockhart was right about how teachers don’t really let students use their own ideas or imagination because if we were able to do this we will be like Vi Hart just drawing an putting out ideas. that probably no one else has ever thought of.

 

 

Great courses being offered in the Spring

Announcements, , , , , ,

Hi everyone,

The following courses are being offered next semester in the Math Ed program –  they are great courses, and the work you are doing in this class is excellent preparation for each of them.  If they fit your schedule, I highly recommend them (one or more!).  If you feel ready to take one but don’t satisfy all the prerequisites, come talk to me (or Prof. Douglas, adouglas@citytech.cuny.edu, head of the Math Ed program).

MAT 3075 Real Analysis
MAT 3050 Geometry I
MAT 3080 Modern Algebra

Best,
Prof. Reitz

Videos- Joseph Ruiz

OpenLab Assignments

1.a https://openlab.citytech.cuny.edu/2014-fall-mat-2071-reitz/?p=312#respond – “Doodling in Math class Infinity elephants”…  This video talked about a game you can play in almost any shape you decide to draw. You pretty much have to draw circles and circles until you fill up the entire shape inside.

b. https://www.youtube.com/watch?v=Gx5D09s5X6U&list=TLDmvTd50jxGk&index=10 – “How to snakes”….. In this video she talks about snakes and how they can be arranged in many different ways like in the game “SNAKE”. She represented the binary numbers by changing the colors of the snakeskin.

c. https://www.youtube.com/watch?v=jG7vhMMXagQ&index=6&list=TLDmvTd50jxGk “Pi is (still) Wrong” In this video she says how instead of PI we should use TAU. Its funny how she is baking a pie while describing PI

 

2. In this video I found it rather confusing. This lady talks so fast and in the video doodling in math class she draws a lot  of different animals and wierd shapes and talks about how doodling in math class is fun. I was a little confused because she jumps from talking about one thing to talking about another. One thing that I learned from the video was how she compared the “series” application into drawing elephants grabbing eachother’s tails infinetely. I found that very interesting. One question I still have is that if she can relate all of these videos to her own math life and how has it helped her?

3. What this video meant to me was inspiration. The way how she described doodling in math is a new form of way of looking at things from a different perspective. I know that sometimes I’ll begin doodling in my other classes like for example in “Number Theory” because I dont know whats going on in there. I will begin doodling about random things that dont relate to math in a sense, however I will keep track of each time I doodle and see how I can relate it to any math topic. This video wasnt really relevent to me in Prof. Rietz’s class.

 

Semester Project – Group Process Paper

Project, , ,

UPDATE 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.

Semester Project – Group Process Paper

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 our mathematics education.  In the past weeks, you’ve all spent some time individually and in groups working on such a problem (the MIU game, Bridges and Walking Tours, and Mutilated Checkerboards puzzles).

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

  • Description of your puzzle, in your own words.
  • An account of working on your puzzle as a group, from playing with the puzzle 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.

Details:  This assignment is due Tuesday, December 2nd.  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.

 

Week 11 Assignments

Assignments
Written work, due Tuesday, November 25th, in class:
Sec 11.0 p178: 3,4
***Sec 11.2 p187: 1,2,7, *In addition, complete Example 11.8 at the top of p180.6
*** NOTE: You may hand in Sec 11.2 on Dec 2nd (after the break) with no penalty)
WeBWorK – WeBWorK #7, due Tuesday, November 25th, at midnight.
OpenLab – ****OpenLab #11 due Tuesday, December 2nd.
**** NOTE: There is no OpenLab #11 – work on your group paper instead!