# Fuzail’s videos

1)

b. Rhapsody on the Proof of Pi = 4:  https://www.youtube.com/watch?v=D2xYjiL8yyE

proves that pi= 4.

This video showed that there are lots of number you can add and the result will be 2. You can say 1+2=2,  ½+½+½+½=2 etc. Also 2 is so friendly and easy number.

This video shows different way to add, devices and multiply numbers. Which is easier to understand and logical.

2)

When I watches the first video, I was lost. I did not understand the proof even though she drow nice. I felt like she was rushing while she was explaining. If she would have take more time to explain the problem then I would understand it. I learned that the students’ understanding is based on the way a teacher teach. My question is, why does a pi relates with a circle?

3)

From my knowledge, this video did not shows a good method of teaching. As I said in last paragraph, it was fast and not clear which makes me confused to understand how does pi=4. It was a poor math teaching video. From this video we can see that if a teacher take time, ask question and explain clearly then the students will more like to understand the concepts.

# Videos : Yuyu Chen

Part 1

A Song About A Circle Constant

A music video about the circle constraint, Tau.

Origami Proof of the Pythagorean Theorem

A visual example and proof of the Pythagorean using nothing but a piece of paper.

Angle-a-trons

Create the angles you need by folding a piece of paper systematically into a quick and ready to use protractor.

Part 2

The video,  A Song About A Circle Constant, talked (sang) about the idea of Tau. Prior to this video, I had no idea what this concept was so I was trying to learn and understand it.  . Vi Hart created a video to explain the concept of Tau, a measurement of 2pi used as a proportion for diameters,  in ways of music, visuals, and geometry. The music and song helped to internalize the idea of Tau more concretely as you can hum its tune or sing its numbers.  Vi Hart even used visuals like circles and an unraveled earphone wire to show Tau’s applications and value on paper. The humorous drawings of the two stickmen arguing about Tau cemented the idea that Tau’s value comes from twice Pi, but is a specific term and value used for discussing diameters.

Part 3

By the end of the video, I was very amused but at the same time bewildered. Needless to say, the music and lyrics were very provoking but what was shocking was that I actually learned. In other words, I would never have hoped to think or even imagine that teaching can be in this form. Certainly, I wouldn’t expect this in a school setting. This approach to teaching a concept is incredibly refreshing in my mundane routine school schedule and learning experience. It is math. It is teaching. It is a music video. It is not in today’s schools. It’s disheartening to realize that I have lost my strong youthful enthusiasm for learning. This video was able to revert me back into a child, happily and playfully learning about anything and everything that piques its interests. I wish my future students would achieve, and even go beyond, the same level of enthusiasm that I had when I watched this video.

# Rahat Javed Videos

Part 1:

Angle-a-trons: https://youtu.be/o6W6P8JZW0o

This video showed that one can make angles and shapes without actually using or carrying a protractor. Adding on that, if one knows the basic form of the 60, 90, and 180 degree angles they can use paper folds to help them mimic the job of a protractor.

Borromean Onion Rings: https://youtu.be/4tsjCND2ZfM

This video showed how to cook onion rings in a unique shape called the “Borromean Ring”. This edible rings were used as a topper in the video. Moreover, the video explained the concept of how the Borromean Rings are linked and how to link the onion rings the same way.

Re: Visual Multiplication and 48/2(9+3): https://youtu.be/a-e8fzqv3CE

This video was trying to shed light on a new multiplication method and also to explain how crucial proper math notation is. Lastly, that there are more than one way in math to solving a problem.

Origami Proof of the Pythagorean Theorem: https://youtu.be/z6lL83wl31E

This video explained the proof of the Pythagorean Theorem by folding different triangles into a paper. It explained the basic concept of the a^2, b^2, and c^2 sides, and how and why all the sides add up and work.

Part 2:

For this part of the assignment I chose to focus on the “Re: Visual Multiplication and 48/2(9+3)” video.  I found this video so fascinating because not only was it a response video to a concept or trick used for multiplication that I was unaware of, but because of what I learned through Harts simple statement and showing that there are  more than one way to solve equations. Like I have previously mentioned, the video was in response to a multiplication trick, but the fascinating or knowledgeable part to me was when she didn’t know how to multiply 6*7. She then shows a alternative way, despite the trick, which was to draw a whole bunch of dots and multiply by grouping simpler numbers that once can multiply then multiplying the remainder. I just thought one needs to know there times table. Moving on, the second half of the video also interested me and I learned something new. She explained how crucial math notation is. I mean, I always new how crucial it was but not until I saw the video example of how one can mess up on a simple multiplication and division equation if it was not in the right form. Since math is my major, I could easily identify how to do it, but I can also see how tricky the equation would have been for someone not so passionate about math. They wouldn’t have the necessary skills to pick up on bad notation. In conclusion, the video was well explained, leaving me with no questions.

Part 3:

Well I do believe that this video was math, probably not numerical or algorithmic actual type math, but it used these concepts to explain the fact to not look at every single mathematical problem in one way. Sometimes, there are more than one way to do something that might be more convenient and easy to understand. While for others the conventional way would be best applicable. This of Hart’s lesson, yes, i do think i would use in my future teaching career because not all students learn the same. So its always beneficial to keep options and various methods on hand of doing problems, catering to the students needs. This way math breaks out of its ‘boring’ or ‘usual’ ways, hence making it fun. This also connects to Lockhart’s idea of making math fun and actually introducing new concepts into math, allowing students to explore on there own, beyond the conventional boundaries. In conclusion, Hart’s video do shed a more concrete and visible light on basic math and notational importance, so well that these will, for sure, aid in my steps to my career and once I am there.

# Videos Josiel Nunez

Part 1.
Wau: The Most Amazing, Ancient, and Singular Number
This video literally talked about the most interesting number called Wau! WOW! A number that is so complex there are infinitely many ways to express it itself. You can use it in conventional ways but with complexity, you will end up with wau.

Infinite Trees Are Super Weird
This video talks about infinite numbers. She goes on about how you can create a number tree and this number trees has branches and nodes to it so essentially you can go along these branches and reach these numbers infinitely. Also wonders if there is a pi node.

Math Improv: Fruit By The Foot
She wants to know if there are math elements to fruit by the foot, and does something interesting with the candy. She relates it to the famous mobius strip.

This video amazed me. I honestly don’t know if wau is real I didn’t bother searching about it but it blew my mind. She kept comparing wau with fractal fractions and e and derivatives, and it was mind blowing what this ‘wau’ number is. What I actually learned in this video is that if you infinitley take a pattern for example (x+x^y+x^(y^x))/(y+y^x+y^(x^y)) and so forth, equals wau. My question is, why don’t they teach us this in school?

Part 3.

I believe this video could mean nothing to my own math teaching. I mean, it’s talking about a topic that isn’t even teachable. It seems like just a concept, something to get you thinking. Wau would make a great excercise in terms of the idea of infinite patterns in math. I believe this concept is math but it isn’t teaching. It is an idea that will leave everyone wondering. And the reason for that is math, well numbers in general is a complex idea that we as humans have taken control of the topic. It’s like measurements for example. Measurements were created by people to define a set of rules and precision. But no doubt, there is ‘no such thing as measurements’ we’re just safe with them. Do you understand? Like we know what pi is but we don’t really know what pi is. This is wau. I believe that in Lockhart’s Lament, it was the same idea.