Tag: OpenLab 8


Part 1

This video shows the relation of simple doodling to demonstrate and compare the relationship between the Fibonacci sequence and real life.

This video demonstrates the use of symmetry and its reflection in order to create a pattern shaped as a braid. The use of this type of pattern may be used to produce a sound braid shape such that when notes are added to it there will be harmony. Mathematically speaking this sound braid is considered a an object exsting on a two-dimensional plane with space time.

This video gives details on the different types of infinity and impresses on the difference between countable infinity and uncountable infinity.

Part 2. My favorite video of the three is the Doodling in Math video. The video was eyeopening for me because I never knew how much of a connection a sequence can be related to real life. I loved the use of a pineapple and a pine cone, which already are two amazing things, the video left me wanting to know much more about the Fibonacchi sequence. I learned that in fact a pine cone of any shape still follows the order of the Fibonacchi sequence. One question I have is there a way to show that the pine cone’s leaves on the top reflects or follows the sequence as well?

Part 3. Thia video has inspired me to be creative when I teach math in the future. I believe videos like this or even examples related to this, could have helped me get a stronger foundation of math because it might have kept my attention a little but longer than the more traditional way of teaching where a teacher gives direction and leave the student to apply the concepts to solve problems. One may ask, is this way of teaching math? I declare that it is indeed math and this type of teaching may prove highly relevant in teaching students at any grade level, and it is done in a way that will help a student remember and apply it to other forms of sequences and patterns. There is a big connection between this video about the Fibonacchi sequence and the reading Lockhart’s Lament, because Lockhart professes that there is a need to teach students in a way in which they get a full understanding of the meaning of things instead of memorizing a formula. The example he used with a box whose space is shared by a triangle and using the triangle as part of the rectangle is a very useful way to show students why the formula of the area of a triangle works in turn helping them understand that the imagination is what helps you understand the notion. The author states that something as simple as drawing a straight line connecting to points on the rectangle gives a drawing more meaning. Accordingly, Vi Hart shows that she has the same sentiments by having a video where she explains the sequence but takes her time to demonstrate what a sequence meant and proved it in various ways using a pine cone and a pineapple giving the sequence more meaning. The use of real life examples is a effective way of teaching, I find that students may pay more attention and they will most likely remember what was taught without using memorization.

Videos, Jeron

Doodling in Math Class: Stars
This video involves the concept of factoring using stars. The stars total points are factored and you are able to create 1 dimensional stars with those factors.

Doodling in Math: Sick Number Games
This video is about turning numbers in specific triangles and creating patterns that would make it easy to guess the numbers that would follow.

Rhapsody on the Proof of Pi=4
This video involves breaking down a square with perimeter 4 into even smaller ones until you almost get the shape of a circle. Other shapes were used and were broken down until they became almost straight lines.

Part 2
The video I chose to discuss is Doodling in Math Class: Stars which explains how you can make factors of star points useful. It was the first video I watched so it completely intrigued me at first glance. The quick drawing with precision and accuracy made the presentation that was displayed appear visually entertaining. When I then looked at what was being said I became even more intrigued since it showed at first how stars can be easily made by using 2 of the same shapes. These shapes included a triangle, which came first, then a square and finally a hexagon. Then she went into factoring these stars and made 1 dimensional stars that correlated to the factors. It was like making factoring, which she said was barely discussed, into a more enlightening scope than a formal one.

Part 3
This video reflects to my math teaching since it can help to make people think outside of the box. Factoring might be simple but there is never a fun way to teach it. By creating stars and then factoring them then factoring can lead children to see the fun in math. People usually remember entertaining teachings but tend to forget the boring ones. It can even lead you to start your own ideas since one perspective can lead to many others. By looking at this video I was able to broaden my understanding of star points where they can be made using regular shapes instead of having to draw every single point one by one. This sort of correlates to Lockharts Lament since this sort of teaching of factoring would make children think and to not see things with a formal approach but a creative one. By doing this, it might spark creativity in them as well making them real mathematicians instead of just the copy and paste ones.

Videos – Ismail Akram

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.