November 2011
20 posts
Mathland - Nick and Ramzi (The Room)
Our project was modeled after the description that a classmate – Felipe – gave of what his ideal Mathland is. Essentially, Felipe expressed that he wanted math to be more like a casino – both in terms of the probability and random chance aspects as well as the problem-solving feature that plays a role in gambling and specific games available at casinos. In an attempt to emulate and...
Mathland camp To Infinity + Beyond (by Eva,... →
October 2011
100 posts
MusicaLand! The Experience →
This is the actual link to Suzanne, Lena, and James’ Mathland Project. Enjoy!
Mathland Scratch Project: Brittany, Danya, Dani →
This is the scratch portion of our mathland project which incorporates sports (high jump) and math (clearing the bar when solving a math project correctly).
Mathland: Learning Math through Movement
(Brittany, Danielle M., Danya)
We wanted our Mathland to be like playing a sport and designed it for Danielle Pike, who said she wanted math to be more like learning sports where it becomes mindless after you teach your body how to do it. When we were thinking about how to create our Mathland, Dani (Moscovitch) used the example of pole vaulting. When learning to pole vault, a pole-vaulter must...
Our Mathland -- Annie Stella Alex
We did a guess-and-check, “figure-it-out-as-you-go-along” baking project! Annie, who is quite the novice when it comes to baking anything, attempted to make chocolate chip cookies without any recipe. Perhaps simple for some, this actually turned out to be quite the task for rookie Annie, who struggled to decide the best measurements and ingredients. Because she has eaten cookies before she, of...
Nested Triangles
HELP! Agh! While I understand the concepts of 2.4, I am confused about how to actually do it in scratch. I worked on the nest triangles for a while, but alas, its not looking like it should (though at least they are triangles!) I’ll have to think more about this one.
Suggestions?
Mindstorms Ch.5 Response
I definitely agree with Papert that to learn something you need to relate the new material to something you already know and then you have to make it your own or somehow internalize it. I follow this learning pattern when I am learning math and other subjects. As Papert pointed out, math usually requires prerequisites since math concepts build upon each other. This is helpful in that you can...
Ruby and Project Euler
I read some more about Ruby and tried out a couple problems from Project Euler using the repl.it website to test them out.
I started trying to solve problem 10, adding all the primes below 2 million. I made an array and practiced some loops, just to get more comfortable with Ruby. I was having trouble making my nested loops work, but I finally realized that I left off one of the “end”...
Mindstorms Chapter 5
First of all, I really liked this chapter. I thought that Papert brought up a lot of good points and had an interesting perspective. Often times when I read his work I find that I think to myself “of course, that’s obvious” but he really does lay things out in a new way which I really appreciate.
I thought the whole idea of prerequisites was extremely interesting. Prerequisites...
Mindstorms Chapter 4
What was most interesting to me about this chapter was the entire process of debugging. As a person who is not the biggest fan of math, when I was younger I would often just ignore what went wrong when I made a mistake; I was too frustrated that I had made one in the first place. I think that Papert has a lot of logic when he talks about the process of debugging. It is often easiest for people who...
WatchMathland Project Video #3
WatchMathland Project Video #2
WatchMathland Project: Video #1
Ch 5
This chapter was interesting to me because I had an especially hard time learning physics in high school. The author discussed the importance of “finding ways to relate it to something they already know,” which I think is important because as he pointed out, it’s hard to see Newton’s laws in action unless you are in a car skidding on ice. Pappert pointed out that the best way to learn physics...
Triangle Recursion
After reading Ch.2.4 in Turtle Geometry, I decided to give the nested triangles a go in Scratch. I started with a specific length of the side of the first triangle and then divided that in half to get the length of the next triangle and then did that again. I feel like I cheated the program since I hardcoded where the sprite should go, instead of making a variable, but I wanted to make an...
To Infinity and Beyond- Scratch Program
Here is the Scratch program we used at the To Infinity and Beyond math camp:
http://scratch.mit.edu/projects/grease1978/2115581
Our Mathland - To Infinity and Beyond!
For out Mathland, we decided to create a “Summer Math Camp” that was more interactive and conceptual than existing “Math Camps”. We filmed a sort of commercial advertisement for the program highlighting activities that can be done at To Infinity and Beyond. The theme for these activities was Circles. Two “students” who were having trouble with math were encouraged to attend To Infinity and Beyond...
MusicaLand
(Suzanne, Lena, and James)
For our Mathland, we tried to create Dani Moscovitch’s idea of musical collaboration, improvisation, and composition. We envisioned a collection of musical loops (percussion, harmony, and melody) that could be played one at a time, played together, or used as the foundation for further composition or improvisation. We did it using Scratch, by assigning each loop to...
Mindstorms Chpt 5
Sorry this is not a video.
I actually agree with a lot of what the author said in this chapter. It struck me when he mentioned the fact that when you look at courses in college course catalogs, you usually see a lot of prerequisites listed. This is understandable, especially for upper level courses, because there is not enough time for the professor to teach all the basics that you may need to...
Ch. 5 Response
I’m home for the weekend so sadly this will have to be a written post this week :(
A lot of things in this reading made a great deal of sense to me. The whole concept of “perquisites” is something that made a lot of sense to me. At Tufts there have been math classes that looked extremely exciting to me, but that I didn’t have the prerequisite for, and I had no interest in...
Improved Turtle Geometry Experiment!
Hey all,
After looking through the polygon vs. star problem during class, I realized I had a similar problem a while ago with a project of mine. I had tried to make this shape:
But I ended up with something like this:
The link to my former project is here.
This is the result that I eventually got:
The link to the new and improved project is here. I thought you had to change the angle...
Mindstorms Ch. 4 Response
I agree with Papert when he proclaims “No knowledge is entirely reducible to words, and no knowledge is entirely ineffable.” When I was reading the beginning of this chapter, I thought immediately of dance rehearsals and how performing arts practices/dress rehearsals are like ‘debugging’. Running through the process in order and seeing which versions of steps work best...
http://scratch.mit.edu/projects/ngwoolf/2100857 →
This is a project I’ve been working on for a few weeks that would an example of my Mathland (or at least part of it). It’s a Monty Hall problem that let’s you try and figure out which of 3 doors a car is behind. I looked up how to do some of the programming for it and looked at other people that made them on Scratch for help.
There’s still some bugs, the biggest being that...
NY Times Article →
Thought this was really cool and somewhat applicable.
Dani and Brittany discussing Mindstorms Chapter 3...
Mindstorms Chpt 4
I think this idea of “developing descriptive languages for talking about learning” is really interesting. When the author pointed out that many people think they should learn physical skills just by doing them, I thought about my own experiences in learning physical activities. I definitely think about learning dance differently than I do learning sports like basketball, tennis, or...
Mindstorms Ch. 3 Response
The comparison to Euclid’s and Descartes’ systems of geometry helped me understand the unique qualities of Turtle Geometry more, but I got stuck when Papert said that the floor turtle and light turtle carry a “powerful idea” in that “Two physically different entities can be mathematically the same (or “isomorphic”).” I think this might be because of...
scratch
To create the spiral, I worked with what I knew about making a circle on scratch. I have been doing that by means of making the turtle move 1 step, 1 degree and making it repeat 360 times. To create the spiral, I took that idea and tried to figure out a way to intercept that 360, move the rotation in a bit, while still creating the continuous circular motion moving inward. I thought the best way...
Mindstorms Chapter 3
This chapter is essentially an attempt by the author to lay out the many reasons why Turtle geometry is superior to other methods of teaching and learning mathematics. In many ways, I do relate to this. I think that TG is presented in a way where math doesn’t seem as daunting to learn.
I think this is a really good way of explaining the benefits of using Turtle. He describes the concept...
Attempts to make a sun
So after looking at Turtle Geometry and Mindstorms and seeing the flowers and spirals that were created, I decided I wanted to create a sun. For my first attempt, I used two different sprites hoping that they would overlap and look like a super sun. It didn’t work out super well though:
Then I tried to make a sun by individually creating each sun-tip, but quickly abandoned that...
Mindstorms chapter 3
In general, it seems that in this chapter, Turtle Geometry is being hyped to a level that I am skeptical of. The author lays out multiple arguments for why TG learning is more effective than the ways in which math is taught today, but many of the things he says about it don’t even seem far off from the way I learned math, nor a more tangible method.
One thing I noticed, was the...
2.1-2.3 Turtle Geometry Experiment
For my (absurdly late - my apologies Alec!) experiment with Chapters 2.1-2.3 of Turtle Geometry, I tried to make an equiangular spiral, as seen here:
First, I started out trying to write the code for a spiral on my own. Retrospectively, I now realize that both my starting degrees and distance were too big.
I ended up using a code that I found on the Scratch website. However, this gave me...
Mindstorms Chapter 4 Response
When Papert introduced that the central theme of chapter four would be to display how learning a physical skill can be, in many ways, to building a scientific theory, I was intrigued to see how he would tie in this concept. Essentially, Paper was claiming that
“an important part of becoming a good learner is learning how to push out the frontier of what we can express with words. From...
Discussion by Danielle, Eva, Hannah, and Lena!
Avoid by Smell/Find by Sight
I decided to try to do a predator/prey problem where the predator is trying to find the prey with sight and the prey is trying to avoid the predator by smell. I made the knight the predator and the lobster is the prey. Since Scratch has the commands “point towards” and “distance to” I decided to use those instead of figuring out the distance between sprites using the distance formula....
Turtle Geometry 2.1.1. - Scratch Play
I was curious about this how changing the A1, A2, D1, D2 values would affect the shapes. It took me a little while to translate the TurtleGeometry language into scratch, and once I set it up, I tried different experiments with these numbers.
Above, this was kind of a mess, I think I let it go on too long.
Above, I was trying to mess around with what the chapter was talking about regarding...
Turtle Geometry Chase
I liked the idea of the chaser and the evader, so that’s the project I worked on. I tried to make the chaser and evader like in section 2.2.2 of Turtle Geometry.
I started out just making the two sprites face each other and move towards each other until they touched (plus the evader turned 90 degrees each time). This is what it looked like as a result:
After this, I changed the steps of...
Mindstorms Chpt3
I was somewhat skeptical about how many mathematical concepts and ideas kids could really learn from doing Turtle Geometry, but after reading this chapter, I can see that you can actually learn a lot about geometry and develop good problem solving skills.
As you start out making simple shapes using the Turtle, you are advised to walk the shapes with your body and figure out what you are actually...
Proving "4 Ants" distance problem
One of the problems at the end of chapter 2.2 of Turtle Geometry was to set up the four bugs simulation and have the system calculate the distance traveled by each bug, in order to prove the book’s claim that the total distance traveled by the bugs is equivalent to the perimeter of the square they form at the start.
I already had a program in Scratch for modeling the four ants, so I...
Eva and James discussing chapter 3 of Mindstorms....
Mindstorms Chapter 3 Response
As stated in the title of Chapter 3, turtle geometry truly is a mathematics made for learning. As Papert states, Turtle geometry is unlike Descartes’ analytic style and Euclid’s axiomatic style. Instead, turtle geometry is a computational style of geometry. I thought it was very interesting that this innovative new style of math actually used a primary part of Euclidian math -...
mindstorms ch3
so this chapter was kind of cool, providing examples of kids trying to figure out how to build a garden. i really liked the idea of intuitive learning, using a turtle as an embodiment of our mind and to actually see our ideas coming to life, so to speak. i agree with papert when he says that we have disassociated our bodies, and therefore our mind, with learning. when we “learn” math,...
