exploring the quantitative world

I am glad that Papert finally addressed the connection between a LOGO environment and schools.  I have really enjoyed reading Mindstorms and found Ch.8 to be my favorite chapter to read.  I liked is comparison of a LOGO environment to the samba schools.  To him, the samba schools were his mathland where math is a real activity and novices and experts are learning together.  This type of environment reminds me of a Montessori classroom where students of different levels are learning from one another while engaging in different activities.  The role of the teacher is to get the students started on the activity and to guide them if they need it, but otherwise the student is mainly in charge of their learning.
I definitely agree that math is cultural and that the computer can be used to unite multiple domains.  But what is really important is the process, not only of mathematics but of other subjects too.  I think that is why computer programming is such a powerful too because the skills that are learned through it are important to all areas.  Computer programming also gets away from the idea that there is only one answer.  Plus the process of debugging is just as powerful as programming.  

In order to implement a LOGO environment or even to fully integrate computers into the classroom there needs to be a complete redoing of the math curriculum.  I liked Papert’s comparison to the change of how skiing is taught and learned.  In order to change math in school the content, pedagogy, and technology all need to be reformed.  Unfortunately, I think we are a long way from this reform ever happening and that by the time the math curriculum is reformed, there will  be something even better than computers with which you can teach math.  However, I think until there is a reform of the math curriculum, computers can be used enhance the current curriculum.  I think the biggest hurdle in fully implementing computers is the state math standards and standardized tests.  Since there is a set math curriculum for schools, there is little room for students to explore math and other domains with computers.

            In Chapter 8 of Mindstorms, Papert finally answers the question that he has been building towards for the entire book: what is the ideal social context in which his type learning might take place? Up until this point, Papert has emphasized and reemphasized his computer culture that moves away from the traditional mathematic one, allowing us to learn (in the traditional sense) as well as “learn about learning” (177). The culture that he has described, to this point, has incorporated humanized learning with almost personal relationships with knowledge, allowing the learner to supplement their experience with other students and teachers. Papert addresses the idea that whenever talk of schools ceasing to exist is brought up, people are naturally inclined to go on the defensive, as “most of us spent a larger fraction of our lives going to school than we care to think about… the concept of a world without school is highly dissonant with out experiences of our own lives” (177). Despite, he does suggest that if we are to move in this direction, it is vital that we begin to plan “elaborated models of the nonschool activities in which children would engage” (178).

            I felt that the most intriguing aspect of Chapter 8 was Papert’s subsequent discussion of Brazilian samba schools as an example of such a model. As he explains,

“Every American disco is a place for learning as well as for dancing. But the samba schools are very different. There is a greater social cohesion, a sense of belonging to a group, and a sense of common purpose. Much of the teaching, although it takes place in a natural environment, is deliberate… and focused. Then it dissolved into the crowd.” (178-179)

Papert then astutely connects Brazilian samba schools back to Turtle Geometry and the LOGO environment, claiming that they are alike due to the fact that any mathematics associated with either samba school or Turtle Geomety is “a real activity that can be shared by novices and experts. The activity is so varied, so discovery-rich, that even in the first day of program, the student may do something that is new and exciting to the teacher” (179). Furthermore, he elaborates on this by bringing up yet another similarity: the quality of the human relationships each creates. The way in which teachers intervene in learning in the setting of Turtle Geometry mirrors the way in which expert dancers in samba school assist and learn from others. Instead of having a traditional curriculum or lesson plan, teachers working with Turtle Geometry answer questions, provide help, and facilitate students by providing insight that will help to expand their horizons. Similarly, expert samba dancers will help to assist those who are struggling, answer questions, and – just by dancing – allow others to visually model what they need to do. Additional, Papert describes how the samba school and Turtle Geometry share a third thing in common: “the fact that the flow of ideas and even of instructions is not a one-way-street” (180). In Papert’s own words:

“The environment is designed to foster richer and deeper interactions than are commonly seen in schools today in connection with anything mathematical. Children see programs that produce pleasing graphics, funny pictures, sound effects, music, and computer jokes. They start interacting mathematically because the product of their mathematical work belongs to them and belongs to real life. Part of the fun is sharing, posting graphics on the walls, modifying and experimenting with each other’s work, and bringing the ‘new’ products back to the original inventors.” (180)

The only thing standing in the way of such a learning environment and the subsequent growth of popular computer cultures, according to Papert, is a cultural obstacle. The remedy, therefore, is also cultural, and thus Papert hints that in order to advance his model learning society, we must “advance the art of meshing computers with cultures so that they serve to unite… the fragment subcultures that coexist counterproductively in contemporary society” (183).

I took Intro to Cognitive and Brain Science last year, and in that class we were introduced to the concept of the “self” being an oversimplified illusion, and not displaying the complexity of what is really going on in the brain. Having been raised with the language of Eastern religions often around me, such as Self with a capital S, this was an interesting thing to ponder, and still is. In that class we also had a couple of lectures on Artificial Intelligence. Minsky’s article discussed the two together (selfhood and AI). When I heard the lecture on AI in the CBS class, I remember being struck by how abstract, “math-y”, and boring the whole thing was presented as. I liked the first three minutes of the lecture, because it introduced how computers could be used to understand human minds, and vice versa in some cases. But then the lecturer went on to introduce abstract formulas and concepts that were totally divorced from things I could relate to. This experience connects directly to Mindstorms Chapter 7, where Papert is emphasizing that studying how one learns is just as important to learning what one learns—and that the two are not separate, but that actually, as shown in the “learning to ride a bike” example”, understanding the process can help you achieve the skill. In trying to teach AI, the lecture failed to see how the process of “accessing” AI is just as important as understanding the different algorithms and formulas that allow for AI programming. 

Something I want to bring up is what I see to be great hypocrisy in both of these articles in how they seem to view science as a more valid form of learning than other fields. Minsky writes, “so ‘consciousness’ yields just as sketchy, simplified mind model, suitable only for practical and social uses, but not fine-grained enough for scientific work” (Minsky 15), while Papert writes “By restating Newton’s laws as assertions about how particles…communicate with one another, we give it a handle that can be more easily grabbed by a child or a poet” (Paper 172). There is clearly this concept that science is “real” in a way that a poet or a social scientist is not. While I understand that Minsky is arguing that we are deceived by our daily experiences of selfhood, the reality is that this is what we experience. He himself says that it would be too risky to suggest seeing humans as something other than selves, given how our societies are so structured around this concept. So those “lowly disciplines” that take the experience of selfhood into account, while perhaps are not getting at the reality on the neuronal level of processing, are getting at the reality of experience. And to invalidate this type of knowledge as lesser, as their language of scientific-centrism does, goes against Papert’s whole argument about making math more accessible and meaningful. While perhaps it is not contradictory, if he really means that math should be packaged so that less robustly scientifically intellectuals can still make sense of it, I have always gotten the sense that he is more talking about showing the interconnectedness of knowledge. And so if he is against the fragmentation of knowledge into supposedly separate disciplines, why the need to locate science as this separate body of knowledge that is more “real” than other forms?

The line in Mindstorms chapter 7, “the dynamics of lift are fundamental to flight as such, whether the flyers are of flesh and blood or of metal” (Papert 171) certainly connects to the Minsky article, because Minsky is trying to lessen the gap between human brains and computers, and show that they don’t have to be seen as so fundamentally different. Here too, Minsky is emphasizing the process of flying, versus the body that is doing the flying. I think part of why this is a hard concept to grasp is because of our “self-oriented” mindset. Socially and culturally, we rely so much on the idea of an individual and distinct self that we place great focus on “who” is doing the action. Minsky is saying that the “who” is less important, in that the human brain isn’t so different from the computer brain, and the processes are similar. And Papert is saying that the process shouldn’t be separated from the end result—that the process can be illuminating, in fact.

So I replied to Nick’s e-mail about meeting up to video chat, but I later found, in my spam folder, an e-mail saying the message was not sent (there was a problem because I didn’t use the e-mail address that is on the list for the turtle geometry google group list), so that didn’t work out. We talked about a lot of this in class already, so I will just write a little bit about what I think.

Reading these did actually change how I think about AI. I didn’t really have a clear definition of AI before. I just thought of it as being machines or computers that think like humans somehow, but I was not sure what that meant. Now, I think of AI being characterized basically by machines or programs that can learn things. This way, they can improve or adapt for future possible events as they gather more data and develop a history to help them predict future problems. 

In Mindstorms, the author mentions AI being a way computers emulate human intelligence. I think the idea of intelligence is hard to define, but I liked the example of people studying the flight of birds in order to create airplanes. Airplanes are machines that emulate the flight of real birds, so airplanes appear to have the intelligence of birds, even though they are machines made of metal. I think this concept of AI still needs to be developed and refined over time as people research more into this area and create new technologies. 

The author in Mindstorms also goes back to his point from earlier about breaking difficult concepts into microworlds (like the physics microworld) in order to learn them better. He also mentions that computers can help children construct their own microworlds, and he provides a few examples. I can definitely see how computers and Turtle Geometry can help people understand and practice this concept of breaking difficult problems into smaller, more understandable concepts. The use of functions or methods in programs demonstrates this very well, but it is also about thinking of how you would do things yourself in basic terms so that the computer will understand how to do them.

Reading the Minsky article in conjunction with the mindstorms chapter made me think a lot about the computerized chess program, specifically “Deep Blue” which was a computer-chess player that ultimately won against the chess champion human. Before finding this out, my instincts were to say that a computer would never be able to beat the best human chess player because of a factor of human’s creativity, spontaneity, and ability to predict moves ahead of time and also predicting the other players moves by evaluating the way they’ve been playing. It’s a little startling that these conditions that I thought were unique to humans with alive and functioning brains are things that a computer is capable of doing. It brings into question of whether the ultimate goal of computers in a world of technological advancement, is to imitate and reproduce the workings of a human brain. Is that just creating humans, then? 

I still believe, because of personal experience, unlimited expanding knowledge, unpredictability, and interaction with similarly-capable brains, that humans maintain an upper-hand of creative capabilities and understanding over computerized systems. There is still the sense that we control the computers, that we make them do things, and that any sense of “personality” we try to instill in them, really is just a projection of human choices stemming from our unique capacities/traits. 

Here is my attempt at embedding triangles in another shape! 

Once I got ruby processing to work on my computer, I decided to give it a try.  I looked over some of the example codes in the Learning Processing with Ruby in order to get a sense of how it worked.  I ended up just messing around with the code and changing things in the code to figure out what the code actually meant.  

My program creates a square and then everytime you click, it creates another square that is larger than the previous square.  The program also changes the colors of the squares after each click so that the colors are getting lighter.  If you want to start over you can press any key and it will reset the size of the square to the original dimensions.  I really did not have a project in mind when I started working with ruby processing so this is just what I came up with.  

Here is the code:

class Squares < Processing::App

  def setup

    background 255

    smooth

    @rect_x=150

    @rect_y=150

    @rect_size =50

    @rect_fill = 50    

  end

  def draw

  stroke 0, 90, 0

  rect @rect_x, @rect_y, @rect_size, @rect_size

  fill 0, @rect_fill, 0

  end

  def mouse_pressed

    stroke 0

    fill 0,0,@rect_fill

    @rect_size +=10

    rect mouse_x, mouse_y, @rect_size, @rect_size

    @rect_fill +=20

  end

def key_pressed

    background 230, 0,0 

    @rect_size=50

  end

  end

Squares.new :title => “Squares”, :width => 500, :height => 500  

I was also still working on the triangle recursion from Turtle Geometry in BYOB, but when I create a function that calls itself, I cannot seem to get it to work.  I am going to continue to work on it and see if I can get it working.

http://scratch.mit.edu/projects/ngwoolf/2146678

Here’s my attempt at making a program to simulate recursion in Scratch. I based it off of a project made in scratch that used a similar method to make shapes and animals that kept growing… However, I couldn’t figure out an efficient way to make it keep repeating/growing forever (or at least, for more than 5 steps), as I could only get to 4 or 5 levels before it broke down. Furthermore, I’m still working to get it so the shapes are smaller and fit on the screen as well as to install a counter that allows you to adjust the level.

Hi everyone! Our video discussion of Ch. 6 of Mindstorms can be found here: http://www.youtube.com/watch?v=kI0y5x69uPI

I posted this on Monday, but it doesn’t seem to be showing up. Third time’s a charm? We’ll see.

Cheers,

Suzanne

This chapter of Mindstorms references a lot of the earlier chapters and sort of builds on those ideas. There are also a lot of new ideas that the author introduces, all the while building on the concept and methods of learning. 

The author discusses a lot of the different methods of learning, including learning facts versus learning skills.  He also brings up the idea of ‘propositional knowledge’ versus procedural knowledge”. One thing that I found interesting is the idea that the author creates a connection between the scientists and children. He says that scientists and children have the same way of thinking and there is a relationship between their thought processes and patterns. I agree with this relationship, although I had never really thought about it before reading this chapter- the author laid it out in an interesting way.

Another thing that I found to be interesting and true was the idea that teachers should help students learn intuitions rather than just facts. In one of my classes this semester, the teacher discusses gaining skills and intuitions rather than just memorizing. I think I’ve begun to listen to this idea more and more, and have slowly started trying to figure out how to gain those kinds of skills. It’s much better to understand something rather than just trying to figure out how to memorize it. With an understanding of things, one can learn how to apply them in other situations. The author, in this scenario, uses the example of Turtle. 

Over all, I think that the author comes to interesting conclusions in this chapter. I think that there is a fundamental thing missing in our learning processes, and that fundamental thing is the idea that we need to learn and be taught how to be better learners. No matter what we study, this skill is extraordinarily important. 

What stood out to me the most in Chapter 6 of Mindstorms was the focus (early on in the chapter) on how computers can be used in to influence the way children learn in a positive manner but, conversely, can also be used in ways that only reinforce our society’s traditional outlook on “real science” versus “school science.” Relating this back to previous chapters in the book, Papert explains a paradox concerning commonly held notions of children’s learning styles and abilities:

“Although most of our society classifies mathematics as the least accessible kind of knowledge, it is, paradoxically, the most accessible to children… The thinking of children has more in common with ‘real science’ than ‘school science’ has with the thinking either of children or of scientists.”

Papert goes on to elate this paradox into the aforementioned way that computers can be used positively or negatively to either diverge from this train of thought or, rather, to strengthen it. According to Papert, adults talk about learning experiences using the terms “getting to know”, “exploring” and “acquiring sensitivity” — descriptions that are an accurate reflection of the way in which children learn. However, children use a different kind of language - semantically - to explain the way they learn, reflecting the specific model of learning engrained in the minds of grade school children. This model revolves around the learning of skills rather than “getting to know” an idea (i.e. understanding or grasping it), solely because it is “easier to enforce the learning of a skill than it is to check whether someone has ‘gotten to know’ an idea.” Essentially, school focus on learning skills and facts in such a way that children are influenced into thinking about learning in a very concrete, uncreative way.

However, Papert contends that working in an environment such as the Turtle micro-world, students are able to learn facts and skills without memorization or repetitive practice of these skills; they learn by exploring the interface and what the Turtle’s capabilities are. He then relates this concept of ‘getting to know’ an idea to being introduced to a new community, in which you just want to be exposed to a bunch of people and not just learn everyone’s name and memorize them. 

Personally, the idea Papert is getting at in his description of “school” learning versus “real” learning is one of the biggest fundamental problems in our current education system. Placed in a highly competitive environment, students are taught that grades and success on report cards, tests and projects greatly outweigh how well one can grasp a concept (or, essentially, learn). Thus, students are forced to learn through memorization instead of learn by focusing on whether or not they understand what they should be internalizing but are instead memorizing for a test, after the taking of which they can forget everything they memorized. The type of learning Papert advocates is much more beneficial and much more relatable for students, as they are not forced to memorize dull, boring concepts and facts that make their mind go blank. He explains:

“Yet the Turtle is different — it allows children to be deliberate and conscious in brining a kind of learning with which they are comfortable and familiar to bera on math and physics. And, as we have remarked, this is a kind of learning that brings the child closer to the mathematic practice of sophisticated adult learners… We must not forget that while good teachers play the role of mutual friends who can provide introductions, the actual job of getting to know an idea or a person cannot be done by a third party. Everyone must acquire a skill at getting to know and a personal style for doing it.”

Through the use of Turtle, children are able to internalize Physics concepts, for example, without the direct help of a teacher and without having to memorize boring facts or concepts. It is a way in which children can, early on in their learning experiences, ‘get to know’ a formal subject by ‘getting to know’ its main concepts through interactive experiences in a friendly environment. Furthermore, if computers are used to just allow children to carry out more complex ways of memorization - making graphs or executing calculations - they are put “at a very high risk as learners. They are on the road to dissociated learning. They are on the road to classifying themselves as incapable of understanding…” Essentially, if computers are not used to teach children how to go about working through conceptual problems, as Turtle geometry does, it only reinforces “the need for drill and practice in arithmetic” will continue to exist.

(Sorry again that this is not a video. I hope that is okay. It is difficult to coordinate a time to meet up for the video as I do not really know people in the class that well and groups have already formed to discuss the weekly reading responses.)

This chapter referenced many ideas mentioned in earlier chapters of Mindstorms. The author reflected on the idea that children naturally think about thinking and use procedures as part of everyday life (such as the examples of giving someone directions or playing a game). Teachers should help students improve their natural intuitions and develop their own styles of learning and using procedures. The author mentions that many successful scientists think in the same ways as children, which I do agree with. There are many highly intelligent people who seem child-like in the way the act and perceive the world. I do think that this has to do with their ability to learn because children are natural learners. It seems that once people start school, some children lose this natural curiosity and become discouraged by their struggles to learn the way subjects are taught in most schools today. When a student’s intuition tells them one thing, but they know that this answer is not correct, teachers usually use equations to prove the correct answer to the student. Just like the author says, this strategy is not very helpful because it reinforces to the student that his/her idea was wrong without actually helping him/her to understand why this intuition came about. Teachers should instead help students alter their intuitions so that their intuitions will be correct. 

It is true that when you learn physics in school, you are usually taught the formulas and quantitative reasons before understanding the qualitative reasoning behind these results. This makes it hard to identify these new physics ideas as something similar or related to what you already know or what your intuition tells you. The author says that by learning Turtles, you can “get to know” what it is like to actually learn a formal subject, and this is how Turtles can help with subjects like physics, not just basic geometric and computer science concepts. I would really like to see an example of this approach in order to see if this actually works, how well this strategy works, and if learning Turtles helps most people rather than just a few students.

I think it is interesting to look at learning other subjects (like mathematics) in the same way as learning computer science. When you think about something in mathematics that you do not fully understand, you can think of this problem as arising from a difficulty you have with the actual procedure of doing the concept (like adding). Rather than just avoiding wrong answers, you can examine the bugs or what went wrong with the procedure and think of this as a normal part of the learning process. 

I think this idea of altering intuition and learning how to be better learners is a powerful way to think about teaching. It is discouraging when you ask a question about something you do not understand, only to be told again what the correct answer is. You can be told the correct answer 100 times, but that may still not help you understand why exactly you thought the answer should be different. We should be able to think about our thoughts and analyze our intuitions to better understand how we can arrive at the correct answer.