week 3: Turtle Geometry: A Mathematics Made For Learning, Languages for Computers and for People

“An important part of becoming a good learner is learning how to push out the frontier of what we can describe with words.” 

Things to think about:

  1. The LOGO Turtle taps into children’s ‘body knowledge’, i.e. their sense of how to move with their bodies. What’s an example of something that makes learning a task easier by tapping into body knowledge?

  2. Papert talks about 3 kinds of mathematical knowledge: ‘school math’ (selected to be the core knowledge everyone should learn), ‘proto-math’ (background that’s assumed without being explicitly stated), and a third category of knowledge that’s neither selected not assumed, but ought to be included in education. Drawing from any field you’re familiar with, what are examples of these different kinds of knowledge?

  3. Papert writes, “You learn in the deepest way when something happens that makes you fall in love with a particular piece of knowledge.” In Mindstorms, Papert describes how many children came to LOGO hating numbers as ‘alien objects’ and left loving them. Think back to an experience of falling in love with an idea. What features of it led to this feeling? Or conversely, what barriers prevented you from falling in love with an idea?

  4. Papert describes how drawing spirals with LOGO is more empowering than solving algebra problems, or how making computer poetry is more empowering than memorizing parts of speech. Drawing from any field you’re familiar with, how could we teach a piece of knowledge so that it more readily empowers the learner?

  5. In Chapter 4, Papert describes how to teach juggling more efficiently by ‘thinking computationally’ (e.g. thinking in terms of procedures, breaking a problem into parts, debugging individual parts, etc.) Think back to learning a complex skill with your body (such as swimming, dancing, juggling, riding a bicycle, etc.) Did computational thinking help you learn this skill more effectively? If not, how might it?

Cool resources/links:

Rosa: Kids create their own language naturally to create space from parents and parental authorities... would be cool if they could transfer those natural impulses into computational slang.  DOPE idea :-)

Book suggestion: Pedagogy of the oppressed

Rosa's project: Wanted to share some of my favorite Papert ideas... the reason I decided to read Mindstorms and dig deeper

Fun quote:  "YES! Laughter is an invitation" - Rosa


1. In learning how to roll a kayak, you have to first learn a move called the 'hip snap'. I've noticed that kayaking & learning to roll seem to come more easily to people with dance experience, I think this is because they have prior body knowledge about staying loose, separating upper & lower body movements, swaying hips, etc..
2. For the third kind of knowledge, I think the answer to 'why do we need to know this?' is often unsatisfying to students. See also: http://www.smbc-comics.com/comic/a-new-method 3. Having to memorize a lot of information was a barrier for me to fall in love with many subjects in school. 4. 5. When learning to roll a kayak, there are tons of stumbling blocks you can run into. I read a great book that used a debugging philosophy, spelling out each of the different components of a roll, listing the commone ways that people mess them up, and how to fix it. I found this very helpful in learning to roll, and it helped me iron out my bugs.


1. How to feel words: https://drive.google.com/file/d/0B6JcX4ZukFrpLW9HRTM0UjJzZWc/view?usp=sharing
2. Teaching children about their body, especially their brain, suffers from “school knowledge” which is experienced as the information not being presented in an interesting and deep enough manner to satisfy children interested in their changing bodies. In part due to assumptions of “proto knowledge” like we all are currently using a body and brain so we must understand something about it. Education could go further to personalize knowledge through addressing cultural differences in students, exploring the social and historical drivers of misconceptions, and helping students develop their own algorithms for growing, learning and staying healthy.

1. 2. 3. I remember in high school, sadly, not being able to fall in love with physics. The majority of the examples my teacher used in class and on exams had to do with football and other sports, and these were things I actually did not have any interest or knowledge of at all. 4. 5. Coincidentally, I also learned to juggle at some point. I do remember it taking at least a number of weeks for me to learn to cascade juggle three balls. While I don't believe I used the type of computational approach described by Papert, I do remember that the method I employed (which was described in the book I consulted at the time) involved learning to toss one ball with a good form, before moving to two, and then finally juggling three. I have found, though, that the art forms I have started engaging more with in adulthood -- dancing and playing musical instruments -- have seemed to become more easier by a computational sort of approach -- or, I have enjoyed the learning process more because I now am likely to automatically find something like a computational approach, thereby making the activity appeal to my other interests. While I do feel that these physical activities are perhaps a bit easier with a computational approach, there is still an 'art' to these skills that is difficult to directly map to a step in the computational process