I just finished reading Seymour Papert’s book Mindstorms for the second time and I have the urge to read it again soon. It is so rich in ideas, both in depth and in breadth, and it includes many illuminating examples. The book is very old (second edition published in 1993) but this doesn’t diminish its value at all. Papert chose computational thinking as the thinking model and he explained how the programming language LOGO, part of it Turtle Talk, that he and his colleagues developed, could be used to help children explore and learn mathematics, physics, and grammar, the subjects children usually don’t have many opportunities to explore freely and discover by themselves, especially the parts that the formal methods and conclusions seem to be in contradiction with our intuition in daily life. Though the book talked a lot about children’s development, the essential ideas about learning and thinking Papert introduced should be useful for people at any age.
Papert seems to be a very colorful character. He described himself in the Afterword of the book like this. “I have always considered learning a hobby and have developed many insights into its nature by cultivating sensitivity to how I go about doing it. Thus, I have perhaps engaged in deliberate learning of a wider range of material than most people. Examples of things I have learned in this spirit include chapters of science (like thermodynamics), reading Chinese characters, flying airplanes, cooking in various cuisines, performing circus arts such as juggling, and even two bouts of living for several weeks with distorting spectacles (on one occasion left-right reversing glasses, on the other a rather complex prismatic distortion of the visual field).” It takes certain personally to try the distorting spectacles, I would imagine.
By training, Papert is a mathematician and psychologist. He was heavily influenced by Jean Piaget’s work on children’s intellectual development and he certainly expanded Piaget’s work in many significant ways. His research interest was not just to understand how children learn and think. He was an interventionist. He wanted to use his understanding to create an environment for children in which they can achieve the best learning and understanding.
The scope of learning Papert referred to is much broader than the learning in the traditional sense. Beyond learning facts and picking up skills, he also talked about how to make sense, how to develop and debug intuition. Here the examples he provided and his analysis are some of the best parts of the book. He paid great attention to the process of learning. He strongly believed that if you could externalize your thinking, if you could put your thinking in a form or procedure that you can name, manipulate, change, and critique, you have much better chance to develop a thorough understanding of whatever you want to learn or do. He disagreed with J.S. Bruner on his “influential classification of ways of knowing.” According to Brunner, “Some knowledge is represented as action, some as image, and only the third category as symbols. Bruner has asserted that “words and diagrams” are “impotent” to represent certain kinds of knowledge which are only representable as action.”He observed that in the history of science or in personal intellectual development, progress was often marked by seeking and finding a new descriptive language for what can not be grasped without it before. One example is calculus that Newton invented to help him work out the planetary motions.Papert believed that people could learn better if they can constantly push out what words can express. His own attempt in the book was to describe juggling in a computer-program-like procedure. It is a hierarchical design. He analyzed the motion and figured out what needed to be done to carry out juggling successfully. Then he moved into the component skills, which are essential to complete each step of the main procedure. With the clarity of all the identified component skills and procedure steps, it’s easy to isolate and trap bugs. For example, he mentioned that some people fail to juggle two balls because they track the balls with their eyes and they can’t track two balls at the same time. The solution was to fix your gaze at the apex of the balls’s trajectories.This example impressed me so much when I first read the book.
Papert thought that the affective aspect of the learning was as important as the cognitive aspect, if not more. He observed that what one can or cannot learn in many cases are not determined by the content, but by the personal relationship between the learner and the subject. He said, “New ideas are often acquired as a means of satisfying a personal need to do something one could not do before.” He thought that “The best learning takes place when the learner takes charge.”With this understanding, he considered rote learning as the worst model of learning since it is a dissociated model where material is treated as meaningless. On the other hand, Papert considered Piagetian learning highly effective. It is the type of learning that is embedded in other activities, and it is without curriculum or deliberate, organized teaching. Teachers for Piagetian learning could help the students by answering questions, working on projects side by side with the students, or showing something interesting to the students spontaneously. One of the vehicles Papert created for Piagetian learning is Turtle Talk. Children could start with Turtle geometry. Compared with the basic construct, point, in Euclid’s geometry, the turtle has a position and a heading, while the point has only the position. Children could apply their personal knowledge of how they move their bodies to instruct the turtle to move and trace out interesting patterns. I played with it a little and it is powerful and impressive. It is a full blown programming language. I plan to introduce it to my daughter this summer.
In Piaget’s line of thinking, children are builders of their own intellectual structures. Built on that, Papert argued that builders needed building materials and the source of those building materials is in the surrounding culture. Papert’s work implied that one of the best ways to help children learn is to make children’s environment discovery-rich by supplying them with many “seeds” of powerful ideas and models to think with. He related one of his own examples. When he was two years old, he discovered a set of differential gears. He played with them and fell in love with them. He internalized the gears and could imagine that he himself was the gears. He told us how much this model of gears in his mind helped him learn algebra effortlessly in school. He realized that not everyone was able to fall in love with gears. But somehow he hoped that the computers would have universal appeal. Turtle Geometry demonstrated his vision of what a model-to-think-with for children was like. It is a great model. It’s really too bad that it doesn’t seem to catch on more widely.
Papert’s understanding of how mind works is computational and it could be summarized with the Society of Minds theory. According to this theory, components of intellectual structures are more like people than precise and logical rules and propositions. The interactions among those components are more like social interactions than mathematical operations. He believed that thinking was to a large extent retrieving. “People can think only because they can draw on larger pool of specific, particular knowledge.”Based on this, he thought that logic and formal learning is continuous with social, bodily, and concrete learning. Following the same line of reasoning, it’s always helpful to relate the new material, whatever it is, to our diverse personal knowledge. The components, Papert called them agents, are modular and simple minded. They are often in conflict with each other. The conflicts are resolved by other simple-minded agents. There is no logical consistency in our intellectual system. One advantage for that is when we learn something new, if it’s in conflict with something old we already possess, we don’t need to reorganize our intellectual system to eliminate the inconsistency and to make use of the new knowledge or skill. Learning is essentially a local event. The implication is that we can put our new acquisition in our tool box as a tool. The more we practice this tool, the better we are able to use it. By introducing this new member to the old members, we learn when it is appropriate to use what tool. The interactions among those tools might bring global change in our intellectual system, but only very gradually. During the process, we can still function decently.
Papert had a very sharp observation about learning process. To paraphrase his idea, he thought getting to know a new domain of knowledge is like coming into a new community of people. We have to endure and enjoy the initial overwhelming and chaotic feelings. Details seem to be a blob of mess. They are not differentiated in our minds at all. When we get to know the community of people, we might have the luck to meet one or two important people to develop deep relationships with in the beginning and those people become a bridge for us or we can ask mutual friends to make introductions for us.If we are capable learners, we can pick out a few powerful ideas in the new domain and develop a personal relationship with them first. If we don’t have enough skills to do so, we can use a good introduction which can help us bring the new knowledge into contact with the familiar ones. Introductions can certainly make learning easier, but we all have to do our own work of getting to know. To make sense, to understand something back and forth till nothing more can be said about it, to perform a skill as if it is an instinct, to make the new knowledge our own, we have to give ourselves time to play with it, to learn the component skills and their combinations, to work with what we’ve got, and to “make something new with it in a personal and playful way.”
Papert talked about many learning enablers with in-depth examples. Other than the discovery-rich environment, models-to-think-with, articulating and analyzing one’s actions and thinking, developing and debugging intuition, he put great emphasis on developing qualitative frameworks, which are something you use to think about various problems before you decide what formal methods to apply. To Papert, it is important to separate the powerful ideas from their formalism. Many powerful ideas scattered around the book, and most of them came from the context of computation. Several of them influenced me a great deal. Here are some ideas that have influenced me a great deal:
·State and state-change operator
·Variables and procedures
·The concept of structured programming
·Self-contained world in which certain questions are relevant and others are not
·Finding intermediate case when dealing with two conflicting cases
Computer could be one of the biggest learning enabler. By providing Turtle Talk, “learning for kids becomes more active and self-directed.” Papert pointed out the two important functions computer could serve. “First, the computer allows, or obliges, the child to externalize intuitive expectations. When the intuition is translated into a program it becomes more obtrusive and more accessible to reflection. Second, computational ideas can be taken up as materials for the work of remodeling intuitive knowledge.”
How about if we want to help other people learn, as parents, teachers, or mentors? Papert had a very interesting point. He said that “all curriculum development could be described as reconstructing knowledge” “in such a way that no great effort is needed to teach it.” In developing curriculum or learning environment, here using mathematics as example, he emphasized three principles:
·Community principle: “The mathematics must be continuous with well-established personal knowledge from which it can inherit a sense of warmth and value as well as ‘cognitive’ competence”
·Power principle: “It must empower the learner to do personally meaningful projects that could not be done without it”
·Principle of cultural relevance: “The topic must make sense in terms of larger social context.”
It also helps if we can figure out the structure of knowledge we want to teach and modularize it to make it mind-size bite so that “it’s more communicable, more assimilable, and more simply constructable.”
Other than the ideas about learning and thinking, this book also gave me a refreshing insight about differential calculus. In essence, differential calculus connects the local and the global. Papert said that the “differential calculus “derives its power from an ability to describe growth by what is happening at the growing tip. This is what made it such a good instrument for Newton’s attempts to understand the motion of the planes. As the orbit is traced out, it is the local conditions at the place where the planet now finds itself that determine where it will go next.” Interestingly, this reminds me of life itself, to a degree.