“Certain notions of mathematics are not sufficiently embedded in the culture for children to learn in their natural way, so they come to school to learn them. Once children are in school, we try to impose mathematics on them in much the same way it was imposed on us: we begin by making them work at unimportant and uninteresting problems on little squares of paper. If before we ever allowed children to dance we insisted that they spend hundreds of hours drawing dance steps on square papers, and only when they could pass a test on the ability to draw dance steps on paper would we let them actually get up and dance, many children would find dancing impossibly difficult. Those gifted in dance would give up. And I think this is exactly what we do with mathematics. We teach it to the children in a way quite analogous to drawing dance steps on paper, and only those who can survive twelve years of that ever get to use it, to dance with it.”

Papert, S. (1984). Computer as Mudpie. Intelligent Schoolhouse: Readings on Computers and Learning. In D. Peterson. Reston, VA, Reston Publishing Company.

FredWith dance you can get up and “do it” but you might be doing it wrong (even if you yourself as a child are having fun) and learning to dance well once you realize what you are doing is just randomly jumping around takes a lot of time and repetition. Is the equivalent with math to just play with numbers and symbols without worrying if it is wrong or even meaningless until you get to a point where you want to do it the right way? What would be considered important and interesting problems that could be solved correctly without learning and building up the basic foundations? Is anyone doing that now 30 years later?

ihor CharischakMy experience with young students is not that they are either right or wrong, but rather they come with misconceptions. My first misconception was thinking that since 2+2 was 4 and that 2X2 was also 4, that multiplication and addition had the same rules. I soon discovered that was not the case so that misconception went away to be followed by other misconceptions or as Papert would say I encountered “bugs” in my thinking. Debugging is the most important skill that a young person should have.

JoeyMy two boys, ages 8 and 12, are learning how to code in Scratch and having a marvelous experience. Computational thinking skills and strategies can be developed by clicking & dragging blocks and seeing the results of their choices. Making mistakes & learning how to “dance” is safe in this environment and they both want to dig deeper to learn more so they can complete a game or storyline that they are developing for others to view.

GermanWelcome back!!. We missed the daily food for thougth.

Seymour predicted educational achievements, that only years after, the technologies are making possible….

Dan MeyerFred’s question is a good one, basically asking Papert to elaborate on the math side of the dancing analogy.

One example is to have a class of students pick any three whole numbers they want and a) add them together and b) multiply them together. We write up everybody’s numbers on two different sides of the boards and start looking for patterns. Someone notices that all the sums are divisible by three. Someone notices that all the products are divisible by 2 and by 3. Someone ELSE notices that they’re divisible by 6. Students pick more sets of numbers and add and multiply them to see if they can break these patterns.

Once we’re satisfied, we prove. We’ve taken the number play, the investigation, the pattern-seeking, and locked it down tighter. It’s not enough to have fun noticing, the mathematician says, we have to know WHY.

That’s one example of how the play can turn into practice.