I talked to my son about how magical Pl is. How it appears in so many places in nature. It was observed. Ancients measured the circumference of the circle and it’s ratio with the diameter. That remained constant irrespective of the circle – PI. It also shows up in so many places in Physics.
How many people tried calculating PI including 5th century mathematicians in China / India, Archimedes and Srinivasa Ramanujam. We talked about how hard it is to calculate PI. How it is an irrational number and no repeatable patter. Then I said we will beat Archimedes today… in one afternoon.
Creating a sense of mystery and adventure I feel is key to getting kids excited about learning any thing new. They always want to play. Why not?
Then we talked about the intuition behind the Archimedes method . If your draw a polygon (multi-sided shape like a square with 4 sides) in a circle and then keep increasing the number of sides, eventually it will come very close to a circle. Archimedes had a simple way to calculate the perimeter of the polygon and thus approximate the circumference of the circle.
Archimedes stopped at a 96 sided polygon. Using simple excel or a more sophisticated program in python we can go to MNs of sides to estimate the perimeter easily.
The interesting thing about using the Archimedes method is that it requires application of Pythagoras theorem, infinite series and basic geometry.
Learning happens in the mind of the kid. Only when they reconstruct pieces and learn to assemble seemingly unconnected pieces (Pythagoras theorem interacting with infinite series) will real learning happen. This is the essence of Constructionism.
- Calculating PI like Archimedes did
Kids should be taught programming. But not with the purpose of writing computer programs.
Instead they should learn programming to develop a new way of thinking – concepts such as iterations, use of variables, reusable blocks, error handling to refine the solution. To give them a powerful tool to simulate real life and refine their mental models. To allow them to visualize outputs in interesting ways than just drab equations.
Can we unteach physics or math or biology or even languages thru programming?
Does programming offer a safe and a low cost way to fail in the journey of solving a problem?
Will programming develop abstraction of ideas and their implementation?
Seymour Papert defined a concept he called Constructionism ,  in his proposal  to the National Science Foundation. This concept can be a very powerful learning model to rethink how you can unteach to kids.
The word constructionism is a mnemonic for two aspects of the theory of science education underlying this project. From constructivist theories of psychology we take a view of learning as a reconstruction rather than as a transmission of knowledge. Then we extend the idea of manipulative materials to the idea that learning is most effective when part of an activity the learner experiences as constructing a meaningful product. 
Constructionist learning is when learners construct mental models to understand the world around them. Constructionism advocates student-centered, discovery learning where students use information they already know to acquire more knowledge. Students learn through participation in project-based learning where they make connections between different ideas and areas of knowledge facilitated by the teacher through coaching rather than using lectures or step-by-step guidance. Further, constructionism holds that learning can happen most effectively when people are active in making tangible objects in the real world. In this sense, constructionism is connected with experiential learning and builds on Jean Piaget’s epistemological theory of constructivism. 
This can be translated into 3 key ideas as we think of a new way of learning and teaching:
- Learners need to reconstruct what they learned … assemble the pieces like building Lego models … and they finally assemble a mental model of how things work in their own mind
- This activity of recontructing is more effective if the end product is a tangible real life meaningful object
- The role of the teacher is to facilitate that reconstruction and call out the reusable pieces as you go along (Interestingly this is very closely related to the concept of learning thru Chunking and connecting the chunks, Barbara Oakley talks at length in these videos on Chunking )
- Wikipedia page on Constructionism (Learning Theory)
- Situating Constructionism by Seymour Papert and Idit Harel
- Educational Psychology Open course by Atlantic International University
- Constructionism: A New Opportunity for Elementary Science Education
- Learning to Learn: Videos on Chunking