Connected Knowledge, Problem Solving Tools and Estimation
Only connect! That was the whole of her sermon… Live in fragments no longer.
- EM Forster, from Howard’s End
The Value of Connected Knowledge
Facts or ideas we know, are often disparate and unconnected. As we grow, we make more connections, thereby creating meaning, and are able to not only deepen our understanding of individual facts and ideas, but also use what we know effectively. This process is described by the ‘knowledge lattice’ analogy below.
Every dot marks a piece of knowledge—a fact or an idea. Now add bonds between neighboring pieces of knowledge, with a probability 𝑝bond for each bond. The following figures show examples of finite lattices starting at 𝑝bond = 0.4. Marked in bold is the largest cluster—the largest connected set of dots. As 𝑝bond increases, this cluster unifies an ever-larger fraction of the lattice of knowledge.
For long-lasting learning, the pieces of knowledge should support each other through their connections. For when we remember a fact or use an idea, we activate connected facts and ideas and solidify them in our minds. By using the tools described below, we can help young learners, master in a few years, what might have taken us a couple of decades to master!
Problem-Solving Approaches/ Tools
The tools/ approaches below help learners connect disparate facts and ideas and promote long-lasting learning.
GenWise had an exchange with Prof Sanjoy Mahajan, Associate Professor, MIT on the importance of building these skills in middle- and high-school children, which he strongly encourages us to pursue.
The GenWise approach to getting middle- and high-school learners become better problem solvers is to encourage them to apply the above tools to conceptualise problems, list down their assumptions, get them to reflect on the quality of their assumptions (and refine the same), arrive at estimates through multiple routes (demand side, supply side, etc.), appreciate Orders of Magnitude, validate for reasonableness and so on. Learners quickly transition from “I can get all my answers these days on Google” to getting hooked on to these new ways of structuring and consolidating knowledge/ facts/ ideas.
Below are examples of (a partial set of) courses (and specific problems we have tried to solve) where we have used these tools; answers to many of these could be “it depends!”, and that is exactly where interesting conversations start…
Wicked Problems: Urban Transportation
For travel between Chennai and Bengaluru, which is more fuel efficient - flying or road travel?
For Mass Rapid Transit, which is better - Bus Vs Train?
Nature, Society, and the Individual
What is the contribution of automobiles to New Delhi’s air pollution?
Estimate the quantity of waste generated in your housing community
Is a Vegan diet friendlier on the environment?
How much money does a small dairy farmer in India make per litre of milk?
How large is Greenland, relative to the African continent, area-wise?
Estimate the diameter of the earth
Estimate the population density of an Indian urban centre, say Bengaluru
Estimation Techniques
# of leaves on all the trees in Cubbon park?
# of animals of an endangered species, say the Bengal tiger, in India
# of barbers in Bengaluru :-)
Mass of air in our classroom
We are confident that many teachers are already supporting learners with these principles/ tools. A more conscious approach to incorporating these formally in the classroom could go a long way towards solidifying, consolidating knowledge and connections for your learners - we can easily see applications in Geography, Social Sciences, Physical Sciences, Business Studies, Economics, Environmental Science, Mathematics - literally everywhere!
Some References
The Art of Insight in Science & Engineering; Mastering Complexity Most of the input for this document is thanks to this excellent resource, which has been put together on the back of a course at MIT, Boston, USA.
Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin