When Math Gets Abstract: The 6th Grade Shift
If you do math homework with kids, you might observation that as math becomes more abstract, more students starts struggling. Until K-5, math textbooks are grounded in applications and everything has strong correspondence in real world. With 6th grade this starts to change. 🧵 https://x.com/TaliaRinger/status/1681410191278080000
The situation gets much worse in college level math. First year of college is when many former top high school students gets humbled at their first encounter in Linear Algebra, Statistics or Real Analysis. The drop out rate in first year due to math can dwarf other numbers!
Let’s take example: eigen vectors! Take virtually any pure linear algebra textbook and you will see series of propositions/proofs endlessly laid out without much in the way of interpretation, application or any other context. See how many of these you can appreciate or remember.
Now take a look at Python Notebook explaining PCA/SVD and how this results in beautiful algorithms for filtering, clustering, feature extraction etc. Then go back to same textbook, look at same propositions/proofs and see if you feel differently about them :).
I think we are on cusp of changing education dramatically. Previously, textbooks were static and knowledge distribution was monopolized by few experts. With LLMs, textbooks are dynamic, conversational and customized for everyone. It is hard to convey how huge of a leap this is.
We are wired to learn things differently and that’s our collective evolutionary advantage. If you make everyone learn something only in one way, you will end up creating class system of smart and stupid. Once that constraint is removed, world would be a very different place.