Also if you, dear reader, have suggested #thresholdconcepts for #mathmatics, please reply with your suggestion. (I do already have a bunch of research on this, so things like "negative" numbers and sets are strong candidates for threshold concepts.)
Link about threshold concepts (in case this term is unfamiliar): https://www.ee.ucl.ac.uk/~mflanaga/thresholds.html
Fermi estimation may be a #thresholdconcept - it has something to do with number sense, which is not unrelated to mathematics.
Calculating with symbols, certainly - a hurdle for some students when the numbers fall away from the maths lesson.
A Fermi estimate is one done using back-of-the-envelope calculations and rough generalizations to estimate values which would require extensive analysis or experimentation to determine exactly. Physics is celebrated for its ability to make extremely accurate predictions about tough problems such as the magnetic moment of electrons, the deflection of light by the Sun's gravity, or the orbit of the planets around the Sun. However, accuracy often comes at the cost of great difficulty in calculation. …
The idea of proof, the idea of proof by induction and the idea of proof by contradiction are #thresholdconcepts
The idea that mathematics is the study of pattern
The idea that numbers are just equivalence classes
Something about axioms too, as possible whimsical and arbitrary and not necessarily modelling a reality - that mathematics is a game, sometimes with applicability.
The Librarian 🌷
Ed S
Blake C. Stacey