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

The Threshold Concept

Here is my list of candidates (their level of troublesomeness varies with human development) so far:
metaphor
symbol
collection
pattern
number, numeral, digit
addition
additive inverse
place value system
big-little principle
scaling/ratio
unknowns (@bstacey 's algebraic variables. Are these ideas different? I suppose it depends on what we mean by algebra)
sets
functions
slope
continuity (orig. limit and derivative, but this seems the more foundational concept)
proof, esp. inductive (h/t @EdS )

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.

https://brilliant.org/wiki/fermi-estimate/

@thelibrarian @bstacey

Fermi Estimate | Brilliant Math & Science Wiki

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. …