Dependent variable vs name of function

Description of bottleneck

In mathematics and in particual in the STEM disciplines one often does not symbolically distinguish the name of a function and its dependent variable.

For example, the time dependence (independent variable, symbolized by $t$) of an electrical charge $q$ (dependent variable, symbolized by $q$) might be described by a certain function $f(t)$, i.e. $q=f(t)$. Here different symbols have been used for the dependent variable $q$ and the functional relationship $f$ (between $t$ and </q>). It is, however, customary to conflate this and to use $q$ to do denote both dependent variable and functional relationship. This results in the using the experession $q(t)$.

Interestingly this possible Bottleneck was revealed during an Decoding interview on students' difficulties with describing piecewise defined functions. The interviewers got confused by interviewee's simultaneous usage of a symbol as the independent variable of a function and as the name of the functional relation.

People interested in this bottleneck

Peter Riegler