From algebraic equations to algebraic thinking: troubleshooting technical systems

When you have an equation like this:

10xy^2+15x^2y-5xy = 2xy^2+3x^2y-xy

…to solve it you will perform a methodical sequence of operations to isolate the variables.

That process, conceptually, is exactly what we do when troubleshooting and diagnosing the problem of a system, whether that system is a diesel engine or a piece of computer software, we determine the problem through diagnostics, a sequence of procedures to that isolate the variables which could be causing the problem.

When the instruction of algebra is confined to the solving of equations, failing to make the connection to technical systems in the real-world application, you have the pedagogy of uselessness.