Before the beginning – Euclid’s Common Notions

This preamble from Euclid’s Elements is where mathematics education still goes wrong, even after 2000 years or so.

Sound notions of what equality is are required as a bedrock of algebra.  Dynamic approaches of teaching equation solving, in which terms and numbers move and change sign, seem to work at first but lack the simplicity of mathematical logic and create all sorts of problems when randomly, but apparently sensibly, applied.