Algebra

t-Formulae and parameterisation of the circle

t-Formulae are used in integration to tackle rational expressions of tigonometric functions.  After a spell in the cold, when they were not included in some A level specifications, they are now back in sixth form lessons. It all starts with the subsitution, from which the following functions can be derived, ,  ,  . These derivations …

t-Formulae and parameterisation of the circle Read More »

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 …

Before the beginning – Euclid’s Common Notions Read More »

Abstract algebra, the un-codified implications of which need to be fully understood at school to gain good grades in exams.  School algebra and numeracy is all about persuading pupils that the numbers we have work by these rules, and not by the various coping patterns they learned earlier in their education.

This 7th century visualisation of quadratic algebra, thanks to Islamic scholars, is a great place to start the academic year in mathematics.