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I have several Maths-related ideas that run along these ideas. The first concerns the terms 'plus' and 'minus'. The main thrust of my idea is to replace minus with opposite (direction) and, for the moment, to replace plus with forward* (direction).

*

*This is because of the number line.*

*6 + 3 => 6 forward 3 = 9.*

*6 - 3 => 6 opposite 3 = 3.*

The Power achieved by this switch is by making explicit the use of the minus sign to indicate opposite. In my experience, the two most common mistakes that students make in Maths are multiplying/dividing signs and multiplying/dividing units. Look at how this would change:

forward x forward | = forward |

forward x opposite | = opposite |

opposite x forward | = opposite |

opposite x opposite | = forward |

It is probably the last one that causes the most problems. If you ask someone the opposite of opposite they will usually answer, "the same". So -(-3) is the same as 3 therefore -(-) = forward.