Maths is about logical reasoning

Maths is all about logical reasoning. If we have already solved a problem, then we already know the answer and we don't have to solve it again. If we have already worked out what to do to solve a problem, we don't have to work out what to do a subsequent time, we just do the same things that we did last time. This is the basis of the routines that are taught in schools as mathematics. But they are not mathematics. Learning and using these routines may be variously described as "arithmatic", "algebra", or "geometry", but they are not mathematics, they were once, when they were being thought out and developed, but they ceased to be mathematics once their development was completed and they became established routines. Mathematics should refer to the application of logical reasoning to a problem.
So maths education should be about learning how to interpret the facts presented within a problem, and how to apply sound reasoning to manipulate those facts. Calculation or manipulation of data using established routines is not mathematics. That it has become to be to termed as such is simply terminological inflation (in the same way that over the last 30 years school "pupils" have become school "students").

When I sat my A level maths, nearly 40 years ago, I was advised that, were I running out of time, I should do the logical reasoning part of the question, convert the problem into mathematical form, and calculate it until I arrived at a numerical expression, whereupon it would be acceptable to write "hereafter arithmatic", and leave it to go onto the next question. This advise underlined the distinction made then between maths and calculation, a distinction that has since become blurred.

Puppet Maths encourages its pupils to use logic to solve problems. We teach the routines that are the known solutions to problems, and in doing so we show the logical reasoning behind the routines, and encourage the pupils to use that logical reasoning when using the routines, rather than just remember the routines and and regurgitate them (which is what so many traditionally taught pupils do).