I Hate Math

@mathsman:

I don't know how the syllabus is designed, but I would think it right to assemble a group of leading professionals in various non-academic careers - architects, accountants, engineers, scientists, journalists, shop managers and the like - to establish between themselves what is the best blend of basic mathematics for pupils not yet ready to decide on higher-education and career choices.

At up to GCSE Level.....

Obviously money is a priority for everyone and anyone, including those listed above, so I would add a thorough grounding in percentages and loan / debt calculations to the basic money arithmetic; including understanding what the words mean and how to realise when the lunch is not free. (e.g. to avoid tricks like 'Buy Now - Pay Later' and the nature of credit-card purchasing).

I would also add simple Statistics - at GCSE Level not necessarily things like Standard Deviation but averages and means, and with particular reference to understanding the crucial difference between Risk and Hazard, and the compounding effects of % on statistical counts.

Plane, and simple Solid, Geometry - basic geometrical rules, and Trigonometry, you can use for all sorts of practical purposes in all manner of different fields.

Areas and volumes - circular and trinagular as well as rectilinear.

Algebra - introduced early, not so much for its own sake beyond its own rules as necessary, but as a tool in much the same way knitting-patterns, chess notations or cake recipes are short-hand instructions - with the bonus that the rules allow you to customise the instructions to the task. So early understanding of simple algebra can then be used in the other topics, to show it's not merely a puzzle thing that terrifies everyone with its weird x.

Graphs - line, bar, column, also polar, for added interest. A practical application for these is the tachograph, such as used in the school buses; and indeed a sample tachogram formed questions in the GCSE exam I took. Graphs showing simple algebraic equations, as well as the sort of non-linear graphs given by statistical studies like age-ranges and the weather. The trigonomentrical graphs - it's possible to show rather elegantly, the relationship between sin & cos, the triangle and the circle, graphically.

Basic Theoretical Mechanics - as adjunct to qualitative studies in Physics. The lever (a neat algebra illustration of the [ab = cd] type), inclined-plane and its screw-jack equivalent; simple planar force diagrams and how they are used daily in various areas of work. I'd leave circular motion to an more advanced level though it's not especially hard.

Further co-ordinates - introducing (x, y, z) as Ordnance Survey points. (NGR and altitude). No need to delve deeply into the abstractions, but it illustrates you can count in 3 dimensions and a map of real countryside is a very good introduction, especially if a local example is used. (When I tried A-Level Physics, at school, the local brickworks chimney was the object at infinity for telescope studies. It was about a mile away, near enough infinitely far for an optical-bench telescope!)

I think that lot would be a pretty good start!

@ArishMell: and take rather more time than currently allocated, lol.

However, remember too, that most (all?) of what you have suggested requires that students accept its usefulness before they actually need it; much as they have to now.
For example, "money", regrettably, students don't have much and don't spend much, and don't need to use loans, although % are very valuable in understanding retail duping. It would be useful to be able to understand all that is printed on product labels.

So, yes and no, to all that you suggest.
And the grand plan by "experts" has been suggested many times.

@mathsman:

Thankyou. I intended the "grand plan" to be influenced by actual experts, who know what maths and arithmetic their trades need because they or their staff use such calculations daily. How are school syllabi set? I appreciate the details would need to be designed by experienced teachers, but thought it an idea if they also consulted external, genuine users of sums.

I know students don't have much money - and if they go on to university most will certainly be in debt. All the more reason to teach them how money works for or against you.

Would that list take up more time than whatever is taught now? I didn't think it any greater a volume of work than that GCSE course I took, and I based it on what I remember it included. That was once a week for a school year: not several lessons a week over a few years.