I Hate Math

@mathsman:

Is there a fundamental flaw in education generally, in not explaining why we are taught things beyond merely for passing artificial exams?

Like Viviscarlet, I could not understand the point of Maths at school, because to me, it seemed just a lot of impenetrable puzzles for their own sake, taught by various characters of whom one or two made it boring and impenetrable. I did not really start to appreciate Mathematics' point until I'd been working at semi-skilled factory-floor level for quite some years - and only grasped how Logarithms work as indices, the general nature of Algebra, and what Differentiation does, in my 50s!

@ArishMell: I think a major problem with the school maths curriculum is that it is not constructed with a view to being usable at the time of learning.
Whereas, it's fairly straightforward to present other curricula as relevant.
The whole maths curriculum seems to be presented as a sequence of topics, each leading to another development, rather than as useful in itself at the time.
The fact that so much of our lives is significantly based on maths doesn't cut-the-mustard.

@mathsman:

I wonder why that point about significance is so hard to put over? Is it because Maths at school level is inherently rather abstract? I did feel similarly about French - apart form not having the memory to learn a difficult language anyway, the notion that an entire nation live by it was just not put over, so it became a chore of irregular verbs and strange noun-genders.


Your point about a sequence raises what I see as a basic difference between UK and US maths teaching, that I have noticed in many posts on SW, EP and Wikipedia's 'Answers' site. It's a difference that affects how the sites' users discuss maths education.

It looks as if the American schools do not teach Mathematics as a set of curriculum topics within a single Maths syllabus, but as quite separate syllabi. This comes out in users remarking on exams etc. in Algebra OR Trigonometry OR Geometry... I was going to type Calculus until I remembered never seeing it mentioned in such debates: it was within the GCE O-Level syllabus. I have asked this a number of times, but never received a satisfactory answer whether I am right. It might explain why some contributors complain about Trgi or Algebra rather than Maths, even allowing for individuals finding certain topics harder than others.

One major flaw the UK system revealed to me was the removal of the O-Level syllabus, so the logical progression from Ordinary to Advanced level was thrown away. I discovered this when I took GCSE then A/S Level courses in evening-classes some 20 years ago, for work reasons. The effect was a much more fragmented syllabus overall, with a huge jump in both topics difficulty from lower to upper.

I think a flaw common to both is in not clearly explaining Algebra's real role - a topic capable of, and taught as, standing in its own right, but far more useful as a short-hand system of instructions for solving applied all manner of practical maths problems generally.

@ArishMell: I could be writing as essay about several of your points. Algebra: a wonderful way to generalise, but rarely needed to solve any issue related to school-age kids, which can be resolved by inspection or trial-and-improvement. Simultaneous equations are a good example, no use whatsoever at age 11 - 14.

@mathsman:

I recall exercises in simultaneous equations sometimes included such matters as diagramming train movements - "where would the 7:55 from London pass the 8:15 from Leeds?" Actually, only the railway staff needed to know that - the passengers' concern is reaching Leeds or London on time!

That GCSE course included Matrices - and these were so divorced from anything even in the rest of the syllabus, and so abstract and poorly explained, I failed utterly to grasp them. I know how to do adding and times sums - I don't need boxes of them though!

@ArishMell: matrices are presented so abstractly, their use cannot be discerned. I can tell students how they can be used for solving simultaneous equations, but it's quicker without matrices. However, their use can be demonstrated, usually through inequalities and linear programming.

@mathsman:

I turned to a work colleague for help with Matrices. She was employed as a mathematician, and she told me parts of her work involved massive blocks of simultaneous equations - 100, perhaps 100s - of unknowns at once; and matrices were the only way to solve them. The computer did the donkey-work but she still needed to understand the principles. This though, is highly specialised work far above anything encountered in schools, nor indeed by most people generally!

@ArishMell: quite so, telling students something might be useful later is no way to progress with teaching. So many processes use multiple simultaneous/linear or polynomial equations/inequalities. So, what's to be done with school maths, lol?

@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.