By the time any child reaches secondary school they should be able to do the 3Rs and some algebra. They should be able to think abstractly (which is a learnable skill). In essence they should be ready to do their GCSEs by year 10 (the old 4th year). In general we get students needing help with Maths, English and science. These days the general requirement is for a vocational, ie job-orientated skill base. Exams were invented in the mid 19th century because the government were unable to recruit enough aristocrats, the only people who had any form of real education other than the upper middle-class. Shortly after that formal education to higher junior level was available for the masses. Essentially exams are for those that want to work for the government which is why the system at present only favours those who are naturally good: that is to say, the schools aren’t interested in doing anything for those that are struggling because they would be of no use to the civil service. They have no sense of teaching for a general ability but for a specific set of skills that are suitable for the civil service, hence English maths and science: music has been down-graded as “discretionary” however such liberal arts are essential for a rounded personality.
The need for maths became obvious to me in the mid-90s when the bulk of my students were English and Music. Many parents starting asking if we were able to provide maths tuition. Consequently I did some research and found that maths as such was not being taught in a systematic way, indeed there was not even any awareness of the difference between maths and arithmetic.. As a result we set up a special maths course which more or less guarantees a “C” grade to the average student.
English, and proficiency in it, is, and always has been, a question of reading, both in depth and breadth covering a wide range of styles and not forgetting the classics like Dickens and Austen to name but two as well as Shakespeare and the many great Poets such as Byron and Shelley as well as more modern poets such as Heaney. Cross-cultural poetry has also become a big theme.
Science is not just a subject but a way of thinking: most universities talk about “evidence-based” theory which is just another way of talking about science. The accumulation of evidence and opinions based on that evidence. The division of subjects such as chemistry, maths, biology, physics are simply for the purposes of examining, in reality science is the whole and maths is the “language” of science.
History is a useful way of developing reading skills and develops writing skills too by the use of narrative writing.
These are the main subjects covered but enquiries regarding others are welcome.