Three of Churchill’s comments, respectively on education, communication, and examinations, can be of great help to us in solving current problems. The first two are his tribute to his teacher of grammar, who showed him how to construct a sentence, and his statement that, “Broadly speaking, the short words are the best, and the old words best of all”. Children do not, for the most part, know enough Latin and Greek to understand the basis of terminology derived from them, and this terminology too often creates a mystique that obscures learning instead of promoting it.

In geometry, for example, the difficult word Isosceles is just Greek for two equal legs, and a theorem is something that we can prove on the basis of things we already know. I was taught many theorems at school without anyone ever explaining to me what such a thing actually was, and similar problems persist. Maths compresses language, frequently inventing its own vocabulary and symbols to do so. All of this needs to be unpacked and practised if most children are to learn maths – going past anything that is not understood creates a block that can last a lifetime. Churchill’s principles of communication are as important and effective in education as they were in politics.

Of examinations, Churchill said that, “the questions … were almost invariably those to which I was unable to suggest a satisfactory answer. I should have liked to be asked to say what I knew. They always tried to ask what I did not know. When I would have willingly displayed my knowledge, they sought to expose my ignorance. This sort of treatment had only one result: I did not do well in examinations.”

In the security queue at Westminster some weeks ago, I met two ladies who were principals of Further Education colleges in London. One told me that she had over 2,000 students retaking maths and English at GCSE. That seemed a lot, until the second announced that she had 4,000. A friend’s son, in charge of maths in a home counties college, has 3,500 students. Each of these figures is larger than almost any school. The unfortunate lecturers have around eight months to get to know the students and turn round a lifetime of disappointment, with predictable results – the failure rate last year was 70 per cent, the highest I’ve ever heard of in a public examination.

The students are acutely aware of their situation and, unsurprisingly, hacked off with it. My friend commented that his son could cope with all sorts of difficulties in learning maths, but was now faced with sustained unwillingness to work. The reason is not hard to grasp. Almost all of us, setting out to achieve something important – and everyone knows that maths is important – give it our best shot, and are prepared, like Robert the Bruce’s spider, to keep trying if we don’t get it right first time. But if we’ve been failing for eleven years, and are given material that we have no hope of understanding, because we don’t know the elements on which it is based, or understand the language and symbols in which it is expressed, we are worse off than the spider. We don’t have a thread to climb.

Unsurprisingly, the two college principals felt that their sector was a poor relation, and that their lecturers were hard-working people facing an impossible task. By co-incidence, one of them was head of the college that had asked me to lead a revision day last year, so that I had seen the truth of their situation for myself. Sir Michael Wilshaw was asked at the presentation of his final annual review if the requirement for all students to resit GCSE “wasn’t working,” and he replied diplomatically that it may be worth considering “some form of test of fundamental skills.”

Sir Michael was right, and his comment brings me back to Churchill. The foundation level of these maths papers, which most resit students take, has far too many questions that insert a twist to force students to apply what they know in a situation that is not obvious. An example from a sample paper is a question asking them to prove that a triangle in a diagram is Isosceles, when it is deliberately drawn without two equal sides. Another is to ask them to calculate the cost of providing some cakes for a party, involving five separate calculations, ending with the amount of change they’ll receive.

These little steps and twists add appropriate rigour to higher level papers, but prevent foundation students from showing what they know in a straightforward way, and shove their limitations down their throats. GCSE foundation papers, and not just in maths, need to be redesigned on Churchill’s principles.

This posting first appeared on Conservative Home.