The diagnosis by the Qualifications and Curriculum Authority is spot on: the children were relying too much on sound, rather than recognising that "knowledge" contains "know". In other words, they were ignoring morphology, the internal grammatical structure of words.
Of course, once you know the spelling it's easy to see know inside knowledge; but what about the child who doesn't yet know the spelling? How easy is it to hear "know" in "knowledge"? And how can teachers help?
The pronunciation does its best to make life difficult because the vowels are different. "Know" has the same vowel as "no" and "notice", but "knowledge" sounds like "not" and "novice". Even the morphology doesn't help much, because the second half of "knowledge" is completely bizarre.
What kind of a suffix is "ledge"? We have no idea where this came from. We could recognise "knowing" or "knowage" or even "knowment", but "knowledge" is just baffling.
Disappointingly, the real experts can't help; for example, Eric Partridge's "Origins" - a wonderful resource for etymology fans - gives the "ledge" an "o.o.o." ("of obscure origin").
In short, it's not at all obvious from the pronunciation that "knowledge" contains "know". On the other hand, the two words are certainly closely related in meaning. If thoughts are what you think and dreams are what you dream, then knowledge is definitely what you know. But those links don't help much with spelling - does "thought" contain "think"? What do you say to the brilliant pupil who spells it thinkt? Not an encouraging model for spelling "knowledge".
This all sounds very negative, so let's see if there's a solution to the problem of "knowledge". How do you help a poor speller to remember the k? There's actually a very easy answer: think "acknowledge". Don't worry about the spelling - just listen to the pronunciation. The k phoneme is a reminder of the k in the spelling of "acknowledge", which obviously contains "knowledge". If you want to get technical you can show that the "a" at the beginning has the same origin as the "ad" in "adventure", so the k must belong to "knowledge" rather than to the prefix.
But most learners will probably be satisfied just to be reminded, thank you very much.
And if you're looking for mere reminders, try Eric Partridge again for words related to "know": "can", "uncouth", "cunning" and "keen", every one with a clear k sound. Seeing (and remembering) these links is no harder than hearing the link between "knowledge" and "know".
Richard Hudson is professor of linguistics at University College, London Geoff Barton is headteacher of King Edward VI School, Bury St Edmunds, Suffolk