How many of your family or friends’ phone numbers can you remember off the top of your head?

I only ask because increasingly we all rely on our electronic devices to remember such information for us.

But when the idea of allowing students to use search engines in exams was suggested recently, the immediate fear was “dumbing down”.

Only a few years ago, there was a similar debate about the use of calculators.

For the 11-year-olds sitting their national curriculum tests, often known as Sats, in England this week, the emphasis is on mental arithmetic.

Calculators are no longer permitted.

Their use will also be limited in the new GCSE maths exams, for which students will start studying this autumn.

No dictionaries

Dictionaries have had a similarly chequered track record in foreign language exams.

They were banned 15 years ago, after research suggested they gave the brightest students a greater advantage.

Newly redrafted GCSEs in French, Spanish and German will be introduced in 2016.

As part of its recent consultation on the exam, the regulator Ofqual has asked about the ban on dictionaries.

In the responses, opinion was divided, suggesting this is not a settled debate.

In different ways, these are all dilemmas about the boundary between knowledge and understanding, between retrieving information and manipulating it.

And with search engines, it is very much a digital conundrum.

Imagine for a moment the pre-digital equivalent – allowing students to roam through a vast library.

They simply would not have time to find the references they needed and return to their desk to complete the exam.

Now unimaginable amounts of information lie at our fingertips.

But does the act of memorising and then recalling information mould our brains in a different way?

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