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- re. claimed benefits from ‘playing’ with ordinary calculators  i.e. just ‘trying out’ : This is learning by osmosis

- re. “Should the goal not be the correct answer rather than an estimate”? Ultimately, usually of course yes, but only if one gets there by a process one understands, rather than by using ordinary calculators or rote manual working. Estimating acts then only as a means- to engage the mind, because to estimate one cannot generally do by rote.  

- re. concerns about Qama’s ‘slowing things down’:
 Slowing down WHAT?   fast, ‘mechanical’, insight-less operations?

In fact, youngsters leave us in no doubt where the slowing-down goes in to:
Usually, when we hear them quietly snapping  “Wait!” -  they are announcing they just started thinking.
Who in their right mind would want to get in the way of that

- Regarding the time issue in general:

The purpose of time-limitations in maths is questionable altogether. Where maths is actually being used, it rarely matters how long, within reason, it took to get the result. What matters is whether it is right. Regarding exam situations, surely, getting 100% in two hours is better than 80% in one. (Timing should come in only to discriminate between equally performing students, but this can be done by means other than time limits.)

Pragmatically, regarding the use of QAMA in an examination, the solution should be to simply extend the duration of an examination by a certain amount that is considered reasonable for doing the required thinking.

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US Patent 6820800

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