There are known knowns; there are things we know that we know.
There are known unknowns; that is to say, there are things that we now know we don’t know.
But there are also unknown unknowns – there are things we do not know we don’t know.
– Donald Rumsfeld, the then United States Secretary of Defense in 2002.
I know the 12 times table and at a pinch I could probably recite the 13 times table quite quickly too. I was drilled at school. I can also tell you that the square of the hypetonuse is equal to the sum of the squares of the other two sides, though I have no idea of its relevance.
Hypotenuse (n.) is an interesting word for some folk: 1570s, from Late Latin hypotenusa, from Greek hypoteinousa “stretching under” (the right angle), fem. present participle of hypoteinein, from hypo- “under” (see sub-) + teinein “to stretch” (see tenet). Formerly often erroneously hypothenuse.
Thankfully I didn’t study Greek at school, but Latin was a pain. I thought I could remember the conjugation of the verb amo (to love), but had to check here only to discover that the infinitive is amā́re.
Those two bits of etymology … now three … are available in my Webster’s New World College Dictionary which sits on my home desk and is way too heavy to carry around. Naturally, I’ve copied and pasted from the internet rather than copying and formatting verbatim from that tome.
Learning by rote to the nth degree in order to pass exams is a pain!
The nth degree – maybe.
However, learning basic techniques and rules of operation etc. in subjects are a necessary basis for enabling answers to one’s curiosity. Regarding the use of calculators, I now quote freely from Wikipedia, the open source encyclopedia.
In most countries, students use calculators for schoolwork – but not generally in Indonesia. There was some initial resistance to the idea out of fear that basic arithmetic skills would suffer. There remains disagreement about the importance of the ability to perform calculations “in the head”. I can do simple calculations in my head and give rough estimations, and that’s all I need: I’m not an engineer or a scientist.
Research suggests that inadequate guidance in the use of calculating tools can restrict the kind of mathematical thinking that students engage in.
That’s possibly true; I’ve no idea what a lot of buttons on my calculator mean, let alone what they do, or why, but that surely is of very little importance. Maybe it’s cos it’s no sin to not know.
Some curricula restrict calculator use until a certain level of proficiency has been obtained, while others concentrate more on teaching estimation techniques and problem-solving.
Perhaps a balance is needed between the two.
Others have argued that such use can prevent understanding of advanced algebraic concepts.
That’s not a problem for most of us; I don’t even understand most simple algebraic concepts,
In Indonesia teachers have to teach to tests written by those who can’t teach and, yes, I do know that I’ve written about that umpteen times before.
However, in a recent debate organised by the British Council* and the World Innovation Summit for Education (WISE), Professor Sugata Mitra argued that students be allowed to use the internet to answer exam questions.
Take away the paper and pencil and say this time you have to answer the [exam questions] differently. All you have is [an internet enabled device]. You can email your friends, you can look up on the internet, do whatever you like. And answer the questions.
If you do that the entire system will change. Teachers are intelligent people; they will start immediately to teach differently. They will insist that you don’t memorise; you can look it up on StartPage or Ixquick which “were the first search engines to use automatic encryption on all connections to prevent snooping.”
Teachers will insist that you do not need to know the 17 times tables because the machine will do it for you. They will insist that you do not need to have good handwriting because you will not hand write at all, you will type. They will insist that you don’t need to memorise spellings because the tablet corrects spellings for you, that you do not need good grammar because the machine suggests grammar for you.
What it does not do is tell you how to discriminate. So, [students] will concentrate on how to discriminate between good info and bad info. The present day teacher, the existing teaching system does not do that. Because the examination system is obsolete. Teachers are trained to prepare students for an obsolete examination system. Such teachers are themselves obsolete.
Well not yet, especially in countries such as Indonesia which has only had 15 years to undo the blinkered control mechanisms of colonialism.
But one can dream of a time, of future generations of students who learn to know what they want to know, even if in so doing they wish to remain unknown.
*Anyone wanting to know about the role of the British Council in “Internationalising Higher Education” in Indonesia can download a 31 page ‘Country Profile‘ .pdf file for a mere US$200.00.
Alternatively, you may want Student Insight – Indonesia .pdf which is based on data collected from more than 2,600 prospective international students from Indonesia. That’s the same price but just 19 pages.