Einstein on SATs

James Coombs's picture
 19

Einstein captured the issue in a single sentence.  “Sometimes what counts can’t be counted, and what can be counted doesn’t count.”  With Maths in particular it’s possible to get very good marks in standardised tests just by applying various methods without the need to engage in any deeper thinking/learning such as why does this work.  For other subjects, substitute mathematical methods for historical facts or a tick list of grammatical idioms the examiner will be looking for.  Being able to churn out a drop in clause, just for the sake of it, doesn’t make me a good writer.

Our current education system was designed by the Victorians to produce convergent thinking production line workers in the days when a ‘computer’ was a job description and there was a real need for a consistent thinking workforce.  The SATs tests themselves are inherently OK.  The problems arise from the current political obsession for ‘raising standards‘ by blindly applying the McKinsey Maxim: “What you can measure you can manage.” without pausing to consider what standardisation actually means.

Michael Armstrong (1999) explained, “a standard is a measure… but the most dynamic characteristic of learning, which for want of a better term I will call its creative aspect, cannot be measured…  Moreover, a standard is a measure of conformity whereas education is as much, if not more, concerned with non-conformity: with exception rather than rule; with the novel, the unexpected, the re-described and re-constructed; with the revival of learning no less than its transmission, and with innovation as well as tradition.

A very standard looking workforce

This focus on standards worked well in the C19th producing a consistent workforce needed for the industrialised production lines but for the C21st we need innovation and creativity in order to prosper as a nation.

Einstein or McKinsey? Who should guide education policy?  One of the greatest thinkers the world has ever known or a bunch of accountants?

 

References

Armstrong, M. (1999) ‘The Quality of Learning’, in O’Hagan, B. (ed) Modern Educational Myths: the future of democratic comprehensive education.  London: Kogan Page Limited, pp.109-120

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Douglas Hainline's picture
Wed, 18/05/2016 - 16:42

There is clearly a lot of truth here,  although I don't think I agree that the new requrements of the 21st century have anything to do with it.

We have always needed creative thinkers. We have always needed people who can multiply two three-digit numbers together.

These two things are not necessarily counterposed.

If 'creative thinking' can't be 'counted' .. that is, cannot be measured ... then there is no way of knowing if the schools are doing anything at all to advance it.  If that's the case, we should not make the schools try to do something that is evidently impossible to detect. 

Religous people claim that their prayers for the ill will help them recover, with no evidence whatsoever that this is true, but we shouldn't spend taxpayers' money on untestable claims.

However, we can detect whether the schools are teaching children how to multiply (and all the other things they ought to know, such as who fought whom in WWII, how to write readable English sentences, what an electron is ... ).  I don't think we should give up trying to measure how well they're doing the latter. But is anyone advocating that we do?


rogertitcombe's picture
Wed, 18/05/2016 - 17:31

"Moreover, a standard is a measure of conformity whereas education is as much, if not more, concerned with non-conformity: with exception rather than rule; with the novel, the unexpected, the re-described and re-constructed; with the revival of learning no less than its transmission, and with innovation as well as tradition.

Michael Armstrong was surely right.

What he describes about 'education', distinguishes it from 'training'.

The Global Education Reform Movement (GERM) does not distinguish education from training. The marketisation paradigm assumes that education is just a form of training. It is behaviourism. That is why as GERM unfolds in the English education system through further Academisation, this is accompanied by the onward march of behaviourism.

The consequence is the replacent of deep, slow learning by content and memory drive teaching to the test.

This is further explored here.


Douglas Hainline's picture
Wed, 18/05/2016 - 17:42

I think that at this level of abstraction, we can all agree.

Creativity, critical thinking ... good.
Meaningless rote memorization, learning to parrot whatever Authority tells us ... bad.

But the devil is in the details.

I believe that if you don't know Newton's three laws of motion, you haven't learned much.
I also believe that if you don't know how we ought to test the claim that eating raw onions will prevent colds, you haven't learned much.

If we can all agree on both of those things, we ought to be able to have schools that we are all happy with: schools where kids learn the factual knowledge they need, the algorithms they need, the things they need to know by heart ... and also where they learn how to build things that no one has built before, write creatively, criticically take apart the latest Government (and/or Opposition) lies ...

I don't see these two ways of approaching education as in conflict.

Needless to say -- or perhaps it's needful to say -- we ought to be spending a LOT more money on education. Every state school ought to have the same physical provision as Eton, and the same level of teachers.


Janet Downs's picture
Thu, 19/05/2016 - 08:33

I don't know Newton's three laws of motion, therefore I haven't learned much.  Might as well chuck my BA down the loo, it appears.

However, in studying my apparently useless degree, I met Pope's statement:  

'Nature and Nature's laws lay hid in night;  God said, Let Newton be! and all was light.'

Whether God had anything to do with it is debatable.

 

 


rogertitcombe's picture
Thu, 19/05/2016 - 10:25

Janet - You will not be surprised to know that I agree with Douglas on this.

The observation about Newton's Laws of Motion  is not important so much for what they state, but for how counter-intuitive they are. Daniel Kahneman is relevant here. Humans have been dropping things and trying to kill people and animals by hurling rocks at them for at least half a million years, but no-one, not even the brightest spark in the cave, ever noticed that small, light rocks fall at the same rate as big, heavy ones. Kahneman gives the answer - System Two (reflective and metacognitive) thinking is required. It was not until the Renaissance that original thinkers, experimentalists and trouble makers like Galileo (one of my heroes) sprung up. There is a parallel with teaching and learning. Behaviourism is Kahneman's System One and Piaget's Concrete Operational thinking. Even Aristotle, a very clever person indeed, never made that jump to System Two in relation to science. Developmental learning theories like those of Piaget and Vygotsky lead to Shayer and Adey's concept of 'plastic intelligence' and to the the pedagogies of developmental teaching for cognitive growth including the current version of it in the form of Dweck's 'growth mindset'. The marketisation paradigm of GERM based marketisation is degrading the entire English education system and making our kids dimmer while they leap ever rising 'benchmarks' at younger and younger ages accruing ever more worthless qualifications. All this is relected by PISA.

Douglas highlights Newton. My favourite is Michael Faraday, because he demonstrates not just the power of System Two thinking combined with experimentation, but was a personal embodiment of 'plastic intelligence'. Through his work he progressed from being a 'science lab technician' operating at Piaget's Concrete Operational Level, to being the intellectual giant on whose shoulders James Maxwell and Albert Einstein stood in order to produce the masterpiece Theory of General Relativity. (Maxwell really was Scotland's Einstein).

Of course your BA is not worthless. Science and maths are not the only subject areas where System Two thinking can lead to penetrative, analytical thinking, as you demonstrate all the time in your articles and posts. But not being taught Newton's Laws of Motion in a way that  is properly understood is a failing of any education system. I too missed out on loads of stuff on the arts side that I am only now beginning to appreciate.

That is why all pupils must have a full broad and balanced education at least up the age of 16, which we agree on.

I thank the author of this article because it shines a light on so much of the poverty of practice now taking place in our marketisation-debased school system.

Time for a plug. This is what my book is all about.

 


Douglas Hainline's picture
Thu, 19/05/2016 - 08:54

Janet: you SHOULD know Newton's three laws. They're part of the intellectual/cultural heritage of the human race, as much as Shakespeare. Pope wrote that couplet for a reason.  If you're ignorant of those laws, you can't understand why the International Space Station doesn't fall down, or why it's quite wrong to say that there is 'no gravity' on it.  

However, I do appreciate -- believe me! -- that Newton's Laws, and the rest of science and mathematics, can be taught in a dull, soul-destroying, rote way, convenient for exam-setters and -markers but actually conveying little or nothing of genuine science to the children who are subjected to this sort of 'education'.

But this isn't a new problem -- see C.P. Snow's essay on the 'two cultures' written more than fifty years ago:( https://www.rbkc.gov.uk/pdf/Rede-lecture-2-cultures.pdf ).

Throw your BA down the loo? Of course you shouldn't! Any more than I'll throw my History BA down the loo.  We ought to recognize that to be educated means knowing Newton AND Pope. 

By the way, if you know Newton, then you'll be able to appreciate Einstein (and the other great scientists who transformed Newton's worldview in the 20th Century), and appreciate the riposte to Pope's hailing of our emergence from darkness to light:

"Then the Devil,  shouting 'Ho!', 

said 'Let Einstein be!'  ... and restored the status quo."


Janet Downs's picture
Thu, 19/05/2016 - 12:01

Douglas - thanks.  Love the riposte.

I have now looked up Newton's three laws and answered all the quiz questions correctly.  http://teachertech.rice.edu/Participants/louviere/Newton/law1.html

My ignorance is entirely my own fault.   I started Physics in the Fourth Year (this was over 50 years ago) and my 15-year-old self found it 'boring' (my interests at the time were elsewhere - namely the boys from the school next door).  I dropped it.

My interests (apart from boys) veered towards English (although not the dull, boring teaching of formal grammar I was subjected to).  I did A Level English at night school: C P Snow's 'The New Men' was one of the set texts.  As part of my OU course, I studied the history of science in the Enlightenment (eg Lind's 'Treatise on Scurvy') - Newton's importance was recognised (eg Principia Mathematica) but we didn't have to learn the scientific laws just understand how his work influenced Enlightenment thought (and Blake's antipathy towards Newton - you might enjoy this Royal Academy of Arts article https://www.royalacademy.org.uk/article/william-blake-isaac-newton-ashmo...).


Douglas Hainline's picture
Thu, 19/05/2016 - 12:16

Janet -- I don't think it's "your own fault". It's OUR fault that we have designed, or allowed others to design, an education system that crushes all the interest and mystery and fun out of as many subjects as it can, science and mathematics being especially vulnerable.

Or so it appears to me.  The Open University is brilliant -- or the people who design the courses are -- and they should be put in charge of the entire education system. 

Thanks for the link!


Janet Downs's picture
Thu, 19/05/2016 - 13:07

Douglas - to be fair to my Physics teacher, Miss McReady, she did her best to make the subject interesting - we did lots of experiments and so on.  I loved the section on heat and light but hated mechanics and electricity.  I didn't do homework (except to write 'Ohmwork' on the top of some homework about electricity) and fell behind.  

On the other hand, I had a brilliant maths teacher, Mrs Dearns, for five whole years (continuity very important).  She gave us demanding stuff to do: trig, geometry, graphs with parabolas, (2H pencil - no other would do) quadratic equations.  The work was a mixture of practical (eg cutting up circles to discover relationship between radius and circumference), theoretical (stuff she explained clearly) and analytical (solve this problem).  I owe my O level pass to Mrs Dearns.

 


Douglas Hainline's picture
Thu, 19/05/2016 - 14:19

Janet -- a strange symmetry!  I am a maths/sciencey kind of person, but my maths and science teachers in school (this was Texas in the 1950s) were not inspiring -- nor was the cyllabus and approach to education. But I had two brilliant, wonderful English teachers -- I wouldn't have gotten beyond two pages of Shakespeare if one of them hadn't pushed us on until we began to be able to deal with the unusual (for us) idiom.   It's the teachers, mainly -- which is why we need to have a different sort of syllabus, and to have pay and working conditions that don't force great teachers to have to make material sacrifices in order to teach.  (An additional symmetry between us:  the distracting, tormenting presence of the Opposite Sex, just at the age when your brain wants to absorb the results of the transmission of ideas from the previous generations, while your body begins to demand the transmission of your genes to the next one.)

"Ohmwork"!  Wonderful!  


Janet Downs's picture
Thu, 19/05/2016 - 16:19

Douglas - Miss McReady was not impressed.  She wrote that if my work was as good as my witticisms, I would do much better in Physics.  Alas, I took no notice.


Douglas Hainline's picture
Fri, 20/05/2016 - 14:20

Janet -- there is a lot of room in science for witticisms.  Look at XKCD.com (yes) and work back through this genius' cartoons.  (Here are two  of my favourites: https://xkcd.com/1489/  ... and  https://xkcd.com/435/) Some of them make no sense unless you have a basic understanding of science, and some of them still make no sense (to me, who has only that), but by and large they're brilliant. A selection should be posted in every classroom in the world.  (You can do a mouseover on the cartoons and get more information.)

Now I feel it's my duty to try to help repair what the educational system didn't do. So... on to Newton's Three Laws. (You can retaliate with literary advice -- my worst subject at university, where I had to do one year of English [this was the US], and I still recall how near-suicidal I became because I couldn't write in a minimum of three pages anything intelligent analyzing  "Golden boys and girls all must, as chimney sweeps, come to dust." Isn't the meaning obvious: we all die, rich or poor? What else could I say? I still have the mental scars from that. But others found it easy. Too bad I couldn't have swapped assignments or something with you.)

First Law: If you want to make something start moving, or move faster, or slow down, or swerve -- you've got to push it or pull it. It won't happen on its on.  If it's moving, it'll stay moving, if it's sitting, it'll stay sitting, unless it's pushed or pulled.

For example, when you throw a ball, as it flies through the air, things are pushing on it (little bitty air molecules and bits of dust and stuff floating in  the air, which it's got to shove out of the way, thus speeding them up and slowing it down),  plus it's being pulled on by everything else in the universe, but especially by all the little bits of the Earth, all of which are being pulled by it as well, so they and the ball move toward each other -- they move only a teeny teeny teeny bit, while the ball moves a lot -- we say the ball 'falls' towards the Earth.

But ... what if there were no air or dust or anything in the way of the ball?  And what if the pulling of all the other little bits of the universe  was very very  small, and even those tiny little pulls mostly 'cancelled out' because for every little bit pulling it to the left, there would be another little bit on the right pulling it that way  -- well, what then?  Why, the ball would just fly off, in a straight line, neither speeding up, nor slowing down, nor swerving ... forever.  And ever.

Pretty cool, huh?  (Whoops ... better not use my eleven-year-old vocabulary here.)

Anyway, that's the First Law. It's rather counter-intuitive. Newton wasn't the  first person to understand it,  by the way.

If we thought about it, we'd probably say that when we threw the ball, we gave it some 'energy' (whatever that is), which it then used up to keep flying along, but as the energy we gave it got used up,  then the ball sort of gets tired, and drops down.  But that's wrong.

Maybe it's better to think about rolling a ball along the floor,  or on a pavement, so we can leave 'falling' out of it. We know it eventually slows down and comes to stop. Must have burnt up all its energy, right?  Nope -- according to the First Law, it had forces put on it opposing its direction of motion, from all the little bits of the floor or pavement that stick up and have to be pushed down, or which briefly stick to, the ball as it rolls along, plus the air and stuff in the air it has to push aside (being pushed back in return, but that's the Third Law,  which we'll talk about later).

 What if we could eliminate these little bits? Maybe instead of ball, have a disc, like a hockey puck ... instead of a floor, have a special metal 'floor' with little tiny holes and compressed air shooting up thru them, so that our hockey puck 'floats' instead of scraping along. We would see then that it would go a lot further before coming to a stop. (At well-financed private schools they have tables built along just these lines. Every school -- every primary school -- should have one.) The hockey puck would go a lot further, but it  would still come to a stop eventually, because of the air etc in its way.

What if we could eliminate the air?

Suppose we could such a table inside a big tube which we could pump all the air out of?  Well then that hockey puck would float along at whatever speed we gave it to start with ... forever.  And  ... we would have invented the super-fast, low-energy, maglev vacuum train of the 21st Century, which our descendants will use to shoot over to Melbourne in two hours -- provided we don't destroy ourselves first.  (Read about these trains  via that admirable socialist institution, Wikipedia: https://en.wikipedia.org/wiki/Vactrain).

Now, come on!  This can be explained to ten year olds if we wanted to. Throw in a 'vaccuum table' with a floating hockey puck, some videos of the people floating around inside the International Space Station  (where there is plenty of gravity, by the way, but that's for a future 'lesson') ...  How could this not be easy, and interesting, fascinating, for kids, including ones whose real genius is for literature?  (And anathama to anyone who asks, 'How could we put this on a standardized multiple-choice test?')


Janet Downs's picture
Sat, 21/05/2016 - 09:00

Doglas - thanks for your entertaining explanation.  I like the idea of vactrains.  As someone who doesn't drive a car (it's safer for the rest of the world if I don't), I would appreciate being able to whizz about so quickly.

Re the 'chimney sweep' quote - I read the whole speech at my mum's interment (not internment, as I kept telling everyone until someone gleefully pointed out my error).  It's one of my favourite Shakespeare quotes along with bits of The Tempest' - when Prospero talks about 'cloud-capp'd towers' dissolving like the 'great globe itself'; or about our little lives being rounded with a sleep - and Henry V's speech before Harfluer (Cry God for Harry, England and St George!) and Agincourt (never fails to send a shiver down my spine when Kenneth Brannagh says it https://www.youtube.com/watch?v=A-yZNMWFqvM).


Douglas Hainline's picture
Sat, 21/05/2016 - 15:52

I am so grateful to my "9th Grade" English teacher who pushed us bodily through Shakespeare. We had to memorize various passages, which I know to this day.  It's sensual. A miracle.

 "Internment"! Wonderful!  (I'm trying to think how I can suggest this particular wordplay to whoever delivers my anti-eulogy.)

On to more Newton. (By the way, they should really be called "God's Three Laws" or "The Universe's Three Laws". Puttting them to someone's name suggests, to me at least, that they are something arbitrary, 'socially constructed', etc.  Which they are not, even though we know that they're actually not quite the full description of motion.)

It's best to skip the Second Law and do the Third before we get to the Second. The Third Is, roughly, You can't push or pull something without being pushed or pulled yourself, just as strongly, but in the other direction.   Just as you can't touch someone, without being touched -- it's just in the nature of the way things are. 

Another way to put it: forces always come in pairs, twins, both 'looking at' each other, or both with their backs to each other.

We don't instinctively see this law to which we are totally subjected because so much else is going on that obscures its operation, and/or its effects, or see its effects on both sides, because on one side they are too tiny to perceive.  The Earth pulls me down, rather strongly, as I can prove by jumping off a roof.  I can see the effects on me of doing that, as I speed toward the ground. What I can't see is the earth rising to meet me -- both of us moving, in upside-down proportion to the amount of stuff which make us up -- there's not much of me so the force of the twin pulls between me and the earth result in me speeding up a lot ... whereas there's a lot of stuff in the Earth, and so it moves much -- much much much much -- more slowly towards me. (We both 'stretch' a bit too.) The forces are equal, but their effects are not.  If I should suddenly swell to have the mass of the Earth  -- and thought experiments like this are very useful in physics, which is why it is or should be an inherently creative enterprise to study it -- then the Earth and I would speed towards each other at equal speeds.

It's an easy Law to learn -- forces come in equal pairs oppositely-aimed -- but not always easy to see in operation, just like the First Law.   I suppose there is a clutch of metaphors for human interactions  hiding in these laws, especially this one, for imaginative writers . We need more Tom Stoppards!


rogertitcombe's picture
Sat, 21/05/2016 - 16:26

Douglas, I am looking foward to your explanation of the 2nd Law. This is most important law in probably the whole of science except the 2nd Law of Thermodynamics, because it defines Force and hence Work, Energy and Power. These concepts have universal application applying to electricity and magnetism as well as pushing and pulling things.

This isn't simple at all is it? How do you explain that Force = Rate of Change of Momentum is equivalent to Force = Mass x Acceleration?

The progression distance/speed/acceleration and travel graphs are not easy either.

The 2nd Law of motion cannot be taught as a series of facts. The concepts have to be developed. Piaget and Vygotsky apply here.

As we know from investigations of concept formation, a concept is more than the sum of certain associative bonds formed by memory, more than a mere mental habit; it is a genuine and complex act of thought that cannot be taught by drilling, but can only be accomplished when the child’s mental development has itself reached the requisite level.

Newtons Laws of Motion have a lot of counter-intuitive implications. You mention those relating to the 1st Law. But, What is the difference between Momentum and Kinetic Energy? Why is Momentum conserved in all collisions, but Kinetic Energy is not?

I applaud your appeal not to be afraid of science, but it is wrong to present it as something easy, that all the student has to do is listen to the teacher and learn what is told. This does not solve the issue of difficulty that so concerned Shayer and Adey. To solve this difficulty then behaviourist pedagogy will not work. The developmentalism of Piaget and Vygotsky does work, but not quickly. The teaching and learning methods have to be right and the teacher needs to know what they are doing.

 


rogertitcombe's picture
Sat, 21/05/2016 - 16:27

Douglas, I am looking foward to your explanation of the 2nd Law. This is most important law in probably the whole of science except the 2nd Law of Thermodynamics, because it defines Force and hence Work, Energy and Power. These concepts have universal application applying to electricity and magnetism as well as pushing and pulling things.

This isn't simple at all is it? How do you explain that Force = Rate of Change of Momentum is equivalent to Force = Mass x Acceleration?

The progression distance/speed/acceleration and travel graphs are not easy either.

The 2nd Law of motion cannot be taught as a series of facts. The concepts have to be developed. Piaget and Vygotsky apply here.

As we know from investigations of concept formation, a concept is more than the sum of certain associative bonds formed by memory, more than a mere mental habit; it is a genuine and complex act of thought that cannot be taught by drilling, but can only be accomplished when the child’s mental development has itself reached the requisite level.

Newtons Laws of Motion have a lot of counter-intuitive implications. You mention those relating to the 1st Law. But, What is the difference between Momentum and Kinetic Energy? Why is Momentum conserved in all collisions, but Kinetic Energy is not?

I applaud your appeal not to be afraid of science, but it is wrong to present it as something easy, that all the student has to do is listen to the teacher and learn what is told. This does not solve the issue of difficulty that so concerned Shayer and Adey. To solve this difficulty then behaviourist pedagogy will not work. The developmentalism of Piaget and Vygotsky does work, but not quickly. The teaching and learning methods have to be right and the teacher needs to know what they are doing.

 


Douglas Hainline's picture
Sun, 22/05/2016 - 19:24

Roger ... Whoa, whoa, whoa!!  I don't think science is easy!!! They/it/whatever didn't make an easy universe. 

I know that looming ahead of my notional ten-year olds are the laws of thermodynamics, Maxwell's equations,  relativity (special and general), quantum weirdness, second-order partial differential equations, tensor calculus, chaos theory, turbulence  .... and, if they want, endless embroilment with the Philosophers of Science.  And if they master all of that -- that is the one-tenth of one-percent who might -- they/we still won't be able to explain consciousness. So much to discover yet! 

Contra Feynman -- Peace Be Unto Him -- I do believe that a healthy interest in the things that the philosophers worry about is very important, and needs to be inculcated (sorry, brought out) from as early an age as possible.

So I try never to use phrases like "mass is... " or "energy is ..." but rather  "We use the word 'mass' when we want to talk about  ...."  "We use the word 'energy' when we're trying to explain the following facts ..."   (I say I "try" not to use the ''X is Y' approach, but I often fail.)

I leave the Second Law until last because it does involve an equation.  But even here, I try to sneak around it. So ...  (Janet, are you sitting comfortably?)

What happens when we push or pull on something? Well, we start it moving, or speed it up or slow it down if it already was moving, or make it swerve ...  that's the First Law.  Now, we notice this:  if I've got one thing which has a lot more stuff in it than another thing --- I use the term "more massy" -- then the same amount of push or pull will change the speed of the second, less massy thing,  more than it will do for the more massy thing.  It's easier to picture this: say a small model car, next to a real one, and you give the same amount of push to both.  

If I could find a good video of  two objects floating around in space, or inside the International Space Station, one much more massy than the other, but both being given the same push -- say from two similar 'baloon rockets' -- I would show it. I don't know of one though.

This is sort of common sense.  Now for the dreaded equation.

(By the way, I use what are sometimes called 'formula triangles' to teach all relationships involving binary commutative operators and three elements ((ie. addition/subtraction and multiplication/division)). I know there is controversy about this,  and that they can be misused and become mechanical means of avoiding understanding, but I believe they need not be, and that in fact they can give learners a deep appreciation of such relationships in a way that linear 3 x 4 = 12  or F = MA  formulations cannot.)

Anyway ... we note that the more massy something is, the harder it is to push or pull it. Common sense, really. And we can note another common sense thing: the more strongly we push or pull it -- the greater the force we apply -- the faster it speeds up, slows down, or swerves. 

Now ... we can express that this way: I can't reproduce my triangle here, but I'll do my best:

First, I need a single word for 'how fast it speeds up, slows down, or swerves'.  Here is what everyone else uses for that, so we'll use it too: "Acceleration".  It's a seven-dollar word, sorry about that, I'd rather say "Changeyness" or something, [perhaps the literary people can suggest a better term],  but we'll get used to "acceleration" as our shorthand for "how fast the speed or direction is changing". [If I'm able, I'll have had my pupil(s) rote-learn a definition of  'acceleration' beforehand, as I'll explain, but that's not always possible, as it isn't here.]

Here, I usually have a diversion: I ask them to imagine that they've just been given a new car. But ... when they get into the driver's seat and look at the speedometer -- and it's useful to have a picture of a speedometer (not a digital one but an analogue one, with a needle that sweeps around a circle -- when they look at the speedometer, they see a tiny little miniature car glued to it, with its tiny little wheels on the surface of the speedometer ... and when, using my Magic Magnifying glass, they look inside at the dashboard of this tiny little car, they see a tiny little speedometer ... this little speedometer measures how fast the little car is being swept around the face of the big speedometer, when the needle moves. If the big car is just sitting there, not moving, so also will the little car be sitting there, since the big car's speedometer is on zero and stays there. Or, when the big car is zooming down the motor way at a steady 70 miles per hour, or any steady speed, the little car won't be moving around the speedometer face -- the needle that holds it onto the face will just be pointing steadily at 70. That little needle will only move when the big car speeds up (or, if it can move backwards, and it can, when the big car slows down. If we had a film of it from the start of a journey to the finish, we'd see that little speedometer needle moving along from zero, as the big car accelerated up to motorway speed and the speedometer needle swept around the face of the speedomter ... but then falling back to zero as the car got up to seventy and stayed there, since it only moves when the big car's speedometer needle is moving.

In words, this is hard to see: it needs to have visuals. But what I've described is, of course, acceleration: the little car's speedometer needle measures the big car's acceleration -- its speeding up or slowing down [not, however, it's turning -- for that I'd have to set the whole minature speedomter in a floating compass or something, and this becomes too complicated]. When the big car is crusing at a steady speed, the little car is not moving at all around the speedometer face and so its speedometer shows zero.

By the way, I would have had my pupil(s) do some rote learning before we got to Newton's Laws, along these lines: Q: "What do we mean by the word 'Speed'?" A: "Change of location in space!"!  Q: "What do we mean by the word 'acceleration'?" A: "Change of Speed!"  -- to be shouted out as a Question, and shouted back as Rote-Learned Answer,  as close to daily as possible, over a perod of a few weeks. That would include some Wrong Definitions for them to shout down, such as, "Q: If my Speed is changing, am I ALWAYS going faster or slower?"  A: "NO!! You can be turning!"  "Q: If I'm accelerating, does that mean I am always speeding up?" A: "No, you could be slowing down, or turning!"  These catechismical responses need to be shouted out, with enthusiasm. 

So ... finally ... to the dreaded equation.   I show it like this:

                                                       Force

                 division symbol here    division symbol here

Acceleration                                x                           Mass

I invite them (you) to notice: the more force, the more acceleration. The more mass, the less acceleration. Just what our common sense tells us. If I wrote it as a linear sort of equation,  I would not have   Acceleration "equals" force/mass, but instead of "equals", I would have the proportion sign, to be read as  "Acceleration is directly proportional to Force, and inversely proportional to Mass."  (Of course the idea of proportion, and "directly proportional to" and   "inversely proportional to" would have to be already something they were happy with, via some rote-learned chanting plus some simple arithmetic examples: Q: What do we mean by the phrase  'directly proportional'? A: "The more of this, the more of that". Q: "What do we mean by the phrase "Inversely proportional"? A: "The more of this, the LESS of that!"  (All to be chanted loudly, as usual.)

Janet, there you are. The Second Law: the more force you put on something, the more it speeds up or slows down or swerves.  But the more massy it is, for the same force, the LESS it speeds up, slows down, or swerves.   And this relationship is "linear": double the force, double the acceleration. Double the mass, halve the acceleration.  (There are plenty of relationships which are not "linear" -- such as the relationship between how fast something is zooming towards the ground, and how long it has been falling.  But that can wait.)

Now I think this is a hell of a lot easier to learn than  the difference between metaphor, metonymy and synecdoche ... but it does get harder.

Okay  ... Roger .... I've totally dodged the 'real' Second Law, which is about rate of change of momentum, not just velocity. I haven't even used the word velocity, much less 'momentum', nor the concept of energy (which as most people reading this know, was not a concept Newton or his contemporaries arrived at), nor power.

But it's how I would start teaching 'mechanics', at late Key Stage 2 or  3.  I would love to hear critical comments.

I would like to expose to critical scrutiny some of my other methods for teaching physics and mathematics, but this post is too long already. 

I should say that I don't think in terms of behaviorism vs constructivism, or whatever. I have never even been able to understand these disputes, because they usually don't get down to what one would actually do in front of kids. I don't even know what it would mean to teach in a way inspired by Piaget or Vygotsky.  Maybe I already do that. If not, maybe I should ... but I would have to know what it meant.

 I like Paul Hewitt's approach to physics, I like Hake and 'concept inventories', I like the Flying Circus of Physics ... and the Cartoon Guide  approach.  I've tutored kids in science  -- from state schools and private schools, and at all levels of ability --  for 20 years, and I have almost never encounted one who seemed to have learned any real science in school, much less one who was turned on and excited by what they were taught there.   To take just a small point: none have ever had any idea, not even roughly, of the size of an atom, or many particles a 'mole' of particles is, or how far away the nearest star (besides our sun) is.  Nor have I encountered kids who have learned how we should decide on someone's claim that eating brocolli will reduce your chances of bladder cancer.  Yet it seems to me that these things should be included in what we teach our young people about science.

 

 


rogertitcombe's picture
Sun, 22/05/2016 - 20:15

What is new and exciting for me is marrying up Shayer & Adey's Piaget/Vygotsky with Matthew Syed's, Learning from mistakes

Syed comes to learning through the learning to avoid crashes that has been become institutionalised in the airline industry, but not in acute hospital care.

If you are struggling to see the connection it is through Vygotsky, metacognition, and the learning potential of honest, open, supported sharing of personal metacognitive inner explanations of things that are hard to understand. It is like a debate Janet might share with four or five other interested learners in a physics learning group that might be supported by a teacher like you.

Syed comes in with the part played by mistakes in all learning. Vygotsky with the power of talking to oneself about the personal struggle to understand, for example,  the phenomena you describe in relation to Newton's Laws.

It is first necessary for students to experience air tracks and the inertia possessed by large and small masses. When students can then talk to themselves about their difficulties, they acquire the tools to talk to each other and a teacher in a group, opening up to each other the true depth of their cognitive conflict so  helping each other resolve it. That is not the culture of the disciplined classroom of compliant and obedient rows of immaculately uniformed recipients of knowledge.

What Shayer and Adey Claim is that the cognitive growth that results from this process is transferable to all other learning. In other words the student becomes cleverer in a general sense.

This is what Carol Dweck refers to as a 'growth mindset' shared between teacher and students. It is a learning mindset that seeks out 'hard stuff' and relishes the mental anguish needed to come to a resolution. They call this an attitude of 'learning resilience'.

The opposite is the pages of neat maths problems all correctly solved by a pupil laid out in two neat columns of her execercise book with a neat little tick by each and the comment 'excellent work' written by the teacher. This sort of stuff does not prepare the pupil for tackling problems where first attempts result in mistakes and failure. Only there can deep learning be found and personal general cognitive growth achieved.

That's the main idea. There is more in my book and on my website

 


Douglas Hainline's picture
Sun, 22/05/2016 - 21:42

I've (mistakenly) replied by email, so this will be repetitive. Some of this is new to me, and I look forward to reading about it. I ordered your book a couple of days ago. In general, I absolutely agree about the rows of sudents writing down rows of neat answers, regurgitating them (hopefully) on exam papers. Pointless. Why not just memorize some of the poetry that Janet could recommend -- it would be more valuable.

My understanding of some of this is as follows: much better to guide the students -- scaffold them -- thru various experiences, such as the air track, and let them talk about it, maybe propose hypotheses, test them, etc...  but knowing they will not re-disover the Laws of Motion on their own  (or perhaps this is my own belief only). At the end of the day the teacher will have to explain the Laws of Motion and show how they are consistent with observation. Or maybe that's just my reading, or rather my belief.  (How I remember those dreaded physics labs, sretching springs and timing things rolling down inclined platforms, hoping to get 'the right data' and faking it when we didn't .... the motive I suppose was Good, but the actual practice was useless. ) 

 


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