Teaching inductive reasoning

[Mister Noodle]

Inspired by the 'concentration activities' thread, I have a question for anyone else who may have pondered it:

How do you teach inductive reasoning to children (of any age)?

Our entire culture celebrates deductive reasoning: given a set of rules, determine the facts.

All of the puzzles and games and children's shows and other activities out there are geared towards this half of the reasoning process.

This is fine, but as someone in the IT support industry, I'm constantly gobsmacked by the complete and utter lack of people's ability (or inclination) to handle the complementary function: generating an inductive hypothesis.

People just don't model systems in their heads. They'll see a set of behaviours (from a piece of software, ferinstance), and they more or less learn them by rote. They don't look for patterns in them and try and condense them down to rules that can be easily understood and extrapolated. So when they run up against novel or broken behaviour, they're at a complete loss, because they don't know what to do next.

This process - wondering what rules would cause a set of behaviours, and proposing a working model to explain what they're seeing - is the entire first half of the scientific method.

And it's completely alien to a frightening percentage of the population (it's certainly frightening in engineering students I work for).

But really, this lack is hardly surprising, given that nobody teaches it to kids. There aren't any games where the object is to work out what the rules are. We don't have classes where children have to work out how the innards of a machine are wired up. We don't have anything that teaches people to black-box, reverse-engineer or otherwise make mental models that explain phenomena.

This entire cognitive faculty goes completely unexercised until way late in people's lives, so it never becomes second nature to them. We don't give them the training, and we don't give them the tools.

So, my question: how could we do this? What kind of games or activities would encourage kids to sketch out hypotheses - which they could then test with their perfectly-well-exercised deductive faculties?

How could we make it fun and interesting, for any given age group?

[sweetsugardumplin']

I'm really inspired by what you are suggesting. :yes:

I'll get back to you on some thoughts and ideas. :idea:

Mumma

[Pixie]

You are looking at a child's world through adult eyes.
To require inductive reasoning from a child is like asking them to carry out a gymnastic routine before they can walk, or asking them to write a play before they have learned the alphabet.
Induction requires a comprehensive understanding of the rules and parameters of the field and experience working on problems in the area under investigation. So I am saying that the prerequisite level of knowledge is high and so unless the child is a prodigy in the field in question, it probably won't be until, late secondary or even tertiary education, when they will be confronted with that type of challenge.
That is also probably why the great minds of history with some exceptions (Gauss) tended to deliver on their talents only during adult life. Forms of induction are taught in university level maths and statistics, and no doubt other fields such as philosophy. So the reason you have not run across any material is perhaps because nobody has been able to consistently teach it to children.


Just like to add that was written by my DP, Noodle as I knew it would interest him + I have no idea watcha talking about...:laughing: them big words N all :D

[Mister Noodle]

Hm. I'd argue that they spend their entire early childhood doing it on an instinctive/intuitive level: from finding their hands and feet to learning to see to developing the theory of mind, they *infer* their entire world, almost from scratch.

It just seems wrong that we either don't or can't provide tools for them to do this consciously, and/or with abstract concepts.

I'm not speaking of mathematical proof by induction, by the way. (yes, Gauss was a little cleverclogs)

All I'm talking about is the ability to clear a mental space to visualise (or some more abstract form thereof) the underlying structure of something, from a handful of clues.

An example: cut a tennis ball in half, put a ball bearing inside, glue a card with a hole in it over it to fit, then glue the other half back on.

Just by shaking it around, a person should be able to work out the existence and position of both card and hole, by the way it rattles. The same if there are two holes, or no card, but the ball bearing is on a spring, like those cat toys.

Our cerebellums are very good at this kind of thing.

Our forebrains can be good at it too, if you give them a little practice, in a form that can be generalised out. We work out that other people think like ourselves, and that's no small leap to make.

Are you sure this kind of skill can't be taught as a general principle?

[Lirael]

:confused: my brain hurts :D

[Shanaynay]

So, my question: how could we do this? What kind of games or activities would encourage kids to sketch out hypotheses - which they could then test with their perfectly-well-exercised deductive faculties?

How could we make it fun and interesting, for any given age group?

The Wisconsin Card Sorting Test.

[Mister Noodle]

Hey, cool - now, to implement something related in chunky yellow plastic, with lights and bleeping noises and pictures...

[DQ]

:confused: my brain hurts :D


Mine too Cel!!!!!!! *insert "ouch" emoticon here*

[ThreePinkFaireez]

:banghead: :detective: I've gone to consult a thesaurus (spelling?) dictionary to spell with and someone who is way way smarter then me!!

[pegasus]

I do agree somewhat with Pixie (or her DP as she suggested), but my other answer (in short) would be - backward chaining. As a therapist who has worked with both children and adults, I would suggest that you definitely need to take into consideration where that child is at from a developmental psychological perspective (consider Erikson, Piaget or Jung's developmental stages).

Problem Solving skills are one of the greatest tools to teach a child so that they can generalise knowledge. A thirst for knowledge is the other thing and this goes hand in hand with the problem solving.

Teaching from a Gestalt perspective is going to enable a child to utilise IR.

In all honesty - I believe a child will be able to understand (without realising it) the concept of IR before age seven when they develop identity constancy or after age eleven when they become able to consider a problem in the abstract. (See Piaget's cognitive developmental stages.).

[MariaO]

Isn't that what talking dolls are for? My brother thought so anyway when we were kids. (i.e. to cut the back off to see how the talking mechanism works)

[Rhys'Mum]

lol

This is a really interesting discussion. Thanks. I didn't know it had a name I just knew some people could and that others seemed only to know how to do things by rote (interestingly I did IT support and BA work for a lot of years). It has often frustrated me and I just couldn't 'get' it. I will be interested to hear what you find. Would love ways to encourage it in the little man as he gets older, I love creating opportunities for incedental learning.

[Ana Gram]

Hmmm, Mr Noodle, did you think it's not done because it is coma indusing? Seriously I've had to force myself to read this and the very thought of doing what you are suggesting made me cringe, groan, roll my eyes and want to fall into a deep coma.

[MrsMiggins]

The concept is partially tested for in some IQ tests. I believe it is definitely something you are born with, but can be nurtured (rather than taught). Although having said that, I think everyone has it to some degree.

In the US in the 80's it was something they were very much into introducing at elementary school level & as such, my brother & I both experienced teaching experiences geared towards getting kids thinking "outside the square" so to speak.

[mysonroger]

[
I remember reading the preface in the Baby Whisperer book by Tracey Hogg (god rest her soul) and she explained that part of the reason she has this 'whisperer' ability was because of the influence her grandmother had on her as a child. if , for example, they were walking down the street and saw a dress on display in the window, her grandma would ask her a series of questions. from how, do yu suppose, it was made,
the factory was in which country,
who ,do you suppose, were the people who made that dress,
how did they come to work in that factory
the logistics of getting the dress from the factory to the shop etc.

so that she just didn't take it for granted that dresses just 'appear' in shops......

for me, this is an important aspect of raising my children....to be able to think like this, and not accept things blindly. I'm good at improvising so maybe i have the inductive reasoning....i just didn't know it was called that. i believe that when teaching somebody something it is good to explain each step of the way so they understand every element, so that they can improvise when somethign goes wrong, or come up with a better solution themselves, or improve or remove unnecessary steps to a task even.

i'm starting to do this with my 2.5 year old DS with the aid of puppets and home made bits and bobs.....i've done the whole transition from caterpillar to butterfly thing, tadpole to frog, i'm about to do bird to egg to bird . pretty basic, but i believe i'm on the right trail.

[mysonroger]

Oh good holy god, i've just read all the other posts and i feel my approach is maybe a bit too simplistic for Mr. Noodle.......

anyway, i believe , myself, that i'm on the right trail. please someone tell me if i got it all wrong?? I mean...there's people quoting Erikson, Piaget or Jung's developmental stages, and Gestalt, and here i am quoting the baby whisperer.........ha hah hahahahahaha.

its ok to laugh at me.............

[Mister Noodle]

Hmmm, Mr Noodle, did you think it's not done because it is coma indusing? Seriously I've had to force myself to read this and the very thought of doing what you are suggesting made me cringe, groan, roll my eyes and want to fall into a deep coma.

What, you mean algebra?

[Pixie]

DP is still at work I told him you responded this morning but he was running late for a meeting if he will he'll reply tonight :D

we had a long chat about it this morning, I said how as a kid I switched the light switch on and off on and off trying to work out how a switch on the wall worked the light over there, so later that night I took apart the switch and saw the wires I took the wires out...light doesn't work, reattached wires, differently to see if light would work it didn't DP explained why I forget now :o so I wired it back the proper way and hey presto light works...

Just it just depend on how curious you are as a child, I didn't go to school so I spent a fair bit of time trying to work things out for myself....still am actually :D

[Ana Gram]

What, you mean algebra?

algebra is already taught at schools and yes I found it incredibly boring.

[Mister Noodle]

heh 'chelle, that was my point - algebra nearly killed me.

But that doesn't mean its either impractical or a bad idea to teach it.

[Ana Gram]

Didn't say it was but as I said it is already being taught so now I don't know what your point is.

[Mister Noodle]

um, there seems to be a communications breakdown here.

Algebra: boring, painful, taught anyway.

IR: (IYHO) boring, painful, and so shouldn't be taught.

Whence the asymmetry?

[Ana Gram]

Perhaps they don't want children to either sleep or wag half the school day if they did both.

[Pixie]

OK This is Pixies lesser half!

I should have stated at the outset that I have no qualifications to comment on developmental psychology, I was just making unsubstantiated assertions, based on generalisations.
So having made that clear, I obviously misunderstood your points. I participate in a lot of problem solving activities and have noticed that with adults more frequently than I would hope, that when the problem is even slightly out of their field of expertise, experience or knowledge domain they are missing the ability to deal with circumstances that are out of the ordinary, to the extent that they also seem unable or unwilling to apply basic problem solving techniques. I extrapolated this to my assertions regarding children, apparently unsuccessfully.
I have however come up with a different model to put forward. (please remember my earlier disclaimer)
How about this?
I see generalisation to be an important skill, it is an important part of how our senses help us to keep up with all of the things that are happening around us in the world, filling in bits we miss and leaving out non essential details.
I think that for abstract thought we need a sufficient level of experience in order to be able to consciously fill the gaps.
In your example of the ball cut in half one would have to assume the child had seen and held a ball before , had previously experienced the impact of an object falling and so on.
So inductive reasoning is natural and it appears can be exercised , but i still think the level or complexity of problem the child is able to handle will be limited by their past experience. So no statistical inference or calculus for infants, except for, little savants.

[Mister Noodle]

Yah - I was thinking of a *much* simpler level than that!

Maybe some simple computer games.

Ferinstance, a 3x3 grid of paint puddles, with a roof over the top so you can't see what they are. If you roll a soccerball through from any given point, it soaks up the paint in splotches from all three of the puddles it rolls through - though in no particular order. The object of the game, of course, is to guess the pattern underneath. (with some cute graphical reward if you get it right)

Little things like that.

[mysonroger]

see...no one is taking any notice of my post because i didn't use enough big words.

[Lirael]

:confused::confused:













:sleeping::sleeping:

[BlueGin]

Ferinstance, a 3x3 grid of paint puddles, with a roof over the top so you can't see what they are. If you roll a soccerball through from any given point, it soaks up the paint in splotches from all three of the puddles it rolls through - though in no particular order. The object of the game, of course, is to guess the pattern underneath. (with some cute graphical reward if you get it right)

Little things like that.

Would "MasterMind" be an appropriate game then? I am no expert in this area (I am actually not that sure what type of thinking you all mean as a lot of the posts are over my head) but it sounds a lot like the paint game to me. I remember playing it from around 4-5 years old, and apparently I have lots of smarts in odd areas and am a box-skirting thinker.

MySonRoger - I would reply to your post if I could, as I could actually understand it unlike the others :o :p but am so lost on what MrN was originally saying that I don't think I'd know if you were on the right track or not! XX

[mysonroger]

i was thinking that i could be so far off the track that people are so embarrassed for me and don't have the heart to tell me that i just didn't get it.

but i'm quietly confident

[Mister Noodle]

Yah - Mastermind was great. I used to play that lots when I was a kid.

Though really, you'd need to make things a little less pin-downable than either to keep it out of the realm of simple deduction - maybe if the colours *mixed*, so it wasn't just a matter of putting together permutations... hmm.

[Lirael]

i was thinking that i could be so far off the track that people are so embarrassed for me and don't have the heart to tell me that i just didn't get it.

but i'm quietly confident

I cant even bring myself to read the OP I have tried about ten times but my eyes go cross eyed and I start blanking out:D
so dont worry about not getting it, I rarely get Mr Noodles posts he is just way to smart for his own good:p
(BTW i dont know if you got it or not lol:o)

[Mister Noodle]

MSR: no, you're quite right - asking kids open-ended questions, requiring them to construct answers from scratch - "So, how was that made then? No, don't guess - take a look and see what you can work out" is a great approach.

Apologies for not getting back to you earlier :o

[mysonroger]

oh no, don't apologise. i thought you were being an intellectual snob.

hey, i reckon you make your posts so hard to
read that it scares people off when really you could actually be spreading a good and worthwhile message that average Joe can understand and actually have some influence.

people are getting concussion here.....it doesn't have to be that hard.

[Mister Noodle]

Um, thanks... I think.

And sorry - this is just how I talk. I'm honestly not putting it on, I promise.

Ask Beany how irritating I am in person...

[mysonroger]

i have no doubt in my mind that you do talk like that.....and i have no doubt that its for real too.

but far out man..........

[MrsMiggins]

Oooh! Mastermind!! That was my mum's favourite game for us to play!! Except that she must have thought we were all brainiacs, because she started us playing it at like 6 years old!! :laughing:

I was thinking this evening as well, does anyone think that inductive reasoning & imagination are closely linked?

The thing that got me to thinking was that my 13m old has these coloured balls she plays with in the bath. About 2 weeks ago, she picked up the yellow one (always the yellow one for some reason) and pretended to eat it like it was a piece of fruit or something. I just thought - wow! That is pretty remarkable! But tonight I started thinking about that & the whole inductive reasoning thing & how she would make the mental jump from eating a real piece of fruit to pretending (and she was obviously pretending; she knew what she had was not edible and was pretending to bite a piece off and make chewing motions & sounds) to eat a plastic ball.

[pegasus]

Hm. I'd argue that they spend their entire early childhood doing it on an instinctive/intuitive level: from finding their hands and feet to learning to see to developing the theory of mind, they *infer* their entire world, almost from scratch.


See this is one area where I think the learning styles of kids gets confused a bit.

Pixie's partner got it in one when he talked about generalisation.

As far as I can discuss - babies learn from trial and error - which teaches them cause and effect. (ie if I do a, b happens)

Inference suggests that they have the backward ability to see an outcome and work out how they got there (eg. if they touch their feet, they know how they got there, in my example, they get their feet by accident and gradually - through doing it more - they learn that the action of reaching with both their hand and foot at the same time they'll get the same result)

IR can only happen when the person can generalise skills - as then they have a large enough bank of information to take from.

BTW - Chelle and Cel - I get what you are saying about going crosseyed too - only reason I'm here is my baby suddenly decided she wanted a feed and I'm hoping if I do it now I'll be able to sleep later than 5am. (Usually doesn't eat between 6pm and 5am).

I don't even know if I make sense at the moment...

[Pixie]

Hey girls this is Pixie not her Lesser half...good to see he knows his place HA HA.

Sometimes things go over my head, most of the time actually, don't worry about it just read and enjoy, I understand this thread NOW lol but yeah took me like 20 times reading it over and over lol

That splodge game sounds cool but isn't that a memory game?

MrsM my mum and dad were the same I was the youngest and they would ask me questions, lucky I had my brother on my team!

[Mister Noodle]

Pixie: it wouldn't be a memory game if you couldn't tell the order of colours - and less so if you couldn't tell the individual colours, just the effects of mixing them.

it's *hard* to nail the process down, innit?

[Mister Noodle]

Peg: Asher is (albeit slowly and minimally) developing rough concepts of "people" and "objects" - whereas to start with, he was very evidently awash in nothing but a sea of individual sensations.

He's starting to sift the astounding mass of raw input, and creating entire concepts from scratch to file them under.

That's grandmasterclass inference, if you ask me.

Now that'd be a cow of a computer game for adults: you're presented with a vast array of unlabelled knobs and dials, with a big siren that goes off at intervals.

Your job is to work out what it all means, and how to keep the siren from going off.

They would of course be hooked up to the sensorium and muscles of a virtual baby (and the siren would be crying in distress)- but you don't tell them that. They have to work it all out from scratch, like a baby does. (and even then, they'd have a huge advantage, because they already have so many useful real-world concept to draw upon)

Reckon anyone would ever crack it?

[Rhys'Mum]

Oh good holy god, i've just read all the other posts and i feel my approach is maybe a bit too simplistic for Mr. Noodle.......

its ok to laugh at me.............

hey, I thought your post was great, makes total sense to me. That's pretty much what my parents did (and still do) with me whereas my husband thought it was totally weird. Well guess who can think outside the square and problem solve in this family....

You took a complex idea and gave it a practical basis. I love it.

[pegasus]

Peg: Asher is (albeit slowly and minimally) developing rough concepts of "people" and "objects" - whereas to start with, he was very evidently awash in nothing but a sea of individual sensations.

He's starting to sift the astounding mass of raw input, and creating entire concepts from scratch to file them under.



See - I'd see this as being a bit of Gestalt understanding - "seeing the object as a whole rather than a sum of it's parts".

To me (or how it was taught to me) inference is seeing an outcome and deducting what has occurred from observations. Eg. Observing a sign knocked over and a cars front end pushed in - the inference is the car ran into the sign and knocked it over. Most likely correct, but an inference rather than based on fact. It's an outcome deduction based upon previous experience of the event.

I like the story of the three(?) blind men and the elephant. (I think there's more men, but I forget the parable)
1st man feels the side of the elephant and thinks it's a wall
2nd man feels it's leg and thinks it's a tree
3rd man feels the trunk and thinks it's a snake.

They all have made their assumptions based upon their previous experiences, but have made them based upon a part of the whole. A generalisation at this stage would be false, but that's what they've tried to do.

That's what I'm trying to say about very young children - their sensory systems are still in the very early stages of development (heck, our brains don't stop developing until we're in our twenties), so it is impossible for them to be able to properly generalise information for a few years as they experience more.

By definition in Inductive Reasoning we reach general conclusions from a number of specific instances. What I'm suggesting is that until our sensory systems are more integrated (would love to talk more on sensory integration - very much up my alley), our conclusions are not always correct enough to draw generalisations.

Inductive reasoning involves generating hypotheses - this is where young babies can't do it as they haven't experienced enough of the world. The more they experience, the more they'll move towards being able to do it. Trial and error is the first way they experience stuff and accidentally they'll get it right a few times - this is where a parent's role of identifying desired behaviour and giving positive reinforcement is so important - it allows them to go to the next level. I'd suspect that some of the young people you've talked about coming through your work place didn't get enough of the consistancy and reinforcement in early years to encourage the next level of learning.