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The knowledge economy myth
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You yourself insulted nice guy 80. As an advocate of aggressive moderation I can't complain about being reported.
I didn't edit my post because it was insulting to you but because initially I misunderstood what you'd typed. When I read the quoted text again i realised that you didn't say that you teach the syllabus no matter what but that you know people who do.
You might be an excellent teacher but your colleagues who teach from a predetermined plan would need to be miracle workers to make up for that initial disdvantage.
I hope that teachers who teach according to a strict plan determined by the department of education are insulted and offended. It is now clear that you are not one of those teachers. But you did defend them.
Fair enough, and I have already contacted the mods to say that you edited your post. I will do the same with mine, but in my defence, I was told to 'shove it up my _______'
I didn't start the aggression, I had no reason to.
I was only defending them on the basis that it is hard to teach the way that you want to teach if you have inspectors breathing down your neck, almost forcing you to do exactly 3 and a half hours of Irish per week (I know one or two schools where this happened). I don't think many teachers like teaching in such a way.
Personally, I don't see the reasoning behind the dept guidelines (ie giving Maths and Science less time than Irish). The guidelines were brought up in the context of the discussion on the knowledge economy, as you know!:)0 -
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By barebones logic I meant formal logic, truth tables and so on. Construction games, lego etc don't have anything to do this or logic in general. I think they're fantastic for kids but don't really strain your logic skills. For games, yes I think dice based games are excellent, teaching someone to win by calculating percentages is a good mental workout.
Actually Lego mindstorms teaches programming with different sensors to solve problems and you get to play with lego.
Its like win/win
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Actually Lego mindstorms teaches programming with different sensors to solve problems and you get to play with lego.
Its like win/win
Yeah, Lego Mindstorms, just another toy I wished was available when I was that age. All I had was programming on a ZX Spectrum/Apple II to keep my mind occupied in primary school.
At least I'll get to buy them for my son in a few years.
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Yeah, Lego Mindstorms, just another toy I wished was available when I was that age. All I had was programming on a ZX Spectrum/Apple II to keep my mind occupied in primary school.
At least I'll get to buy them for my son in a few years.
I've been playing building lego robots using Arduinos a bit recently. Do that too, its a lot of fun! I'd say it'd be a great teaching tool for people towards the end of secondary school. That's where my comments on lego are coming from btw, I've been thinking a bit recently about how much cool stuff I learned when playing with it as a child - its funny how you can fall into the same forgotten modes of thinking doing an old task like that - I was surprised at the complexity of some of the stuff I remembered how to do.0 -
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I'm not sure I think its a good idea to directly try and teach kids advanced formal logic in primary school. I think at that age they should be learning to use and apply general concepts of deductive reasoning, and if they can do this fairly well, then they've made great progress.
Games like Cluedo (aka Clue) are a great introduction to the subject of reasoning logically, and you can go almost as far down the road of teaching people logic with it as you'd want.
For example, check this out: http://cs.gettysburg.edu/~tneller/papers/flairs06.pdf
"In this section we describe the game of Clue and explain why
it is well-suited to the teaching and application of propositional logic."
I'm not sure its all at as straightforward as that.
Without trying to get into some pretty serious debates here, are you familiar with programs like SHRDLU, and the 'Blocks World' domain it uses?
I remember playing with lego as a kid, and I distinctly remember having to do things like trying to look ahead to how I could rebuild a certain thing I was working on to try save a piece, or make a cleaner solution, and having to do things like model where the bricks would go in my head, and do things like see the bricks I would change, and even 'backtrack' to some extent when I reached a bad solution etc.
There's a lot of deduction and planning and reasoning that goes on there, and while I wouldn't quite claim that we do it using formal logic inside our heads, I would say that way we think is similar to how we later reason about algorithms and logic.
Possibly, deep down, we are using a process a bit like SHRDLU (probably with more intuitive pruning of some sort) - I certainly think this is more true at the start, and then we get good at building more intuitive shortcuts later. But I acknowledge this is very much just opinion :-)
I mentioned 'towers of hanoi' - I played with that a bit as a kid - teaches recursive thinking. I've also used it as a tool to teach something about how recursive thinking works, if a teacher could do this, it'd be an excellent lesson.
You mention truth tables - thinking along the lines of 'if I capture that pawn, and the other player doesn't move his king, then I can checkmate him, or if I move my bishop here, and he doesn't move his queen, then I can pin his queen to his king' isn't exactly doing truth tables, but its laying some of the ground work for them later.
Again, I think the way to go is to have people play games that are heavily supportive of learning these concepts, and then introduce the concepts as useful tools that can add to the understanding of the games.
Learning through games, its the future! :-)
Well honestly I think we're talking about slightly different things here. Pure logic is a very specific thing, it's very limited because of this! Broader analytic skills aren't covered completely by logic, only a minority is. I think I'm using a narrower definition of logic than you are but that doesn't mean either of us is wrong.
I did get introduced to formal logic in primary school at the age of 7 when teaching myself to program dealing with if/for/not loops and so on (and honestly earlier in logic puzzle books kinda). But then that wouldn't be typical of the age group. If you can comprehend this kind of stuff easily, it's a boon, but if you don't have that kind of mind I'm not sure it'd be of benefit to you. A bit like how a primary school kid of sufficient intelligence can learn Calculus at a LC level fairly comfortably, but it doesn't mean all primary school kids should be introduced to Calculus that early.0 -
Well honestly I think we're talking about slightly different things here. Pure logic is a very specific thing, it's very limited because of this! Broader analytic skills aren't covered completely by logic, only a minority is. I think I'm using a narrower definition of logic than you are but that doesn't mean either of us is wrong.
I'm not sure I like the use of 'pure' there - at one level, I'm not sure there is a logic more pure than "if I move there, he'll take me, and I don't want him to take me, so I'm not going to move there".
Unless I'm mistaken, I think I understand what you talking about as 'formal logic'.
I would say that formal logic is very well related to good reasoning skills. I think this a large part of why formal logic is useful. If it wasn't closely related to general 'logic' or rational reasoning skills, I don't think there'd be much point in teaching it to people, particularly not as part of a general curriculum.
Because I think the two are closely related, I see the good general logic skills as being useful, both in themselves, and as a stepping stone to a later understanding of more formal logic, which should also, in turn, enhance and expand the general reasoning skills.
Even if you restrict what you are talking about to just very formal logic, I think that games such as chess, and especially cluedo, can serve as very good introductions to this. Unless you are talking about something more formal than the propositional logic described in the cluedo document I mentioned?I did get introduced to formal logic in primary school at the age of 7 when teaching myself to program dealing with if/for/not loops and so on (and honestly earlier in logic puzzle books kinda). But then that wouldn't be typical of the age group. If you can comprehend this kind of stuff easily, it's a boon, but if you don't have that kind of mind I'm not sure it'd be of benefit to you. A bit like how a primary school kid of sufficient intelligence can learn Calculus at a LC level fairly comfortably, but it doesn't mean all primary school kids should be introduced to Calculus that early.
What is a 'not' loop? :-)
I don't really think that for basic things like this, some sort of 'innate' intelligence is much of a factor. Really, what kids understand when it comes to this sort of thing depends on what they are previously exposed to, and if its presented to them in a way that they like.
Anyway, I wouldn't propose teaching kids formal logic on its own - very dry stuff. But I would propose teaching them general logic and reasoning skills through games, and eventually moving into elementary formal logic from that, where they are interested in learning about it, because the see it as useful to progress their understanding of the games they play.0 -
I'm not sure I like the use of 'pure' there - at one level, I'm not sure there is a logic more pure than "if I move there, he'll take me, and I don't want him to take me, so I'm not going to move there".
Unless I'm mistaken, I think I understand what you talking about as 'formal logic'.
I would say that formal logic is very well related to good reasoning skills. I think this a large part of why formal logic is useful. If it wasn't closely related to general 'logic' or rational reasoning skills, I don't think there'd be much point in teaching it to people, particularly not as part of a general curriculum.
Because I think the two are closely related, I see the good general logic skills as being useful, both in themselves, and as a stepping stone to a later understanding of more formal logic, which should also, in turn, enhance and expand the general reasoning skills.
Even if you restrict what you are talking about to just very formal logic, I think that games such as chess, and especially cluedo, can serve as very good introductions to this. Unless you are talking about something more formal than the propositional logic described in the cluedo document I mentioned?
Honestly, from some of the formal logic I've seen in Philosophy, I'd argue that some of it isn't very closely related to more general reasoning skills! Predicate logic is, well, messy.
I agree with you, I think it's just my choice of language that's causing problems. I suppose the way I'm coming at this is, that something quite dry and staid like formal logic is useful for developing reasoning but it's unsuited to general education in a classroom (seriously, even at college level formal logic doesn't necessarily sit well except with self-selected students and even then if you go beyond basic predicate logic you can have trouble). Games are great for reasoning, chess etc all played a vital role for me anyway and I will introduce my son to them as he gets older for exactly the same purpose (Go is one I highly recommend, it's all about pattern recognition similar to chess but contains the same need to mentally have a picture of the board several moves ahead to do well in). I don't however see much of a point in introducing such games into the classroom which is what we're really talking about.What is a 'not' loop? :-)
A nor loop for the overly fast typer.I don't really think that for basic things like this, some sort of 'innate' intelligence is much of a factor. Really, what kids understand when it comes to this sort of thing depends on what they are previously exposed to, and if its presented to them in a way that they like.
Honestly, single loops fine, multiple nested loops give people more trouble though. I don't really want to get into a gifted vs normal intelligence debate since it'd be unhelpful I think but it's building from the basics that is important and intelligence does have an effect here. Forming your own algorithms to find something or test for something isn't trivial once you get beyond simple examples. The thing is, arguing a complex point often follows such nested logical patterns and the ability to deal with complex abstract concepts often necessitates a grounding in such. I don't see an easy or obvious way to teach how to do this on your own though, examples sure but then you're depending on the kids to "fill in the dots" and your mileage will vary with that from kid to kid I imagine.Anyway, I wouldn't propose teaching kids formal logic on its own - very dry stuff. But I would propose teaching them general logic and reasoning skills through games, and eventually moving into elementary formal logic from that, where they are interested in learning about it, because the see it as useful to progress their understanding of the games they play.
Perhaps. I'm not convinced a one size fits all approach works with this stuff though. In the average classroom you'll have vastly varying degrees of aptitude for this stuff. At least you will if my experiences in school were anyway typical.0 -
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Yeah, I mentioned 'Go' in my initial list there, I don't play it much but I found it a really interesting learning experience to learn it.Games are great for reasoning, chess etc all played a vital role for me anyway and I will introduce my son to them as he gets older for exactly the same purpose (Go is one I highly recommend, it's all about pattern recognition similar to chess but contains the same need to mentally have a picture of the board several moves ahead to do well in).
Fair enough - personally, I definitely would.I don't however see much of a point in introducing such games into the classroom which is what we're really talking about.
People don't necessarily play games like that outside school, and, it looks like we both think they were a vital part of our learning. I do think in primary school they'd be more beneficial than reciting times tables, or rote learning verbs etc.
Hmm - now I'm really confused! I know of for loops, and operators like NOT, and conditional statements like If - is Nor here a n-ary operator, or is a nor loop something from more formal logic that I haven't heard of?A nor loop for the overly fast typer.
Yeah - I very much agree with you here - its one of the key things I'm trying to build my argument on; I see a distinct similarity between being able to argue a complex point and being able to deal with such abstract concepts as you mention. (From what I know this isn't obvious - its very much up for debate about whether how we reason internally would be related). I guess I'm just going another step and saying that the reasoning in games with lots of branching, depth, and conditionals, is also related, and that as such, worth learning - in school.
Honestly, single loops fine, multiple nested loops give people more trouble though. I don't really want to get into a gifted vs normal intelligence debate since it'd be unhelpful I think but it's building from the basics that is important and intelligence does have an effect here. Forming your own algorithms to find something or test for something isn't trivial once you get beyond simple examples.
The thing is, arguing a complex point often follows such nested logical patterns and the ability to deal with complex abstract concepts often necessitates a grounding in such.
Well - maybe I'm wrong, but I think that at a young age, games help.I don't see an easy or obvious way to teach how to do this on your own though, examples sure but then you're depending on the kids to "fill in the dots" and your mileage will vary with that from kid to kid I imagine.
No, a one size fits all attitude isn't the best - but, we get to a question of resources pretty quickly if we try customise teaching at a young age.Perhaps. I'm not convinced a one size fits all approach works with this stuff though. In the average classroom you'll have vastly varying degrees of aptitude for this stuff. At least you will if my experiences in school were anyway typical.
Given that we already have a one-size-fits-all curriculum, I think we could make it better. I'd hate to see the fact that its one-size-fits-all be used as an argument for lowest common denominator teaching... that's the real problem.
I guess I also have a lot of faith in the abilities of individual kids to learn stuff if its presented well - just where I fall on the nature/nurture issue. I think theres a huge amount of BS about natural ability that's wheeled out as an excuse for poor teaching, uneven resources, and underlying social inequality.
One-size-fits-all garments should be stretchy, or adjustable - not just XXX-large!0 -
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Hmm - now I'm really confused! I know of for loops, and operators like NOT, and conditional statements like If - is Nor here a n-ary operator, or is a nor loop something from more formal logic that I haven't heard of?
It's just a logical operator you can use in If or For statements. It's used in electronics as well as formal logic: http://en.wikipedia.org/wiki/Logical_NOR
It's a very simple concept really. But you can build very complicated entities from such simple logical beginnings.I guess I also have a lot of faith in the abilities of individual kids to learn stuff if its presented well - just where I fall on the nature/nurture issue. I think theres a huge amount of BS about natural ability that's wheeled out as an excuse for poor teaching, uneven resources, and underlying social inequality.
Yeah, I think we disagree fundamentally on this one. I agree completely that it's abused as an excuse for poor teaching and uneven resources but I'd argue the opposite tabla rasa stance is abused equally with absurd notions that any kid can be exceptional academically which is blatantly false. The truth lies in between these two extremes. Nature and nurture are both true, your intelligence is mostly dictated by your parents' intelligence but this is only partially genetic the environment your parents provide is dictated by their intelligence and their opinion of education (which is dictated by their own experiences!). We could go around and around in circles for ever on this really.
I'll recommend a book actually that shaped my own thinking a lot: http://www.bookdepository.co.uk/book/9780007240821/Nature-Via-Nurture0
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