Just as a library is dependent upon writing, and writing is dependent upon an alphabet, and an alphabet is dependent upon language which is dependent upon verbal speech. Until one is either developed or taught/learned and understood, the next cannot come about.Quote:
Originally Posted by cafolini
However, you can have an speech, language, alphabet, and writing, but if paper and ink are not developed, there is no library. So, philosophy depends on engineering to be able to be recorded.
First, 4+2=12 (base 4).Quote:
Originally Posted by cafolini
I don't think it's necessary to teach number bases along with arithmetic. At that age it would confuse and frighten most kids besides achieving little. It would go more suitably later on with topics such as modular arithmetic and Fermat's Theorem. Number theory is, however, largely (and very unfortunately) neglected in elementary schools.
A more natural way to teach arithmetic could implement objects, grouping and counting them, anything to develop a sense of numbers rather than rote memorization.
I came upon an interesting essay recently that I think pertains to this topic: http://www.maa.org/devlin/LockhartsLament.pdfQuote:
Originally Posted by Paulclem
As for fighting fantasy games – I really don't see how that relates to math, or English. The level of writing appears to be quite mediocre.
I like the essay you posted. Some good ideas and I agree with the general thrust of the argument.Quote:
Originally Posted by cl154576
The fighting Fantasy book can relate to both. It's how it is used and adapted. The writing is mediocre - but that then lends itself to improvement. Puzzles/ problems can replace the simple dice challenges. You just have to be creative with extracts.
The are no truths unto themselves without relationships with anything else.
Agreed. That's perhaps why maths teaching and how it has been presented is so dry and abstract. The attitude has been that maths is a truth unto itself. Clearly rubbish.Quote:
Originally Posted by cafolini
Now this is a beautiful question!
And, in my opinion at least, not impossible!
In fact, it's ripe with possibilities. Just think about how creative you can get, searching outside the proverbial box for ideas to present these two subjects cohesively together! It could be the beginning of something fantastic, a new way to teach.
There are many who form the opinion that you are either an English, or a Maths person. In the end, I think it has to do with interest, effort, and time.
I think the way I would present a lesson plan to tie English and maths together would be very similar to an assignment given when I was younger that I will never forget.
The teacher gave us the outline of a story that we were to fill out in our own way, but must reach particular conclusions. Within those boundaries, I made a fantasy story, but it could have just as easily become science-fiction, or adventure, or anything my young heart could have desired.
I'm not sure about the exact words, but we were to write a minimum amount of pages... We had to write our outline first, with a short summary of characters, settings, etc. The only restrictions we were given is that our protagonist was either the 'prince' or 'princess', and they were to meet in a 'secret garden' at the end of it.
A similar 'make your own story' plan could be reached, with a different conclusion, and different chosen characters, etc. It was simply a wonderful way to focus us, as young writers.
I should also add that mathematics can get very exciting when you think about how it's in the world around us, especially with physics, celestial bodies, and molecules. Maths tie in very heavily with science, and all of these can be an exciting, enjoyable playground for children. It's difficult for kids sometimes, myself included, to get their head around numbers. But concepts are a children's dream.
It's just a matter of thinking about how many ways you can utilize the use of a paper clip. Divergent thinking. :)
My example project would go something like this:
You're to write a 5-page story about a man, or woman who has been chosen by a secret government organization to build a Teleportation Device (Or camoflage, or light speed engine, etc, etc. Limitless possibilities). Be sure to name your machine!
You may begin your story anyway you wish. The scientist, or mechanic, or engineer, or whatever they are, could be working in a lab, or on their way to McDonalds. Be creative! But, no matter what, they will be approached to build this contraption. It's up to you to decide how.
In the end, they must be able to explain how their device works. An example: The uncertainty principle, light speed, atoms, etc. (Be sure to explain these theories to them in a simple way first, perhaps making consequent lesson plans that tie in with the writing portion.)
I know it might sound as if this stuff could really go over the heads of kids, but if done in the right way, explained well enough, and brought together in an engaging manner, I think you could pull this off. Give the kids the benefit of the doubt, believe in them, and you can be incredibly surprised at the results. Don't sell them short!
Just my own thoughts on the subject. :) You could make things more simple too. It's just an outline.
Their protagonist could go back in time and meet a mathematician, or the protagonist could actually be historical in the first place, a best buddy of Einstein that nobody knew about.
If you want to bring in more of a literature element than simply writing, perhaps provide a list of writers in literature, assign them an author, or let them choose one, and give them a few chapters to read. Then, have them attempt to write in that author's style without plagiarizing. :)
I hope that this helps bring about exciting new ideas. :)
the number 4 doesn't exist in base 4, just like the number 2 doesn't exist in base 2 (binary). but if it did it would equal 10, and 10 + 2 would be 12.Quote:
Originally Posted by cl154576
The person is trying to equate the meaning of 4+2 in base 10 with 12 in base 4, which is correct.Quote:
Originally Posted by Cunninglinguist
When you say that the number 4 does not exist in base 4, it is meaningless. What you meant to say is that the symbol 4 does not exist in base 4, which is correct. Any quantity (number) can be expressed in any base. That's the independence of quantity from symbol.
No, I meant to say number. In common use, using "number" to refer to the "symbol" isn't incorrect...strictly speaking, yes, mathematical objects can only be the referents of such. If you really want to get pedantic then it ought to be called a numeral, not a symbol. I'll tell you what is meaningless, though. 4 in base 4. :PQuote:
Originally Posted by cafolini
Ha! So speak more strictly instead of insultive. The difference is paramount and not open to vote. Case closed. You don't know what you are talking about. Cunning? Yeah! Solong.Quote:
Originally Posted by Cunninglinguist
Interestingly enough, the Govt in the UK have decided to scrap what were our L1 and L2 qualifications for English and Maths to be replaced by something calle Functional Skills. Apart from being a much more demanding qualification that actually comes closer to GCSE as the standard English and Maths qualification, it has a significantly greater amount of English in it than the former multiple choice qualification.
They have been designed like this in order to attempt to place mathematical problems into a real world context, so there are extended problems on the uses of shape and space, statistics etc, often requiring a sentence or two on why a choice was made, and why it was better. The questions are open, so that there's more than one method and answer for the learners to approach the problem. Some of the questions involve quite a lot of reading and make use of seperate information sheets.
Informality is hardly paramount in this context. It's certainly not as egregious as using 4 in base 4, which is tantamount to using A as a numeral in base 10. That's certainly neither formal nor informal -- it's just wrong. Anyway, you doubtless understood that I was referring to the numeral when you tried to correct me, which means it served its intended function. And saying case closed isn't an effective way to win a debate. Case closed! :yikes: Anyway, we're totally off topic now so I'm going to stop responding.Quote:
Originally Posted by cafolini