I'd like to hear some ideas that anybody might have for tying Mathematics in to a 6th-10th-grade (actually, *any* grade, really) English classroom. What sorts of materials (books, articles, films, presentations, anything!) might you suggest using?
I imagine that a lot of the reading would tie-in with history and historical figures, but I'd like to be able to have at least a few lessons up my sleeve that might be able to highlight the importance of that much-loathed subject. :)
You may not like this answer, but sometimes we can't tie everything together. It is very hard to tie math and English together. If you think about how the subjects are split up, you'd need to collaborate with the math teacher. Who knows how flexible that person is going to be when trying to cover the curriculum. They will be pressed for time. You will probably want it brought into your class, not the other way around. With that kind of collaboration, there may be more flexibility. Are you thinking about this for an interview or if they ask you in an interview? If so, I'd just emphasize the collaboration piece.
Math word problems- break them down step by step, this way they can analyze what is asked of them- can be a good English lesson. I am a special needs assistant in a middle school.Quote:
Originally Posted by jpveedubs
I agree with that part, definitely.Quote:
Originally Posted by KCurtis
The other part has to do with the way arithmetic is taught. Algebra is the laws of arthmetic properly taught. People are taught to learn artithmetic by rote and repetition. When they get to algebra they hate it because they don't realize that what they already learned is useless for thinking. All the laws of algebra are within arithmetic, but students are not taught associative, commutative, factoring, etc. and etc. They are taught useless tables by rote. Raw memory is the number one enemy of mathematics.
The third part has to do with symbolism. And for children to grasp it, they must be taught number bases. In base ten, for example, 4+2 = 6 but in base 3, for example, 10+2=12 (6 in base 10), and in the binary, base 2, 100+2=110. You can count in any base you please. In base 4, for example, 4+2=11. And so on. Knowing the use of symbols reveals the independence of quantity from expression.
As much as I'm for cross subject teaching in school, i don't think math and English can, or should, be tied together. It seems like the attempt would be so convoluted (the above suggestions seems a good example) it would end up confusing students, or just completely shutting them off. English goe great with history, politics, even science ... but I just can't see any coherent link that could be made between the two. I could be wrong.
How about fighting fantasy books? Do you know them? You take a character and they make decisions about which option to take in a fantasy story. If they come across an enemy, then they fight them on the roll of a dice.
http://en.wikipedia.org/wiki/Fighting_Fantasy
http://www.amazon.co.uk/s/?ie=UTF8&k...l_7n53zgnvh1_b
Of course the maths could be quite limited, and I'm unaware of the levels you would teach and the topics you could cover.
You could adapt the idea though and throw apprpriate puzzles to solve a simple story. These - you may know this - were the precursor of video games back in the 80s.
Like Paul said, it all depends on the curriculum elements you would like to integrate; however, I am all for Maths and English elements being introduced into different subjects. In real life subjects do not come in nicely labelled, separate boxes, do they?
There are always opportunities for exploiting... For example, reading and writing large numbers, volume and area calculations (which means shapes, measuring and long multiplication), comparing numbers, average calculations can very easily be introduced into English lessons.
This does not mean you need to "teach" them all these but provide opportunities for them to practice.
Here's the problem I see with this: what does it teach them pertaining to English (or math) and does it do so in a more effective or productive way than keeping the subjects separate?Quote:
Originally Posted by Paulclem
Like what, though? That's what the OP was asking. I'm stumped as to specifics.Quote:
Originally Posted by Scheherazade
Here is an example:
While teaching different types of text, I asked the students to write informative pieces on life-long bags offered for sale by different supermarkets. They compared the prices, the material they were made of and their strength, the weight they could carry as well as their volume... All required various use of their numeracy skills.
At the end, they put their findings into an informative article... Which was the main aim of the lesson.
Later on, they compared Easter Eggs (weight/calories/sugar/price as well size) on sale in a similar manner and wrote a persuasive piece.
Interesting.
As I see it, math is just another language. There is no problem in translating math to English, or any other language. The big difference is that one page of math would take many pages of English. Of course there are many aspects of English that are not suitable to be translated into math. But there is not a thing in math that cannot be, however painfully, put in English.
So integrating English with math is a matter of being able to speak math in English.
There's a debate that been going on over here for some time about how to teach maths. he accepted view is that maths exists as a seperate entity as a truth unto itself, and previously it was taught in this way without reference to anything else.Quote:
Originally Posted by Mutatis-Mutandi
As a result a visual learner like myself was stuck in a magnolia classroom struggling and not succeeding with abstracts.
The current view of those who are trying to improve the quality of maths teaching is that it is not an abstract self evident truth, but is the result of human endeavour in maths in a particular context.
So one way of looking at maths is to include Babylonian base 60 as part of the lesson. Base 60 is the foundation of our time - seconds and minutes. Our learners struggle with time questions at a certain level. Giving a bit of history on Babylonian base 60 might just reinforce that concept of 60 seconds/ minutes by providing an interesting stream of though with which to refer to.
As for the fighting fantasy games - well i don't really know the age of the kids and how suitable it is, but a lot can be gained by fun. Playing and replaying is sutrely better than completing a sheet of boring algorithms.
This is excellent, we do this in middle school also. And students need this to take the MCAS, which incorporates math and english into word problems and they MUST write a very short paragraph explaining their results. They must be able to read the word problems and decipher what is asked. One math problem is a page long.Quote:
Originally Posted by Scheherazade
Teach them to write proofs, maybe. Or if they're not ready to do that they could write solutions. If it's an elementary level geometry class, you could have them write detailed instructions for compass constructions, etc. Being able to communicate your ideas well is one of the most important skills in math.
However, this makes the assumption that it's not an entirely exercise-oriented class ... it would be extraordinarily tedious to write solutions for computational problems and basic algebraic word problems. There should be some creativity, some artistry, involved.
Try reading some problem solving blogs, or math lectures and essays; for the most part it's all expository writing.
The teaching of algebra without a previous elementary course in Eucledian geometry is a brutality. It has no place in experience. So much for the more advanced analytic geometry without trigonometry, or ridiculous calculus without analytic geometry. Knowledge builds on knowledge, not on memory.
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