COMMON CORE MATH: TWO APPROACHES: REAL MATH IS ABOUT PROPER PARTNERING ...
Ok, Common Core is a disaster; we get it. What else could it be with the federal goobernment, profit hungry "testing" corporations, and busybody billionaires behind it, right? Well, I've been hearing horror stories about common core math, so I had a bit of free time this past week when I was laying in bed miserable with tonsilitis, and I actually found two helpful videos which I'd like to share. The first one actually makes sense - at least to me - and, as the presenter, Dr. Raj Shah, indicates, learning certain things the way he presents them also lays a deeper foundation for algebra and (if you're really following him, calculus). So I had no real difficulty following it, and no real difficulty with why certain things are being done:
Ok, I get it Dr. Shah, and, from my point of view, it makes sense. I've even seen math problems where students are supposed to draw arrays for simple multiplication problems, which are counted wrong if the student draws the array in the wrong way. Ok, I get that too, for I suppose that it's a helpful idea to lay the foundations for matrices and linear algebra early on. The trouble is, the bewildered parents looking at the right answer to a problem with the wrong array may not understand why the fundamentals of linear algebra are being taught in elementary school, and how obscuring the principles of commutivity so early on are beneficial, and of course, they have every bit as rational a point as the array addicts of Common Core. When I saw these array problems, I began to scratch my head and wonder also. And even with Dr. Shah, I wonder how the approach of visualizing a problem like 23 x 451,002 using the bright shiny new method helps either. Now we could do it Dr. Shah's way, and invoke all sorts of new and eminently rational steps complete with subdivided rectangles and the implied differentials(but let's not use that word yet because we'll scare everyone away), or do it the old fashioned way, with fewer steps. So in my tonsilitis-medicine-induced stupor, I chalked it all up in the "maybe" column, with a lilttle mental footnote that the "tons of research" Dr. Shah opined existed, suggesting the success of the "new methods", might be taken with a grain of salt. After all, tons of research suggested various trendy things - like getting rid of the classics, history, geography, Latin, and Greek - was a good idea to the likes of Dewey, Thorndike, and the progressivist edubabblers of a century or so ago. And what stellar results that has produced.
But, before you start hurtling rotten fruits and vegetables at me, there's this wonderful bit of splendid nonsense that I also found, which puts poor Dr. Shah's purely rational mathematical approach to shame, and this is, I suspect, the real common core math, and its such eminently sensible, and sexy, rationality:
You're kidding, right? Nine is "partnered" with one because we're in a base ten system? (See? doesn't that make so much more sense?) "Oh what fun!" my loopy drug-influenced brain was thinking. "Why, this means that numbers are all partnered with each other! It's like an orgy! Hey, I'm very comfortable with that! I'm achored now, baby!" But then, dreadful thoughts! How to explain the inherent homoeroticism of partial differentials? the unnatural polygamy of factorals? the pro-female bias of having to solve for x so many more times than for y? Why, even the Lorentz transforms were apparently non-gender neutral with the x transform displaying, once again, a gender bias for x (female) and not y (male), or better, z, which is neither and therefore, much better! Shame on Lorentz (and Einstein too for propagating it)! And because we're all in polite company here, I won't even begin to describe the thoughts I was having, contemplating what was partnered with Euler's theorem or the Hopf torus, nor the manifold positions in which they were anchored, or even if any of them were comfortable, even though they all looked entertaining, but it did inspire several new and very exotic ideas for sex toys, which I'm hoping to patent. And you can imagine what this approach means for basins of attraction and topological probes! Why, it's a positive orgasm of mapping functions. And...oh!...."The Sexual Fantasia of Riemann's Zeta Function"... well, that was just a "WOW!" I had to have a cigarette after THAT one.
So thank you Common Core! I'm truly impressed! This is truly a work of simple genius and inspiration! What has been missing from mathematics all along is proper partnering and sex and the feeling of being anchored and comfortable.
See you on the orthorotation...
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get off the tonsil meds. can’t imagine what the dreams must be like between standard american meds and these vids.
hang in there and thank you
ps. make tea or chew em and let em stick to your molars. will sooth the throat for hours.
Also, one more thought…how the hell do the French deal with arithmetic when some of there basic numbers seemed to be so messed? For example, ninety-seven (90+7) in French is quatre-vingt-dix-sept (4×20+10+7).
Having just watched those two videos, I have to admit that I don’t really have any problem with this new method of teaching math. The second video is kind of dumb (and obviously dumbed down for the television audience) but Dr. Shah’s explanation is logical. But isn’t the bigger issue that “Common Core” is overly reliant on standardized testing and technology featuring expensive equipment and software all for the obvious benefit of corporate profits?
As for the math techniques themselves, I rather like the graphical approach that Dr. Shah explains. When I was a student I did fine with arithmetic in the younger grades. Geometry was no problem either. But I strongly struggled with algebra and frankly it didn’t make any sense to me until I studied calculus which basically united geometry and algebra into a sort of united theory for me. After that, it “clicked” and I had no problem with algebra whatsoever.
Then I went to university where I majored in electrical engineering or 3 years (before switching majors) and those courses were almost exclusively advanced math. Matrices, differential equations, etc. The ironic thing to me was that at that point there was almost no numbers involved in most of the equations, you would have a sheet of paper filled with Greek letters. Any of the difficult numbers such as the speed of light were represented with a letter (such as “c”) in a kind of short hand notion and then the few actual numbers that would show up in the equations were usually representative of a simple relation such as 2, 3 or 4.
At any rate, I’m glad to be done with schooling.
“…it’s a helpful idea to lay the foundations for matrices and linear algebra early on.”
For me, this brought up a possible AI agenda, possibly off-planet based.
Humans have worked out clever and simple ways of doing math over the lifetime of our species. It probably began as ‘survival’ math, given that you better have an answer as to whether you can reach that tree before that tiger gets to you. Slim, swift, and based in reality.
On the other hand, matrices and such are inherently abstract. Divorced from the world. Useful, but only if you are carrying-around a personal computer.
In that way, we are being subtly ‘conditioned’. Divorce a matrix-trained person from their computer, and he/she is lost. As a consequence, there is a background ‘need’ to remain in the technological system at a deep, fear-based level.
The earlier you can instill this ‘mode’ of thinking, the more deep-rooted it will be in the personality. If you also move to minimize the ‘natural’ math, you have them subtly ‘subject’ to you…
Hmm, I wonder if that’s how the Rainman (1988) figured out how many toothpicks were on the floor?
In my case, my mental math skills improved greatly after a significant friend, in days of yore, taught me how to, basically, mentally subtract or add in extraneous numbers ie 432+519 = 430+520+2-1 = 950+2-1 = 951. I’d have two tracks running in my head at once; the main numbers and the extraneous numbers off to the side… well, actually, it’s more like three tracks: the larger round numbers, the plus numbers, the minus numbers.
This helped me to figure out simple math problems without needing to write them down, which, I had no problem in doing, I just didn’t want to HAVE to write them down, because sometimes, there IS no paper and pencil handy.
And maybe most important of all, it made me see math as something OTHER than what I’d always thought it was: tables of numbers. I was able to visualize it better, sort of like the blocks in the first video, although not exactly like that.
I wonder what THIS says? I had to ask my husband HOW I was supposed to hold the pencil when I was teaching myself to draw at age, roughly, 40, 😐
I always thought that artists just plucked things out of their heads to paint, draw or whatever. WHAT does that MEAN?
What better way to promote their publically correct and gay rights agenda, start indoctrinating them young. That way you keep the sexes separate, frustrated, and eventually traumatized. Everyone knows that frustrated and traumatized people spend more on things they don’t need than happy, well adjusted people. Everyone profits except the poor unwashed masses who live miserable lives.
The exciting math, for those of age is where the numbers “hook-up” and multiply.
For me, the best way to teach is one-on-one teaching.
Not some nationalized one-size fits all recipe, step-by-step coloring in by-the-numbers.
The real math being done is: who counting the numbers of greenbacks made in this scam?
As in voting, it doesn’t matter who votes; it’s who counts the votes. The same analogy applies here.
Or, as in geography: the world is not flat, round, nor pear-shaped; it is crooked. It’s easy to get lost looking for a straight way in a crooked world.
Fix the crooked money, and you’ll fix the crooked world.
Then the numbers will add-up.
Here is a comfortable way to multiply 45 and 24: 45×24 = 9x5x2x12=1080. Why bother to teach long multiplication at all? Why not allow students to find the own creative ways to multiply numbers. Another example: 17×19=(18-1)x(18+1)=18^2-1^2=324-1=323. The students that aren’t interested in being creative can use a calculator, or, even better, spend their time reading Charles Dickens.
Problem is math bores me unlike reading you have to know your multiplication and division tables to use it. With reading you could misspell words but if you understand what your reading and the meaning of the words in the context there being used you can inform yourself using them. Math is sold as some kind of magic unless your have to calculate in designing and making things it is of little use to me. You could be a math wiz and still be a klutz and you could be a math illiterate and still think and understand the concept you just use visuals and god forbid pictures to get the idea. And math has been used down through time to sell dodgy ideas.
Lol. One of your best posts, and it even makes sense. Nothing wrong with math like I learnt it, carrying the digits, alone and single, not craving the polynomial comforts of partnering.
Feel better Doc!