The Federalists Papers helped me a little. The image is from their site and supposedly shows a homework assignment to which a father responded. The Federalist Papers said that the father's response was awesome.
It looks like the photo started in Twitter (Ell_mari78) with 438 re-Tweets (as of today). That is where the Federalist Papers (School sends home) picked it up and pushed it to Facebook. There were responses/comments posted on all three sites: Twitter (19), FP (129), FB (48 with 244 shares).
I wrote a few responses (in the following order). All of these are a continuation of discussions in this blog and at the truth engineering site. It's nice that Common Core might offer some material to further the theme using a technical subject.
- 6:49 pm The problem here is that the visual representation does not show the proper perspective. The leaps go from 100 to 10 to 1. Someone, earlier, mentioned that they would rather use a slide rule which was a functional piece of equipment used by many over many years (yes, it had a real mathematical basis, namely logarithms). --- This type of thinking focused on logic may have some merit, but it stinks. Russell gave it up Common Core folks. He and Whitehead took hundred of pages of terse, tedious logic to prove simple addition of two natural numbers. Then, our friend, Bertrand got smart. --- The Common Core folks ought to consider looking into an intuitive interpretation. It might just go much further. -- It may be that we best leave the dry logic to the machines (verifying their basis and extensions, as we are the masters - don't worry, it will not lead to the singularity).
- 6:52 pm It would be funny if the results were not so sad.
- 7:36 pm The parent is over complicating things. It's the same problem that adults get with the 5th grader comparison. Actually, a difference of 427 and 336 would have been more interesting. ... These differences are not those of differentials. But, the person was probably irate at the thought of this type of approach. ... The approach shown here is one of many rules that one could come up with. The trouble with some class work is that things like this are taught as if deus ex machina (all I have to do is appeal to Galois' experiences with the minds of the day). Why not teach a few principles and let the kids discover their own little tricks? Then, don't rate someone's result against another. If they have the right answer, what difference does the method make (path independence, so to speak). ... I told one of my early teachers (later on in life) that the first thing that I forgot was the times table. She was upset, a little. I told her that remembering the diagonal (squares) was sufficient. Everything else comes out by simple rule (eventually leading to the fingers). ... Of course, others have their own little tricks. Are any better than others? ... Well, when we finally get to where optimization is required (all sorts of reasons) then we might have the justification to evaluate and rate these types of rules of thumb. ... Otherwise, live and let live, especially in mathematics, in an operational sense.
- 7:41 pm Try the method with 427 and 336 to make it interesting. ... Why not drill the squares and then use logic (loosely used) to fill in the table? Have fun with it? ... Mathematics is more amenable to the general populace than the experts will allow (arguable, but definitely one of the arguments against the singularity).. STEM will not stem the divergence between those with the supposed best-and-brightest approaches versus the rest. However, the rest, many times, are more broadly based in being-ness. ... It's sad that we have the lasting repercussions from the early travails caused by over-zealot idiots (an idiot is world-class when they impact a lot of others' lives; an idiot with a small sphere of influence is tolerable).
My first reaction was that this an example of mathematics being misused. As in, teach someone a little of the subject, and they become dangerous (like the bosses of quants). The approach is tedious and not really intuitive. But, as the second reaction shows, the thing is not as bad as it appears, albeit it's flaky (as in, more complicated than necessary). Finally, the push behind this type of initiative is to teach and assess the effect of teaching.
That there seems to be a bias toward the more formal approaches is troubling. But, we have gone over that a lot. Mathematics is not our God send. Rather, if one looks at the troubles of the world that are economic, a lot of the mess comes from world-class idiots abusing mathematics and the enabling computational system.
So, thanks Common Core. I'll have to catch up on what they're up to before proceeding.
Added this comment at the Federalist Papers site (03/22/2014 - 12:40 pm):
|My mathematician friend (old-time professor) used to joke that engineers didn’t do math. Engineers open a book and find equations, he noted. On the other hand, by the time someone obtains an engineering degree, their mathematics exposure is far more than most math teachers face. Too, the engineer just might have a better grasp given that they bump up against the most reliable of truth processors. Nature. So, we’ll let that be.|
I have not paid attention to what Common Core is up to. From a brief look, it seems that they want to partition people into those who can handle this type of tedium and those who cannot (not unlike a whole lot of scholastic testing). Yes, tedium, of the utmost extreme (cast that upon the number line).
Now, how that bifurcation of people will play out is something that we will have to see. Some of it is, like Scott says, to determine the class that will be subservient to the masters.
I am upset that the general educational community has bought into this warped way of thinking. From where I sit, they will cause even worse incursion of interlopers into mathematics than we have seen now.
From my long years of experience, this type of thinking is the culmination of gaining computational prowess. After all, are we all not worried by the Singularity? Supposedly, in some minds, tackling things this way will help us compete with computers and stay ahead.
No so. Mathematics (the real one) is peripatetic in nature (some of those who are drugged into submission now could very well be misunderstood geniuses).
Marie, in one sense, mathematics starts with our fingers and markings on what might be a line (however, not conceptually, but rather in the real life of being). Then, objects are the key thing (think sets and then classes). What we call the number lines come much later (remember, it took Russell and Whitehead hundreds of pages to get to proving a simple addition).
The older methods for teaching these simple maths were more intuitive (in the sense of the finger, and toes for that matter). And, many more got through the rigor than we see with the approaches that force feed supposed superior insight.
The kids ought to use operational means and see them work. Then, slowly the abstract can be introduced. Generalizations are best made upon something known. That there is some type of abstraction that teachers can claim has support, that support did not drop out of heaven. Rather, years of work went into the framework.
Given that this teaching method is new to me, I’ll look at the Common Core site and see what’s up. This introduction, though, is not encouraging as the world-class idiots (who, many time, could handle the above tedium) have over-laid us with an insidious entrapment that will cause hell on earth (even worse than we have seen so far). For some reason, I never suspected the teaching community as being meant to perpetuate such an infernal viewpoint.
03/23/2014 -- Turns out that there was a story involved and that it was written.
03/27/2014 -- Based upon other examples that I've seen (say, friendly numbers), this whole thing aligns with my complaints about the misuse of mathematics. It has not been shown that mathematics is the way of truth (despite its operational successes), necessarily. As we know, numbers can be manipulated via interpretation (that is the human lot). To impose on young minds, the methods, etc., of elders, in the case of rules of thumb, is onerous. We need to bring out the "universals" to teach. Let the youngsters then discover their own approaches. What? Yes, look, mathematics came up with path independence in one area. There is a generalization of this. If the student gets the right answer, and the teacher cannot follow their thinking, blame the teacher (ala Galois' story).