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Thursday, July 24. 2014
A few reasons. First, my younger son loves sports and sports analysis. Statistics were something he followed from an early age. My older son did not. Secondly, my older son had different teachers and slightly different math programs. These programs mimicked the comedian's schtick:
I had an extremely difficult time helping him learn his math based on the program offered by his school. I was unable to learn the principles they were making him learn, how could I provide any assistance?
My younger son's experience, on the other hand, engaged a teaching method similar to that mentioned in the first four paragraphs of the article. He was using life experience and discussion with friends to learn the basics. The math program he was taught was significantly different from his brother's, the methods similar to those I from which I learned (I know the way I learned math was different from public school kids - my Catholic school was outperforming other local schools on standardized tests for years).
Ultimately, it's important to realize math is the basis of logic and reason. A deficiency in math skills may go a long way to explaining why so many Americans think they can get something for nothing from the government. Common Core may have fine intentions, but its implementation is a disaster, and is heavily politicized. It is unlikely to solve the issues it is designed to fix.
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Math is not the basis for logic or reason, in fact you have it backward, logic and reason are the basis for math, or at least two of them
Attempts to reduce logic to pure mathematics have in the end always failed.
Hello chicken, this is an egg.
I won't dispute logic is not purely reducible to math. I think it is improbable to be particularly good at logic and not understand math.
Wake up and smell the coffee.
I blame genetically low IQ blacks and Hispanics. Races are real, and racial differences are real. The US scores low on these international tests because we have many low IQ blacks and Hispanics. Once the test scores are separated out by race, American whites do as well as European whites, and American east Asians do as well as east Asians. Blacks and Hispanics do as their co-races do.
You guys claim to be psychologists. Is that just bullshit?
Low IQ or low-performing? It does not take a high IQ to do algebra.
I'm not a psychologist nor have I made that claim.
I don't agree with your premise, either. But your welcome to think as you see fit.
I'd blame their schools, their teachers, their parents (or lack of), and the inner-city culture.
And maybe that "New Math". I learned the old math, and it's worked for me.
Are you talking about the New Math, the New New Math, the New New New Math, the New New New New Math or the New to the nth Math? Every five years or so there is a new educational fad- not just in math.
BTW, as a student I very much liked the New Math I was exposed to in the 1960s, with two caveats. First, I had a very solid grounding in basic arithmetic operations before I was exposed to New Math. Second: the proofs and such that New Math emphasized were good for the top students, but not so good for the not so good students.
I didn't have new math, just the traditional algebra and geometry, the latter a prove it yourself class in the traditional mode. It was geometry that introduced me to logic and proof, both of which I think are missing from modern math education.
I also spent three days reading through my teacher's notes on set theory from his college course on the topic. That was as close as I got to new math.
You are correct. My children recently took geometry in high school. One of the math teachers specifically told me they no longer do proofs. I was flabbergasted! That was the only part of Geometry I enjoyed (and did very well at). I still am trying to figure out exactly what they teach during Geometry nowadays. It should say something that 3 of my kids HATED Geometry and it was their worst math grade (each had varying skills, but even the one with the best grades tanked in Geometry).
In my state, at least, their whole high school math situation is very confusing. They have Algebra I, Algebra II, Algebra II Honors, Geometry and then other math classes that don't include Trigonometry, so I have no idea what it is called these days. Algebra II and Algebra II Honors are actually separate classes with different goals...but if you finish Algebra II before your senior year, you take Algebra II Honors next. Color me confused. Wish they would just go back to what I knew:
One of the math teachers specifically told me they no longer do proofs. I was flabbergasted! That was the only part of Geometry I enjoyed (and did very well at.
The sequential thinking required for constructing geometric proofs is useful in all disciplines, not just in math. And not just STEM subjects.
Before I was exposed to constructing proofs, I was indifferent to math. After being exposed to constructing proofs I discovered that math could be fun.
Certainly proofs were not unique to New Math. Look at Euclid.
My wife is a very smart lady— a straight A student, gifted, really, in math, science and music. About 15 years ago, a neighbor lady was talking to her about the problems her eighth grader was having with algebra. My wife offered to help the kid, but she was confused by the book they were using and the way they were teaching algebra. It was totally alien to her experience. I feel sorry for the kids who were struggling with it.
Similar experience here. I somehow made it thru StuyHS & Finance, but found myself unable to fully comprehend my youngest child's HS "mathematics" - the text itself was beyond useless. Bought him the "For Dummies" version - now he's in Engineering school...
Americans stink at math because it pleases our lords and masters that we do ... how else can we be convinced of global warming and the multitude of other frauds being foisted upon us?
From the anecdote:
"Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray. "
I knew Americans were terrible at math, but not on this scale.
I don't know if math is the basis for logic and reason but it is the disciplinarian of them. It is quite easy to reason yourself into a false belief. But not in math, or at least not in the "old" math. Math requires structured organized thought. That unforgiving structure then bleeds over into the softer fields.
As for why Americans stink at math, it is how it is taught or really not taught. Note how many people are learning math, finally, through Khan Academy. Note that Khan Academy doesn't use the stupid methods of the education cartel.
No, I meant that in a technical sense.
Logic, the "science" of correct reasoning (and here science is meant in an older sense), is rather different from the broader "reasoning" you are talking about here, where rhetoric and moral valuations, metaphysics or general philosophic issues and modalities may obtain. These sort of "conclusions" that lead to "beliefs" involve other considerations than formal logic.
Thus, it is not strictly truth that " It is quite easy to reason yourself into a false belief.". In a strictly formal logical sense this is not true at all. Again, logic is not concerned with "beliefs" or even meaning, but with clearly stating and logical proving propositions, etc. Certainly, higher level discussions of ethics or other philosophical issues, or even religious issues employ logic, but other factors come into play as well. The point here is that "logic" in and of itself is unambiguous in these discussions. statements are either logical true or not, and we know why they are so in either case.
This is the problem of conflating the discipline of "logic" with the colloquial notion of its application. When we say "your logic is different than mine", we do not really mean that both "logics" are valid from a formal point of view, because they cannot be fi they reach radically differnt conclusions. What we mean is the other factors come into play, such as assumptions about values, tactic assumptions, rhetorical approaches (false metaphors, etc), and etc. This is something we run into all the time in politics, for example.
Likewise, it is quite possible to develop mathematical systems that have nothing whatsoever to do with "reality", and yet they are quite mathematical valid. Moreover, it possible to use math is such a way to confound the "mathematical logic" under consideration with the conclusions. In both of these cases, Statistics, and all the scientism and pseudo-science that can crop up around it, comes to mind.
So it is quite possible to "reach" false beliefs "employing mathematical logic" in a practical sense, if you are willing to be a sloppy about what "mathematical logic" actually is. We see this all the time in the "soft sciences" such as Political science, Sociology of Psychology.
Beyond that, when i said that attempts to make logic as subset of mathematics--the idea that math is the root of logic--I again meant this is a formal, technical sense. I was talking about people like whitehead, or, in other areas, people like Quine or Wittgenstein--and then there is always Godel.
None of these attempts is a formal sense were successful, and for various reasons.
Of course, there is a lot of debate about this, particularly in the area of proofs, but I would say from a formal POV, mathematics uses a subset of logic, which is reasonable given that it is dealing with a smaller "solution space" if you will.
In my mind this why attempts as "computational logic" (which is an attempt to automate formal logic)so often fall short. We can come up with systems that are reasonable in lower order logic, but as we add higher levels, these systems fall apart.
This may seem like nitpicking but it is not really any such thing. We need to be clear about what we mean.
Common Core is neither well intended, nor well conceived to provide a rigorous education. Genuine accomplishment by the majority of students is not what it is intended to do.
Learning to use math in everyday life is a great treat compared with sitting and reading formulas, or going to the blackboard to demonstrate your incompetence. HOWEVER, there are very, very few teachers who are able to manage an engaging curriculum of mathematics. I was fortunate to have found two late in life and they were a blessing. Prior to that I had had my share of miserable math teachers.
Americans don't do well at math because it often is taught poorly, even at the grade school level, and at higher grades the teachers (being often unionized education majors with little real world experience in how higher mathematics is used) aren't able to bridge the expectation gap of poorly prepared students. Mathematics is one of the pillars of a real education ... which gets short shrift by schools and the education industry in favor of social engineering.
Math is unlike many other subjects, because you can't bullshit your way through it. It has hard, discrete, concrete answers. You either got it, or you failed to get it. It is less susceptible to manipulation in the evaluation phase than any other subject. This isn't a skill the modern education estate or our ruler-elites value or want passed along, particularly to the rank-and-file. They prefer soft slippery subjects where weasel words and turns of phrase will win the day. And they certainly don't want an educated middle class than can reason that they are destroying us economically by critically evaluating the crap information they feed us.
It turns out that one of my daughter's is a math prodigy. She is also musically gifted. Somehow these two things are interconnected, and it's probably not hereditary, or if it is, it skips a generation.
Yes, that link has been identified. It seems that music and math are somehow linked.
Which is why, for right or wrong, all children in our district (and I'm sure many more) MUST take up an instrument in First Grade and play it for 4 years. It is based on a belief that playing an instrument will help with math skills.
Didn't help my first son, but it could be a legitimate belief.
I'm not sure what the link is related to, but it is intriguing. My sister (outlandishly liberal wacko) made all her kids learn an instrument at an early age. One is gifted, all are adept at music. All are also very good at math.
I think the connection is more math languages and physics music. But the categories can be somewhat fuzzy.
Well, I made it mostly through the article which is in a ward: tedious. We do learn
The cognitive-science research suggested a startling cause of Americans’ innumeracy: school.
So they "changed" math. Only to discover the new method is highly dependent upon the "Great Teacher" problem. All in all, most teachers cluster somewhere around the average, not on the Great side.
And surprisingly, the author does point out that the Ph.Ds at the Ed schools, like Ph.Ds in all the "schools" don't like or want to teach how to teach or whatever their subject is. They'd rather teach whatever if their fancy of the semester. All college education goes this way. Teaching undergraduates is tedious but pretending to teach them is the only way the Ph.D can get money so they teach whatever, instead of the basics.
So we have mediocre teachers, untrained in the actual techniques of teaching (but boy, did they get that "understanding"), using poorly conceived and written books to induce a hatred of math in students at an early age. We should also note, these are the geniuses who think that a poor student, especially one who had trouble with math should goi into the skilled trades.
You know, I can't help but see that while the old, terrible, formulaic methods, disliked by the Ph.Ds may have been based on repetition, they weren't depedent up on the "Great Teacher" fallacy. Even the mediocre could teach math.
Just wanted to put in a plug for Singapore Math, if you've got a young person in your ambit. You can get a full set of the materials for under $100 a year, including a guide developed for homeschooling parents (i.e. meant for you to just pick up manual and go with it). It's clear, to the point, and child-focused. They have one version that aligns with common core as well, so you just ignore all in-school teaching and re-do the work with Singapore materials at home. Frustration and stupidity are optional... just opt-out.
As an added bonus, you get to see exactly how much dead space normal school takes up-- it's totally possible to keep up with, or even exceed, the pace of institutional school math courses with only 2-3 hours per week of one-on-one instruction. Go year-round, even better. (Some schools reported gains of 20 percentiles in a single year after introducing Singapore Math.)
I'm so glad homeschooling is getting some traction--there's a huge variety of high-quality material out there for parents (or whoever) to take charge of your young person's education, whether just fixing one problem area or keeping them moving at the speed they're capable of.
Who ever wrote the article either stinks at statistics or intentionally misrepresented the issue. Americans do not "stink at math". What Americans do is count everyone when they create the database of students and results. Do you honestly think China or India count their students who fail out of school or cannot go to school? They only have data for the students who were smart enough to compete for the limited seats in class rooms. If we did the same and only collected the data from our best students we would look like a nation of genuises.