That’s just a matter of the limitations of low-level standardized tests: they are little more than an IQ test by any other name. And though IQ tests do have an important purpose - they are effective at discovering severe limitations in cognitive ability, general or specific - they have a severe weakness in that there is so much you can learn from making students solve basic problems in a short period of time. The long and short of it is that SAT or ACT tests are great for determining a student’s potential to be able to learn higher level math, but not their actual knowledge. The actual knowledge tested on those exams, while in principle going up through algebra 2, is rather sparse and easily learned just to pass the test.
More substantial knowledge can only be obtained through a full class, with all its homeworks, exams, and projects. Perhaps that explains why high school GPA is more predictive of college performance than standardized test scores.
re Neodymium’s point: If the pace of teaching does not outpace the ability of the students to “get” the math, then any pace is okay, and the students may be advantaged by going quite fast. The US pace can create some ego issues for students who are potentially very strong, but who have not had the faster pace or special math courses/camps/online work, etc., when they find themselves surrounded by those who have had such experiences. The non-advantaged US student has to recognize that he/she is at best “untested,” and go from there.
Well you do highlight a few of the important major issues in grade school education.
The first is that there is no strong degree of standardized curriculum - every school system teaches to its own standard, and there are of course those special courses that some have access to, others do not. Though there are plenty of political reasons for it, there are no real valid academic reasons why the students in some schools should have one curriculum, while the students in a different school should have a different one. So students will end up on an unequal footing early on.
The second is that students and their academic ability is not fixed at birth. Yes, there are some students who are “naturally” smarter than others and genetics does have plenty to do with that. But the other issue is that early development also plays a pretty big role in how students turn out. If students are given a poor math education, then chances are they will be poor mathematicians. I know a lot of people who were “bad at math” who had an early instructor who made them change their ways (and often major in math) and I also know that a lot of the reason for the slow teaching in early US math is as a result of risk aversion on the part of parents who themselves are fearful of math, who think the curriculum should be dumbed down further. Perception of ability at an early age does a lot.
For example, look at the common core standards for the first few years of school: http://www.corestandards.org/Math/
A lot of the first few years is far too simplistic to really foster a good proper education. I have seen enough from very young kids to see that they aren’t stupid, and that it seldom takes them three school years to understand how to count to 100, how to understand the difference between a square and a rectangle, and to add and subtract. Most students don’t start to develop a math aversion that early because the pace is far less than that which they are capable of. Multiplication is the first spot where you start to lose people, because that is a significant step up from addition and subtraction in both speed and difficulty, and some children are discouraged by how quickly the difficulty level is ramped up (though they would probably be just fine if they had been used to a faster pace). Then division, exponentiation, more advanced geometry and graphing, algebra, etc., and as the difficulty ramps up so unevenly students start to have trouble as it gets harder and harder rather than just merely more advanced.
When you push students harder in a reasonable fashion, they will generally develop more. Very few students are going to push themselves harder than the standard that is given to them, and if that standard is well below their capabilities, then they will not develop all that much and will just feel that they can coast through on natural ability until it is no longer possible to do so. And the standard as set in the US is just too low to teach young children math at the level that they need to be able to develop as math-friendly students. The constant and annoying jumps in difficulty are discouraging for everyone, and it seems that those who succeed are mostly those who are capable of coasting on their natural ability for longer than most others. Not really the kind of result you would want from a structured and effective math program.
At the college level, it makes more sense to say that some people are better at math, and some worse. And the people that “can’t do calculus” are incapable of doing calculus not because the innate ability doesn’t exist, but because weaknesses in math have built up to such an extent that there is no reasonable way that they could learn what they needed to to catch up to the pace of the calculus class. But by then it’s a bit too late to do anything because it was in grade school that these problems should have been addressed.
It’s not just the students - many math teachers readily embrace those memorization strategies. The “FOIL” method of binomial multiplication is a great example of this; Algebra I teachers almost invariably teach the acronym, leaving teachers in higher-level math classes to break the habit as they explain that “first-outer-inner-last” won’t work for a trinomial.
And I think that’s a problem that extends beyond math. I’m reading a book now that emphasizes the need for problem-solving rather than memorization in organic chemistry. When were afraid of a subject, we have a solution to actually learning it: memorize! But tricks and shortcuts don’t truly solve the issue, they just makes it harder and scarier. The US may produce great critical thinkers, but it’s not because of a superior teaching style.
I’m curious how you would actually measure who has more critical thinkers. Not that critical thinking isn’t important but it seems impossible to measure and compare.
I don’t have access to those articles. By the abstracts they seem to be rather lacking in their conclusions, mostly either just making very nebulous statements or creating a measurement model of their own which is hard to corroborate. And that’s my point: it’s really hard to say one way or the other what is best for fostering “critical thinking” and I don’t think that it’s right to just say that one educational system is better at it than another when it’s hard to define critical thinking success in any well-accepted manner.
I would love to, though I’m not all that inclined to try to get through the paywalls. A summary of what criteria you have for making a judgment one way or the other on who is better or worse at critical thinking would be much appreciated.
Though I didn’t enjoy algebra much as a kid, it does play an important part in your everyday life. Learning algebra helps you to make decisions better.For instance it helps you to decide what car to buy.By drawing up a graph and by weighing the best option you can get the best value out of your money. Finally interest rates, you will have a hard time to choose what company could give you the best if you cannot figure out the graphs and understand the concept of percentage. In order to be safe in this world you need to know your math
Lack of mathematical depth of knowledge indeed has a high social price. The Great Recession of 2008 was caused by predatory sub prime lending enabled by lack of mathematical sophistication on part of the population at large.
OK, Americans, want to return to the level of math that was available to the early agricultural communities, 5,000 years ago and forgo all knowledge that was accumulated later. Geometry that was available to ancient Egyptians, trigonometry, that existed during Columbus times, Calculus that was widely used since Renaissance.
Are we sane even to discuss it? Humans developed math, because they need it. Desperately. Math is the earliest science, that became available to humans. Math is a foundation of everything, I mean, everything that we have today. Do you think you would have internet chat rooms without math? Hollywood movies without computers that operate because of math? What kind of world do you envision, without math? Cave man already knew how to count mammoth in the herds.
Somebody argues to abandon math for the sake of … (what)?
I was offered subprime mortgage and realized the consequences, instantly. It was not a trap. My colleague took a subprime mortgage, that was eating over 60% of his monthly income. However, he did it with a full understanding of consequences. He bought a house, renovated it, flipped it, made money. Subprime mortgages are useful, if you know how to handle them.
The dilution of math curriculum, substitution of real math with something soft, like “financial literacy” will just deepen the social gap. Some people would know, how to make and count money. Others would believe in lotteries / casinos. Wall Street is very mathy.
< Finally interest rates, you will have a hard time to choose what company could give you the best if you cannot figure out the graphs and understand the concept of percentage.>
I suspect the problem was more that people who took out those loans incorrectly assumed they’d always have a job to cover the payments. It wasn’t a problem with understanding math. It was a lack of knowledge about economics and history.
I wouldn’t expect the layman to understand the details of strange financial instruments because they are convoluted by design. An economics approach of, “don’t take strange loans you can’t understand because that rarely ends well” would work better.
The thing is you’ve got to do your research before making any major purchase. That goes beyond math. If you don’t have the ability to figure it out yourself, you find a reliable source to help you out.