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My observation is that, where students really fall down, is when algebra hits. When I was in school, 7th & 8th grade ease you into working with "x" - type equations, and that's when people start to struggle. If that isn't taught well, 9th grade algebra is a lost cause. After I worked hours every night on algebra homework, only to get a hard-won C grade, I found out that I'd gotten the highest grade in algebra of anyone in my family, including my parents! Crazy. I aced geometry, though.
So IDK, but there seems to be a problem with the way algebra is taught, and how it's prepared for in earlier grades. One poster said, that in Russia, they're already formulating basic math functions as "x" equations in 3rd grade. That would probably help. I remember the whole "x" thing coming out of left field as a totally new concept that had to be explained, in 7th grade. It's a difficult transition for many students, to start thinking in those terms, suddenly, at 12 years of age.
I tutor students from four school districts and a couple of private schools. Although Algebra I is where kids and parents tend to realize there is a problem, the problem has been going on for years. I have ninth graders - algebra students - come to me not knowing how to divide without a calculator. They have not memorized the basic multiplication facts. They add and subtract on their fingers. And they haven't always mastered the traditional multiplication and subtraction algorithms. They struggle with basic word problems and have very little grasp of percent and proportion. The parents and teachers might think that "x" is the problem, but it is deeper than that.
I tutor students from four school districts and a couple of private schools. Although Algebra I is where kids and parents tend to realize there is a problem, the problem has been going on for years. I have ninth graders - algebra students - come to me not knowing how to divide without a calculator. They have not memorized the basic multiplication facts. They add and subtract on their fingers. And they haven't always mastered the traditional multiplication and subtraction algorithms. They struggle with basic word problems and have very little grasp of percent and proportion. The parents and teachers might think that "x" is the problem, but it is deeper than that.
When I was in school, kids weren't dependent on calculators, and knew how to divide, and had memorized the multiplication tables. Most students had a challenging adjustment to working with "x" and other pre-algebra concepts in 7th grade, though, and 9th-grade Algebra was agony!
Speaking personally, you may have a point, though, in that I never mastered calculating percents. Even after getting a tutor to review it all after 6th grade, I didn't retain it. (I could use your services even now, as a middle-aged adult. ). I still think it's a good idea to start working with "x" in grade school. Students will be used to it, by the time they have to learn more complex equations in middle school. There may be other issues as well, as you say, but at least they'll be comfortable with "x", and will have a facility for it to a certain point, by 7th grade.
My son who just started college figured out a way to complete calculus problems much faster than the way they were being taught. He had the correct answers, but be got marked wrong (0), because he did not do ti the tong overly complicated way that often resulted in incorrect answers because it was so complex. If he did it the long complex way and got a wrong answer he would get a better grade than if he did it efficiently and got the right answer. He had the final victory though when he got a 4/5 (or something like that) on the Calc AP test and the teacher had to give him an A in the class.
Making things more efficient might work in some cases, but it might fail in others. So, it depends on whether it's just another way to solve the problem, or a shortcut. Very rarely do students just come up with a new "shortcut" that can be rigorously proven; though it does happen, look up the Three Radii Theorem. Anyways, I'd say it's really harsh if it's just a different way of solving the problem. The Russians have a different method for finding the determinant of a 3x3 matrix. It may be more somewhat less complex than the American way, but it's not a shortcut, just a different way to do it. So I'd say it depends on what he's doing.
I also struggled through calculus, so I can understand.
Nobody holds your hand like American schools/ Education Systems. Education elsewhere especially eastward is do or die. Education in America is ‘Dont worry honey, you can try again next year’..... all the way through college. Very forgiving, maybe too forgiving given the skills people lack in college.
There were moments where i really hated school growing up (Memorizing Multiplication tables to 12 in 3rd grade comes to mind) but I’m so grateful for the type of education i got now.(Not Russian, but similar in tone, application and intent)
But thats not to say it didn’t have its own problems.
I actually prefer the longer explanations in American books, it leads to a more deeper understand. So, in that case hand holding is actually good.
The American education system is a somewhat different issue.
Making things more efficient might work in some cases, but it might fail in others. So, it depends on whether it's just another way to solve the problem, or a shortcut. Very rarely do students just come up with a new "shortcut" that can be rigorously proven; though it does happen, look up the Three Radii Theorem. Anyways, I'd say it's really harsh if it's just a different way of solving the problem. The Russians have a different method for finding the determinant of a 3x3 matrix. It may be more somewhat less complex than the American way, but it's not a shortcut, just a different way to do it. So I'd say it depends on what he's doing.
I also struggled through calculus, so I can understand.
I do not think it was a shortcut and not something new, just a more efficient way. He said it was obvious. I thing we teach a less efficient way to get the answer so each step is clearly visible and easily understood. He basically said you do nto need all those steps, the answer is right here. I do no tthink he was the only one doing the problems more efficiently. He is extremely bright in all areas, but not a math genius
I never had much math so I do not know. He is also done with math as he placed out of all of his math classes in college. Kind of too bad, but I can hardly chastise him for not taking any more math as I took philosophy classes to avoid math..
I do not think it was a shortcut and not something new, just a more efficient way. He said it was obvious. I thing we teach a less efficient way to get the answer so each step is clearly visible and easily understood. He basically said you do nto need all those steps, the answer is right here. I do no tthink he was the only one doing the problems more efficiently. He is extremely bright in all areas, but not a math genius
I never had much math so I do not know. He is also done with math as he placed out of all of his math classes in college. Kind of too bad, but I can hardly chastise him for not taking any more math as I took philosophy classes to avoid math..
One big thing with math is learning the process on simple problems so you know how to do it with complex ones. Could well be his professor is trying to teach a process that can be generalized and by "being more efficient" he isn't learning the process.
This sounds reasonable, but I'm a child of a time when we did memorize everything, and Americans were still notoriously bad at math. So it must be something other than memorization, although that would certainly help. Could it be that American schools waste a lot of time during the day on unimportant things and don't spend enough time on math? My child spends maybe 45 minutes a day on math in his 5th grade classroom, and I know I probably spent less. But I remember lots of cutting and pasting and social studies and "library time" and music class and art class - not to mention the 10 minutes it took, 3 or 4 times a day, for everyone to line up to walk down the hall. Or is it that there is little extra help available for kids who don't get it? Are classes here bigger?
I'm going to postulate something that I know will be controversial, but needs to be discussed:
American students have a hard time with math because American teachers are themselves afraid of math. They pass this fear on to the children so by the time they get to middle school, they're convinced that math is this enormous obstacle they can't overcome. They expect to be bad at math so they don't try. Then they get to college and what do they take? Science or engineering? Nope, too much math. So what they can take that has the least amount of hard courses? Education. They become teachers and perpetuate the circle.
And you're right about the time spent in other work. STEM -- Science, Technology, Engineering, and Mathematics, was coined to reflect the need for more students to study those courses. So what have schools done with it? Turned it into STREAM so they don't have to focus on those dreaded "hard" subject. Why don't they just call it "school?"
I do not think it was a shortcut and not something new, just a more efficient way. He said it was obvious. I thing we teach a less efficient way to get the answer so each step is clearly visible and easily understood. He basically said you do nto need all those steps, the answer is right here. I do no tthink he was the only one doing the problems more efficiently. He is extremely bright in all areas, but not a math genius
.
It sounds like, the way they taught him in school had extra steps, in order to teach logic, so the kids would understand the concepts and process. But once you understand, you don't need all the baby steps. And you say, that in college, he's being graded down, because he's not including the baby steps? Did I understand that right?
This sounds reasonable, but I'm a child of a time when we did memorize everything, and Americans were still notoriously bad at math. So it must be something other than memorization, although that would certainly help. Could it be that American schools waste a lot of time during the day on unimportant things and don't spend enough time on math? My child spends maybe 45 minutes a day on math in his 5th grade classroom, and I know I probably spent less. But I remember lots of cutting and pasting and social studies and "library time" and music class and art class - not to mention the 10 minutes it took, 3 or 4 times a day, for everyone to line up to walk down the hall. Or is it that there is little extra help available for kids who don't get it? Are classes here bigger?
Are you saying, you don't think 45 minutes, which is one class hour, per day is not enough? How much time do you want them to spend on math? A class hour/day is plenty. The question is: what methods are being used to teach it? Is your child learning the math, and building competency? That's all that matters. My schools didn't have cutting and pasting beyond about 2nd grade, nor was there "library time".
One class hour per subject should be enough for any subject, including social studies, which is often about the history of civilizations, or contemporary political affairs, or a semester dedicated to studying Latin America, or whatever. It's an important topic.
I agree that art class is a waste of time, the way it's done in the US, because it doesn't teach skills and concepts. It's just more or less free-drawing time, or art-project time. There's no structured curriculum to build skills, scheduled by age-appropriateness (brain development), like there is in Europe. Kids who can't draw never learn to draw, they just get bad grades for years, so in that sense, it's waste. But making kids sit through an extra hour of math instead, isn't going to address the problem with math instruction.
I'm going to postulate something that I know will be controversial, but needs to be discussed:
American students have a hard time with math because American teachers are themselves afraid of math. They pass this fear on to the children so by the time they get to middle school, they're convinced that math is this enormous obstacle they can't overcome. They expect to be bad at math so they don't try. Then they get to college and what do they take? Science or engineering? Nope, too much math. So what they can take that has the least amount of hard courses? Education. They become teachers and perpetuate the circle.
And you're right about the time spent in other work. STEM -- Science, Technology, Engineering, and Mathematics, was coined to reflect the need for more students to study those courses. So what have schools done with it? Turned it into STREAM so they don't have to focus on those dreaded "hard" subject. Why don't they just call it "school?"
I never liked math until I came to university. Most of my teaching assistants were from China, Vietnam, India, etc. They were all brilliant, and their depth of knowledge really gave me a deeper understanding. Maybe it's the difference between being taught by a PHD student and some with a high school teacher with a bachelors.
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). I still think it's a good idea to start working with "x" in grade school. Students will be used to it, by the time they have to learn more complex equations in middle school. There may be other issues as well, as you say, but at least they'll be comfortable with "x", and will have a facility for it to a certain point, by 7th grade.
