Do the math: too much calculus? (2012)
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Do the math: too much calculus? (2012)
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Re: Do the math: too much calculus? (2012)
#2I think this is just another example of standardized testing (specifically AP course exams in this story) almost creating a niche-like education for students.
Maybe that's an odd way to put it, but some students wind up spending hours and hours studying AP/SAT/ACT/etc.-specific materials (literally 500+ page textbooks for each type of standardized test). Sure this method of studying helps them achieve great scores on the standardized tests, but my impression as a recent student in academia (finishing college now) is that this creates an issue where students are almost "overly" dependent on more specialized areas.
I don't know if it's an issue of not having time to learn "street smarts" (so to speak) because standardized studying takes up all their time, or if it's something else. But there's definitely some improvement that can be made.
Re: Do the math: too much calculus? (2012)
#3>This is not true for students who take Advanced Placement calculus
I hated BC calc. Bad teacher. I learned the same material at the same time in AP Physics, and loved it.
I think a related issue to the author's point, though, is that students are taught in a way that implicitly suggests that calculus is the pinnacle of mathematics. Which is blatantly wrong.
Re: Do the math: too much calculus? (2012)
#4I think this is just another example of standardized testing (specifically AP course exams in this story) almost creating a niche-like education for students. Maybe that's an odd way to put it, but some students wind up spending hours and hours studying AP/SAT/ACT/etc.-specific materials (literally 500+ page textbooks for each type of standardized test). Sure this method of studying helps them achieve great scores on…
A pattern that you see almost everywhere is: imperfect incentives/objectives + strong competition = perverse outcomes
Over the last decades, we're increasingly seeing this in academia (publish or perish), the corporate world (boost the bottom-line at the expense of everything else), politics (win the election even if you have to burn your own party to the ground), and many other walks of life, as the world has gotten more competitive.
To fix this, you can either fix the objective (which may be very difficult), or you can reduce the level of competition.
Re: Do the math: too much calculus? (2012)
#5I think this is just another example of standardized testing (specifically AP course exams in this story) almost creating a niche-like education for students. Maybe that's an odd way to put it, but some students wind up spending hours and hours studying AP/SAT/ACT/etc.-specific materials (literally 500+ page textbooks for each type of standardized test). Sure this method of studying helps them achieve great scores on…
A pattern that you see almost everywhere is: imperfect incentives/objectives + strong competition = perverse outcomes Over the last decades, we're increasingly seeing this in academia (publish or perish), the corporate world (boost the bottom-line at the expense of everything else), politics (win the election even if you have to burn your own party to the ground), and many other walks of life, as the world has gotten…
This also causes some odd results. If the MIT/Caltech/Harvard/etc student bodies are generally less intelligent than you might expect and often boring people.
You see the same thing at most national level high school competitions. The surface details may seem very diverse, but underneath that they tend to have a lot in common.
Re: Do the math: too much calculus? (2012)
#6I think we teach Calculus wrong in a deep fundamental way. We should incorporate more high math concepts earlier into education BUT people are always afraid of anything past 4th grade math!
"A minority of students then wend their way through geometry, trigonometry and, finally, calculus, which is considered the pinnacle of high-school-level math.
But this progression actually “has nothing to do with how people think, how children grow and learn, or how mathematics is built,” says pioneering math educator and curriculum designer Maria Droujkova."
...
"“Calculations kids are forced to do are often so developmentally inappropriate, the experience amounts to torture,” she says. They also miss the essential point—that mathematics is fundamentally about patterns and structures, rather than “little manipulations of numbers,” as she puts it. It’s akin to budding filmmakers learning first about costumes, lighting and other technical aspects, rather than about crafting meaningful stories."
http://www.theatlantic.com/education/archive/2014/03/5-year-...
Why is calculus the pinnacle when I actually feel that pre-calculus would be better students even make it into middle school? These concepts of patterns and structures is the foundation of not only math but also of language and reading.
Re: Do the math: too much calculus? (2012)
#7> Too many students experience a secondary-school calculus course that drills on the techniques and procedure that will enable them to successfully answer standard problems but are never challenged to encounter and understand the conceptual foundations of calculus,” he said.
As I get older I've realized that I learn better when I understand the concepts about things. I then get excited to apply what I've learned into practice.
I think that if I learned about "why calculus", what problems did it solved at the time it came around, and how we use it in practice I would have been able to grok it quicker and deeper. I didn't end up getting above a 3 on the AP calculus exam.
I did however get a 5 on the US government exam. I had a teacher who did a great job throughout the course having us work out essays and testing arguments in class to help solidify our knowledge as opposed to memorizing facts.
Re: Do the math: too much calculus? (2012)
#8>This is not true for students who take Advanced Placement calculus I hated BC calc. Bad teacher. I learned the same material at the same time in AP Physics, and loved it. I think a related issue to the author's point, though, is that students are taught in a way that implicitly suggests that calculus is the pinnacle of mathematics. Which is blatantly wrong.
I have had the pleasure of pushing many female students into taking calculus but my success rate was about 50%. Each one of my children's friends LOVED STEM and were thinking about going into engineering. All of them said that they were the only girl in the class and were intimidated and the other said it was REALLY boring. Calculus should be easily made fun just exploring the actual concepts in real life similar to a good physical science teacher.
Re: Do the math: too much calculus? (2012)
#9I think we teach Calculus wrong in a deep fundamental way. We should incorporate more high math concepts earlier into education BUT people are always afraid of anything past 4th grade math! "A minority of students then wend their way through geometry, trigonometry and, finally, calculus, which is considered the pinnacle of high-school-level math. But this progression actually “has nothing to do with how people think,…
Berkeley EECS grad. I didn't go the device physics route but I used calculus about twice in 4 years except in physics classes.
Re: Do the math: too much calculus? (2012)
#10AP Calculus was the most useful course I took in high school. It was rigorous, and I scored high enough on the exam to get two free college classes and start freshman year at the sophomore level, which left room at the end of my college career for more specialized courses.
There should be some vetting process for the students who want to take AP classes. A lot of the students in my AP Calculus class had no business being there. One guy got a 4 out of 50 on a test once, another guy didn't even take the AP exam, and another guy just put his head down on the desk during the AP exam. But this is really a problem for individual schools and has nothing to do with College Board.