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From the university perspective, it is not particularly helpful for them to know a little engineering at the expense of the math/physics/chemistry they might otherwise take. I feel quite certain that engineering schools are good at taking students with a solid foundation of math and basic physics and getting them to where they need to be in engineering. They are not set up to take students who think they know engineering and remediating the math, physics, etc. that they should have as prerequisites.
I don't teach engineering, but I do teach calculus, and I have a similar problem. I would rather have students who have never heard of a limit or derivative, but can do algebra and trigonometry. The 40% of the class that come in with the backward set of skills (a little calculus, but not enough algebra) really struggle.
This is extremely good to know. I believe it. I'm pretty sure rudbeckia hirta has said the same thing over the years.
oh gosh. Speaking of rudbeckia, I found this terrific post from 2006 while Googling her blog. I should probably print that one out and scotch tape it to my collection of as-yet unused calculus textbooks.
9 comments:
I understand exactly what you are saying...
The problem is that there are still those (http://www.districtadministration.com/pulse/commentpost.aspx?news=no&postid=49557)
that refuse to acknowledge that there is a problem...
How do you teach engineering without maths in the first place anyway?
I guess you could teach the complusion to test everything.
Does it also follow that AP Calculus AB, since it covers fewer topics and presumably in more depth, is usually preferable over AP Calculus BC in high school?
One of the commenters on another thread advised that students NOT test out of college calculus.
If a student is not going to major in science, math or engineering, does it make a difference?
--Does it also follow that AP Calculus AB, since it covers fewer topics and presumably in more depth, is usually preferable over AP Calculus BC in high school?
No, because it cant' be assumed that the topics are covered more in depth at all. The main assumption is that the students are slower, basically, not learning more depth.
--One of the commenters on another thread advised that students NOT test out of college calculus.
I was the first person to say this, and several commenters agreed, and at least one disagreed, yup.
--If a student is not going to major in science, math or engineering, does it make a difference?
It depends. Are you sure they will never ever see any math at all? In the social sciences, they will--econ, psych, poli sci. All of those courses are becoming more and more theoretical, and more and more mathematical. They should take the calc because they'll learn it to the point where they actually get something out of it.
If they intend to be an art historian forever, then I guess testing out is fine. But which of us knows what we'll be later in life? Better to learn what you can to mastery, given the various tradeoffs.
If a student is not going to major in science, math or engineering, does it make a difference?
If they change their minds in the future, it will. Also, as Allison says, maths shows up all over the place.
A sound basis in mathematics equips you to make decisions that balance objectivity and subjectivity, fact vs. emotion. At the most abstract level, that's what a math education gives you.
Math wars are, I think, a battle between two camps; one driven by emotion, the other driven by fact. The heart of the battlefield is the essence of math itself.
On the one hand you have folks who, driven by their desire to have everyone feel good about math, create a non-judgemental tu-tu style environment. This has given us the spiraling curriculum devoid of mastery and books that focus on discovery.
On the other hand you have folks who, driven by their hierarchical logical nature, create a judgemental, mastery based environment. This approach gave us (note the past tense) crisp curriculum and books that focused on repetition and algorithm.
Could it be that both camps are actually suffering from an imbalance in their own natures? And isn't it true that sound teaching actually involves striking some balance between these extremes in the classroom?
If a student is sitting in a college calc course, they didn't perform well on the AP exam because they do not understand the subject in depth.
Many students do very well in AP calculus for many reasons. Two of which cannot be addressed in college. They have an entire year to learn the subject rather than a semester. They have an oppotunity to transition into calculus in a familiar, supportive hs setting.
Personally, I think it's a good idea. I wish that my high school would have offered it years ago.
Students in my Calc II class who had taken AP calc in hs and performed well on their exam seem to have a much better foundation that those of us who had taken it in one semester in college.
"Math wars are, I think, a battle between two camps; one driven by emotion, the other driven by fact."
I see it as a difference between low expectations and high expectations. Nobody claims that Everyday Math is more rigorous or better than Singapore Math. All you have to do is look at the Singapore Math placement tests.
Because of their low expectations, they redefine math as numeracy and assume that most kids can't be expected to reach algebra in 8th grade. They hide their low expectations behind a lot of fancy scientific and pedagogical mumbo-jumbo.
Educators want everyone to see that this is just a difference of opinion between two equals; a diffence between skills and understanding. It is no such thing. They want balance, but this doesn't make any sense when you are talking about low versus high expectations. Balance also doesn't make sense when you redefine math.
"One of the commenters on another thread advised that students NOT test out of college calculus."
This really depends on where you are going to school. If it is a large research university, and you are going to be doing more math then testing out is probably not such a good idea. If you are not going to be taking more math, or you are at a small university (like mine) then testing out is probably a good idea. My comlaints about high school students in calculus were about the ones who did not pass the AP test. A lot of them have had a pre-calculus course that spent too much time on beginning calculus, and not enough time on algebra.
"If a student is not going to major in science, math or engineering, does it make a difference?"
If you're talking about the AP test, maybe it doesn't make a difference. My original post was about being upside down with respect to your college class expectations, and I've noticed that in teaching just college algebra this semester (students who know a little bit of everything, but their foundations are weak and they don't know anything to mastery). What that means where I teach is that if you come in without a solid knowledge of basic algebra, it will probably take you more than one semester to pass off your general education math requirement. (If you're not going to college, then I don't know what matters. Everyone needs to know something, but what that something is varies so much that it seems dangerous to make broad statements about it.)
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