What's So Great About Calculus?

Parents Forum
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<p>One of the issues I see a lot, whenever a student is suffering with higher level maths, is "too much, too soon" preparation. A member of my family is currently going through this, taking Algebra in sixth grade. While parents are very pleased, poor kid is getting tutoring, miserable, and losing confidence. If kid ends up with a low A or B in class, he'll be lucky. Where does this put him later on? When he takes Algebra II? When he takes Pre-Calc? Every year will be more difficult than the one before; every year the student will lose a little bit more ground, because the initial foundation was weak to begin with. What is the big hurry?</p>

<p>It used to be that Algebra I was a high school class, taken in 9th grade and followed with Algebra II, Geometry, and PreCalc (including Trig and Advanced Geometry). Only the accelerated kids got through Calc, by taking Algebra I in eighth grade instead of 9th. NOW, 7th or 8th grade is considered the norm for starting Algebra. Are they really getting the foundation? Or, because of the maturity level and experience, is the teacher putting a lot of "fluff" into the grading, such that a B/C student gets A's because of notebook checks, homework credit, extra credit, and projects? </p>

<p>I'm a proponent of strong math foundations. My kids didn't start Algebra until 8th grade, and they did fine. Actually, with very few exceptions, their cohorts that started Algebra earlier ended up washing out of maths and either didn't take Calculus at all (Stats instead), or suffered dearly taking Calculus as juniors. Only the math-gifted students excelled in the accellerated program, but that's to be expected.</p>

<p>As a music teacher, I see the same issues- kids who get propelled through music books that lack a good reading/technical foundation for later studies. They end up washed out when they try to advance into significant musical literature.</p>

<p>Sorry for this behemoth of a post.</p>

62

<p>Most kids I know, (I'm a college sophomore) had Algebra in sixth grade, like I did. No challenge at all, it's simple once you get over your fear of the topic. An open minded 3rd grader could learn it.</p>

<p>Padad,
I agree with you completely about it being a shame that most popular science books are written for the scientifically literate. I guess it's because there aren't enough scientifically literate people for a book written for them to become successful.</p>

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<p>Too much to address for me to get back in the thick of things here but I completely disagree with you doubleplay-- math was much to slow for me and I thnk for many here in this country, and we're getting destroyed overseas because of it.</p>

<p>I wish my math education was at least 1.5x the speed.</p>

64

<p>JHS, another example that I can give you is on probability. Most of us think of probability in terms of counting frquency. Most of us can predict my chance of getting a certain number from a roll of dice, a simple counting problem. Probability becomes a bit more complicated in real life example, where we don't have all the information to do proper counting. For example, if you want to test a new drug, say a new second generation of an existing lung cancer drug. You want to show that it prolongs the survival rate of users from a median time of 12 months to 16 months. So how many patients do you test it on so that you can be somewhat confident, very confident or sure bet. If you are a patient and knowing that the newer drug has a bit more side effect, don't you want to know what all the calculation means? The example here requires a branch of calculus used in Bayesian probability. It is widely used in any probability estimates where frequency cannot be readily predicted.</p>

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<p>Wow, I'm astounded at the cruelty of the statement (a third grader can do it). I guess I run in different circles; I've not known many third graders that can do Algebra, and in my opinion, my nephew who struggles with it in sixth grade is not a dim bulb. </p>

<p>Just like it is arrogant for a philosophist to denigrate an engineer, it is equally arrogant to denigrate a non-mathematical student. Like someone else said, everyone is good at something. And no one is good at everything.</p>

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<p>I didn't mean it be cruel, I'm sorry.</p>

<p>I wasn't trying to imply that your nephew was dim, or even that many third graders can do Algebra, almost none of them can.</p>

<p>But there is a sort of fear of math and science and technology in society that makes it harder to learn these subjects. Kids get the idea that math is supposed to be hard, and so they believe it's hard and make it harder on themselves. It's almost impossible to learn something if you're terrified of it. Same with other sciences and especially something like computer science, even though these subjects are really not that hard and scary and can be taught at a young age.
By third grade, you should have arithmetic down, or at least that's what I remember, and that's more or less all you need to move on to Algebra. But somehow, in American schools they manage to cram three to five more years of math between when kids learn arithmetic and algebra.</p>

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<p>So kay phatalbert. You are, I'm sure, quite good at math in general. It's hard to understand when other people aren't good at things that seem so easy. I go through this all the time with teaching music. </p>

<p>I am also not sure what passes as "algebra". When my kids were in sixth grade, I remember attending the open house and the math teacher telling us the students would be learning algebra. However, this was not really high school/college level beginning algebra class- they were just introduced to some of the concepts of algebra in their accelerated sixth grade math book (titled "pre-algebra"). </p>

<p>I was addressing some of the issues CGM mentioned- her D's having to take two years of Calc. I can only imagine they must have started algebra by 6th or 7th grade if they are taking calc in 11th and 12th (or before).</p>

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<p>In my district, the top 30-40% are in an honors track and complete 7th grade and 8th grade math in one year and are done with algebra before leaving middle school. Ninth grade is geometry, tenth is trig.</p>

<p>That's still slower than most countries in the world and still too slow to be honest. It's not a matter of it being too difficult for kids of a certain age to understand, it's a matter of having elementary school teachers who are actually well prepared to teach math, which is by far the minority of elementary school teachers.</p>

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<p>My son was told he was doing algebra in 4th grade. 3 + x = 7. Is not algebra in my book. Nor is coming up with an addition to a pattern block animal that you will add to by repeating the same pattern of additions.</p>

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<p>Yes, she did have Honors Pre-Calc/Trig last year as a junior and did well. Her teacher recommended AP Calculus for her and it seemed a natural progression. The class she will drop down to is essentially the same class she had previously but is Senior level course Honors rather than a Junior.
I did call a couple of colleges she is interested in for next year and each said the change would not hurt her especially since she is looking at Political Science/English & Literature majors.
Very interesting thread....such passion about the topic.</p>

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<p>Post #68</p>

<p>
[quote]
That's still slower than most countries in the world and still too slow to be honest. It's not a matter of it being too difficult for kids of a certain age to understand, it's a matter of having elementary school teachers who are actually well prepared to teach math, which is by far the minority of elementary school teachers.

[/quote]
</p>

<p>That is not the only problem with teaching math in US schools. There are other related problems:</p>

<ol>
<li><p>The textbooks are too thick. Sixth or seventh graders are scared to death to see an algebra book with more than 500 pages and several drill problems.</p></li>
<li><p>Teaching math by the subject. Asking kids to learn algebra in one year then learn geometry in another year is too much. It’s probably better to have kids learn some algebra and some geometry during the same school year.</p></li>
<li><p>Teaching math by drill or memory instead of teaching problem solving.</p></li>
<li><p>Math is only taught in schools. Parents can help kids familiar with mathematical concepts through life experience or plays before kids start school. Here is an interesting book:</p></li>
</ol>

<p><a href="http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=901%5B/url%5D"&gt;http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=901&lt;/a&gt;&lt;/p>

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<p>I agree coolweather, completely. NYS has done away with "algebra, geometry, trig" and has instead moved to an "A,B" system which teaches all three intertwined as it makes sense to learn them.</p>

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<p>NY found Math A and B such a disaster they are going back to the Algebra 1, Algebra 2, Geometry system.</p>

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<p>What's so great about calculus? It is fascinating, it makes so much sense, it works perfectly, and it so accurately describes so much.</p>

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<p>They're really going back? That's a complete shame and misdiagnosing the problem with NY math...</p>

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<p>Back again, briefly.</p>

<p>Doubleplay, I had the equivalent of Algebra I and Geometry I, mixed together, in 7th and 8th grades, circa 1970. It was completely successful. I am positive that I haven't retained any math I learned after 8th grade. I agree with the others who say we probably go to slow. High school math was completely easy -- constant review, very slow introduction of new concepts, and a bunch of memorization. I could do it without paying much attention.</p>

<p>By the way, I did not find calculus hard. I didn't develop any fabulous respect for engineers by studying it. (Not that I don't respect engineers, but their facility with calculus doesn't enter into it.) It was just math -- a tool you use when you want to do something that I usually didn't care much about doing. It had roughly the same status in my world as high-class gardening equipment did. Appreciating how well it worked didn't give me any desire to use it more.</p>

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<p>I took calculus in college and it was the first time I liked math--you can really DO things with calculus.</p>

<p>30 years later I barely remember any of it, but I find myself groping for the tools that would let me analyze data effectively--and those tools are actually functions which is pre-calculus. I have to go ask one of the 20 something analysts to run my analysis for me. I know what needs to be done; just don't remember a thing about how to do it.</p>

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<p>We have a generation of kids who can't analyze the news- who often just repeat what they hear, but can do "hard math"</p>

<p>Someone said that in order to say, understand bioethics say regarding stem cell research, you need calc...huh?</p>

<p>No, i am not a doctor, and I never studies medicine, but I have a decerning mind</p>

<p>I learned to look at the source of the information I am being given, look at what their agendas are, who funds them, what their religion might bring to the equation, along with the real science involved, which is just as, if not more important for the average person to be able to due, than some math formula</p>

<p>Does Calc teach me how to look at human nature, how to look at the sources of the information...don't think so</p>

<p>SO saying, well, you need calc in order to analyze current social issues is just plain hogwash, and in fact a harmful way to approach the subject</p>

<p>Also, this attitude that doing higher math is somehow one of the most valid ways of decerning thinking skills is also hogwash</p>

<p>My brother in law is highly intelligent, but somehow got through life with no trig</p>

<p>I don't need to know how my engine works exactly in order to drive my car, i do need to know however, when to trust my mechanic and when to be worried</p>

<p>i don't need to know how the airplane lifts off the ground in order to fly</p>

<p>I don't need to know all the formulas in statistics, but I DO need to know what questions were asked, of whom, how they were phrased, when they were asked in order to determine if I should trust the survey </p>

<p>I love math, and am actually very good at it, but I didn't get sucked into this false belief that taking years of Calc is necessary to be a learned, intelligent, visionary, complex thinker.</p>

<p>My oldest D is okay at math, but she can hold her own in any debate, she can see the big and small picture simuletaneously, can analyze situations and data without more than a year of Calc</p>

<p>Her ethics class and US government class will take her further in life than another year of Calc ever would have</p>

79

<p>Let me preface this by saying I plan on becoming a Ph.D. mathematician, and that I love math and do math for fun much more than most other people do their favorite things for fun. Ahem.</p>

<p>I think calculus is overrated. Yes, it's beautiful and useful and certainly necessary for scientists and engineers, for whom it is indispensable. But for the average intellectual, it is not at beneficial as other types of math might be. I believe the reason it is taught as a required math course is that it is deemed easier by most mathematicians. In fact, it is trivially simple once one gets the hang of it. But that's beside the point. Humanities majors do not need to know any calculus.</p>

<p>But I do think that we should make them study math, just like they make us study literature. But then the question arises: what math? Well... I would recommend discrete math. Teach them methods of proof, number theory, some graph theory, discrete probability, automata, logic, etc. These things are much more interesting, IMHO, and are definitely more mind-expanding than mere calculus. Plus, discrete math gives one a much better picture of what mathematics actually is, whereas calculus is usually watered down into a problem-solving course, where you rearrange equations and solve for x. That's no fun. Proving that the square root of two is irrational is much more intellectually stimulating... although it is harder for the average student. Then again, they don't go out of their way to make lit easy on us, do they?</p>

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<p>Wow! A completely new, informed point of view!</p>

<p>Tell me more about this "discrete math" and its mind-expanding qualities.</p>

<p>(I've heard the same thing in an earlier, offline version of this conversation from an acquaintance who is a professor of math education.)</p>