Calc or Stats
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 cjmcjmcjmcjm
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Calc or Stats
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In HS, do you feel calc really deserves its spot as the "top" maths or are there other maths fields that are more relevant to a wellrounded education?
In HS, do you feel calc really deserves its spot as the "top" maths or are there other maths fields that are more relevant to a wellrounded education?
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Re: Calc or Stats
I feel that most of the 'general use' topics in statistics(e.g., identifying common, "lowlevel" fraudulent or misleading uses of statistics) could be effectively taught in a few weeks; after that, there's a quite steep learning curve towards acquiring a "deep" understanding of statistics. As such, it would seem more appropriate to devote a year to teaching calculus, which will be integral to a good deal of work in most STEM fields.
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Re: Calc or Stats
torgos wrote:calculus, which will be integral to a good deal of work in most STEM fields.
I see what you did there.
Why not have both? If you move algebra to 8th grade in place of whatever the hell math is taught in 8th grade now, there is plenty of time to take stats and calc in high school.
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 KestrelLowing
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Re: Calc or Stats
jmorgan3 wrote:torgos wrote:calculus, which will be integral to a good deal of work in most STEM fields.
I see what you did there.
Why not have both? If you move algebra to 8th grade in place of whatever the hell math is taught in 8th grade now, there is plenty of time to take stats and calc in high school.
In my school, you had to take algebra in 7th to get calc and stat in (assuming one math per year).
7th Algebra
8th Geometry
9th Algebra II (works more with functions and such)
10th PreCalc (I've seen this be a trig class, but precalc does include trig)
11th AP Calc
12th AP Stat
Here's the typical schedule:
7th Geometry + etc.
8th Pre Algebra
9th Algebra
10th  Geometry
11th Algebra II
12th PreCalc
The majority of honors students did the first schedule one year back (they took Algebra in 8th) and they either chose AP Stat or AP Calc. I only know of 4 who did the first schedule, although some of them chose to continue onto calc 3 at the community college instead of AP Stat.
Our school was slightly unusual in that we had many AP classes (Calc AB, Calc BC, Physics B, Chemistry, English Lit, English Language, Biology, Statistics, European History, American History). We had more choices than the average school. For schools that aren't so large, it may be saddening that they can't offer Calc and Stat. If I had to choose one though, I'd go with calc. Calc has a much higher probability of replacing classes in college than stat.
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Re: Calc or Stats
jmorgan3 wrote:
Why not have both? If you move algebra to 8th grade in place of whatever the hell math is taught in 8th grade now, there is plenty of time to take stats and calc in high school.
It would certainly be nice to be able to teach both; this may not, however, be feasible. If they have to make a choice between the two, offering calc is probably the better choice. They can also fold the relevant areas of basic statistics/probability theory into other math classes(which they generally do) or some 'field' course for which these tools are relevant much more easily than they can with calculus.
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 ThinkGravyTrain
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Re: Calc or Stats
I guess this is the Americancentric view of the way maths is taught. I don't really know what it's like in other countries but I do know that the majority of students who take maths in the UK as an AS or A2 level do maths with either the applied module of Mechanics or Statistics. I don't recall there being much on probability in the curriculum but I think we did cover the idea of data collection and analysis on a veeeery basic level. We knew means and modes and basic probability but arguably that could all be forgotten and never applied for most people. I remember learning binomial, poisson and normal distributions were actually pretty exciting, especially hypothesis testing. I can see the guys point but at the same time, I remember needing integration for certain probability functions. And lots of other odd bits I learnt in "core maths" coming up in statistics whereas I never needed anything from any other fields to carry on learning calc.
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 katethegreat
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Re: Calc or Stats
I haven't taken Stat yet, but will be next year. I had to study precalc over the summer to take calculus this year (junior year).
While I'm excited about stat, I'm a bit apprehensive because the AP Statistics class does not involve any calculus (and therefore won't count for college credit, same with Physics B, the noncalc physics course). I don't really see the point of studying something when you don't understand the reason behind it.
While I'm excited about stat, I'm a bit apprehensive because the AP Statistics class does not involve any calculus (and therefore won't count for college credit, same with Physics B, the noncalc physics course). I don't really see the point of studying something when you don't understand the reason behind it.
 gmalivuk
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Re: Calc or Stats
This is why I think it's reasonable to prefer calculus as the toplevel high school math course. To have any chance of a deep understanding of probability or statistics or physics or economics or any number of other things, it's necessary to understand calculus.katethegreat wrote:While I'm excited about stat, I'm a bit apprehensive because the AP Statistics class does not involve any calculus (and therefore won't count for college credit, same with Physics B, the noncalc physics course). I don't really see the point of studying something when you don't understand the reason behind it.
On the other hand, for students who *aren't* planning to focus on one of those fields in college, it might indeed make more sense to ensure they have at least a basic understanding of how people will try to lie to them with statistics in their daily lives. That skill is useful for everyone, whereas calc definitely isn't. As such, maybe fold some basic stats into a precalc class, to make sure that everyone who gets to that level or beyond has at least a basic understanding of the subject.
 doogly
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Re: Calc or Stats
Trying to teach a stats course without calc is making me suffer. I so want to say "you do an integral here." These charts with z scores and confidence levels are complete and utter blackboxes that I can barely even hope to have students understand in a meaningful way. Some of em kinda get it. It's not completely awful. But it's absolutely undesirable.
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Re: Calc or Stats
At my high school, you can take AP Statistics senior year instead of AP Calculus or General Calculus. I took both and hate myself for it. AP Calculus is amazing, the teacher is amazing. AP stat is boring, I see why a lot of schools in my area have it as a sophomore class. Even our teacher (who is decent) admits its more of a literature class than a math class. While there are important things that you learn in stat, the class is so elementary, so common sense, that it isn't fun. It doesn't help that all but me and 3 other people are complete mathignoramuses and the teacher teaches to their level. We probably have spent 3.5 months learning or relearning zscores.

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Re: Calc or Stats
I believe that in the battle of the obviously highest maths in HS, Calc and Stats, if you decide which is best to take or hardest or any thing, you will inevitably come to the conclusion that... They are equal in most every way.
Re: Calc or Stats
^ I find that very wrong. Calculus and Statistics are very different. One is math, one isn't. (I'll let you guess which one is which).
 gmalivuk
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Re: Calc or Stats
I can guess which one you think isn't, but the more relevant bit of information conveyed by your post is that you don't know what you're talking about.
Re: Calc or Stats
At least the AP Stat course was not real math. I'm sure that if they taught Statistics differently, like the theory behind it, it would be. But I was told they didn't do that because a deeper understanding on statistics required higher level calculus that you don't get to in high school, so I don't think that counts.
 Internetmeme
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Re: Calc or Stats
I had this conversation with myself this week, and decided to take AP Calc senior year (next year).
I could choose stats, which is easier than calc, and really boost my weighted GPA. But, I'd be bored out of my mind.
I could also choose calc, which is harder, and would only kinda boost my weighted GPA. But, a couple people said a few problems would take a long time.
Both are AP, both can count for college credit.
Calc makes the most sense to take, however, because I'm at the tail end of a Precal course. If I take stats next year, I'll be waiting a whole year (at least) before taking a "real" math class in college. Which means that all the stuff I learned in PreCal would be forgotten more than I would like. Before this PreCal class, the last math class I took was a year before in my Sophomore year, Algebra II. It took me (and the class) a few weeks of review before we got into new stuff.
Plus, it's not looking so hard so far. We're just getting into derivatives right now, and just did a bit on limits. I'm feeling a lot better at taking Calculus.
tl;dr: Calculus is the better choice because it's fresh on your mind in HS. You can always take stats your freshman year of college.
I could choose stats, which is easier than calc, and really boost my weighted GPA. But, I'd be bored out of my mind.
I could also choose calc, which is harder, and would only kinda boost my weighted GPA. But, a couple people said a few problems would take a long time.
Both are AP, both can count for college credit.
Calc makes the most sense to take, however, because I'm at the tail end of a Precal course. If I take stats next year, I'll be waiting a whole year (at least) before taking a "real" math class in college. Which means that all the stuff I learned in PreCal would be forgotten more than I would like. Before this PreCal class, the last math class I took was a year before in my Sophomore year, Algebra II. It took me (and the class) a few weeks of review before we got into new stuff.
Plus, it's not looking so hard so far. We're just getting into derivatives right now, and just did a bit on limits. I'm feeling a lot better at taking Calculus.
tl;dr: Calculus is the better choice because it's fresh on your mind in HS. You can always take stats your freshman year of college.
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Re: Calc or Stats
I took both this year (Calc BC, not AB) on alternating days, and I have the same teacher for each class.
From my viewpoint, calculus is better for someone who likes and is good at math, whereas stats would be better for someone who mostly wants an AP math credit. It seems that stats contains a couple of things that the average nonSTEM person would care about, which is not true for calculus, but as a mathlover I find calculus much more interesting and I'm sure I'll use this stuff in any school career I would want to take.
I'm in an American school, though, where the stats curriculum is much easier than the calc curriculum and doesn't really involve a lot of math. I'm not saying that statistics has no basis in math, but the methods they teach us require mostly calculator manipulation and arithmetic. I thought we were about to get into fun stuff when we started a probability unit, but it doesn't even go indepth enough to get to xchoosey.
From my viewpoint, calculus is better for someone who likes and is good at math, whereas stats would be better for someone who mostly wants an AP math credit. It seems that stats contains a couple of things that the average nonSTEM person would care about, which is not true for calculus, but as a mathlover I find calculus much more interesting and I'm sure I'll use this stuff in any school career I would want to take.
I'm in an American school, though, where the stats curriculum is much easier than the calc curriculum and doesn't really involve a lot of math. I'm not saying that statistics has no basis in math, but the methods they teach us require mostly calculator manipulation and arithmetic. I thought we were about to get into fun stuff when we started a probability unit, but it doesn't even go indepth enough to get to xchoosey.
Re: Calc or Stats
My high school in Israel had an interesting approach to it. I am pretty sure that that was the standard approach in Israeli schools, at least at the time.
In middle school everyone takes the same math classes. When they proceed to HS, the students are divided into groups, depending on how well they did in middle school maths. Those who did well study analytical geometry, calculus, basics of linear algebra, etc.; those who did worse, study a somewhat watereddown version of the same stuff; finally, those who are "mathchallenged" study basic algebra, geometry and... stats. I am not sure how in depth they studied stats, probably just the basics of normal distribution.
In middle school everyone takes the same math classes. When they proceed to HS, the students are divided into groups, depending on how well they did in middle school maths. Those who did well study analytical geometry, calculus, basics of linear algebra, etc.; those who did worse, study a somewhat watereddown version of the same stuff; finally, those who are "mathchallenged" study basic algebra, geometry and... stats. I am not sure how in depth they studied stats, probably just the basics of normal distribution.
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Re: Calc or Stats
As someone who has gone to school in a different country until 7th grade, I can honestly say that the American "approach" to maths isn't the best. Where I came from, I studied up to the equivalent of Algebra II by the 6th grade. When I came here, I had to wait until my junior year of high school to learn any new maths. I pleaded my guidance counselor to allow me to take AP Statistics and AP Calculus in the same year, and he thought I had a weird sense of humour. When he realized I was serious, he told me that there was a "one maths module per year" rule. He then questioned my sanity for wanting to take two "extremely challenging" courses in one year. He then signed me up for AP Statistics based on the logic that most people dread calculus and both courses would "make me want to kill myself."
So I moved on to university without having taken AP Calculus, and took my first calculus module here.
Getting to the point of this story, I honestly do not understand why the word "calculus" springs up such fear and disgust in people's faces. It is simply maths. When anyone asks me what classes I'm taking, they always seem to hate the answer, especially other girls. Everyone seems to think that calculus is the most difficult maths you could ever encounter (which is obviously untrue) and therefore have come to hate / fear it. The future of technology is STEMbased, yet people in this country are still dreading a maths class.
So, to the OP (and anyone else reading), take calculus. Take every chance you get to take any maths courses you can. You will be happy you did. Calculus isn't overly difficult or anything of the sort, don't let its reputation scare you away because most of it isn't true. It is more straightforward than Trigonometry, and less busywork than Algebra II.
So I moved on to university without having taken AP Calculus, and took my first calculus module here.
Getting to the point of this story, I honestly do not understand why the word "calculus" springs up such fear and disgust in people's faces. It is simply maths. When anyone asks me what classes I'm taking, they always seem to hate the answer, especially other girls. Everyone seems to think that calculus is the most difficult maths you could ever encounter (which is obviously untrue) and therefore have come to hate / fear it. The future of technology is STEMbased, yet people in this country are still dreading a maths class.
So, to the OP (and anyone else reading), take calculus. Take every chance you get to take any maths courses you can. You will be happy you did. Calculus isn't overly difficult or anything of the sort, don't let its reputation scare you away because most of it isn't true. It is more straightforward than Trigonometry, and less busywork than Algebra II.
Re: Calc or Stats
Having had the luxury to take both AP Stats and AP BC Calc, I can say both have their merits. Calculus did wonders for my comprehension of physics. Given that I'm majoring in ECS, it's something that I'll need to know. As a class, I found calculus to be more rigorous (although this is probably set entirely by the AP curriculum. I have a friend who was taking graduate level statistics courses  those were scary!)
Statistics, on the other hand, is probably a lot more useful on a regular basis. I came to appreciate random sampling, margin of error, what all of that polling nonsense means, etc, etc.
Perhaps the main difference is the thought process the courses promote (at least, did for me):
Calculus: That's an interesting problem. How do I solve it?
Statistics: That's an interesting result. How do I explain it?
The particular kind of reasoning we as a society want to promote, of course, is up for debate.
Statistics, on the other hand, is probably a lot more useful on a regular basis. I came to appreciate random sampling, margin of error, what all of that polling nonsense means, etc, etc.
Perhaps the main difference is the thought process the courses promote (at least, did for me):
Calculus: That's an interesting problem. How do I solve it?
Statistics: That's an interesting result. How do I explain it?
The particular kind of reasoning we as a society want to promote, of course, is up for debate.

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Re: Calc or Stats
At my school in NZ we have a more generalised system up until year 13 (final year of school, not sure what you'd call it). In years 911 we learn Algebra, Geometry, Graphs etc., and in year 12 we have 5 exam papers, which are Algebra, Calc (basic differentiation and integration), 'nonlinear curves', coordinate geometry and Trig (more graphs than triangles). Then in year 13 you can take Calc, Stats or both. I took Calc, which also includes things like complex numbers, conics and trig identities. Apparently the first day of Calc is harder than the Stats exam.
Re: Calc or Stats
I think Calc or Stats is a false dichotomy; there's many other options that would make sense. For example, further algebra (say, field theory and group theory) , number theory , etc.
Sure, one might argue that those are less practical (and is that really true? Nowadays, fields and groups + number theory are used for so much in, say, computer programming see cryptography or general number field sieve , for example), but statistics is not much more 'useful' to 'the average Joe' (and in higherlevel math, should we be making sure the 'average Joe' can 'use it in his daily life'? I say no; it's nice if he can use it, but not necessary.) , especially calcfree statistics. Sure, it's best that people understand how people fudge statistics, but that takes a day or two, not a course....
Sure, one might argue that those are less practical (and is that really true? Nowadays, fields and groups + number theory are used for so much in, say, computer programming see cryptography or general number field sieve , for example), but statistics is not much more 'useful' to 'the average Joe' (and in higherlevel math, should we be making sure the 'average Joe' can 'use it in his daily life'? I say no; it's nice if he can use it, but not necessary.) , especially calcfree statistics. Sure, it's best that people understand how people fudge statistics, but that takes a day or two, not a course....
 doogly
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Re: Calc or Stats
I think you are missing a lot.
Firstly, this question is about which AP course to take. These exist only in calc and stats. So the dichotomy is real. If this were a "design the best curriculum" then it might not be a dichotomy, but in a "what should do I take next year" thread, it's a real thing.
Probability and statistics are also used in CS at least as much as algebra, and are also essential in every field that gathers data. Which is quite near all of them.
Firstly, this question is about which AP course to take. These exist only in calc and stats. So the dichotomy is real. If this were a "design the best curriculum" then it might not be a dichotomy, but in a "what should do I take next year" thread, it's a real thing.
Probability and statistics are also used in CS at least as much as algebra, and are also essential in every field that gathers data. Which is quite near all of them.
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Re: Calc or Stats
cjmcjmcjmcjm wrote:http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education.html?awesm=on.ted.com_1G
In HS, do you feel calc really deserves its spot as the "top" maths or are there other maths fields that are more relevant to a wellrounded education?
Is the top question, is it not? That says nothing about AP.
Re: Calc or Stats
gmalivuk wrote:This is why I think it's reasonable to prefer calculus as the toplevel high school math course. To have any chance of a deep understanding of probability or statistics or physics or economics or any number of other things, it's necessary to understand calculus.katethegreat wrote:While I'm excited about stat, I'm a bit apprehensive because the AP Statistics class does not involve any calculus (and therefore won't count for college credit, same with Physics B, the noncalc physics course). I don't really see the point of studying something when you don't understand the reason behind it.
On the other hand, for students who *aren't* planning to focus on one of those fields in college, it might indeed make more sense to ensure they have at least a basic understanding of how people will try to lie to them with statistics in their daily lives. That skill is useful for everyone, whereas calc definitely isn't. As such, maybe fold some basic stats into a precalc class, to make sure that everyone who gets to that level or beyond has at least a basic understanding of the subject.
Would it be possible to roll some basic statistics into the probability section of algebra I or II? I've taken the AP class, and the very basic things (what is standard deviation, the difference between mean and median in statistical context, probability in a statistical context, some basics of experimental design, probably forgetting something but hey I just woke up, and a little bit of statistical significance) did not require more than a good understanding of algebra and a graphing calculator. It wasn't until the second half of the year that we got into some of the things that required precalculus levels of math. Most of the first month of class was focused on learning how to interpreting data, rather than math.
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 TheDancingFox
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Re: Calc or Stats
Both important, but it depends on what you're doing. Honestly, if you're ever going to do any hard science later, you'll presumably need both, but you'll definitely need Calculus. And even if you aren't planning on doing any advanced math or science related challenge after high school (Something that probably doesn't apply to most here!) then statistics is going to come in handy now and again anyway, so it's still worthwhile.
At my middle / high school the standard setup was
7th: Prealgebra
8th: Algebra 1
9th: Geometry
10th: Algebra 2
11th: Math Analysis (which I think was like precalc / trig? I forget)
12th: Calculus / AP Calculus, or Statistics / AP Statistics.
Of course you could stop after like Algebra 2 or maybe even Geometry and still graduate, but that was the full length of it. I ended up skipping prealgebra, and so in 12th grade after finishing AP Calc I opted, instead of taking statistics, to take the next math class up at UC Berkeley which was right next to my school. I could've taken AP Stat, but I figured if I wanted to learn real statistics, I'd do it in a college stats class, where I'd learn it properly. And I plan to!
At my middle / high school the standard setup was
7th: Prealgebra
8th: Algebra 1
9th: Geometry
10th: Algebra 2
11th: Math Analysis (which I think was like precalc / trig? I forget)
12th: Calculus / AP Calculus, or Statistics / AP Statistics.
Of course you could stop after like Algebra 2 or maybe even Geometry and still graduate, but that was the full length of it. I ended up skipping prealgebra, and so in 12th grade after finishing AP Calc I opted, instead of taking statistics, to take the next math class up at UC Berkeley which was right next to my school. I could've taken AP Stat, but I figured if I wanted to learn real statistics, I'd do it in a college stats class, where I'd learn it properly. And I plan to!
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