Article: Rush to Calculus is Bad for Students and their Futures in STEM

[MarkT]

http://www.scientificcomputing.com/articles/2015/11/rush-calculus-bad-students-and-their-futures-stem

 

sent to me by my DS 15 !

 

This topic has been discussed before.

 

 

[Serenade]

Thanks for posting this.  I'm going to share it with my husband (an old school EE) who thinks it's nuts the way calculus is pushed on high school students today.

[Arcadia]

Mark,

 

I think it would be good to send to your DS15

 

Regentrude's reply to your thread

http://forums.welltrainedmind.com/topic/581316-stem-precalculus-or-college-algebra-dual-enrollment-considerations/?do=findComment&comment=6753751

 

and this thread if he is interested in engineering as a potential career choice

http://forums.welltrainedmind.com/topic/581065-if-your-child-was-planning-career-in-chemical-engineering-or-electrical-engineering/

 

From reading the AP Report to Nation for my state and for Calculus, my opinion is that those taking AP Calc AB were likely rushed while those taking AP Calc BC were ready for it.

 

Looking at my own district's past results for algebra 1, geometry and algebra 2 state testing, the accelerated track pulled in much better results a grade younger.

 

What is probably needed is multiple math tracks instead of one or two tracks in public school. As a homeschooler, you can set the pace of a subject to the pace your son can cope with.

[Brad S]

Mark,

 

I think it would be good to send to your DS15

 

Regentrude's reply to your thread

http://forums.welltrainedmind.com/topic/581316-stem-precalculus-or-college-algebra-dual-enrollment-considerations/?do=findComment&comment=6753751

...

 

From reading the AP Report to Nation for my state and for Calculus, my opinion is that those taking AP Calc AB were likely rushed while those taking AP Calc BC were ready for it.

 

Looking at my own district's past results for algebra 1, geometry and algebra 2 state testing, the accelerated track pulled in much better results a grade younger.

 

What is probably needed is multiple math tracks instead of one or two tracks in public school. As a homeschooler, you can set the pace of a subject to the pace your son can cope with.

 

Regentrude's comments are very important for context.  My observations are also similar to Arcadia's.

 

 

[MarkT]

1) From reading the AP Report to Nation for my state and for Calculus, my opinion is that those taking AP Calc AB were likely rushed while those taking AP Calc BC were ready for it.

 

2) Looking at my own district's past results for algebra 1, geometry and algebra 2 state testing, the accelerated track pulled in much better results a grade younger.

 

3) What is probably needed is multiple math tracks instead of one or two tracks in public school. As a homeschooler, you can set the pace of a subject to the pace your son can cope with.

1) I looked at the Calc AB versus Calc BC distributions - wow 31% of AB takers got a 1.  That is sad.

 

2) My DS goes to a public charter - they accelerated him into Algebra 1 in 7th grade - I would have preferred an Honors Prealgebra such as AoPS at the time.

    His Geometry class back in 8th grade was comprehensive but not that challenging and he is now worried about that. I had only supplemented him with Algebra, Trig and some Stats.  He kicked butt on the AZ Algebra 2 EOC exam last year in 9th.

 

3) We supplement at home.  We did part of the Great Courses The Art of Problem Solving with Zeitz over Xmas break. Back to school this week.

 

 I love the info I get from the hive.  

 

I was proud that DS15 was even reading stuff like that and thinking about. He certainly is maturing. 

[LisaKinVA]

I'm assuming this means nothing if kids aren't being "rushed." ;)

 

The other question is...Am I reading this correctly?  A student can SKIP Calculus AB and just do BC?  Is that correct?

 

DD (starting 9th grade next fall) IS slotted for Precalculus.  However, she has completed through Algebra 2 (using Foesters, Life of Fred and parts of AoPS), LoF Trigonomentry and AoPS Counting & Probability and Number Theory (intro books).  She'll be working through AP Statistics through the summer, as well as reviewing Algebra 2 in preparation.  I honestly don't know where to go at this point OTHER than precalculus.  She'll have to review math prior to the PSAT her junior year.  I am planning for her to take Precalculus at the DoDEA school.

 

DS (starting 11th grade next fall) is completing a full College Algebra course and a full Trigonometry course before starting Calculus.  I'm trying to figure out placement (AB or BC).  He will also be doing Statistics over the summer.  I was planning for him to take Calculus at the school as well.  Although, I could swap that for AP Comp or AP English Literature.

 

The plan is for her to complete 4 years of math in high school -- BUT -- we do not have local colleges or DE available that would go beyond Calculus BC.  We do not anticipate moving back state side until at least June 2019 at this point.  I do know that Dana Mosely has offered to take DD through Calculus 3, though...should she NOT do this?  She is very gifted in math, and far exceeded my expectations for her.

 

She does NOT want to graduate early, either.  None of my kids do :D  I see no rush.  Especially if they have things they enjoy exploring and doing!  

[flyingiguana]

I think doing calc twice (like the way our system does algebra twice or more) can be a really good thing.  So doing calc in high school for advanced students might even be something to strive for, but with the understanding that the student is going to do it again in college. 

 

There is a big benefit, (I've found with my kids and myself) to just doing it all over again in college.  The 2nd time around, the concepts are just a whole lot clearer, since you're no longer struggling to get down the mechanics.  I've got one kid who only did it once  -- starting with calc BC and then going right into calc 3 in college.  I've never been sure that she's had the concepts down as well as my "slower" kid who did calc in high school but didn't study hard enough to take the AP test and had to do it all over again when she got to college.  The repetition seemed very helpful.  Both these kids would have been in the math-gifted group if they were in regular high school, so they weren't rushed into calc at all.  That's just the pace they were moving at.

 

I've heard similar things from my boss and his three kids, some of whom were in enrichment programs that put them through even higher math before they got to college.  It didn't necessarily stick as well when done earlier.  And once you have the calc/diff eq credits, you're not likely to go back and do those classes over again.  His most gifted son was kind of at a disadvantage later on in college because of this.

 

I think many schools are pushing calc so they can get more kids taking more AP tests.  This pushes them up in the rankings.  What score the kids get on those tests doesn't count in the rankings.  There's also just a feel-good thing about having more kids in more advanced math.  Parents just *think* it means their kids are getting a better education.

[regentrude]

The other question is...Am I reading this correctly?  A student can SKIP Calculus AB and just do BC?  Is that correct? 

 

Yes. Calculus BC contains all the material of AB.

 

From the College Board website:

 

 

 

The difference between AP Calculus AB and BC is one of scope, not level of difficulty. AP Calculus AB includes techniques and applications of the derivative, the definite integral, and the Fundamental Theorem of Calculus. It is equivalent to at least a semester of calculus at most colleges and universities.

 

AP Calculus BC includes all topics in AP Calculus AB, as well as additional topics, such as differential and integral calculus (including parametric, polar, and vector functions) and series. It is equivalent to at least one year of calculus at most colleges and universities. AP Calculus BC is an extension of AP Calculus AB, and each course is challenging and demanding and requires a similar depth of understanding of topics.

[MarkT]

 

 

1) The other question is...Am I reading this correctly?  A student can SKIP Calculus AB and just do BC?  Is that correct?

 

2) DD (starting 9th grade next fall) IS slotted for Precalculus.  However, she has completed through Algebra 2 (using Foesters, Life of Fred and parts of AoPS), LoF Trigonomentry and AoPS Counting & Probability and Number Theory (intro books).  She'll be working through AP Statistics through the summer, as well as reviewing Algebra 2 in preparation.  I honestly don't know where to go at this point OTHER than precalculus.  She'll have to review math prior to the PSAT her junior year.  I am planning for her to take Precalculus at the DoDEA school.

 

3) DS (starting 11th grade next fall) is completing a full College Algebra course and a full Trigonometry course before starting Calculus.  I'm trying to figure out placement (AB or BC).  He will also be doing Statistics over the summer.  I was planning for him to take Calculus at the school as well.  Although, I could swap that for AP Comp or AP English Literature.

 

2b) The plan is for her to complete 4 years of math in high school -- BUT -- we do not have local colleges or DE available that would go beyond Calculus BC.  We do not anticipate moving back state side until at least June 2019 at this point.  I do know that Dana Mosely has offered to take DD through Calculus 3, though...should she NOT do this?  She is very gifted in math, and far exceeded my expectations for her.

 

 

1)  Yes you certainly can if you cover all the topics.  We are not rushing this taking AB first.

2 + 2b)  A good Precalculus is the right choice. You may need to supplement if the DoDEA is not honors level. My DS also completed Alg 2 in 9th grade. I would not do Calc 3 in HS IMHO.  Try Discrete Math or Linear Algebra.

3)  Sounds good to me.

[Arcadia]

3) We supplement at home. We did part of the Great Courses The Art of Problem Solving with Zeitz over Xmas break. Back to school this week.

Has he tried AMC10 or AMC12? The event is in February. If his school doesn't host, he can register at another site that host.

 

The keyword is "Rush". Anything that is a rush job is bad whether it is an academic subject, sports, construction etc. Schools are unfortunately a lock step system and customization within a class is hard.

 

My parents paid for a math tutor for me because school maths was too slow. I appreciated that.

[Lanny]

Thanks for posting this.  I'm going to share it with my husband (an old school EE) who thinks it's nuts the way calculus is pushed on high school students today.

 

Your DH is correct IMO.  Best for STEM students to take Calculus in the university they enroll in, not in High School or Community College.

[Lanny]

http://www.scientificcomputing.com/articles/2015/11/rush-calculus-bad-students-and-their-futures-stem

 

sent to me by my DS 15 !

 

This topic has been discussed before.

 

 

 

Mark thank you for posting that.   Dead on...   I am going to send that URL in an email to my DD.   I believe STEM students should take things that are foundations for their majors in the university they enroll in, not in High School or a Community College.    

[Arcadia]

Best for STEM students to take Calculus in the university they enroll in, not in High School or Community College.

Best for kids to have their first round of calculus in high school if they are ready for it. Just treat it as prep work.

[dereksurfs]

This article is a good example of the principle that 'correlation does not imply causation.'  Too many mental leaps were made in response to the study referenced.

 

Best for kids to have their first round of calculus in high school if they are ready for it. Just treat it as prep work.

 

I think that is the most important point.  Unlike the article's assumptions, students' abilities vary and as such can move through math at different rates.  So, if one tries to generalize for *all* high school students (one size fits all), the target becomes the average student.  For that group, yes, attempting to complete Calc may in fact be a rush job.  However, that does not take into account many individual factors.  This includes unique students who are naturally gifted and very capable of moving through all the same material and concepts earlier.   In our case, we span the full spectrum.  For our oldest ds, he would get bored if not allowed to progress and move up to the next level of challenge once he has a firm grasp on the prerequisites.  In his case, there is no rush.  It is simply the pace at which he naturally moves.  For our middle dd who struggles more with math, getting to Calc in college may very well be unrealistic, at least without rushing.  For our youngest, its too early to tell.  So far, she falls somewhere in the middle.

 

After reading both the article and referenced research with interest, I soon discovered that this was more of a survey than experiment dealing with actual causation.  I think it provides a good basis for further consideration and research in this area.  The study also surveyed which attributes contribute to greater success in college Calculus 1.  I actually found that more interesting than the focus of the above article.  Methods of instruction (Good Teaching/Ambitious Teaching) matter quite a bit, which seems even more indicative of success rather than merely the age at which the student takes Calculus.  

 

In addition, there are certain inherent problems at the university level when teaching Calculus 1 in one semester.  "Universities meet the challenge of teaching a thousand or more Calculus 1 students in a single term either by using their best instructors in very large classes or by opting for smaller classes where budget constraints often require hiring part-time or less experienced instructors, often graduate students whose preparation and support for teaching these classes may be minimal."  -- http://www.nctm.org/Publications/Mathematics-Teacher/2015/Vol109/Issue3/Insights-from-the-MAA-National-Study-of-College-Calculus/?

Edited January 3, 2016 by dereksurfs

[daijobu]

I guess I don't understand how a student can earn a 4 or 5 on calculus BC without a firm understanding in math.  

[Joker]

Is the idea is that it's a rush to AP Calculus or Calculus at all in high school. It hasn't seemed rushed at all for us with oldest. Honors Algebra I in 8th, Honors Geometry in 9th, Honors Algebra 2 in 10th. She will take Honors pre-calc/trig next year in 11th. She can then decide between AP Calculus, AP or Honors statistics, or DE college Algebra. She's had EOC's in all her math courses and done extremely well. Where else is she supposed to go in math? FTR, I don't see a huge push here. To get into those classes she needs the grades and teacher recommendations.

[AEC]

I guess I don't understand how a student can earn a 4 or 5 on calculus BC without a firm understanding in math.  

 

I got a 4 - I had, I think, reasonable comprehension of calc but in retrospect not an especially good foundation of trig , stats, probability or numerical theory (the last 3 were, as far as I remember, never covered in HS in any detail).  In any event, I could have opted out of taking the first two terms of freshman Calculus (went to a university on a quarter system, so 2 terms would have been 2/3rds of the first year).  I elected to take it anyway and I'm glad I did.

 

The biggest shock was the transition from HS to college math.  HighSchool was 'here is a technique/theory - let me show you how to use this then you can do the same'.  College math was 'I will derive or prove a theorem for you.  Since you've seen the proof you understand what this means and how it works.  So, you are now able to use that proof technique to derive corollary theorems and of course you're all smart enough to figure out how to use this yourself'.

 

It was probably helpful that I'd actually seen the topic before.

Edited January 4, 2016 by AEC

[G5052]

Yes, for me, the fundamentals are absolutely critical. No reason to rush if you don't have your algebra down.

 

I had outstanding math education until I hit calculus in high school. Bluntly, she was a mess both in and outside of the classroom. I dropped it, convinced that I was horrible in math. Then I  rediscovered math while studying economics and taking a computer science course as an elective. I ended up getting degrees in math and computer science and am an IT/CSC professor.

 

My oldest ended up having to take Algebra I twice. He just didn't get it. The rest of high school math was a struggle too, but I was determined to make sure that he really understood it versus trying to get him into calculus by his senior year. We spent a lot of time on math, and he indeed never got to calculus, but he did well on the SAT math portion.

 

For his first semester of college, I put him into what they call "engineering pre-calculus" because there were still some concepts he felt uneasy about, and he's an accounting major. He could have gone straight to calculus, but we decided to step back. I wanted to push him some even though he had been through most of the material already, so he went to the tougher pre-calc. And it achieved that. There were parts of it that he really had to work on, but aced it. This semester he has calculus with the same professor and feels really good about it. After this he'll have two semesters of business statistics and then apply to the business school. So stepping back was fine. He has to have 3-4 semesters of math anyway.

[LisaKinVA]

1)  Yes you certainly can if you cover all the topics.  We are not rushing this taking AB first.

2 + 2b)  A good Precalculus is the right choice. You may need to supplement if the DoDEA is not honors level. My DS also completed Alg 2 in 9th grade. I would not do Calc 3 in HS IMHO.  Try Discrete Math or Linear Algebra.

3)  Sounds good to me.

 

Thank you.

 

I was planning on doing AB 11th and then BC in 12th, so that will be great.  DS will probably still need to take Calc in college anyway.  He has tended toward the side of needing more time for courses.

 

Precalculus -- we're planning on supplementing with LoF or AoPS (DD prefers AoPS at this point).  So, I'm not worried about her understanding.  She has been my, "what do you mean you're done?" kid.  My reason for having Jacobs, Foerster, LoF and AoPS -- because I'll throw her into Foerster or Jacobs and she completes it in half the time...making me certain she can't possibly really understand, so then she does AoPS...in half the time (because she did understand).  Our options for advanced math are very limited (I'm limited, our options here are limited).  She will have completed the AoPS courses related to discrete math (all we have access to, anyhow).  If we can get our internet working at speeds reliably, something on-line may be workable.  Right now, I've been shedding most of our on-line coursework.  I have zero planned for 2016-2017 (aside from a Bible and History course at the elementary level, where we have a lot more flexibility).  Any videos we're using, I have to be able to download (at night, well in advance).  We have just had too much trouble this year with internet that hasn't been much better than dial-up.  At least this isn't something I need to worry about right now. 

 

Thanks again.

[Lanny]

It would be interesting, to know the "success rates" in the College of Engineering, in a  University.  Two groups of students in their First year:

(a) Those who completed Calc when they were in High School (I am assuming the university would require them to take it in the university too)

(b) Those who did not take Calc when they were in High School.

 

There are many students admitted to the College of Engineering who cannot handle it and change their Major or drop out.. I wonder how this factors into the equation? One might assume that those who took Calc in High School would do better, because they had previously been exposed to at least some of the material and it would be easier for them.  Is that assumption actually factual?  Is their ability to apply the Math they learned in High School better or weaker than those who did not take Calc in High School?

 

I recall reading something on a web page of the College of Engineering at Tech, a couple of years ago. It had to do with the fact that Engineering is very rigorous and that those who cannot handle the load will be helped, to transfer out of the College of Engineering.

 

Having completed a course does not mean that one can apply the material...  Regentrude once wrote about that in a post that was extremely interesting to me, about how when some of her students in a Calculus based Physics class have problems, it is not because of their lack of understanding of Calculus, that sometimes it goes back to Algebra 1 or even to Pre Algebra and that they are simply weak in Math.  I hope I remember that correctly, and if not that she will correct me.

 

Another person here on WTM once wrote that her DS was in a class and some of those who were Math hot shots in High School were having a very tough time with the same courses he was taking.

 

There are many people who have Certifications in things related to computers who cannot actually do anything productive on the job.  That is the reason Red Hat required "hands on" testing, in addition to written testing, for their Certification program.

 

The NYT Editorial Mark linked to, and this article he linked to about Calc in High School,  point out that there are failures in the U.S. Educational system, as well as in many other countries.  Playing "Devils Advocate" is frequently helpful, when trying to eliminate flaws from something.

Edited January 4, 2016 by Lanny

[G5052]

And FWIW, the transfer counsellor from the business school my oldest is interested in said they have math issues too. A lot of people say they're going to major in business, but 3-4 semesters of college math derail them.

 

So it has sad consequences even beyond STEM degrees.

[Bootsie]

And FWIW, the transfer counsellor from the business school my oldest is interested in said they have math issues too. A lot of people say they're going to major in business, but 3-4 semesters of college math derail them.

 

So it has sad consequences even beyond STEM degrees.

As a finance and economics professor, I see this a lot.  Many of my students have taken high school calculus but are weak at basic math skills--fractions, order of operations, rounding, etc.  They have learned to "type" an equation into a scientific calculator and hit "solve." but they do not know what the equation means.  

[Matryoshka]

As a finance and economics professor, I see this a lot.  Many of my students have taken high school calculus but are weak at basic math skills--fractions, order of operations, rounding, etc.  They have learned to "type" an equation into a scientific calculator and hit "solve." but they do not know what the equation means.  

 

This whole calculator thing has got to be a big part of the problem.  One good thing I have to say about the local ps' math program is that there is very little calculator use.  I didn't have to buy a graphing calculator at all till calculus - they did learn how to use them before that, but just used them in class for the chapter on that, and not for homework or tests.  Dd does have one for calculus this year, but I barely see her use it.

 

[Arcadia]

Lanny,

 

My alma mater already requires an A for the calculus equivalent on top of good grades for the other two major subjects for local students.

 

However what is requires to survive the first semester is

 

1) hard work - course load is heavy and there is little breather room. Think about what would roughly be equivalent effort to debugging and compiling spaghetti code of your colleagues/clients on a 24hr deadline.

 

2) ask for clarification from lecturers and/or form study groups. Some lecturers were really hard to understand after all so having classmates as backups is good. Besides friends keep friends surviving when the going gets tough.

 

3) foundation from the roots up. There are people at undergrad level who are confused by things like scientific notations. Number sense has to be ingrained. You (general) can go through school, do all the textbooks questions and yet still be weak on concepts. There is a lot of logic in math just as there is a lot of logic in programming. I feel many school students forget to think and just let their textbook or test prep book think for them.

 

Whether you can catch up depends on the college of engineering. Its swim or sink.

 

Prepping and passing the RHCE took me 5 days, four days or crash course and exam on the 5th day. It was a walk in the park after the crazy pace of engineering.

 

ETA:

Scores for AP Calc BC are good for California according to Report to Nation. However there is an abundance of private tutors and tuition centers doing SAT and AP exam prep courses. So quality of education that each child get is hard to gauge.

Edited January 4, 2016 by Arcadia

[SparklyUnicorn]

Apparently not typical here where I am.  They only offer it through the CC.  And they do not offer AP.

 

 

 

 

[dereksurfs]

I just want to say great discussion guys/gals all because of Mark's son asking a question.;)

[G5052]

As a finance and economics professor, I see this a lot.  Many of my students have taken high school calculus but are weak at basic math skills--fractions, order of operations, rounding, etc.  They have learned to "type" an equation into a scientific calculator and hit "solve." but they do not know what the equation means.  

 

You just can't have enough of the fundamentals IMHO.

 

When I was teaching basic computer literacy at the college level, Excel always brought about a lot of troubles. A fair number had no idea about the order-of-operations rules, calculating percentages, and doing simple payroll formulas. I always did a "math" review unit before Excel, and we still had problems.

[MBM]

I would say it's not the rush to calculus but the weak and insufficient teaching of fundamental math concepts that causes the problems colleges are seeing. Retaking calculus in college isn't going to help much if the students do not understand those concepts well.

 

Maybe a better answer is for colleges to design their own placement exams to ensure students are appropriately placed. My youngest had to take a math placement exam and then meet with the director of the undergraduate math department. One of his majors is theoretical math. He placed into junior-level classes and has done very well so far. Kids who do have an excellent grasp of math concepts -- and some do -- should not be held back to do busy work simply as a matter of policy.

[Arcadia]

So true :lol:

 

From Berkeley Engineering

"You may have done well in high school calculus, maybe even scoring high on your Advanced Placement, International Baccalaureate or A-Level math exams. Still, don’t assume you’ve mastered the understanding of calculus needed for college-level engineering courses."

 

The link has sample final exams for Math1A & Math1B. No solutions provided.

http://engineering.berkeley.edu/student-services/new-students/first-math-course

[daijobu]

From Berkeley Engineering

"You may have done well in high school calculus, maybe even scoring high on your Advanced Placement, International Baccalaureate or A-Level math exams. Still, don’t assume you’ve mastered the understanding of calculus needed for college-level engineering courses."

 

 

Okay, I'm going to ask this a second time.  How does one score well on AP calculus without mastering calculus?  Or algebra for that matter?  What's the point of external validation if it doesn't validate anything?  

 

I don't remember AP calculus exam being easy.  (I actually don't remember much at all about my AP calculus exam, but I don't recall thinking that it wasn't a good test of calculus.)  Has the AP calculus exam been dumbed down since the 1980s?  Actually, I happen to have a copy of my old AP calculus exam in front of me and (with any luck) I have attached a copy of the first page.  

 

And maybe someone can explain how does one use a calculator in calculus?  Are students using a calculator during the exam now?  

 

ETA:  File size is too big.  Does anyone know how to reduce the file size?  I'm using my phone to take a picture.  

Edited January 4, 2016 by daijobu

[Arcadia]

And maybe someone can explain how does one use a calculator in calculus? Are students using a calculator during the exam now?

This from collegeboard

"Professional mathematics organizations, such as the National Council of Teachers of Mathematics, the Mathematical Association of America, and the Mathematical Sciences Education Board of the National Academy of Sciences, have strongly endorsed the use of calculators in mathematics instruction and testing.

 

The use of a graphing calculator in AP Calculus is considered an integral part of the course. Teachers should be using this technology on a regular basis with students so that students become adept at using their graphing calculators"

http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/2109.html

 

The public school math textbooks teach kids how to use the graphing calculator, usually the TI83/84/89.

 

No either about AP since I was not educated here. The current Cambridge 'A' levels maths are easier than in the 80s.

 

ETA:

On your phone, select low-res or turn HD off before taking the photo.

 

ETA:

I read on these boards about putting AMC10/12 scores as well on college app if you have good scores. Might be another way to substantiate scores.

Edited January 4, 2016 by Arcadia

[TranquilMind]

Thanks for posting this.  I'm going to share it with my husband (an old school EE) who thinks it's nuts the way calculus is pushed on high school students today.

I completely agree.  The groundwork has to be thoroughly laid first. 

[shawthorne44]

Okay, I'm going to ask this a second time.  How does one score well on AP calculus without mastering calculus?  Or algebra for that matter?  What's the point of external validation if it doesn't validate anything?  

 

I don't remember AP calculus exam being easy.  (I actually don't remember much at all about my AP calculus exam, but I don't recall thinking that it wasn't a good test of calculus.)  Has the AP calculus exam been dumbed down since the 1980s?  Actually, I happen to have a copy of my old AP calculus exam in front of me and (with any luck) I have attached a copy of the first page.  

 

And maybe someone can explain how does one use a calculator in calculus?  Are students using a calculator during the exam now?  

 

ETA:  File size is too big.  Does anyone know how to reduce the file size?  I'm using my phone to take a picture.  

 

 

It is truly amazing what calculators can do nowdays.   Well, I'm over 40 and I remember other students using their calculators in cal 2, cal 3 and linear algebra.   The same students were likely using their calculators in cal 1, but I didn't really interact with other students in that class.  

 

The reason I remember it from Linear Algebra is that there was a weirdly easy problem on the final exam.   If you have a strong test sense like I do, you naturally learn a professors test style.   I remember my internal alarms went off because there was a really easy problem where a medium-difficult problem belonged.  Normally that means that the problem isn't as easy as it appears.  Later I had the same professor for PDE and he saw some students using their calculators in class.  He warned them not to do that and he mentioned the Linear Algebra class where he took out a normal problem and substituted one that would be impossible to do with a calculator.   

 

I had one of the fancy calculators, but I only mainly used it for the Reverse Polish Notation, being able to save about 50 common physics constants, and geek status symbol.  

[Bootsie]

You just can't have enough of the fundamentals IMHO.

 

When I was teaching basic computer literacy at the college level, Excel always brought about a lot of troubles. A fair number had no idea about the order-of-operations rules, calculating percentages, and doing simple payroll formulas. I always did a "math" review unit before Excel, and we still had problems.

This is exactly the problem I have seen in teaching finance.  We get complaints that graduates don't know Excel, but the real problem is that they don't do math.  They have been able to type into a calculator (150 + 25 + 30)(1+.08) =    But they don't know mathematically how to solve for "ABC bought three items, one for $150, one for $25, and one for $30.  They must pay 8% tax on the purchase.  What will the total bill be?"  They can't convert that to a formula to put into Excel.  However, many of these same students took calculus in high school.  

[Sebastian (a lady)]

I'm going to dissent from the conclusion I think the article is drawing.

 

I don't think that the problem is that the students took calculus in high school.  I think that a deeper problem is that the students are being passive in class and assume that because the have encountered the material before, they fully understand it.  I suspect that this plays out with the students not working through the homework or reading through the chapters, because the terms used in class ring a bell from previous studies.  

 

I see this as distinct from the question of if they were rushed into and through calculus.  A placement test should demonstrate when a student doesn't have the fundamentals in place for calculus or higher level coursework.  The placement exam isn't going to identify students who choose to blow off homework assignments or class meetings because they assume it is just review.  I'm not sure that the article really draws a distinction between those who were rushed through without understanding and those who are choosing not to do the work in college and therefore aren't identifying areas where their understanding is lower than they think it is.

 

What I encountered in Calculus 1 over 20 years ago was an absolute assumption by the instructor that the course was a repeat for students.  He actually stated that he "knew" that this was a review for everyone, so he was going to go very quickly to get to harder material.  I had not actually had calculus before and the course was horrible for me.  I have very much had calculus as a goal for my older sons, even though I will encourage them to retake it in college.  I wasn't rushed into calculus.  I also had a good understanding of what came before calc.  I was, however, rushed through calc at college.  This set up a very shaky foundation for subsequent courses.  

Edited January 4, 2016 by Sebastian (a lady)

[Targhee]

I guess I don't understand how a student can earn a 4 or 5 on calculus BC without a firm understanding in math.  

The same way elementary kids can pass a spelling test and forget everything they learned the next week.  

[Mike in SA]

Okay, I'm going to ask this a second time.  How does one score well on AP calculus without mastering calculus?  Or algebra for that matter?  What's the point of external validation if it doesn't validate anything?  

 

I don't remember AP calculus exam being easy. 

 

It isn't that it doesn't validate anything -- it shows that the student has memorized some problem solving techniques. 

 

The problem with AP exams is that they aren't very accommodative of testing knowledge of the underlying theory that is necessary for mastery.  The course itself is substantially lacking, imho.  It's one of the reasons we have DS studying calculus now through a rigorous review of the proofs (no calculator), before he takes a regular BC course to get all the calculator application he can stomach.  Then, we'll do the same for multivariate calc, which is a huge step up at most high schools with the offering.

 

25+ years on, I can still rattle off the definition of a limit without hesitation, and understand what it is saying.  I have to doubt that many AP students can do the same.

[angela in ohio]

I wonder how much of this is due to poor calculus instruction in public schools. My girls took calc at the local PS, and the instructor didn't know the material well. Luckily, I'ma  firm believer in algebra twice and calc twice, so they both took it again at the local CC after that. I regret not just having them take it at the CC to begin with, but they were halfway through before we realized the instructor couldn't handle it. Middle dd tutors math students who came out of bad PS math courses in general all the time. 

 

As far as calculators, we used them in trig and calc back in 90-92 when I was in HS. As soon as my girls hit calc, a TI-89 was required, both at PS and the CC.

 

"No one should rush to calc" seems like a backlash to "all must have calc." Every student is different. Part of the reason middle dd kept homeschooling was because the private school she was going to attend for HS was going to "level her out" in math. So she would have repeated algebra II and geometry. That would have killed her love of math and wasted her time. Instead, she was able to go at the pace that made sense for her as an individual. :)

[daijobu]

Ah, memories.

 

 

 

 

 

Edited January 5, 2016 by daijobu

[JeanM]

The other question is...Am I reading this correctly?  A student can SKIP Calculus AB and just do BC?  Is that correct?

 

In my experience, this depends on the class. Way back when, my public high school gave a choice of AB or BC. Our local public high school only offers AB, but students who are interested can take BC the following year online. The online BC is a one year class that assumes you know everything from AB calculus. I'm pretty sure that I've seen some other BC calculus classes that have AB calculus as a prerequisite. My older ds decided he really wanted to do BC in one year, so he did it at home instead of at the public school.

 

[regentrude]

It would be interesting, to know the "success rates" in the College of Engineering, in a  University.  Two groups of students in their First year:

(a) Those who completed Calc when they were in High School (I am assuming the university would require them to take it in the university too)

(b) Those who did not take Calc when they were in High School.

 

There are many students admitted to the College of Engineering who cannot handle it and change their Major or drop out.. I wonder how this factors into the equation? One might assume that those who took Calc in High School would do better, because they had previously been exposed to at least some of the material and it would be easier for them.  Is that assumption actually factual?  Is their ability to apply the Math they learned in High School better or weaker than those who did not take Calc in High School?

 

I would assume it is largely the effect that those students who took calc in high school tend to be the stronger math students. No wonder the stronger math students subsequently perform better in college.

 

To measure the actual effect of taking calc in hs one should compare students who took calc in hs with students who could have placed into calc in hs and chose not to, or whose school did not offer calc. It makes no sense to compare strong math students with weak math students who did not take calc because they were incapable of doing so and drawing conclusions about the value of hs calculus courses.

 

 

 Regentrude once wrote about that in a post that was extremely interesting to me, about how when some of her students in a Calculus based Physics class have problems, it is not because of their lack of understanding of Calculus, that sometimes it goes back to Algebra 1 or even to Pre Algebra and that they are simply weak in Math.  I hope I remember that correctly, and if not that she will correct me.

 

Yes, that is correct. Basic algebra and prealgebra are the problems - not calculus per se.

[Arcadia]

The other question is...Am I reading this correctly? A student can SKIP Calculus AB and just do BC? Is that correct?

Regarding placing, my local public high school place weaker students to Calc AB and stronger ones to Calc BC via tests and teachers recommendation. Both are standalone. Calc AB is typically in 12th while Calc BC can be taken earlier followed by DE or AP statistics.

 

So I would ask the head teacher for math for the school how placement is done.

[mumto2]

1) I looked at the Calc AB versus Calc BC distributions - wow 31% of AB takers got a 1. That is sad.

I remember teachers offering to waive the final exam if we signed up for the AP exam. It didn't matter how well we did- the AP exam experience was our final. I have been wondering if that situation is generating the large number of 1's in the examinations. Kid's paying to take the exam and get out of school a day earlier senior year.

 

Fwiw both of mine will end up doing both parts. Dd because they were not offering the BC last year, she was ready. We have a request in for her to take the BC portion this year. For DS the experience with the easier exam is needed, he is a more nervous test taker. He could probably be ready for the harder exam but we do have the extra year available so will use it.