Which AP exams earn credits at the most colleges?

[Gwen in VA]

Don't those math teachers realize that in college many of their students won't be allowed to use calculators for exams? My kids have routinely not had access to a calculator on math exams, and woe be unto the student who thinks trig is just a few buttons on a calculator!

[Kathy in Richmond]

I love these conversations, though they fill me with regret for what might have been, had I actually learned some math.

 

Carry on :lurk5:

You're still young, wapiti! Two of my favorite avocations today are hobbies/learning areas I took up in my mid-forties. Have fun with the math alongside those smart kiddos of yours.:)

 

I'm really enjoying this discussion about math instruction and AP calc.

 

Just to insert a very practical thought into the discussion, I would not generalize too far from BC calc to the rest of APs.

 

Exactly true!

 

I have my complaints about some of the exams, like Calculus, but others, for example, Physics C, are very nice courses indeed.

 

I fondly remember at least one Physics class where we were only allowed to use F=ma as a given. Everything else had to be derived. Once we had derived other things, then we could use them.

 

See, that's why I love physics, too; everything is derivable from basic concepts. No memorization!

 

But, that's my passion - theory. Hubby's an engineer and prefers just to use formulas. He knows what they are for (understands the concepts), just feels no passion for the proofs. He's a superb engineer and has been able to figure out solutions to problems that have baffled others on the job. He has no problem at all with creativity.

 

Ditto here, right down to the creative, hands-on engineer husband with intuitive understanding of engineering and math concepts, but w/o a passion for proofs. Funny story: we met when he took my partial differential equations class for engineers at Ga Tech. He had no passion for it & earned a D from me. It came back to bite me later when we married and he was looking for a job! (and lest anyone is thinking I robbed the cradle, lol, I was a very young prof and he was a returning older student who had taken a break from his studies )

[8filltheheart]

-students who take AP calculus merely learn a superficial calculus course without deep understanding, and thereby waste a year forgetting algebra

 

 

I wonder if your textbook writing friend would say the same about AoPS's cal course. I am most definitely not a mathematician and don't even pretend to understand 1/8 of this conversation, but I do believe that my ds does not have a superficial understanding of cal. Our oldest ds is a chemical engineer and he took his cal courses at a local university. I think that the AoPS class was a lot more challenging than oldest ds's experience. (Actually, the weakness I do see is not having more calculator and mathlab or Maple experience! Ds does not like using his calculator at all and it is one of the areas that Kathy had to instruct him in.)

 

FWIW, Kathy has looked at the syllabus for the multivariate cal class my 16 yos will be taking at the local state university here (not a Stanford by any stretch, but it neither is it a poor-quality university.) She believes ds is more than prepared for the course.

 

Kathy, what do you think? Do you think the AoPS course is weak and w/o deep understanding and not the equivalent of a college class??

 

My current plan that I am now seriously questioning, was to have him take BC calc with PA Homeschoolers this year, and then take AoPS calc next year after he had the "mechanics" down.

 

 

I can only share ds's experience. He was bored to tears in the PAH course. My math loving ds dreaded opening up her emails to see what she wanted from them that day. I also know ds would be bored if he had to repeat cal again next yr. He wants to dig into more new and interesting materials. FWIW, my ds does enjoy math, but math is not his first love; physics is. And he didn't even take the AMC. (math competition is just not where he wants to spend his time........dark matter otoh..... ;)

Edited July 9, 2012 by 8FillTheHeart

[Kathy in Richmond]

Kathy, what do you think? Do you think the AoPS course is weak and w/o deep understanding and not the equivalent of a college class??

 

8Fill, your son has a superb background in calculus from his AoPS class. I could see that from working with him this past spring.:) No worries at all in that respect; he should definitely not need to repeat calc 1 in college!

 

The AoPS class is proof-based and offers much harder problems than the usual calculus textbook on the market these days. It's not Stanford honors calc (but that's more like real analysis than calculus anyway!), but it's miles above most courses.:)

[mathwonk]

Here is a question I always thought was interesting, but one seldom sees asked (not in AP syllabus?): what is a real number? if the answer is that they are finite or infinite decimals, as stated on page 1 of Thomas and Finney, 9th edition, then how do you add them? I.e. addition usually starts at the "right end" of a decimal, so where do you start with two infinite decimals? I taught a precalculus course to high school students in which we studied such questions. Without knowing what a real number is, how much can one say he understands about calculus?

 

Here is another property of real numbers referred to on page 2 of Thomas Finney as "hard to make precise": what does the "completeness" of the real line mean? They say it means there are no "holes" in the real number line and leave it at that. This gives a false impression that there is something unusually difficult about it, something beyond the ken of a calculus student. However on page 3 they discuss open and closed intervals as something basic and simple.

 

Why don't they just go on to say that "no holes" means there is no separation of the real numbers into two disjoint open intervals? I.e. given any two disjoint (non empty) open intervals of the real line, there must be some more real numbers in between the two intervals. This property gives us all the "existence" results in calculus.

 

E.g. if no real square root of two existed, then the real line could be separated into the disjoint two open intervals, consisting of numbers x with x^2 > 2, and those x with x^2 < 2.

 

How hard is that? I dislike giving someone the impression there are "hard" topics that are reserved for some other course you have to pay extra for and spend years preparing for, especially if it is not true.

 

By the way this tendency is widespread, even at good schools. The following free calculus notes from MIT open courseware (see pages 202-204), although pretty good in some explanations, give slightly the wrong definition of the Riemann integral (an integrable function may not have a maximum or minimum on a subinterval), and they also skip over the easy fact that monotone functions are integrable, giving the impression, in remark 4 p.204, that after the trivial rectangular cases, one is naturally led next to the continuous case. Remark 3 should logically have been the easy monotone case.

 

http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/MITRES_18_001_strang_5558.pdf

 

When I teach a class I try to adapt it to the needs of the members, their background, their goals, and their mood from day to day. The first day I ask everyone his major, so I can try to throw in references and applications to those subjects. If they do poorly on one test, the next test is easier to reduce discouragement, and I may throw out the previous one altogether. Home schooling can do the same, even better, but it is hard to get that from a canned curriculum or standardized tests.

 

I will try to put the notes from my high school precalculus class on real numbers on my webpage, in case anyone is interested in them.

Edited July 9, 2012 by mathwonk

[mathwonk]

Another simple question that cannot be avoided in a calculus class is: what does it mean to say the area under a given graph is a well defined finite number, i.e. that a given function has a definite integral over an interval [a,b]? Any student who wants to understand calculus should have some grasp of this question and its answer. Here are a couple of little tests:

 

1) Define what it means for the integral of f to exist on [a,b].

 

2) Using that definition, prove, i.e. explain convincingly, why a strictly increasing function on [0,1] always has an integral.

 

3) Give an example of a function defined on [0,1] whose integral does not exist.

 

And for students who know the "fundamental theorem of calculus:

 

4) What can be done about calculating or estimating the integral of an explicitly given function defined and continuous on [a,b], but for which you do not know any explicit antiderivative? (without using a calculator). (Hint: what good is a Riemann sum if you can't take its limit?)

 

 

To me such questions are more fundamental than "what is the antiderivative of sin^2(x)?". Do they ever occur on AP tests? And I'm not restricting myself to math. When I was in college, almost every test was "essay style", written in "blue books", in virtually every subject.

 

Do AP tests ever ask one to explain what the various concepts are good for? E.g. in integration, proofs are usually done using upper and lower sums, while "Riemann" sums are better for estimates, and "precise" (sometimes only theoretical) calculations come from antiderivatives. Do kids learn this?

Edited July 9, 2012 by mathwonk

[Laura in CA]

I think that there's a real void and need for a new kind of calculus class in the middle of the two approaches (the crank-it-out approach and the future mathematician approach) for our future engineers and scientists, etc. Just thinking, but it might be fun to develop one.:)

 

I'm also toying with the idea of running an online AP calc prep group next spring.

 

Ooh! These both sound awesome. Let me know if you need a TA/side-kick/guinea pig; I know my son would love to volunteer!! :D

[swimmermom3]

 

But, just as a practical matter, many WTM type homeschoolers are going to be much, much beyond intro history courses typically offered at state universities. History instruction has probably been much more central to their education for years and they will may be totally out of step with intro courses. So, if the kid is headed to the state u (as are) it may make quite a lot of sense for them to knock off the AP. Instead of wasting a year in a huge and poorly taught section survey of world history for people who have never studied it before, many homeschoolers would prefer to go directly to a more engaging upper level course on an area they've wanted to study more in depth. For a student headed to a top liberal arts college this advice won't apply, but I would suggest students planning on the state u look at APs seriously as an option to help shape a better experience at the state u. APs on the record can help get the kid into smaller, and better, classes much faster.

 

Thank you for expressing this in practical terms. For one of my children, it would be less about the credit and far more about not having to take a section survey of a world history course. Food for thought.

 

This is a delightful and challenging conversation. Thank you so much to all who are participating.

[FairProspects]

Thank you for expressing this in practical terms. For one of my children, it would be less about the credit and far more about not having to take a section survey of a world history course. Food for thought.

 

This is a delightful and challenging conversation. Thank you so much to all who are participating.

 

And definitely have dc take whatever AP it is that knocks out Freshman Composition. It may not matter for Stanford and some of the other elite universities (where I'm sure the content is much more stimulating in general), but I had to sit through a quarter of "crap is not an appropriate word in college writing" (I kid you not) because my high school did not offer that AP test even though my writing ability had been light years beyond that since late elementary school. I could not believe I was being forced to waste my time and money that way because I hadn't been able to sit for an AP exam. My advisor actually laughed at me and told me everyone else with my stats had come in with an AP score excusing them.

Edited July 9, 2012 by FairProspects

[mathwonk]

This advice is probably excellent in some settings, i.e. some colleges but it does give me pause. I never took any AP courses in high school at all, had all A's in everything, and was forced into a freshman writing course at Harvard that taught me to write, to some extent, for the first time ever. In fact it taught me that I hadn't yet learned how. It apparently didn't hurt people who wrote well either. On our first assignment, my more literate friend who got one of the few A's, was simply kicked out and put into honors writing class instead.

 

My older son, who went to a high school where literature and exposition were highly valued, went to Stanford and dominated in his freshman writing class, but not on the strength of an AP English class, but from the spectacular honors writing classes in his high school, created by the outstanding teachers there.

 

Even at a school where the class is inadequate for your needs, I believe the problem of being forced into a class that bores you is one that usually can be dealt with by being insistent and persistent. No one at UGA ever has to take a math class that they do not need, if they come to the attention of the department. It helps a lot if the student knows this and advocates for herself. As they put it in the student guide for incoming undergraduates at Harvard "Never take a low level 'NO!' for an answer."

 

Your advisor, instead of laughing, should have picked up the phone and lobbied to get you into the right class. I have done that many times at University of Georgia, where there are also many classes that are inappropriate for strong students. In fact I have essentially never been unsuccessful at getting rules waived. Students don't seem to realize how much clout professors can have in academic matters.

 

On the other hand if it is a financial matter, and you want credit for the class without taking it, that takes more work. However, even there, we have exemption tests that can be taken by students to award them credit in many cases. Always ask for help when things don't make sense. I have even had deadlines waived for application to a program or a degree that were missed by a semester or a year or even several years.

 

(By the way, we spent July 4th on Vashon, in beautiful Puget Sound, to escape 100+ degree heat in Atlanta! :001_smile:)

Edited July 9, 2012 by mathwonk

[8filltheheart]

This advice is probably excellent in some settings, i.e. some colleges but it does give me pause. I never took any AP courses in high school at all, had all A's in everything, and was forced into a freshman writing course at Harvard that taught me to write, to some extent, for the first time ever. In fact it taught me that I hadn't yet learned how. It apparently didn't hurt people who wrote well either. On our first assignment, my more literate friend who got one of the few A's, was simply kicked out and put into honors writing class instead.

 

My older son, who went to a high school where literature and exposition were highly valued, went to Stanford and dominated in his freshman writing class, but not on the strength of an AP English class, but from the spectacular honors writing classes in his high school, created by the outstanding teachers there.

 

Even at a school where the class is inadequate for your needs, I believe the problem of being forced into a class that bores you is one that usually can be dealt with by being insistent and persistent. No one at UGA ever has to take a math clas that they do not need, if they come to th attention of the department. It helps a lot if the student knows this and advocates for herself. As they put it in the student guide for incoming undergraduates at Harvard "Never take a low level 'NO!' for an answer."

 

Your advisor, instead of laughing, should have picked up the phone and lobbied to get you into the right class. I have done that many times at University of Georgia, where there are also many classes that are inappropriate for strong students. In fact I have essentially never been unsuccessful at getting rules waived. Students don't seem to realize how much clout professors can have in academic matters.

 

On the other hand if it is a financial matter, and you want credit for the class without taking it, that takes more work. However, even there, we have exemption tests that can be taken by students to award them credit in many cases. Always ask for help when things don't make sense. I have even had deadlines waived for application to a program or a degree that were missed by a semester or a year or even several years.

 

It is obvious that you have a passion for your role at UGA. The students that had you as an advisor/prof were lucky to have such an advocate.

 

But, your post also reads like that of a professional teacher and non-homeschooler. ;) Its underlying premise is essentially "the professionals can do it better" and that what is being done outside of the university system is not (cannot be) on the same level.

 

When discussing in broad realistic terms, I agree that that is probably true of most school system classrooms and even amg the vast majority of homeschoolers. However, that same discussion seems discordant (preaching to the choir) when I read it in the context of the ladies responding to this thread. The moms posting in this thread have extremely high standards and none would want to short-change their students in any way. And.......what they are capable (and many have proven via their adult children's successes) is quite remarkable. Their home-made courses tend to produce results superior to equivalent courses at many non-elite institutions' introductory level courses and most definitely superior to what students receive at CCs (and get college credit for at most public unis b/c of reciprocity agreements. :tongue_smilie: I'm sorry, but the suggestion of freshman comp as being a course not to be skipped in general makes me :lol: What I have personally witnessed what goes on in freshman comp in CC courses or even state uni make me..... :tongue_smilie:)

 

Reality needs to separate the conversation into what type of higher institution you are discussing and those at the highest level already impose restrictions by not accepting transfer credit, etc. And those that do, AP courses are going to be better quality than the equivalent course at the CC. (at least that is our experience w/3 different CC systems. The freshman level introductory level courses make me cringe.)

Edited July 9, 2012 by 8FillTheHeart

[mathwonk]

Forgive my clumsy expression. What I meant to say is that there exist good freshman comp courses, and if you find yourself at a school where the one you are in stinks, you should get out of it. I don't think I said freshman comp should never be skipped. I just said it helped me. The blanket recommendation that it should routinely be skipped, and that an AP class is always better, was what I was reacting to. I think no specific rule here applies to everyone.

 

I also did not mean to imply at all that the professionals do it better. Rather I believe and have tried to say before, that home schooling offers the chance to adapt a class as closely as possible to the needs of the student. I am just hopeful of sharing what I have learned about teaching math, and about navigating formal school systems so home schoolers can use it both at home and when they get into a regular school. I greatly prefer small personal classes to the ones I had to teach in university. It is also obvious from the comments here that home school courses can be greatly superior to what is available in schools. Indeed that is the stimulus for home schooling, to do a better job. The significantly home schooled group of children I met last summer were certainly the best prepared class I have ever met in over 40 years of teaching.

 

I think if I had been home schooled I would not have needed that freshman writing course. However I also admit that my son's outstanding high school English and history teachers did a better job of teaching him writing than I could have done. Math? maybe not so much. That does not mean other home schoolers could not have beat my son's professional teachers also in English. We all have different experiences, but probably few of them yield either universally valid or universally invalid lessons, at least in my opinion.

 

I fully support using AP credit to exempt courses equal to or inferior to the AP course. I am just trying to help clarify that this judgment needs to be made in individual cases. In my experience it has certainly not been the case that all AP courses are equivalent to the college courses they substitute for. My hope is to help people decide what level they want to shoot for at least in math and how to get there, whether the AP really satisfies their goals or not, and if not how to upgrade past that level. I am motivated by the fact that in my experience AP courses and tests stop short of what it is desirable to know, but this may be overly influenced by the math tests, and my faith in, and enjoyment of, the value of creative reasoning as compared to mechanical computation.

 

If we try to say that a college course should always, or should never, be replaced by an AP course, we may be falling into the same trap as the trig student who does not want to understand the concepts and just wants to know which buttons to push. One needs to do some homework and make a judgment in each case. So thank you for giving the counterpoints to my own arguments which reflect my bias and lack of experience.

Edited July 9, 2012 by mathwonk

[FairProspects]

Forgive my clumsy expression. What I meant to say is that there exist good freshman comp courses, and if you find yourself at a school where the one you are in stinks, you should get out of it. I don't think I said freshman comp should not be skipped. I just said it helped me. The blanket recommendation that it should be skipped, and that an AP class is always better, was what I was reacting to. No specific rule here applies to everyone.

 

 

I fully support using AP credit to exempt courses equal to or inferior to the AP course. I am just trying to help clarify that this judgment needs to be made in individual cases. It is certainly not the case that all AP courses are equivalent to the college courses they substitute for. Many people know this very well, but perhaps not all.

 

I would agree with your sentiments, however the bolded is not always possible at large universities with graduation credit requirements that can only be fulfilled by the course or AP credits. By the time I was forced into taking Freshman Comp., I had already taken 300 and 400 level English and History courses, and I was studying abroad at Oxford's Saint Edmund Hall, but I was told I would not graduate without this stupid course because it was a graduation requirement. No amount of arguing would have waived it for me. It's ridiculous, but there it is (and believe me, I was successful at waiving many courses in my college career, including all of first year Spanish). That's why I recommend that Moms try to avoid this hoop for their dc if they can.

 

I also commented for swimmermom3 because I thought I remembered that she was in my region, and may have dc applying to the same university who would face the same requirement.

 

Vashon is lovely - I hope you enjoyed your vacation here!

[mathwonk]

I am sorry you had that experience, and I have certainly encountered ridiculous rules that will not go away! When logical argument does not help, I do encourage enlisting an advocate among the faculty. Unfortunately you were off campus at the time. I was always shocked at the way I was received when i called some office on campus and identified myself as a professor. I felt a little like Danny Kaye in the "Inspector General". If you have seen that movie, you know he was a fraud who entered town in a fake uniform and was mistaken for someone of importance to whom everyone showed respect! I felt an obligation to use that uniform on behalf of deserving cases.

 

And thank you, we had a great time in WA!

[mathwonk]

Wow! I guess I lucked out big time. My freshman comp instructor was distinguished historian Nathan Huggins.

 

http://dubois.fas.harvard.edu/nathan-i-huggins-lectures

 

http://en.wikipedia.org/wiki/Nathan_Huggins

 

 

My introductory calculus class was taught by John Torrence Tate. (And i still didn't understand it! )

 

http://en.wikipedia.org/wiki/John_Tate

 

http://www.utexas.edu/news/2010/03/24/john_tate_abel_prize/

 

 

I had fun a few years back communicating again with Professor Tate over a homework assignment he had given. He had asked us in that freshman year class in 1960 to prove that the expansion of the famous constant e begins 2.718281828.... but I never did it. After telling the story to my own class in Fall 2006 while teaching the topic, I felt guilty, since I always expect hard work from my classes. So I sat down and cranked it out. I emailed Professor Tate to tell him I had finally done it, and he wrote a nice message back saying how it made him smile to get a homework assignment 46 years late!

Edited July 9, 2012 by mathwonk

[8filltheheart]

I am a little confused after going back and reading your posts and UGA's AP policy. UGA gives 4 credit hrs for a 4 on the AB exam and 8 for a 5 on the BC (with 4 of the credit hrs being withheld until after the completion of multivariable cal, linear alg, or the recommended honors multivariable math 1 and 2.) http://reg.uga.edu/creditFromTesting/advancedPlacement/uga_ap_credit_equivalencies

 

I did read where they suggest a possible option of calculus with theory (which I assume is the Spivak course w/AP credit still granted), but even w/in that paragraph the recommendation for students w/a 5 on the BC exam is the honors multivariable math 1 and 2.

http://www.math.uga.edu/~curr/Major.html

 

Am I missing something? (From my reading, it does not appear that UGA requires its math majors to take Math 2400-2410 which is open to non-honors students and students w/o a calculus background.)

Edited July 9, 2012 by 8FillTheHeart

[mathwonk]

I'm not sure which of my statements you are referring to. You have done your homework well, and my statements were based on my memory of what the associate department head told me years ago. It is probably me that is missing something rather than you. Things do change and I had not read that catalog advice lately. As I recall he said earlier that those students wanting AP credit were not allowed to take introductory calculus unless they took the honors level course with theory, the 2400 sequence. They might take people in 2400 with 4's and 5's, but I am not sure of the exact requirements.

 

My impression was also that the audience for math 3500 and 3510, the several variables honors calculus, was mostly made up of graduates of math 2400. The page linked says that entering students even with only a 5 on the AP (BC) exam are advised to "consider" taking the more advanced course. That surprises me, but I do not read it as a recommendation to take it. Rather it seems to be a recognition that such a step may be suitable for some very strong students, and to give them further options. Each student in this situation is advised personally by the instructor and associate department head to determine proper placement.

 

To me, making that jump would mean a student who has strong computational skills and a grasp of basic theorems, but possibly without proof experience is being asked to consider a very high powered proof based course. That 3500, 3510 course is really advanced, and jumping into it with only a 5 on the AP is analogous to jumping into the super honors courses at Stanford and Harvard. I don't recommend it myself, but I didn't write that blurb, and there are always exceptions. Dr. Shifrin who often teaches it is very helpful however, and if a student who tried this course will attend office hours faithfully, he has a fighting chance. Any student who refuses to go to office hours however and tries to go it entirely on his own, may be in trouble.

 

The advisors at UGA that I know really know their stuff however, and I think you can trust them. I have been gone for two years and they are there now teaching the course. I am sure e.g. that if a student got into math 3500 and did not find it working out, they would certainly arrange for her/him to go back to 2400 or even to the non honors 2500. The teacher who wrote that also knows what the audience and the current expectations are for the courses involved, so I would put more faith in that blurb than in my statements, which are less current and less precise. I would not choose a course without talking to the associate head, possibly the undergraduate coordinator, and the instructor.

 

So as always, I have my opinions, but one needs to do homework, consult with the professor who will teach the course and make a decision based on that. There is no one simple rule that fits all cases. Does this help?

 

I will also make a recommendation specifically for a student attending UGA. The Associate Department Head, Dr. Theodore Shifrin, is one of the best advisors (and instructors) I have ever known, and he probably wrote that blurb on advanced placement. I would talk to him for specific advice on that program. He is a tremendous instructor, especially for the highly motivated math student, and often teaches the advanced honors math 3500 course. In fact he wrote a book for it.

 

http://www.amazon.com/Multivariable-Mathematics-Algebra-Calculus-Manifolds/dp/047152638X/ref=sr_1_3?s=books&ie=UTF8&qid=1341876566&sr=1-3&keywords=theodore+shifrin

Edited July 10, 2012 by mathwonk

[mathwonk]

In regard to doing ones homework on the internet, this next remark does not apply to the link we were referring to, which looks excellent. But it did remind me that in the past, when I was at UGA, I complained repeatedly that we had three different conflicting web based descriptions of the same course posted, and it was impossible for a student to find out what the actual expectations were if he did not know which one was correct, nor for that matter for a new teacher to know exactly what to teach. Hopefully that glitch is fixed by now, but I suggest always phoning and/or visiting and verifying things with the same people who will implement them.

[mathwonk]

@8fillThe Heart:

 

"(From my reading, it does not appear that UGA requires its math majors to take Math 2400-2410 which is open to non-honors students and students w/o a calculus background.)"

 

This is correct to my knowledge. Math majors are not the same as future mathematicians. We will take all the math majors we can get, from almost any background. But I believe we do recommend 2400 to the ones who want to get started right away with theory and can handle it. Just because a course is designed "for" someone does not mean he is required to take it.

 

math 2400 is apparently modeled somewhat on the course math 11, taught at Harvard in the 1960's, which I took, and which Michael Spivak, the author of the standard book for math 2400 apparently also took. When I took that I had not had calculus in high school nor studied it on my own.

 

Maybe you are (rightly) confused by my use of the word "honors". At UGA, math 2400 is certainly an honors course in the intrinsic sense of high quality and expectations. However at UGA "honors" courses also has a technical meaning, namely courses offered through the official honors program. You should check me on this, but this program may be set up to prevent people from taking honors courses unless they are in the official honors program, and maybe all honors program members are expected to take only "honors" courses.

 

That does not make sense in our discipline where often there are people who are outstandingly gifted in math but do not belong to the honors program. There are also many people in the honors program who cannot possibly handle math 2400. That's why we have two "honors" courses, 2300 and 2400. All this is somewhat complicated and possibly political. Again this is why it is crucial to get current expert faculty advice.

 

I am not sure what the exact requirement is for math majors. Since increasing the number of math majors is a perennial goal, presumably it is not too strict. When I was in college it was something like "advanced calculus and any other 6 semester courses from the department. Again this should be checked but I believe at UGA it is even weaker, i.e. not even advanced calculus was required when I was there.

Edited July 10, 2012 by mathwonk

[mathwonk]

I want to thank 8filltheHeart for fact - checking my statements about AP and UGA math. This inspired me to call them and try to update my data. I reached one very helpful professor, a friend who kept such data up until 5 years ago. I will try again later to get more recent data.

One thing I learned that has happened since I have left, is that the course I would have advised most entering students with AP preparation to take, “honors” math 2300H, i.e. beginning differential calculus for “honors” students, no longer exists. This has several reasons. One is financial. UGA apparently did not offer AP credit to students taking math 2300H, and presumably they or their parents were not willing to pay for a course they could exempt even if (in my opinion) they really belonged in it academically.

 

So this, in my personal opinion the academically best option for most such students, no longer exists. I consider this a direct result of the proliferation of AP courses, and I lament it. Basically schools are forced to offer courses for which there is an audience rather than those which I personally think make academic sense. However, it does not mean there are no reasonable options for entering AP students. I.e. we are always adapting our courses to fit the audience we have, to the best of our ability.

 

The next course, 2310H, still exists and presumably is the one many entering AP students take. This is the course that fueled my frustration in the first place, since I taught it regularly, and most entering students with only AP background, did not do well in it, at least with me teaching it. (This is the one the student with a 93 on test 1 dropped out of.)

I asked whether I had been an “outlier”, and whether such students did succeed with other teachers, but that information was not available immediately. I suspect that may be true to some extent, and this is one reason it is useful for old people to retire. Some of us cling rigidly to standards as they were when we were in school, or when we started teaching and have trouble adjusting the level of our courses continually downwards, as it seems to us. I kept telling myself my students deserved the same level preparation I assumed was available to students at other good schools, since they would have to compete for the same jobs. Probably I was not aware of what was happening also at other schools.

 

Today however, younger teachers who also have high standards, but probably are better in touch with the preparation current students have, and what one can reasonably expect, are likely tailoring the courses to them more skillfully than I did. Even curmudgeons like me were constantly tinkering with our curriculum and test questions to try to teach effectively the people who were actually in the classroom.

I.e. since AP tests and credits are effectively the norm today for entering students, colleges have been forced to make the courses more or less suitable for these students. Thus as old hands like me retire who did not do this as much, the problem lessens. Still the data posted by Kathy tells me some colleges, such as Stanford, are still not doing a good job of calculus placement, i.e. its not just me.

 

Originally Posted by Kathy in Richmond

 

"Over 100 kids started in Math 51h in September; after the first midterm almost 2/3 of the class dropped out."

Edited July 10, 2012 by mathwonk

[mathwonk]

Next I want to discuss the specific topic 8fillthe Heart asked about at UGA, BC scores and placement in math 3500H, the several variable elite honors course. The website says students with a 5 on the BC are advised to “consider” taking this course as opposed to the first year (Spivak) courses 2400H and 2410H, which I myself would recommend. The available (5 year old) data seemed to lump 4 and 5 scores together.

 

So I asked what percentage of the class in 3500H is made up of BC”4/5” students as opposed those who are graduates of UGA’s own “Spivak course”, math 2400H-2410H. It turns out that the majority of the 3500H is indeed composed of entering students with a 4/5 on the BC exam, to my surprise. However, it is also true that this group comprises a minority of the entire group of entering students with 4/5 on the BC. Thus the students entering with a 4/5 on the BC outnumber the entire class size of math 3500, and most of the 4/5 BC students take something else.

 

It is still not clear what the answer is to the natural question: “If my child has a 4/5 on the BC exam, should he/she take math 3500H at UGA?” I.e. according to the professor I spoke with, he did not know immediately how many such students were actually being personally advised to take math 3500, as his impression was that they were essentially self selected, presumably after reading the website.

 

I also did not get an answer to my next question, which was “how successful are those 4/5 BC students in math 3500H, among those who opt to take it?”. I wanted to know if it was the same situation as at Stanford, where 65% drop out after one test, or whether UGA does a better job of placement.

 

I.e. presumably one wants to know the answers to several questions:

1) if my child has a certain score on the AP test, which courses can he/she exempt with credit?

(a version of the title question of this thread.)

2) if my child has a certain score on the AP test, which course do you recommend for him/her academically, if different from 1)?

3) if my child has a certain score on the AP test, but nothing else, and if he/she opts for such and such a course, what are the chances of success, based on past experience?

4) If my child wants to take such and such course, for which AP preparation is not necessarily sufficient, what additional preparation has been found adequate in the past?

 

maybe even, at a school like Stanford:

5) What level of withdrawals from, or failures in, this course, among people having the stated prerequisite, is usual?

Edited July 11, 2012 by mathwonk

[mathwonk]

As a partial answer to question 4) in my previous response, i.e. what does it take, beyond AP scores, to succeed in a particular course, we have Kathy's testimony about math 51h at stanford. Here's what her daughter studied prior to a course whose only stated prerequisite when my son took it was a high AP score.

 

posted by Kathy:

"I love Marsden and Tromba and used it with both my kids for multivariable calculus at home. My PhD advisor worked with Jerry Marsden, so I knew it would be full of good stuff. It's one of the few books that L insisted on taking to college with her!"

 

[Marsden and Tromba was a several variables calc book used at Berkeley! This is miles beyond any AP syllabus I know of.]

 

Kathy again:

"Unfortunately, as homeschoolers, that class had no 'documentation' in the eyes of college admissions officers - just a mommy grade and course description. .......,.,That doesn't mean that ...... I can't add a heavy dose of proofs to my version of AP Calc."

 

Notice again that Kathy greatly enhanced her home AP calc course, even though Stanford gave her no AP credit for this. Nonetheless it seems to have benefited L. I am guessing she also used a better than average book for single variable AP calc, maybe Spivak or Apostol?

 

By the way, when my son took the course it was also taught by Leon Simon, and used Apostol vol. 2. Unfortunately my son had not been prepared as well as Kathy's, even though he had taken intro to calculus at rival GaTech, while in high school.

 

Here is the stanford course description, which still does not give any specific requirement beyond an AP BC score of 5, quite inadequate, in my view.

 

"MATH 51H: Honors Multivariable Mathematics

For prospective Mathematics majors in the honors program and students from other areas of science or engineering who have a strong mathematics background. Three quarter sequence covers the material of 51, 52, 53, and additional advanced calculus and ordinary and partial differential equations. Unified treatment of multivariable calculus, linear algebra, and differential equations with a different order of topics and emphasis from standard courses. Students should know one-variable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on BC Advanced Placement exam, or consent of instructor."

Edited July 10, 2012 by mathwonk

[mathwonk]

Another idea occurred to me that may be of independent interest for home schoolers, possibly in a separate thread. I.e. in some sense the well intended questions I posed above, concerning what are the right prerequisites for a college course, are the wrong questions. I.e. it may be that success in a college course may be more closely related to how a person studies than to whether he/she has specific prerequisites. The data is from a study by Uri Treisman who tried to increase the success rate of certain ethnic groups of students. To summarize briefly, he discovered that students who came in with all the right scores and background and motivation, but were too independent and studied alone, tended to do less well than students who studied in groups, helping, pushing and encouraging each other. However at the top of p. 368 he says the real core was not just group study, but "the problem sets that drove the group interactions".

 

My theory is that students who excelled in poor high schools learn to avoid other students and work alone. When their success gets them into a good college this habit backfires. This may explain my failure in college after excelling at a mediocre southern high school working entirely on my own. It occurred to me that some home school students may have the same problem I had, of not realizing that in a good college the students can help each other, and those who do not take advantage of this may fall behind. I.e. challenging study groups may be advised.

 

Here he is now:

 

http://www.utdanacenter.org/staff/uri-treisman.php

 

And here is the summary of the original study that started it all. The key results are stated on page 366, but the previous (and later) parts are also entertaining and useful background. (Is this study well known?) some dramatic results of the program as well as frustrations (when the funding ran out) are expressed on page 369. There is also a statistic there, possibly from the 1980's that over 40% of all the 600,000 incoming calculus students nationwide fail each year. So my 50% "unsuccessful" figure was fairly typical.

 

http://www.utdanacenter.org/downloads/articles/studying_students.pdf

Edited July 11, 2012 by mathwonk

[Barbara H]

 

My theory is that students who excelled in poor high schools learn to avoid other students and work alone. When their success gets them into a good college this habit backfires. This may explain my failure in college after excelling at a mediocre southern high school working entirely on my own. It occurred to me that some home school students may have the same problem I had, of not realizing that in a good college the students can help each other,

 

I'm sure it varies greatly from student to student based on their previous experiences and their personalities. I suspect many homeschoolers may find the group study process easier than their traditional schooled counterparts. Homeschoolers haven't suffered through years of K-12 years of poorly designed group projects that often end up leaving the bright/motivated kid resenting their role of doing the work of the entire group. Homeschooled kids won't have that baggage weighing them down. I feel like with homeschooling we skipped over all the bad of group work and got straight to the good stuff of working with peers who cared about what they were doing - this happened both through activities and through college.

 

Depending on the environment of the college or the university, professors can make a difference in encouraging students to form study groups. One professor I know of makes the students interact with the students sitting around them during the first week of class and suggests they exchange email addresses with at least a couple of students in class so they have a resource for missed notes or to work through problems. This probably isn't necessary at small schools, but at the big state u I would like to see professors encouraging students to get to know and interact with each other. Interaction with the people around you is really not the culture at a lot of big schools particularly in freshman classes and except for extreme extroverts, it can be hard to make that sort of contact without encouragement.

[mathwonk]

Those are good ideas. Another thing I tried recently was scheduling office hours in a class room rather than in my office. I noticed few students coming to office hours and conjectured that it was intimidating. A classroom was more familiar and attracted a larger group who then solved problems together. I also scheduled them at different times to accommodate people with different schedules.

[Barbara H]

Interesting that students are more willing to meet in the classroom. A lot of students are really intimidated about going to see professors and they will work themselves into terrible situations that probably could have been prevented by just seeking out help earlier in the semester.

[mathwonk]

I think you are right, and this intimidation or reluctance to seek help I think is very crucial. When as students we do not succeed we have a feeling something is wrong with us, that we are not intelligent enough. But my impression is that this is not as crucial as the way we study, how willing we are to ask for help, to go to class and to office hours. I was even afraid to go to class sometimes for fear the professor was angry with me for missing a previous class or assignment. I never went to office hours for help.

 

My time at Harvard persuades me that although many Harvard students are very intelligent, their key distinction is a strong self confidence and aggressiveness in seeking their goals. They know what they want and they go after it to a degree that differs greatly from students at the typical state school familiar to me. I.e. these elite students do better mainly because they try harder, are disciplined, and are not shy.

 

Even many of the questions asked on this forum should better be asked of the administrators at colleges, but some of us are too reluctant to ask there, and prefer to ask our peers here, even though we do not know the answers.

Edited July 11, 2012 by mathwonk

[Kathy in Richmond]

Still the data posted by Kathy tells me some colleges, such as Stanford, are still not doing a good job of calculus placement, i.e. its not just me. Originally Posted by Kathy in Richmond:

 

"Over 100 kids started in Math 51h in September; after the first midterm almost 2/3 of the class dropped out."

 

In all fairness to Stanford, the standard recommendation for kids with a 5 in BC calculus is Math 51, the non-honors version. And the honors 51H course home page has lots of warnings about time commitment and difficulty level. It's the one class at Stanford that you can drop even after the drop deadline w/o penalty! But Stanford also has a policy of allowing kids to try a harder course than might be suggested, if they really want to. Overall, I think that's a good policy.:)

 

I am guessing she also used a better than average book for single variable AP calc, maybe Spivak or Apostol?

 

L's single variable calculus class was, ummm, very different! She's an extreme big-picture, visual spatial learner. The typical calculus text was a huge turnoff. While Apostol worked well for her brother, she didn't want to give it a go (sibling rivalry?! she often refused texts that her brother had used)

 

Since L had been exposed to real analysis at summer mathcamp, but since she still needed that AP calc score for college, I decided to try something completely different. I had her use Calculus for the Forgetful, a slim paperback meant for adults trying to refresh their forgotten math skills. It's very theory-oriented, and has only a few, albeit tough (a la AoPS style) problems. When she finished that book, she then worked through Barron's AP prep guide. She is SO non-detail, non-calculation oriented, that she needed that sort of practice in order to get that darned AP score.

 

Those are good ideas. Another thing I tried recently was scheduling office hours in a class room rather than in my office. I noticed few students coming to office hours and conjectured that it was intimidating. A classroom was more familiar and attracted a larger group who then solved problems together. I also scheduled them at different times to accommodate people with different schedules.

 

Very interesting approach; never thought of it, but it makes sense.

 

I had a different problem at GA Tech. I couldn't intimidate students for the life of me - I looked about 18 years old, even though I was older. My other problem was that the students would come to my office during office hours, see me, and ask me for an appointment to see Dr. Last Name. They thought that i was his secretary! Sometimes I played along, but were they ever embarrassed when they found out. And I knew exactly who wasn't attending lectures.:D

 

My time at Harvard persuades me that although many Harvard students are very intelligent, their key distinction is a strong self confidence and aggressiveness in seeking their goals. They know what they want and they go after it to a degree that differs greatly from students at the typical state school familiar to me. I.e. these elite students do better mainly because they try harder, are disciplined, and are not shy.

 

I've noticed this trend, too. Not to say that state school kids aren't this way, though; some certainly are! but to succeed at schools like Harvard, I think that you need to be this sort of personality.

[regentrude]

Another thing I tried recently was scheduling office hours in a class room rather than in my office. I noticed few students coming to office hours and conjectured that it was intimidating. A classroom was more familiar and attracted a larger group who then solved problems together. I also scheduled them at different times to accommodate people with different schedules.

 

We have been doing something like this for our introductory physics courses for years. We call it Physics Learning Center. All instructors involved in the engineering physics course for 450 people cooperate and offer an open learning environment staffed with one of the instructors and two peer learning assistants (students who successfully completed the course and received training in pedagody) for a two afternoons and two evenings each week. The instructors take turns and use it as substitute for office hours.

For my own smaller courses (110 students and just myself as instructor) I run such a learning center on the afternoon and evening before homework is due.

The biggest advantage is that you can get students to work in groups and help each other and just facilitate their learning by being in the background and only stepping in as needed. I get a regular attendance of about 25% of my students every week.

Edited July 11, 2012 by regentrude

[creekland]

 

My theory is that students who excelled in poor high schools learn to avoid other students and work alone. When their success gets them into a good college this habit backfires. This may explain my failure in college after excelling at a mediocre southern high school working entirely on my own. It occurred to me that some home school students may have the same problem I had, of not realizing that in a good college the students can help each other, and those who do not take advantage of this may fall behind. I.e. challenging study groups may be advised.

 

 

 

Interesting theory. Homeschoolers are not necessarily at a disadvantage for this, but it will depend upon how they are guided. I've always "preached" the value of study groups to my guys based on my Physics undergrad experience - though I make sure they are aware they need to understand what is being discussed - not just copying an answer (as happens in our group work in high school).

 

In his cc Microbio course, my then junior in high school joined a group right away. Within 3 weeks he was leading the group. I asked hubby (who drove him there and worked on a computer while waiting) if the other kids were aware that kiddo was still a junior in high school. He didn't think so at first, but they figured it out by halfway through the course (mainly because he didn't have his driver's license yet). It didn't matter. They still wanted him to lead. Hubby said he overheard them once saying they didn't want to put down an answer in a Study Guide until they knew kiddo approved. My guy got one of 4 As in the class. He was loved as a leader and a lab partner.

 

In his Effective Speaking class similar sorts of things happened. They didn't have one group, but had groups based upon projects being done. Nonetheless, after starting "even" my guy ended up leading and ended up being expected to lead in later groups once kids knew each other.

 

In ps, my youngest almost always leads his groups. He's in ps now, but was hs from 5th - 8th. He'll fully tell you the education was better with our hs, but he prefers the socialization of ps. His biggest beef with his peers in hs is that they don't care to learn at all. They want to know the minimum they need for a test, then they (sometimes) try to memorize that, but they never really care to learn it. They love him as a leader of their groups as they really just want to make sure they have the correct answers and know they have better odds with him. He tries to engage them, but with few exceptions, it doesn't work. Their group-work is copying. It's my belief that this then carries over to their expectations in college group work. (Sometimes is in parentheses because many don't care enough to memorize. My guy's been chided more than once for wanting an A when a C is enough to pass - kids have specifically told him this.)

 

I think who does what in Study Groups CAN be enhanced by homeschooling rather than hurt by it. It all depends upon the foundation the student has and their drive. PLUS, I think many kids in ps might be better off if they had to do their own work more often instead of learning to depend upon a group. Study groups are great outside of school (I had them back in high school and college), but when we create them in school, the kids don't have motivation to learn, they have motivation to get the best grade they can by copying. One teacher can't be supervising every group at once and kids know that VERY well. Kids in our school are missing the foundation. Group work (aka copying) is started VERY early - prior to 7th grade.

[regentrude]

My theory is that students who excelled in poor high schools learn to avoid other students and work alone. When their success gets them into a good college this habit backfires. This may explain my failure in college after excelling at a mediocre southern high school working entirely on my own. It occurred to me that some home school students may have the same problem I had, of not realizing that in a good college the students can help each other, and those who do not take advantage of this may fall behind. I.e. challenging study groups may be advised.

 

I agree. For students who excelled in poor high schools, another aspect definitely comes in: being challenged for the very first time in their lives and struggling, they take it as a reflection of their innate ability.

I went to school in Germany, very good school, but I was still not challenged and never had to work hard. My first semester physics at the university was horrible, because I did not know HOW to study - in my mind, not understanding the material immediately meant that I had to be too stupid. I observe the same with many of my students who breezed through high school and then hit the wall at the university; for many of them, this translates into self-doubt, they feel stupid and inadequate, when all they really need to do is learn how to study, and they'll be fine.

As for you, joining a study group was invaluable for me; it was the tool that turned me from a despairing D-student into a confident A-student within one semester.

[regentrude]

In his cc Microbio course, my then junior in high school joined a group right away. Within 3 weeks he was leading the group. I asked hubby (who drove him there and worked on a computer while waiting) if the other kids were aware that kiddo was still a junior in high school. He didn't think so at first, but they figured it out by halfway through the course (mainly because he didn't have his driver's license yet). It didn't matter. They still wanted him to lead. Hubby said he overheard them once saying they didn't want to put down an answer in a Study Guide until they knew kiddo approved. My guy got one of 4 As in the class. He was loved as a leader and a lab partner.

 

 

My DD had a similar experience with group work in her physics class. She did not belong to a study group, but there is a lot of cooperative activity built into the class, and she often ended up leading the discussion in her group. Explaining material to other students is the best way to develop an in-depth understanding (as every instructor knows: you don't really understand something until you have taught it). Her age never mattered, even though they eventually found out she was only 13.

 

Since last year she has been volunteering as a tutor in my physics learning center (the open learning environment I wrote about in my earlier post). She is respected by the students, even when they find out her age (I overheard them talking about her). For her, this is a fantastic learning opportunity which greatly enhances everything we do at home.

[mathwonk]

I love all these examples of success and methods to it. The following sobering experience of creekland's child beginning to tutor is the challenge facing all teachers in ps:

 

"His biggest beef with his peers in hs is that they don't care to learn at all. ..... He tries to engage them, but with few exceptions, it doesn't work."

 

I never solved this problem for the majority in over 40 years of trying. One obstacle is inherent in the lecture - hw/test -grade, system. I could get through to one student at a time in my office, sometimes with hours of discussion. But I didn't have time/energy for that with two classes of 30-50 students each. Do the math for spending one hour per week with each student. My own freshman college honors calculus class had 135, the graduate analysis course I took as a senior had 110.

 

I remember being thrown out of that last professor's office when I dropped in to show him my solution of a problem he said in class he himself did not know how to do! When my son was at GaTech about 1990, I think 140 - 170 students in Engineering calculus was standard. Comments/questions from the audience seemed discouraged/non - existent on the days I sat in.

 

One tactic one can use to encourage participation is to learn every student's name and call on them. As I aged, this task went from taking 5 minutes to taking 8 weeks but I always did it, even though it was embarrassing recently to ask someones name for the umpteenth time.

Edited July 11, 2012 by mathwonk

[mathwonk]

I love this comment by Kathy in Richmond:

"I had a different problem at GA Tech. I couldn't intimidate students for the life of me - I looked about 18 years old, even though I was older." :lol:

 

I guess I got more scary as I got older. On my first job, at 28, it was sometimes fun to sit down in the class with the students and wait for the prof (me) to enter. I realized at some point I might overhear more than I wanted that way! I guess I wasn't very intimidating either, as one of my students actually threatened me physically, outside class, over his grade. Another one implied suicide if I didn't change his. Teaching can lead to a lot of experiences you are not trained for.

 

Once as a young parent, babysitting while teaching, I brought my 10 year old to class where he sat in the front. The students were puzzled and unsure of his status there, so to confound it further, when no one volunteered to answer a basic algebra question, I spontaneously (and stupidly) called on him for the right answer.

 

Of course this was terrible pedagogy as I sensed it made some in my class feel bad, and I never did anything like that again. But we learn from our mistakes.

 

Inspired by Kathy's teaching tips elsewhere, although in this skill I am still learning from experts here, I try to:

 

always encourage and praise, honestly.

 

not embarrass anyone.

 

admit ones own mistakes, and use it to encourage experimentation.

 

always prepare thoroughly, and show an example of hard, consistent, work.

 

learn when enough is enough, but point to something for later.

 

see why everything is interesting.

Edited July 11, 2012 by mathwonk

[creekland]

I love all these examples of success and methods to it. The following sobering experience of creekland's child beginning to tutor is the challenge facing all teachers in ps:

 

"His biggest beef with his peers in hs is that they don't care to learn at all. ..... He tries to engage them, but with few exceptions, it doesn't work."

 

I never solved this problem for the majority in over 40 years of trying. One obstacle is inherent in the lecture - hw/test -grade, system. I could get through to one student at a time in my office, sometimes with hours of discussion. But I didn't have time/energy for that with two classes of 30-50 students each. Do the math for spending one hour per week with each student. My own freshman college honors calculus class had 135, the graduate analysis course I took as a senior had 110.

 

I remember being thrown out of that last professor's office when I dropped in to show him my solution of a problem he said in class he himself did not know how to do! When my son was at GaTech about 1990, I think 140 - 170 students in Engineering calculus was standard. Comments/questions from the audience seemed discouraged/non - existent on the days I sat in.

 

One tactic one can use to encourage participation is to learn every student's name and call on them. As I aged, this task went from taking 5 minutes to taking 8 weeks but I always did it, even though it was embarrassing recently to ask someones name for the umpteenth time.

 

I definitely try to engage every student (by name) when I'm in a class teaching. I sometimes even create "random name generators" (pieces of paper with each name listed) in order to create some suspense out of it all and try to keep them all paying attention.

 

But my all means, this is where homeschooling can shine. One can go at each student's level and make certain everything is mastered, not memorized. In school you must plod on even if some are left behind. You have a schedule and it must be kept. In math, getting left behind is almost akin to a math death sentence. By high school one ought to be getting more used to a quick pace in order to get ready for college - and learn how to truly study, but for foundations while the math brain is still developing, it sure helps to be able to move at the student's pace without the stigma of being "stupid" because you've been put in a lower class.

 

My youngest was 2 years behind in math when I pulled him out after 4th grade. We were able to catch up and move ahead by being at home. That would have never happened if he'd stayed in ps. Now that he's in high school, he's fell to the common denominator our school offers (at the national average - high for our ps), but he MIGHT be starting to get a little bit of self-motivation to do more as he's starting to see the scholarship advantages to being able to do well on the SAT/ACT. Time will tell. Unfortunately, he's a naturally lazy academic student who happens to grasp enough well to have all As at our ps, but that's not saying much foundationally. He will have to get the motivation to do more if he's to do well at any sort of higher level college. I'm letting that play out as it does at this point. Otherwise, I'm afraid if I'm his motivation here he'll get there and fail miserably. I'll guide, but he has to "do" (or not).

 

Part of why he likes ps is it's easier than what we did - much less work required, and I don't mean busywork. (sigh)

[regentrude]

One tactic one can use to encourage participation is to learn every student's name and call on them. As I aged, this task went from taking 5 minutes to taking 8 weeks but I always did it, even though it was embarrassing recently to ask someones name for the umpteenth time.

 

:iagree:

I feel this makes a BIG difference for the whole dynamic in my class. Students can no longer hide in the anonymity of a 90 student group - they are held accountable. I think learning all the names (I am usually done by week 3) also shows that I care about them. Judging from the comments on the evaluations, they really like that.

 

I like knowing things about my students' personal lives, too, because this helps me relate to them as whole personalities (if that makes any sense). I always ask them on my first day questionnaire to share one thing that they find interesting about themselves - a hobby, or a job, or a special experience. This is also a useful device that helps me learn their names.

[Caroline]

:iagree:

I feel this makes a BIG difference for the whole dynamic in my class. Students can no longer hide in the anonymity of a 90 student group - they are held accountable. I think learning all the names (I am usually done by week 3) also shows that I care about them. Judging from the comments on the evaluations, they really like that.

 

I like knowing things about my students' personal lives, too, because this helps me relate to them as whole personalities (if that makes any sense). I always ask them on my first day questionnaire to share one thing that they find interesting about themselves - a hobby, or a job, or a special experience. This is also a useful device that helps me learn their names.

 

I totally agree with this, too. I teach both high school and colleg math (in Georgia.) I do much better when I know all of their names, which isn't hard in my high school classes, but in my once a week college class, it was hard. I printed out their pictures and learned them that way. Another trick is to split them into groups. I do small lectures to each group. It was a math ed class, and a little smaller. I was totally shocked at the lack of trig knowledge in my college class. I decided to focus on that since these people were going to be high school math teachers.

 

My degrees are in engineering, so I do approach math from that perspective. (I have decided not to take personally the comments disparaging AP Calculus teachers, as many of my students have gone on to ace calc in college. But a lot also get 1s and 2s. They take intro calc in college and do really well because they have a foundation. When mom and dad never got beyond 4th grade, calc can be intimidating the first time through.)

 

I, too, took my 10 year old to class one night. He had a blast and could do the algebra better than my college students. But, he is my kid, and we expect a lot out of him. He did LOF pre-algebra in his spare time at school this year.

 

I have enjoyed this discussion. Mathwonk, I was in grad school at GA Tech right after your son was there. If you get a moment, I would love a private message with some good calculus resources. We are adopting new textbooks this year.

[regentrude]

Once as a young parent, babysitting while teaching, I brought my 10 year old to class where he sat in the front. The students were puzzled and unsure of his status there, so to confound it further, when no one volunteered to answer a basic algebra question, I spontaneously (and stupidly) called on him for the right answer.

 

Of course this was terrible pedagogy as I sensed it made some in my class feel bad, and I never did anything like that again. But we learn from our mistakes.

 

But if a ten year old knows what they should have known but did not, SHOULD they not rightly be feeling bad?

Is it helpful if we focus so much on making the students feel good that we bend over backwards to not make them realize where they have gaping holes in the fundamentals?

I am not meaning to be snarky, these are questions that come up for me every semester. How do I respond if my science majors at a 4 year university can not do 9th grade algebra? Do I do them a favor if I let them believe that the quadratic formula is one of the terribly hard things about college physics - or shouldn't I rather remind them that this has nothing to do with hard physics, but rather is material from early high school?

 

Since you have much longer experience teaching, maybe you can tell me how I can continue to bite my tongue and be patient? Sometimes I am ready to scream "but my 13 y/o can do this, why can't you???" Of course I don't (but I can't help thinking it... how can 20 year olds fail the course that my 8th grader aced with only moderate effort...) Sigh.

Edited July 12, 2012 by regentrude

[mathwonk]

@regentrude, these are wonderful points.

 

I will make an attempt to share my perspective on teaching in spite of my checkered reputation in this regard.

 

I am a pragmatist as well as occasionally an idealist. Of course the students should know this, but we may wish to use our experience to determine what will achieve our goals with the students we have. My goal is not to make my students feel good but to help them improve in math and in life. Thus I want to adapt my responses to them, to what seems to motivate each one.

 

Some students are like me, motivated by challenges, even disrespect, to show that they can indeed excel, even in the face of doubt. But this seems more rare than might be expected. So if I perceive that a certain student is easily discouraged, and responds better to gentleness than reproach, I may choose that. I have to choose whether to give a student what he/she "deserves" or what will achieve the goal I have for that student.

 

It is not so simple of course. Some students, again like me, may respond to failure, by being motivated to return and prove they can succeed, but others may just give up. This makes teaching a fascinating challenge.

 

Once I was teaching children and with my back to the board, asked a question. A student shouted out a spontaneous correct answer and I praised him. When I turned around another student was visibly disturbed. What was going on? I thought long and hard and concluded the disturbed student had the answer also, but had politely raised his hand, and thus been ignored. I went to him and apologized. he seemed relived but to this day I have no feedback as to whether I understood the dynamic correctly.

 

In another case a student came to me with a checkered background of poor attention, poor attendance and poor work habits, but he needed my class, and it mattered to me that he succeed. Normally if a student fails from poor work habits I don't "care", assuming the lesson of failure will be useful, but this student was on his last chance.

 

I told him straight up: " Look here, you have a bad track record, and I don't want to take you unless you intend to show me consistent attendance and hard work. One slip up and you are out."

 

i also knew his history and that this was the expectancy from his family. To me however, as a "insert weak adjective" liberal, this was out of character. This student handed in every assignment and ended up with the top grade in my class. Usually I eschew the role of personal trainer, expecting my students to be self motivated, but I helped this guy by being stricter.

 

there is no right way to behave, but I did observe that in my college classes there were a lot of insecure students so I cut them some slack. (To be honest, my evaluations suffered when I was more blunt as well.)

 

You don't always have to bite your tongue. One of my colleagues once walked out of a class from disappointment at the pitiful response of his class and went to his office to be alone. Frightened, the class eventually sent representatives to his office to ask him to return. I never had this much nerve, but as a very young first time instructor, I did once just sit down in my class and meditate for most of the hour, when people were not paying attention. I wonder why I didn't get fired sooner. Sometimes if your outrageousness surpasses what is expected there is no predictable response.

 

I had a wonderfully supportive advisor, but one day he asked what I had done with a certain paper in German, and I said all I had done that week was translate it. He looked me dead in the face and said, "didn't you feel like THINKING?" I went straight to the library and worked on understanding it as hard as I could for a long time. But that bluntness wouldn't have worked every day.

 

To answer your real question, we want to teach, but not destroy. So it is indeed ok to reproach a student to the extent that he/she realizes we expect more, and that we believe he/she is capable of more. But it is counterproductive with average students to make them feel humiliated. And teachers have enormous power, so must learn great restraint. A few words or even a look have great effect. When I tried to home school my son, I gradually realized that even a very bright child sometimes missed things I had assumed were easy, and yet he was still trying to please me. Students do want to please us, as long as they don't hate us, and we need to be very sensitive to this. if we keep their respect, we can ask for a lot, but we need to realize how hard it is to learn, even when trying. I.e. simply making ridiculous mistakes is not proof that the student is not trying. They may not get it, or they may not know yet how to learn. Experience says it helps to err on the side of assuming they are trying their best and need help. (Easier said than done!!!)

 

Sometimes I tell my class they are my team, and I am committed to help them get in shape and make up any deficiencies they have. I.e. I take them as they are, and if they will work with me I will also commit to them. they can ask anything from any previous class and i will answer. They can also come back to me for help in any future class. Oddly I get few takers on this. It seems indeed many students really don't care to learn, but we are there for them anyway, if they ever do.

 

Hang in there. You sound like you are giving it your all. And remember, your 13 year old is very specially gifted and advantaged. He/she has you as personal teacher and parent.

 

simple minded comment that occasionally crossed my mind: if my students could do what seems routine to me, or learn it by reading, i wouldn't have a job teaching them!

Edited July 12, 2012 by mathwonk

[Barbara H]

 

Once as a young parent, babysitting while teaching, I brought my 10 year old to class where he sat in the front. The students were puzzled and unsure of his status there, so to confound it further, when no one volunteered to answer a basic algebra question, I spontaneously (and stupidly) called on him for the right answer.

 

Of course this was terrible pedagogy as I sensed it made some in my class feel bad, and I never did anything like that again. But we learn from our mistakes.

 

 

I would find it to be terrible if you said to the class "Aw come on a 10 year old can answer it, why can't you." But, just calling on the ten year old I don't see the problem. While I understand it was just babysitting here, there are kids who are in college a lot younger. Does that intimidate some students? Probably. But, I bet there are also male students who are intimidated when female students are learning the subject faster. Pointing it out is not okay, but the fact that a difference exists is and it isn't the instructor's responsibility to prevent people from having their own internal feelings about how other people are learning the material.

[mathwonk]

@ regentrude: Again i ask for indulgence - I cannot give advice on teaching, I only can share my experience.

 

If I am impatient with students who are slower than i am, and insecure when faced with those who are quicker than I am, then whom can I teach? Only students exactly like me?

 

I must learn patience for slower students and modesty for quicker students. This is possible but requires practice.

 

Besides, if I cannot learn to teach, why should I fault students who cannot learn math?

Edited July 12, 2012 by mathwonk

[mathwonk]

Barbara H, good points! Thank you for your indulgence. I feel better already! About male vs female students: that has not come up lately here, but my wife had to put up with male students telling her she should not be in the pre med class they were in because her superior performance was making it harder for them to get admitted to med school! Helloooo!!!! There were also med school profs who were biased against women, but eventually came around.

Edited July 12, 2012 by mathwonk

[regentrude]

@mathwonk:

thanks a lot for sharing your thoughts and perspective.

I perfectly understand what you are saying about different students needing different approaches. My colleague who teaches the big intro course is the drill sergeant type and my complete opposite, I am more the motherly caring type. He reaches students who need the kick in the behind and whom I can not make do the work with my style, but there are also students who cry in his class who thrive with my approach.

 

I am also struggling with my role (and we have discussions among instructors about this very topic frequently): to what extent should I be responsible for their character development? I am there to teach physics to adults - is it my job to make up for shortcomings in their parenting?

For example, it greatly bothers me that we are "encouraged" by the administration to give rewards for attending and doing homework, all things the should be mature enough to just do if they want to succeed - and conversely, not being punished for not doing it if they have mastered the material. Where I went to university, a college student is judged on his knowledge and performance in few rare examinations, not for trying. In a sense, we are treating them like children and are using kindergarten methods to get them to cooperate.

 

Just to make it clear: I do not mind working with students patiently who are working hard and struggling. I was one of them until it clicked. I happily spend whatever time and effort is needed to help them, as long as I see they are putting in time and work.

I do mind being expected to perform the miracle of teaching students who are NOT putting in the effort and who somehow make it my fault that they are failing. I also mind being expected to make up for the shortcomings of public school education and parenting which leave students both without basic math skills and basic work ethic.

Does that make any sense?

[creekland]

I do mind being expected to perform the miracle of teaching students who are NOT putting in the effort and who somehow make it my fault that they are failing.

 

So this is happening in college too? :glare: It frustrates me that we have to deal with it in high school. A student can miss weeks of school, turn in no assignments, pay no attention in class, fail several quizzes and tests, and in the end, it's the teacher's fault. So teachers dumb down their materials and give credit for things like bringing in cans for a food drive... This really hurts those who can do well (not enough foundation) and trains the average student that not much is needed to succeed.

 

We have No Child Left Behind - and I agree with it for the elementary years - but by high school, we need to be able to take those who don't want an academic path and let them choose another (generally trades). If we could make that one difference happen in our high schools, it, alone, would help tremendously. Instead, our country is going the other way and insisting that all these no-shows (physically and/or mentally) need to take even more math/science classes. Again, this is where homeschooling can really tailor an education appropriately IMO. Public schools are far too rigid in what they require.

[regentrude]

So this is happening in college too?

 

Unfortunately, yes.

In fact, almost every student who fails my course does so because of a lack of effort (very very rarely there is one who just does not have the intellectual capability - but that is one in 500 or 1,000).

I have been teaching for ten years. Every single student who fails my course has missed several classes and has not turned in several (and often many) homework assignments. I have never seen a student fail who did every homework and attended every class - because if you simply do that, you'll learn enough to at least pass.

[flyingiguana]

 

By and large colleges that refuse credit at least in math, are doing so in my opinion not to gouge tuition, but because experience shows the inferior quality of these high school AP courses and tests.

 

And it's generally professors who make these decisions about whether to accept AP or not. Tuition dollars are not really on their radar. They just know how students do.

 

Even if the AP class was good, if it's feeding into the next class in a sequence (such as in math and science), the student may be better off taking the course that would have been AP at the college they're going to go to. The faculty do talk among themselves about standardizing approaches and making sure students have the background they need for the next courses in the sequence. This can make a big difference.

 

As always, there are a few students who will do well no matter what they're background. But professors are trying to help all students pass, and they often can't tell which are the really stellar students who will do well despite a less than stellar background. Test scores are really no indication -- AP, ACT, or SAT. There are stellar students who score lower on those and less than stellar students who score really high.

 

I'd advise not obsessing about getting credits out of the way. Of my daughter's 12 pre-college credits (3 were AP), only 5 got her out of any classes. This isn't to say she shouldn't have done the pre-college credits. I think they were of benefit to her in less tangible ways, but they didn't do her as much financial good as friends and neighbors were all telling us they would. In fact, she probably only got the 5 credits she did because I was advising her about the best courses to take. She did the Calculus BC test (which gave her 2 credits) and then took the third semester of calc and a full year of physics at a local college while she was in high school. But I was very careful to make sure she not only took these courses (advisors told her not to -- they were too hard), but that she took the right ones that would transfer into a physics program.

 

None of her humanities credits did her any good. She's in the honors program and those courses didn't count for that. Counterintuitively, the brighter the student, the less likely it will be that credits earned in high school will amount to anything at college.

[flyingiguana]

Unfortunately, yes.

In fact, almost every student who fails my course does so because of a lack of effort (very very rarely there is one who just does not have the intellectual capability - but that is one in 500 or 1,000).

I have been teaching for ten years. Every single student who fails my course has missed several classes and has not turned in several (and often many) homework assignments. I have never seen a student fail who did every homework and attended every class - because if you simply do that, you'll learn enough to at least pass.

 

I always say students have to try very hard to fail.

 

This is tongue in cheek, but I actually did have a student who really hoped to fail. He didn't want to be a doctor, but this was the only way he knew how to tell his parents so they'd really get the message.

 

But I have to admit, I did once have ONE student who came to every class, who turned in every assignment and took every quiz and test who still failed. That was a rare case.

[mathwonk]

Regentrude, what you say not only makes sense to me, it also agrees exactly with my own experience. Unfortunately one of the suggestions I would make a teacher in public school, is to take breaks from the job. I used to have to teach also in the summer to earn money to support my family in years when my research grant was denied. Those years it was hard to return in the Fall with enough enthusiasm to do a good job. Teacher burnout is almost a given. One of the most short sighted policies of the university where I taught was a complete lack of a sabbatical program. Having teachers work 30 years with no chance to "recharge batteries" is a huge mistake in terms of the quality of service they can deliver. Schools with sabbatical programs normally offer a semester off every 7 years, to do research and get a fresh perspective. You owe it to yourself and your students to take time off, so you can come back with renewed energy and optimism, in my opinion.

 

 

flyingiguana: "Counterintuitively, the brighter the student, the less likely it will be that credits earned in high school will amount to anything at college."

 

The no child left behind law actually makes this official policy. I had a brilliant undergraduate student in math who found her real love was biology, switched after a few years with me, then took a PhD at MIT. She directed courses, wrote grants, obtained patents, and had several prestigious job offers upon graduation. She preferred to raise a family, moved to a small community with her professor husband and tried to get a local teaching job.

 

According to NCLB, she should have obtained college credit for certain courses she had taken in middle school! So she was considered to be, not extremely highly qualified, but under qualified, and was not hired. That didn't stop her as she opened a consulting business from home and went right along, but the local school system lost possibly the most qualified person ever to apply. She was the best student I ever had all around in over 30 years.

 

Oh, and after years of believing any student who tried could pass, I also had one counterexample, out of literally thousands.

 

Although I used to give three initial grades: test average (after dropping one or two), homework (sometimes graded only for effort), and final exam (always with possible extra credit), and then gave the student the higher of: either a weighted average of these, or the final exam score, I was considered a very tough grader because I did not guarantee a certain percentage of A's.

 

I was once criticized by a friend in a related department for giving an F to a student of theirs who had average 40% on all work, and on the final, as well as not being able on the final even to state the meaning of the concept we had spent the whole semester studying in detail. Today after many more years of downgrading my standards, I admit that almost sounds a little strict to me!

 

When I started teaching in the south I already had 7 years of college teaching experience in the west and northwest, and had never given an F. I gave one in my first year in the south to a student whose final exam had essentially nothing correct on it. In those days we were using the same standard books that were used at the best schools. We gradually moved away from that stance, but now even schools with much better reputations use much easier books. (I myself am from Tennessee, but even the low level high school algebra books we used in 1956, and which left me woefully unprepared for college in 1960, look hard by today's standards.)

 

Text books have decreased in difficulty noticeably every 20 years or so, according to a high school teacher friend of mine; the following examples are from a study of it that he did.

 

Here is a "C level" (hardest) algebra problem from a 1977 algebra book by Dolciani et al. (most students don't do these at all):

 

{1 - 1/[c/d + 2]} / {1 + 3/[c/(2d) + 1]}. simplify.

 

 

On the other hand here is a problem from an 1895 algebra book, Treatise on Algebra, by Charles Smith:

 

{a^2 (1/b - 1/c) + b^2 (1/c - 1/a) + c^2 (1/a - 1/b)} / {a(1/b - 1/c) + b(1/c - 1/a) + c(1/a - 1/b)}. simplify. Hint: the answer is a+b+c.

 

My friend said that a student who had studied from Smith's book might be able to do this is his/her head! but that he considered it "essentially undoable by either today's students or teachers".

 

(I remark also that in Smith's book, and apparently from Euler's time until maybe 75-100 years ago, the study of infinite series was considered part of precalculus, whereas now it occurs usually in 2nd or 3rd semester calculus.)

 

 

Here is my friend's assessment of the Dolciani book:

 

"Each section gives a rule, but the assignments do not deviate at all from the rule. Each homework problem is a minor variation on the worked examples. In a profound sense, the student need not think, just apply rules. The only reward is the momentary rush of having gotten the right answer. The intellectual goal is to learn to follow the rules. In my opinion it is fair to say this book has no content. Once the rules are forgotten (as they always are) NOTHING remains. An education that consist of rules trains someone to be a teacher, nothing more."

 

This outstanding teacher wrote that years ago and is now deceased and greatly missed. (His school had to hire two more teachers in trying to reproduce the work he had been doing.)

Edited July 12, 2012 by mathwonk

[regentrude]

Regentrude, what you say not only makes sense to me, it also agrees exactly with my own experience. Unfortunately one of the suggestions I would make a teacher in public school, is to take breaks from the job. I used to have to teach also in the summer to earn money to support my family in years when my research grant was denied. Those years it was hard to return in the Fall with enough enthusiasm to do a good job. Teacher burnout is almost a given. ... You owe it to yourself and your students to take time off, so you can come back with renewed energy and optimism, in my opinion.

 

 

I agree. I have taught summer sessions twice, and even though I enjoy the smaller class sizes and more relaxed atmosphere, I do not feel as excited about going back to the more strenuous fall semester.

In our department, people volunteer for summer teaching, we are not forced to. I am fortunate that I am not the sole earner in our fmaily and that I can afford to just stick with my nine month contract and not volunteer for summers; at least I won't as long as I am still homeschooling my kids. the break is wonderful, and I am already excitedly awaiting the fall semester and itching to go back to teaching.

[mathwonk]

Gee whiz, I asked and I got more than I can handle of data on math courses and AP tests at UGA.

 

Suffice it to say a 5 on the BC is good preparation no matter what course a student takes. By far most of the students taking math 3500(H) at UGA come in with a 5 on BC, and about 90% "succeed".

 

Interestingly however of the smaller number who come in with either a 3,4 or 5 on the AB, 100% "succeed"! It seems you can make any case you want with statistics carefully presented.

 

The success rate of students with a 5 on the BC who go into other courses, like the 2400 or 2410 courses I recommend is also about 90%, and a little higher (94%) for those who go to the non honors 3rd semester course 2500.

 

When I asked how those AP students survive 3500 without background in proofs, I was told that since they are the primary audience, a specific effort is made to teach proofs in the course for their benefit.

 

Interestingly among students who apparently started college in second semester science and engineering calculus, math 2260 with AP preparation, the majority who came in with a 4 or 5 on the AB test had about a 75% success rate, compared to a 63% success rate for the smaller number of students who came in with a 4 or 5 on the BC test. Not significant perhaps, but unexpected by the lay person like me in statistics.

 

As a cold statistic, 75% success may sound good, but to a teacher having on average 1/4 of a class get D's, F's, or W's, can be discouraging.

 

Of students entering in first semester non honors calculus, the few who had 3,4 or 5 on the BC had a 100% success rate, and the majority entering with 3,4, or 5 on the AB had about a 90% success rate.

 

I do not know the exact definition of "success" (presumably C or above), or whether people who drop out early are counted at all. I also do not know just how much more preparation these students actually have who only show up on the data as having a certain AP score. As we know, some of those students have also studied analysis and several variable calculus at much higher levels.

Edited July 13, 2012 by mathwonk