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Bostonian

Which AP exams earn credits at the most colleges?

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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.

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I just want to say thanks for this thread! I am intrigued by the statistics on AP Calc, and the discussion among dedicated college professors. It is heartening to see your concern for students and willingness to go the extra mile in your teaching.

 

FWIW, both of my two oldest took AP Calc exams.

 

Oldest took AB because he took a long time to get through Precalc (worth it, in my opinion). He got a 5. He felt well prepared for Calc II and beyond. The large land-grant uni he attended required all AP credit to be verified with a pretest taken before he began his first semester as a freshman (that's common practice at engineering schools). He graduated with a double major in math and CS, and won an award in the math dept at graduation.

 

Next oldest took the BC and received a 5 as well. She felt well prepared for Calc III and plans to either minor or major in math (can't decide). Incidentally, she's interning this summer at the CCQC at UGA. :)

 

I'm really enjoying this discussion!

 

And to the OP, you asked a great question, but there are too many variables to answer. If receiving credit for APs is important to your student, I advise checking potential AP credit with several colleges you think might be a good fit. Ds said that the average number of AP credits with his freshman friends at his uni was 12, but some had more and some had none. Some took a lot of tests but didn't get credit for many. However, almost all of the engineering applicants accepted at his school had physics and at least some calculus in high school. That reminds me of the point Creekland often makes - that the admission requirements posted on college websites are minimums, and most applicants have much more.

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Oddly enough, validating through examination out of my freshman 2st semester English course came back to bite me during grad school. When I went back to get my MS Ed, I was told that I did not have enough course credits in English that specifically mentioned writing and rhetoric, even though my undergraduate degree is in English.

 

So off I went to a Teaching Composition course filled with would be teachers. I can say that I've hardly been in a room of worse writers, who confessed to being bad writers and to not liking to write. But they all completed the course and checked the block. Presumably many of them are in teaching jobs that require grading and even teaching this subject that they did not enjoy and had often not mastered. (This complaint applied to about half of the students in the course.)

 

I learned a substantial amount from my high school English teachers. Four of them were very good, passionate about literature and writing and holding students to a gold standard of grammar and expression. But other than having to sit through that Teaching Comp course once a week, I do not regret having moved on to the honors level English course as a college Freshman.

 

(FWIW, there was nothing I could say to anyone in the administration of my grad program to get them to extend credit for the rhetoric course I'd validated, or to accept competency in a skill that I'd demonstrated in a dozen upper level majors courses. I also could not get them to accept any of my engineering courses (EE, thermodynamics, naval architecture, weapons systems engineering, etc as worthy of a science credit for the purpose of teaching middle schoolers about science. I ended up taking a physical geography course to fill an earth science requirement. I did not find that there was much bending of rules or creativity in how one was allowed to fill requirements. I find the suggestion that a "good" advisor can magically make this happen a bit idealistic or representing the reality at one department in one school at one point in time.)

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: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.

 

Because you didn't get to enjoy the 1970s immersed in American culture, I offer a

of what I think of when the topic of profs of lectures learning names. (Only the first couple moments apply. And I'm sure you're much nicer than John Houseman.)

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Sebastian:

"FWIW, there was nothing I could say to anyone in the administration of my grad program to get them to extend credit. "

 

On the "magic" of making administrative obstacles disappear, indeed it may be I am naive and have a limited experience. And in your university it may be that nothing could prevail. To be clear, at my university the point seems to be that it is not what you say to the administration, but who says it. In my experience it was only when a professor took the trouble to intervene on behalf of the student that the magic happened.

 

All the cases I took on had been unsuccessfully pursued sometimes for months or years by the student himself or herself without success or hope of success. But when I took it on, as a professor, doors opened that had been closed. This may not hold true elsewhere, of course, but I suggest that when frustrated by university administration, it may help to enlist a helpful full professor.

 

It may also be partly how one asks. My approach was to avoid protesting or complaining about the obstacle, and instead just asking the person causing the obstruction how it could be surmounted. They were usually glad to point out the secret to getting something done, when they were brought on as an advisor.

 

Of course there is no doubt some schools have administrations that are much more rigid, and perhaps mine was unusually helpful and friendly. Hence my experience may not extend much to other situations, but I mention it as worth trying.

 

These conditions also change over time of course. You are surely correct this is a function of the administrative atmosphere at a particular school and time. I know professors at some ivy league and other upper level schools who feel they have no administrative clout at all.

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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.

 

I had to chuckle at this... My college major was Physics. It comes with a Math minor (I believe I had to add one class for this, but I did). I also opted to get a Psychology minor just to mix up my classes a bit (plus I loved it).

 

I worked for Litton Industries a little bit after graduation, then opted to stay home and raise my family.

 

When youngest was 3, hubby decided to start a business, so I looked around for a part time job and decided to sub in our local middle/high school. At that time, one could do that with just "a" college degree. I started doing it and loved it (even though I was dismayed by some of what was going on academically). Others seem to think I do a reasonable job as kids often ask why I don't teach full time... The admin started to ask if I'd take a full time job. I told them I wasn't certified. (I'm not.) According to the state, I don't have the classes I NEED to be an effective teacher. It doesn't matter if the admin will vouch for me. It doesn't matter if oodles of kids would do the same. I don't have certain boxes checked.

 

To be fair to my admin, they've mentioned that I could teach while taking night classes for approx 18 months to check off those boxes and MIGHT be able to skip Student Teaching due to 13 years on the job that they'd vouch for), but honestly? I really don't care to jump through those hoops - esp while I'm also raising a family. Who wants night classes then? So, occasionally I work long term jobs (any I agree to where the admin can get legally by), but without those classes, I just don't have what it takes. ;)

 

When youngest heads off to college (2 years) I'm still more or less figuring out what I want to do. We may be traveling a bit. That wouldn't work with full time. I might do tutoring or something though.

 

The good thing about subbing (besides the flexibility) is I get to see pretty much ALL the math/science classes at our high school, so I know what is going on and what is being taught, etc. I also get to see almost ALL the kids at school. I actually do enjoy it. The math/science dept know me well, so I generally get to teach as opposed to babysitting. Even if it's last minute, they don't mind if I change plans to stick with what they would have done had they been there. Or, if I can't change something, I can at least catch up some kids who are missing things.

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Because you didn't get to enjoy the 1970s immersed in American culture, I offer a
of what I think of when the topic of profs of lectures learning names. (Only the first couple moments apply. And I'm sure you're much nicer than John Houseman.)

 

Thanks, Sebastian. I admit I quite like the professor's: "You assumed the first class would be a lecture, an introduction." Maybe I should learn from him...

 

Btw, I do not use a fixed seating chart - they can sit wherever they want. Experience shows, they will shuffle around a bit for the first three days and then find seats they keep for the remainder of the semester. (If they did not, learning names would be much harder)

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I forgot to mention that my daughter DID receive CREDIT for every course she brought in via AP or dual enrollment. What it may not have done for her is gotten her out of a class.

 

Credit is cheap. Lots of colleges give it willy nilly. But getting the requirements out of the way may not happen as the result of AP, so the credit may not be of any use.

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Thanks, Sebastian. I admit I quite like the professor's: "You assumed the first class would be a lecture, an introduction." Maybe I should learn from him...

 

I always hated the first lecture when it was just an introduction. I just wanted to jump right in.

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...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.

 

I don't think it is personality alone. It is part of the culture of the elite prep schools and "that" sort of family to work hard at giving their children this sort of confidence as part of their social skills. They consider it essential. The children who really aren't built to be able to do this are a complete mess by the time they finish high school but most of them come through with a "something" that helps them to go after what they want. I had friends who went to public school and friends who went to prep school and I find now that I can often tell right away which way a person was educated just by the way they approach other people. I'm not saying this is the only thing one needs to be successful or that one can't be successful without this, but it certainly helps when one wants to succeed in an anonymous situtaion like a difficult large lecture class. (I'm also not saying it is only prep schools and "that" sort of family that teaches this. My own family taught a quieter version, I've met people who were born this way, people who developed it naturally as they grew, people who deliberately taught themselves, and people who were forced to learn in order to survive. I'm just saying that prep schools and "that" sort of family value this and deliberately teach and encourage it.)

 

I think the idea of having some office hours in the classroom is brilliant. I had to grit my teeth to make myself go find a prof's office and I had to take several deep breaths to make myself knock. It got easier after the first few classes, but I understand why some students don't even try. If the office hours had been in the classroom, it wouldn't have been nearly as scary.

 

One of the things that worries me about my son's cc experience is that he is learning to work alone rather than in a group because the group situation (once he learned some study/classroom skills from them) has proved to be a him tutoring them situation instead of a mutual help situation. I keep pointing out that this won't be true of all his classes forever, but it worries me that he hasn't had the high school math experience I had of figuring out problem sets together in groups. Lots of adult problem solving works this way, and I consider it an essential skill for a not-brilliant-but-just-brightish person trying to get through engineering school.

 

Nan

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Nan" "One of the things that worries me about my son's cc experience is that he is learning to work alone rather than in a group because the group situation (once he learned some study/classroom skills from them) has proved to be a him tutoring them situation instead of a mutual help situation. I keep pointing out that this won't be true of all his classes forever"

 

This impression a student develops in a weak school, that the other students don't care, that the help sessions are for poor students, and so on, are exactly the habits that I suspect can cause a problem at a good college. All of a sudden, if one has managed to get into the right school for ones abilities, one is no longer an outlier but an "average" strong student. The extra programs are actually designed for you, not for the struggling student, but it is very hard to change our attitude.

 

When I entered college I assumed the other students wanted and needed my help, but they didn't think so, since they too had been the tutors at their high schools. Prep school kids, as you say, had already been taught they were the elite, and had better preparation and study habits by and large. One statistic however that was generally true there, was that the prep school kids were so advantaged coming in academically, that they did not struggle the first year as much as the high school kids.

 

This actually hurt them in the second year, and stats showed that public school kids came from behind to surpass the prep schoolers after a while. Home schooling may have been less common then, but I also remember one case of kid whose parents had been posted abroad, and he had never attended any formal school for his first 12 years of education, who was a star upon graduation from Harvard around 1970, (while I was out working in the meat market in "southie").

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Nerd alert! Did anyone try to simplify the fraction from the Charles Smith algebra book in post #99, either by simplifying the fraction (seems harder), or by multiplying the denominator by (a+b+c) and simplifying that? Did anyone feel challenged by the article's author to do it in his/her head? Did anyone read Uri Treisman's study linked in post #74?

 

 

In fact after one denominator - clearing operation, Smith's fraction becomes:

 

{a^3(c-b) + b^3(a-c) + c^3 (b-a)} / {a^2 (c-b) + b^2 (a-c) + c^2 (b-a)}.

 

A prize to anyone, or anyone's child, who can factor (by hand, no computers/calculators) these expressions completely into linear factors!

 

(Hint: To find factors, try the "factor theorem" or "root - factor theorem", i.e. if f(x) is a polynomial in x, then r is a root, i.e. f® = 0, if and only if (x-r) is a factor. And remember, any letter can be used for "x".)

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What may have complicated things in my situation was that they were not only concerned with my having enough credits for the masters but also with having credits for a teaching certification. For all I know, they had gone down that road in the past with other students, only to have them ground on the shoals of an inflexible certifying agency.

 

I cannot speak much to the effectiveness of having a prof try to get exceptions for requirements. My experience with both undergrad and graduate level was that profs (including advisors) were not often willing to advocate on behalf of the student. This of course depends greatly on the prof, the department and the school.

 

I do agree wholeheartedly with your suggestion that the question to ask is how one would go about requesting an exception, not to just start out with the complaint or objection.

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Sebastian: I agree completely. Your situation may indeed have been one in which nothing could have helped. The kind of thing I helped with was often relatively minor, like someone missing out on being on the honors program because of a single bad grade, or losing a scholarship because of a dropped class because they were in the hospital, and they usually involved missing a deadline. E.g. I helped someone get reinstated in the masters degree program who had waited 5-10 years to apply for it, but who had done essentially all the requisite work earlier.

 

And I also noticed that some professors were disinclined to get involved, either from not having the time, the awareness, or lack of interest. I kind of like being able to make things happen, so I enjoyed it, when I could. Maybe it was a reaction to my own situation in college also, where I may have felt that no one helped me navigate a cold bureaucracy (boy that's a tough spelling word for me, totally unlike my pronunciation of it - I can spell bureau easily!)

 

I learned the other point, about how to ask, the hard way too. Here are two sample conversations with a grant management department of a university:

 

professor 1): Why can't I spend that money on the equipment I want? I wrote the grant, and I brought in the money! All your department does is rake a big administrative percentage off the top and obstruct my use of the funds. etc etc etc...

 

professor 2): I realize this purchase I am trying to make is complicated, and I really appreciate your help facilitating it. Is there some way we can do this, and still comply with all your purchasing guidelines, perhaps by the first of next month?

 

 

Needless to say the results differed for these two professors (both of whom are me, at different times, as you probably guessed). Of course, at first I was obviously infinitely more clueless than most people about the proper approach, and consider myself at best a sort of "Adrian Monk" in diplomacy (if you watch that show), but I think I eventually got up maybe close to average. (My close acquaintances, who know me mostly as prof #1, would probably be laughing.)

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I want to revisit the challenge in post 112, to simplify the C. Smith book fraction from post 99. When I first tried it, all I could think of was to multiply out the denominators, so I multiplied by abc/abc and got the fraction in post 112. Then I had no idea what to do to simplify further, so I used the hint that the answer is a+b+c, and just multiplied the bottom of

 

{a^3(c-b) + b^3(a-c) + c^3 (b-a)} / {a^2 (c-b) + b^2 (a-c) + c^2 (b-a)},

 

by a+b+c, and showed you get the top. I could even do this in my head because it is clear that a times the first term in the bottom, plus b times the second term, plus c times the third term, already gives the top, so I just had to show that multiplying b+c times the first term in the bottom, plus a+c times the second, plus a+b times the third, gives zero.

 

It is amazing what you can do while lying asleep unable to doze off, and in fact you can easily check that b+c times the first term gives a^2 times (c^2-b^2), after a canceling a pair of terms. Now you don't need to do the others because it is "clear" by symmetry, that the second multiplication must give b^2 times (a^2-c^2) and the third must give c^2 times (b^2-a^2). Ok I cheated and didn't really do it all out.

 

But now we get, a^2c^2 - a^2b^2 + b^2a^2 - b^2c^2 + c^2b^2 - c^2a^2 = 0. done.

 

so much for doing it using the answer hint. I claim any algebra oriented kid could have done this with persistence, no creative thinking required. But simplifying it without using the answer is harder as I address next.

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Ok, at first I had no idea how to approach this problem without using the answer, I mean what does "simplify" mean? I know to get rid of denominators, but then what? (And remember I am a seasoned mathematician, but maybe a little clueless about explicit manipulative algebra; i.e. I have friends who would have blown this out of the water in a jiffy, but I felt challenged by it.)

 

Well what does it mean to simplify something like 237/79? Well probably one should factor it. Once we get that idea, we try various small factors like 2,3... But 237 is odd so 2 does not work, but the digits add up to 2+3+7 = 12 = 3(4), so it is divisible by 3. Then since 80 3's is 240, one less 3, namely 79 3's is 237. so 237/79 = 3(79)/(79) = 3. and that simplifies it.

 

So finally it dawns on me we need to factor those big fractions. Once I realize this, theorems like the "Factor theorem" ring a bell, and I try to use them. That says that an expression in x is divisible by x-r if r is a root of the expression, i.e. if the expression becomes zero when x = r.

 

I have no x's but so what, pretend a is x. so I have in the top the expression: a^3(c-b) + b^3(a-c) + c^3 (b-a), which when written as an expression in terms of powers of a, looks like

 

a^3 (c-b) + a [b^3 -c^3] + (bc^3 -cb^3). This is a polynomial of degree 3 in the letter a, with "constant coefficient" (bc^3 -cb^3) = bc(c^2-b^2) =

bc(c-b)(c+b).

 

The factor theorem says if we can find a root r of this, then we get also a factor of form a-r. Now do you remember where to look for roots of a polynomial? The "rational root theorem" says to look in the factors of the constant term, right? I.e. to look for integer roots of x^3 - 7x + 6, we look at the factors of the constant term 6, i.e. we must check ± 1, ±2, ±3, ±6. In this easy case 1,2,3 work. In general you have to remember to allow minus signs as well.

 

Ok the factors of the constant term of our guy are bc(c-b)(c+b). So we have to try setting a equal to ±b, ±c, ±(c-b) and ±(c+b), as well as products of these irreducible factors (ok that's a lot of possibilities, but trust me it isn't that bad here). E.g. setting a=b,

in a^3 (c-b) + a [b^3 -c^3] + (bc^3 -cb^3) gives b^3(c-b) + b(b^3-c^3) + bc^3 - cb^3 = 0, so b is a "root" and hence a-b is a factor.

 

Now can anyone do the rest of it? More important, does your child's algebra program teach these two basic results: i.e., factor theorem and rational root theorem?

 

The moral here is that a problem that is almost hopelessly complicated via plugging and chugging, plops out when one understands the basic principles of algebra, namely the (root/) factor theorem and the rational root theorem, enough to apply them creatively. Those two are the most useful results of algebra in a calculus course, and yet many books do not stress them. Just mindlessly multiplying and dividing symbols together as seems to be the focus of books like those by Saxon, has limited usefulness. Although one should be able to do it, that's not enough. We don't want to limit our algebra knowledge to the types of questions that traditionally appear on the SAT, but hopefully we want to be able to answer any type of algebra question.

 

Here is one more illustration of the usefulness of the rational root theorem, often omitted from books, even ones that include the theorem itself. Many books tell the student that the square root of 2 is irrational but few prove it. However some of those same books do teach the rational root theorem, that the only possible rational roots of a polynomial with integer coefficients, can be written as fractions p/q where p divides the constant term and q divides the lead coefficient. Since the only possible rational square roots of 2 are among the possible rational roots of X^2 - 2 = 0, this implies they must have form p/q where p divides 2 and q divides 1. The only such numbers are ±1, and ±2, and these don't work. Thus any book author that gives this theorem and also implies it is hard to show that sqrt(2) is irrational, just isn't thinking. (arguable rhetorical question:) Do we want our kids learning from such books?)

 

Ok, my apologies, end of stump speech on algebra. Many of you are no doubt better at this than I am. [There is still a prize for the first person, preferably a child, who factors these expressions completely by hand: a^3(c-b) + b^3(a-c) + c^3 (b-a), and a^2(c-b) + b^2(a-c) + c^2 (b-a).]

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I had trouble believing this, and double checked, but if I understood the response correctly there was a sizable minority of UGA students entering "honors" second semester calculus with a zero! on the AB test, of whom 89% "succeeded"! Of the smaller number entering with a zero on the BC test, 82% "succeeded". I didn't even know you could get a zero, much less that you could get one and do just fine. Wow, that's also a (1%) higher rate of success with a zero on the AB test than the small number who got a 3 on the BC test, and only slightly lower than the comparable number who got either 3 or 4 on the BC test. What do these scores mean?

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My guess is that a 0 means they took the course, but not the test since the test only scores from 1-5. Many students do that. My guys studied enough to take (and likely pass) the test, but we opted not to take it. Oldest succeeded in his course, but it was just business Calc. I fully expect middle to succeed in regular Calc.

 

Some might not take the test due to not feeling prepared, but even for them, seeing the material for the second time vs the first ought to help.

 

What are the pass rates for those who come from Pre-Calc or College Alg in high school directly into Calc in college?

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I don't have those, but I could ask. This data I have presented involves over 15,000 students and thus takes a while to compile.

 

Of course that new data will not reflect my idealistic preparation because algebra and geometry in high school are not what they once were. I.e. AP calculus courses in high school have destroyed traditional algebra and geometry courses, causing them to be replaced by test oriented "precalculus" courses. So I would guess that success rates in today's world are very low for students with only modern precalculus preparation. Unfortunately courses must be designed for the audience we have, not necessarily the ideal logical sequence mathematically. (Of course home schoolers have the chance to deviate from the pattern found in public school, but at some risk, hence better based on their own best judgment than anonymous advice.)

 

I myself would suggest the ideal (guided) pre calculus preparation to include Euclid's Elements (of geometry and number theory)

 

http://farside.ph.utexas.edu/euclid.html

 

and Euler's Elements of Algebra" http://archive.org/details/elementsalgebra00lagrgoog

 

 

followed perhaps by Euler's Analysis of the Infinite. (This book is prohibitively expensive retail, and should only be consulted in a library.)

 

 

I can't test this hypothesis because no one I know of has done this course of preparation. But I predict anyone who came in with "just"

Euclid's Elements, Euler's Elements of Algebra, and say Legendre's Elements of geometry and trigonometry, would do rather well in calculus, even without Euler's precalculus: i.e. Analysis of the Infinite, Books I and II.

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I still have no explicit data on calculus performance for students entering uga with "precalculus" only. One reason is the question of how to set a baseline on such preparation. E.g. the SAT test, at least as of a few decades ago, stops at first semester 10th grade math, and it is still true that no trig is tested. so our data shows that sat scores do not predict success in our calculus courses, but they do predict precalculus course success. we have a departmental placement test that is twice as useful as sat scores at predicting calculus success.

 

by the way i previously stated that verbal sat scores predict success in our math courses but my source said today that was a mistake.(??) hey if you can't trust anonymous sources on the internet, who can you trust? (i read the other day that a lot of people are serving time from convictions obtained by flawed FBI lab tests. aren't you glad that isn't you? i am.)

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