<p>I understand more about your situation. I have some comments, though, about the second part.</p>
<p>Typically, AP-Calc does not involve proofs. In fact, MVCalc and Linear Algebra often does not involve proofs. For that, one needs to be in a different level of MvCalc and Linear Algebra. So kudos to your son's teacher if s/he introduced proofs in a Calc 1 class. And it makes sense for your son to want to be exposed to proof-based math.</p>
<p>The second refers to getting a 5 on the AP for only 70% correct answers. In fact, that's the way the exam is devised. Students are not expected to answer everything. I believe points are deducted for incorrect answers. Students can also get points for partial answers (i.e. if the reasoning is correct, or correct up to a point). Some college exams are designed that way as well. So the fact that one can get a 5 for 70% correct answers does not connote weak foundations.</p>
<p>And knowing my kid he probably got a five with more than 90% correct answers since that's how he did on all the practice exams. :) I'm envious that you're school offers such challenging math. My son is taking a MV course now, but it doesn't seem to be that difficult.</p>
<p>Marite, what I meant was that to built a strong foundation in calculus, one need to look beyond 5 in AP.</p>
<p>Mathmom, my DS1's teachers are retiring and their math class may no longer be the same. As to my DD2's school, they have math professor come to teach at high school as dual enrollment. Their Linear Algebra is like junior class for math major so that they are proof based.</p>
<p>It may be true. I would not know. My S found that he was very well-equipped for MVCalc and Linear Algebra. He would have taken the proof-based version of these two classes if they had been offered at times that suited his high school schedule.</p>
<p>I went to a small school that had pretty set schedules (with a small school, scheduling into different than normal classes is difficult), and no APs were offered until junior year with AP US History. My school's history teachers did not like the AP World curriculum and felt that it was too much of a brief survey covering a lot of material. AP math and science courses are mainly for seniors, and AP English is for seniors (though some juniors are suggested to take the AP Comp exam even though they haven't had a course yet). AP Gov, Comp Sci, Psychology, etc. are not offered. AP math and language classes are sometimes taken junior year.</p>
<p>The typical ninth grade curriculum at my school was: English, Ancient History, Earth Science, Geometry, and first year of a modern language. The more advanced students take "honors" versions of these classes, may take Latin II/III, and may take Biology. I should mention that I went to a challenging school that also supported high-achieving students with extra-curricular options and lots of extra challenges within the classroom.</p>
<p>One thing DS1's school does (which I really like) is to compress a couple of the full-year AP courses into single semester classes. Therefore, DS was able to take AP Stat and AP Comp Sci AB each in one semester, leaving time for more electives. The teachers also added more content than the standard AP courses inthese subjects, so it was fast and more advanced, which always sits well with DS.</p>
<p>DS's BC Calc class finished the AP curriculum in December last year. He used to have homework that was labeled as final exams/reviews for second semester calc courses from Dartmouth, Maryland, UMich, etc.</p>
<p>The science sequence there is also accelerated -- they cover a full year of honors Physics in one semester -- ditto all the other sciences, too. </p>
<p>DS's only gripe is that there are no proofs in his HS sequence. He's picked that up outside of school.</p>
<p>Even the basic MV-Calc and Linear Algebra classes do not include proofs. The honors versions do. S had to take the basic classes because of scheduling issues and called them 'plug and chug.'</p>
<p>Our school adopted a block schedule as of last year. How does it work for AP classes that are taught in the fall, with the exam falling in May? And what about AP classes that begin in February, with an exam also in May?</p>
<p>I was also puzzled as to why would inverse's DS want to take two years of Calculus after he passed the BC exam. Especially - why did he take a year of AB Calculus (and even took the AP test!). I actually thought that it was the school who made inverse's DS do it.</p>
<p>I know that my DS would go out of his mind in such a setting (nevermind the additional material, the bulk had to be the AP content anyway, right?). In his turn, he passed Calculus BC in what would be his 6th grade - he was a homeschooler at the time, so I can not tell exactly which grade he was in. Next year, he audited MV Calc and couple more university courses, and after that he returned to school (9th grade) where he was able to take the Advanced version of Linear Algebra, and in 10th grade he moved on to Analysis and other advanced Math courses with no problem. I believe he learned all the proofs he needed in these classes.</p>
<p>I do understand (in theory) the inverse's reasoning about good foundation; but I do not think that in our case that would do any good for DS. In fact, DS actually was thinking about repeating the MV Calculus in 9th grade, because the first time he took it, he only audited the lectures, and did not do any homework. But the professor encouraged him to move ot to the next class, for which I am eternally grateful. It was a blessing for DS: he loved the class, and since then he adopted the risk-taking approach. Now he is not afraid to take a class for which he does not have prerequisites, if he thinks he can do it. Makes for more interesting life. :)</p>
<p>As for the topic of AP classes, DS's school did allow them in 9th grade. In fact, they even had some middle-school kids who were taking classes at the university after they passed AP. They did have some barriers at all grade levels, though (like a teacher recommendations, essays and/or A for the previous course). AFAIK, since then the high school/university program changed the rules, and they now only allow kids into the university classes starting in 11th grade. I do not know what a kid who finished Calculus or Physics in 9th grade (or earlier) is supposed to do now.</p>
<p>My high school was on a block schedule, 4 classes per day, changing every quarter. The typical 9th grade honor student took:</p>
<p>Honors English (2 quarters)
Honors Geometry (2 quarters)
Honors Civics (2 quarters)
Honors Physical Science (2 quarters - 1 physics, 1 chem)
Phy Ed (1 quarter)
7 quarters' worth of electives. Common choices were a second math class (probably Algebra II), foreign language (2 or 4 quarters), band (usually 4 quarters), etc.</p>
<p>Very few if any students took AP classes in 9th grade. I think most of the reason for that was that with the AP's they offered, it was difficult for 9th graders to get ready for them in time. AP stats would be possible, but I think you'd have to take that in the spring and Algebra II in the fall, thus Geometry by 8th grade. AP sciences would be pretty much impossible. And AP social studies classes are really only offered to older students. Those were pretty much all the school offered.</p>
<p>Our HS doesn't have restrictions on what 9th graders can take, but as a practical matter there are few APs they are ready for. My S took AP computer science in 9th by talking his way into it (he showed the instructor the kind of programming he was already capable of.) And he took the 1st AP Latin in 10th grade (after having started Latin in 8th) b/c he studied in the summer to accelerate himself.</p>
<p>(Btw--my son got 5s on all his APs, so he must have been ready.) :)</p>
<p>AP Environmental Sci would be a possible 9th grade course--it's only a semester of college work and not considered too demanding. AP Music Theory could be taken at any age, assuming the student has the background already. </p>
<p>Other than those, the normal sequence begins in 10th grade with AP Euro (or is it American?), AP Bio, and possibly Statistics if the student is sufficiently accelerated in math.</p>
<p>AP Gov't is traditionally reserved for seniors.</p>
<p>Had to add my comments to the thread- gifted education has been a passion of mine for many years. So here are some philosophical, not practical, opinions regarding living in our imperfect world.</p>
<p>It's a shame that some schools restrict students, trying to fit the exceptional (highly gifted) student into the average mold. It is good to have guidelines, especially for pushy parents who think their bright child should always be doing the top/ most advanced curriculum, but to deny a gifted child chances to do what he/she is capable of hurts them. It's too bad that by definition there are always so few at such high achieving levels they can't have the large peer groups the typical child has; parents/society have to sacrifice the optimal experience in at least one area to meet the needs in another...one size/shape never fits all. I am reminded of my early entry (ie one year younger than expected for grade) son's first grade teacher's comment about how she handled comments from the third graders in his reading group about a mere first grader being in their group (it was a grade 1-3 class)- she asked them, can he do the work?, when they said yes she said well, then does he belong in the group?, they said yes... She found a nice way of getting them to accept his presence using logic they could follow. The actual truth was that he really needed a much high reading group but that was the top one in the class and his developmental levels fit first grade best at that age. I don't understand how learning material typically taught in college hurts a young student if they are ready for it, especially when the AP classes keep them with other HS students. High schools let children start later and be held back grades, why can't they seem to handle younger children doing things with older students when they put much older students with the younger ones??? Those gifted students relate well to the older classmates more than to their agemates.</p>
<p>Addenda- of course a qualified freshman could take an AP class in our school district. Trying to skip prerequisites requires proof, such as the student who wanted to skip precalc, he passed the precalc material and did the AP calc class; he's doing the next levels of calc at a local college through Wisconsin's youth options program.</p>
<p>In response to Marmat103, I think that my DS1 believe very much in additional practice in achieve proficiency and real understanding. This is especially true when you accelerate fast. How well you learn is often more important than how early you learn. Other explanation has to do with his personality. Although he aims high, he is always concern about whether the foundation he stands on is solid or not. He tends to focus more to the part of half empty than the part which is half full, the part he don't know than the part he already know.</p>
<p>Up until this year, our high school only offered AP Computer Science for freshmen. But this year they let a number of students, coming from a middle school program for highly gifted kids, take AP Biology as freshmen. I think they were very careful in screening those kids. My youngest, who is highly gifted, will probably go to this high school and I'm very curious to see how these students do in the class, not just on the exam but under the pressure of the workload, etc. Even with highly gifted kids, there are maturity issues that need to be considered but I agree that it is a shame for those kids to be held back from what they may be able to do simply because of their age. Many students at our high school take both AP Biology and AP World History in 10th grade. I absolutely would not let my child take an AP class as a freshman because of how it would "look" to colleges. No college would reject a student because they didn't take AP classes in 9th grade. I would only put him in the class if he wanted to do it and if it seemed to be in his best interests. I think there is also the "burnout" issue to consider. Instead of 9th grade being an adjustment year, it becomes a more intense experience with an AP course.</p>
<p>My freshman year in HS, they wouldn't let me take any AP courses. Yet I self studied for AP chem and AP computer science AB on my own and got 5's on both.</p>
<p>In retrospect I actually like that they didn't offer them to me because:
1) I learned more on how to study on my own
2) The honors chem teacher was sympathetic and just let me take the final exam for the class and excused me from the HW and other stuff completely. I still did the labs cause they're needed for the AP, but it wasn't part of my grade or anything.</p>
<p>I think the very very gifted -- the tippy top -- should not be held back from taking advanced classes, especially math. </p>
<p>What worries me is that in the push to be competitive for selective schools, to get the weighted GPA up as high as possible, kids who aren't ready for APs feel extreme pressure to take as many as possible as early as possible. If you are taking APs because you are bored in other classes, that's one thing. If you are taking them solely because if you don't, your weighted GPA drops -- that's a trend that worries me. For the majority of kids, most college classes should be taken in college, not in high school. I think it's a shame that teachers aren't talented enough to figure out how to make a nonAP class challenging. The most challenging class I took in HS was not an AP.</p>
<p>Excellent point sly_vt. As this thread has progressed I was thinking the title should have been, "AP's for gifted students". For 90% of the kids who are in HS, AP's are challenging, and more appropriate for juniors and seniors.</p>
<p>At our h.s., students usually start with AP Euro in 10th grade, take APUSH in 11th and maybe a science or foreign language AP, and more senior year. I don't think we've ever had a student ready for AP calc in 9th grade, nor has anyone asked to take other APs that early (we offer 8 or 9). </p>
<p>I do see too early APs as a potential problem - for the upperclass students in the class and for the students who burn through the curriculum that early. Why stay in high school? Students do choose to leave h.s. early, but as someone who did it (over 30 years ago) I personally don't think it's an optimum choice for most students. </p>
<p>I think, too, it's different if a building is 9 - 12 or 10 - 12. Either way, the youngest group in a large public school will usually need an adjustment period.</p>
<p>Thanks for all the replies. Yes, as I indicated in some post up above, I know locally students whose response to their local high school curricula is to go out of state to college at early teen age, and others whose response is to enroll in college here in town. But it seems to me, one parent among many, that maybe the trade-offs would be different if AP courses were available at a broader range of ages. It appears that in some places they are. My son (freshman this year) has taken all of the calculus assumed by the AP calculus BC course (in a university course with no AP designation). His calculus teacher thinks it is pointless for students in that program to take the AP test--the program is well known in math departments around the country--but I expect to encourage my son to take the AP calculus BC test anyhow. He is also in two distance learning courses that have AP designation: physics B (which is a conservative course to take for someone with his math background and previous background in science) and United States history (quite a stretch for him insofar as it involves writing research papers). He has one other course that covers much, but not all, of the syllabuses for AP United States government and AP comparative government (and which also involves writing quite a few papers), and I'm mulling over having him take those two tests also. </p>
<p>Parents resolve these trade-offs in lots of ways. Some young people get deeply involved in extracurricular activities and get their challenge that way, even if school is not challenging. My son has been lucky to have, in his math program, a friend who first got him into traveling club soccer (which the friend has now dropped) and Lincoln-Douglas debate (which the friend will co-captain next year). Lacking the local math circle that some towns have, I have also kept my son very involved in math competitions, which has been a lonely activity for him (not many teammates) but one at which he makes steady progress. When an activity becomes sufficiently challenging, there is much to be said for keeping the school classes no more challenging than they have to be. I hope the students in schools with few APs for younger high school students at least have lots of challenging extracurriculars.</p>
<p>Tokenadult:
If you are looking to save $$, I'd suggest that your s not take the tests for AP US Gov and AP Comp Gov. He might not get any credit for those.
I'm of two minds about taking the test for AP-Calc. By the time he is done taking math classes, he will have gone well beyond introductory Calc. However, for the sake of getting credit, he may have to fall back on the test. S, for example, got no credit for the post- BC Calc he took, but his BC Calc score counted toward his eligibility for Advanced Standing.</p>