<p>Our school combines calculus A with trig, so that the most advanced kids can take AP Calculus BC as juniors. They just added multivariable calculus (not an AP course) this year for kids who take BC as juniors and who previously had to go to the local college for senior year math. They also have an AP Calculus ABC (1.5 units compared to 1 unit for other math courses) for kids who want to finish the calculus series in high school but were not above grade level as freshmen.</p>
<p>I really like the way our district handles math—lots of tracks both high and low and chances to move between tracks if that’s right for the student.</p>
<p>My daughter is good but not great at math. At the beginning of junior high she was two years ahead in math and had algebra I in 7th grade. She was not ready for it, and struggled that year (as did about half of the kids placed in the course based on test scores). Her junior high has an “advanced topics” class in eighth grade for kids who took algebra I but did not seem to be ready for geometry yet. That “catch up” year was great for her. She’s in accelerated geometry as a freshman in high school and loves it. I don’t think that would have been the case if she had continued on the two-years-above-grade track. </p>
<p>My friend’s daughter, on the other hand, is taking geometry I as a 7th grader (three years above grade level) and flying through it. For her, the idea of reviewing algebra for another year would have been beyond boring. She’ll take accelerated algebra II in 8th grade and be ready for trig/calc A as a freshman. I’m not sure how they’re going to handle senior year math for her grade since this is the first time they’ve offered geometry for 7th graders.</p>
<p>Edited to add:
The school also offers AP Statistics, which a lot of kids (my daughter included) plan to take along with AP Calc BC their senior year.</p>
<p>When I went to high school, the “regular track” in math was:</p>
<p>9th grade: Algebra 1
10th grade: Geometry
11th grade: Algebra 2, if going to college
12th grade: Trigonometry and Precalculus, if going to college
College freshman: Calculus, if needed</p>
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<p>Knowledge of statistics is definitely useful for many, but the reason that AP Statistics gets no love here is that many do not really consider it to be truly college level (and many universities do not either, since they do not give subject credit for it), even though high schools only offer it because they can stick an “AP” label on it.</p>
<p>My kids are complete opposites when it comes to math. My oldest who is now a sophomore engineering major started off with Algebra 1 in 7th grade. His path was Algebra 1, Geometry, Honors Algebra 2/Trig, Honors Pre Calculus, Calc BC, AP Stats. He started with Calc 3 in College. The math head in jr high approached me about skipping Algebra 1 and starting with Geometry but I really wanted to keep him with his peers. </p>
<p>Now for my younger son math has always been a struggle. I told the jr high math head that I didn’t even want him to take the placement test to see if he could skip 7th grade Pre Algebra. In 8th grade he placed into Algebra which I knew would be too hard for him but I let him start with it. Sure enough when he started earning D’s I finally got him placed back in what the school called Algebra 8 which was a slow paced intro to Algebra. He made it through Algebra 1 in 9th grade, Algebra 2 in 10th grade (with lots of tutoring) and is currently in Geometry (which he really likes). Next year he’ll do Pre calc as a senior. </p>
<p>Now our district makes every 8th grader take Algebra 1. Since it’s a California high school graduation requirement they want the students to have as many years as possible to fulfill it. Many of these students would be better off with Basic Consumer Math.</p>
<p>On solution would be to spread out the super high level Math courses into two years, and include more real world applications.
Use logarithms and limits in creating computer programs to solve a real world problem.
Create your own statistical curves with raw data. Set up physics and chemistry and biology experiments and then do the raw Math. Solve engineering problems with the Math. Apply it to the humanities: use Math to solve how well a marketing technique is working. Economics: measure transactions and their impact.
These things are too important to skip, rush through, and maybe can be handled in more depth for better understanding and retention.
Formulas, problems, tests- no necessarily the best or only way to acquire expertise in these areas.
A curriculum like this can be pre-college level, yet very enriching and valuable.</p>
<p>Our country NEEDS this type of expertise very badly in the workplace…</p>
<p>When I was in high school, any student who completed precalculus in 10th grade was a top student in math, and was ready to go full speed ahead in calculus BC (and get what was for him/her an easy A in the class and an easy 5 on the AP test). Forcing such a student to slow-pace one year of calculus over two years does not make sense when the students who reach calculus in high school (even those just one year ahead who complete precalculus in 11th grade) are the good students in math.</p>
<p>Meanwhile, the “regular” math students who complete precalculus in 12th grade and then go on to college take full speed freshman calculus in college. If they can handle that, why can’t the advanced students who complete precalculus in 11th or 10th grade, if the advanced students were properly placed (as opposed to being pushed ahead of their actual math abilities).</p>
<p>It sure seems to me that slow pacing calculus in high school is done because there are now many students who are inappropriately pushed ahead in math. When I went to high school, the only calculus course was BC, and the students did fine in it and the AP test.</p>
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<p>Typically, AB is considered equivalent to the first quarter or semester of college freshman calculus. BC is considered equivalent to the first two quarters or semesters of college freshman calculus. The BC syllabus includes the AB topics, plus additional topics.</p>
<p>When my D. was in middle school, she didn’t have opportunity to do any accelerated math. she was in the best class, yet they only did algebra I. This year in HS, she is doing algebra II and geometry. </p>
<p>Last year we had a math study group with a girl who had straight As since 3rd grade. The math group met once a week to do some math enrichment. At the time of group, the girl is 2 years older than my D. and one grade higher. Consider she is a A student, I was surprised to find out how poor her math was. Then this girl moved away. This year the study group included one girl who just came from China to do HS. The Chinese girl is also in 10th grade, a grade higher than my daughter, and she is not a straight A student, not even in math. my daughter is definitely struggling to do math with her. The Chinese girl, by the time she was in 8 - 9 th grade, finished all of U.S. high school math.</p>
<p>A couple years back I had a discussion on Math preparation with a retired Professor of Engineering. His view was that great mathematicians are born … not made. Math would hardly unique in this respect … (“Dear Abby, how do I train my daughter to sing like Celine Dion?).” For evidence he referred me to several well-known Eastern European mathematicians that had no formal training at all.</p>
<p>That said, my own experience is that people “get” Calculus at a particular point in their intellectual development … presuming they the subject ever “clicks” for them at all, and for some (like very highly educated DW) it never does. So I think the answer for the OP’s question really depends on the kid. JMHO of course.</p>
<p>@Alh, You specifically stated, “What we consider acceleration is what other parts of the world consider average pace.” You were not referring to “average” scores, but the accelerated programs. The US advanced track is not “average” compared to other parts of the world, IMO. There would have to be a study comparing “advanced” US math students with other countries to determine the accuracy of your statement.</p>
<p>I really like your ideas. But how many of us know public school teachers able to implement such programs? I can think of maybe two individuals. The students I know who have done the type of study you suggest did it on their own outside of a school setting, sometimes with the help of mentors. This is not to be critical of teachers. Some of them are really limited by the curricula available to them.</p>
<p>I wonder how many parents of college math majors, and especially those who may go on to PhD programs, feel public school accelerated math education was adequate? I think it is the content that is the problem. Not acceleration.</p>
<p>Ohiomom: I don’t understand statistics and don’t really understand what the report and tables show. My impression is that our “advanced” public school math students (those doing math strictly at high school and not at outside programs or universities) are not advanced by international standards. This is my impression from talking to young mathematicians. I will be delighted to be proved wrong.</p>
<p>I am not claiming your son, with his high SAT math score, is average and not trying to be insulting. It seems good to me to think about what is really going on with education in this country.</p>
<p>Maybe someone who does understand US and international math education can explain it to us?</p>
<p>However, the two things are linked. If some students are accelerated inappropriately beyond their actual math ability, then the course content may have to be dumbed down (or slow-paced, as the two years for one year of calculus example may indicate) so that the actual good students in math learn less than they are capable of learning.</p>
<p>^^ I did not read into your statements anything about my son. I simply disagree with the notion that the US accelerated math tracks are mediocre by international standards</p>
<p>What I believe is essentially based on hearsay.</p>
<p>I am hoping maybe quantmech or one of the other math/science posters will show up and explain it to us because it is an interesting topic to me.</p>
<p>“The Chinese girl, by the time she was in 8 - 9 th grade, finished all of U.S. high school math.”</p>
<p>I’m sure many of us can relate stories of individual math whizzes. I know of a student who skipped 2nd grade, and had completed all his private school HS math by end of sophomore year and attended local 4-year colleges for math junior and senior year. If he were to go to China, they would be wrong to assume he was typical of all US students.</p>
<p>My feeling about math is that it is really just valuable in what it can facilitate. I don’t see it as some sort of virtuoso competition, like playing piano or swimming the butterfly. I see it as a really important tool for discovery. I guess I would value more the type of student with the breadth to perceive problems and possibilities and then apply mathematics in interesting and new ways. I don’t really think the push to keep doing higher math earlier is necessarily going to produce this type of student who will have potentially the most impact.</p>
<p>Our school also offers Calc AB and BC as an either/or. There is also honors Calc, which is geared towards kids who performed well in CP Precalc and want an honors level course or kids who struggled in Precalc honors and aren’t ready for Calc AB. For kids on the most advanced track, multivariate calculus is offered senior year. IMO, I don’t see why anyone needs to take multivariate calc while still in HS unless they are truly exceptional. Statistics is considered an elective which is supposed to be taken in addition to, not instead of, the traditional math sequence. It is considered an easy AP class. I am not a math person at all but took statistics in college and loved it and did well.</p>
<p>My oldest D, now a freshman in college, was on the grade level track, taking CP precalc as a senior. Math was by far her weakest subject–the math fairy must have been sick they day she received her math gene. She was accepted to 9/10 schools to which she applied, including all the state flagship universities to which she applied. Clearly, it didn’t make or break her college acceptance. I suppose if you are determined to get into HPY it might matter, but for most kids it won’t be a dealbreaker if they finish HS at the precalc level.</p>
<p>Regarding preparation for college, D was not well-prepared in math regardless of having been on the advanced track: calc in junior year, AP stat in senior year. The mom of another girl from her high school who had been on the same track, also commented that her D is really struggling in college math too. Admittedly, both girls are at top schools, but it made me wonder how on earth all the kids on the grade level track handle college work!</p>
<p>I think this is completely false, and probably why there are so many people that have issues with math. You’re not going to get it right away, it’s going to take some work. The problem is that too many teachers aren’t proficient in math themselves, so kids have a poor background. It’ll be hard to understand high school algebra when you have trouble understanding the rules for adding and subtracting fractions! At this point, catching up will be overwhelming. The solution is not to slow down the curriculum even more though, but to make it stronger at the elementary and middle school levels.</p>
<p>Also, to actually answer the OP’s question, I think a lot of it comes from the culture on CC. Calculus can be difficult, especially for someone who hasn’t seen it before - the thinking and intuition needed is different, and you’re not going to get it right away. The only D I ever got on a test was in Calculus, and I had gotten an A in every math class before, and even qualified for the AIME, twice. But to the population in CC, this just sounds like a big risk, and the possibility of not getting an A can be uncomfortable to someone who thinks they need a 4.0 to get into Harvard.</p>
<p>There are three tracks in our small public HS. There is a lot of variation available within the tracks and there is possibility to move up as well. </p>
<p>1st track begins with Algebra in 9th and ends up with Topics in Math (having covered Geometry and Fundamentals of Algebra) or Probability and Statistics, Trigonometry, or Algebra II in 12th. </p>
<p>2nd begins with Geometry in 9th and ends up with Calculus AB, Trigonometry & Analytic Geometry or AP & Reg Prob. and Stat. in 12th.</p>
<p>3rd begins with Honors Algebra II in 9th and ends up with AP Calculus AB, AP Calculus BC, or AP & Reg Prob. and Stat. in 12th.</p>