HS math: is calc a good idea?

Parent Cafe
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<p>ucbalumnus,</p>

<p>We have experienced both of those scenarios, within in a few short years. Older kid is one of “those” kids – who teachers started recommending single subject acceleration while in grade school. It was clear he needed it, but the district refused. It was very frustrating and slow for him, and we made do with outside supplementary classes. Getting him the acceleration he needed was awful, and required principal, parent and teacher support and pushing before the district would ok it. </p>

<p>Then, boom, the district changed its policy (new superintendent) and boom! All of a sudden, kids were being pushed wholesale into algebra in 7th grade just so they could have “early exposure.” The acceleration that was so impossible to get for my kid who desperately needed it was matter of course for my kid who needs it less (but who will be fine accelerated). My sons’ middle school takes a more cautious approach to 7th grade algebra, reserving it for for those who test in and who are well-prepared. This is not true at all the middle schools in the district!</p>

<p>The result? According to the algebra 2 teacher at my older son’s high school? Total disaster. Kids have been given early algebra and geometry but have not mastered the material required (even though they got As). They don’t know what they need to know to be successful. District policy does not allow you to repeat a class taken for high school credit and passed. These kids are in a really sticky place – they lack the fundamentals but the algebra 2 class can’t go back and completely recover algebra 1 (and geometry). They would have been so much better off without the acceleration.</p>

<p>And why? Simply because our superintendent likes to brag that middle school kids are taking high school classes. Without making sure that they’re ready and that the true rigor of high school mathematics is in place. It makes me so mad.</p>

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<p>All of my kids took calculus in high school but don’t obsess about it. The single variable calculus sections at MIT are huge. </p>

<p>I think many kids take calculus in high school because it’s the only advanced math option available. Math, aside from content, is a way of thinking that could be fostered as well with something like number theory, for example. I think calc is offered because at the college level it, along with linear algebra, are the prerequisites for many advanced courses–although not all.</p>

<p>Here’s a contrarian view on calculus: [The</a> Calculus Trap](<a href=“http://www.artofproblemsolving.com/Resources/articles.php?page=calculustrap]The”>Don’t Fall into the Calculus Trap)</p>

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<p>Looks like there is some serious grade inflation. To earn a C or higher grade, the student should have learned the material well enough to be able to use it in subsequent courses. To earn an A grade, the student should have a strong mastery of the material.</p>

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<p>The problem is that not all middle schools are created equally. To earn an A in those classes at my sons’ ms is to master the material. Others are not built the same. Course content and instruction matters a lot.</p>

<p>Back in the day (now 30 years ago), I was accelerated and took calculus sophomore year and then not again until college (engineering). Was totally fine. My older son will take it as a sophomore and then will have so many options of what to study. Of course, he’s way brighter than I am (olympiad level). Younger kid is on track to take BC in 11th grade. </p>

<p>Many, many different paths. Sometimes I think we get obsessed over what’s best and sometimes there’s not one “best” - but rather many bests and sometimes even just best for right now.</p>

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<p>Pie squared, that’s what happened in our district. The kids did indeed test in or get recommended for the two grades ahead acceleration in middle school, and the high school teachers were raising holy heck because they simply couldn’t grasp the material as deeply as they expected. The kids were doing well. They could do the computations, but there are certain things one is simply not ready for because one’s brain has not reached a certain developmental stage. I liken it to trying to potty train your 9 month old. Could be the brightest kid on the planet, still not going to get very far until certain developmental stages are reached. The district administration did listen to the math teachers, and the two grades ahead acceleration was ended. </p>

<p>Now, are there a very few students still accelerated at that rate? Sure, but there are no longer whole classes of kids. Tiger families are far more common than students who truly need the more advanced courses, and I applaud the district for listening to the teachers and taking a step back.</p>

<p>Here’s a question for you, though. Why don’t we ever discuss grade levels ahead in English? Seriously, in more than 20 years in higher ed, I’ve never encountered a student bragging about being grade levels ahead in English (the way they do in math). Is English just that much harder?</p>

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<p>OP, there’s nothing wrong with the advanced track your kid is on. I can’t speak to the curriculum - but it seems that those who know have spoken to that.</p>

<p>DD will be a Mechanical Engineering major in the fall and has had Calculus AB. She took Algebra in 8th grade. It wasn’t offered in 7th here at the time, but it is now. Her AP test results exempt her from Calculus I, but she’ll take it anyway (recommended by her engineering school). She’s right on track with the bulk of her peers in engineering. Most will enter Calculus I.</p>

<p>My general rule of thumb is that my kids be challenged. Take the most accellerated track possible to achieve the balance of success (avoid frustration) and challenge. So far that’s worked out. :)</p>

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<p>DS 1 did the advanced track all the way through taking AP Calculus in 11th grade and Ap Statistics in 12th grade. He is now a Mech Eng major in college. Interestingly, he retook Calc 1 in college and feels it was a good idea.</p>

<p>We backed DS 2 off a bit after 8th grade and he took Honors PreCalc in 11th grade and will take AP Calc as a senior. Interestingly, his SAT and Math 2 Subject scores are higher than his older brothers. So I think his sequence has lead to deeper understanding.</p>

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<p>AP level is theoretically a grade level ahead of normal college-prep 12th grade English courses, given that sufficiently high AP English scores are allowed to exempt students from frosh English composition courses at many colleges.</p>

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<p>My son did Saxon Algebra in 6th, Bob Jones Geometry in 7th: both courses homeschooled. He went to 8th grade and took Honors Algebra II online, 9th PreCal, 10th AP Cal AB/BC, 11th College Linear Algebra online and this year will take Cal III. He is not a genius, but is very bright. He doesn’t love math, but does have a knack for it. He has been very successful and is glad he did this sequence. </p>

<p>I know lots of people are saying scrap the Saxon; however, my son and I both feel that Saxon really gave him a firm foundation for some of the later concepts. The repetition was beneficial to him. That being said, some students (my second) really struggle with the format of Saxon.</p>

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You don’t need to do calc by 11th grade to pursue math-heavy fields, like engineering. The vast majority of my electrical engineering class at Stanford did not have math beyond calculus in HS, and many repeated calculus again in college. The “standard” EE 4-year plan at Stanford starts with calculus at an accelerated pace for the first 2 quarters. It is not until the spring quarter than you get to multi-variable and linear algebra.</p>

<p>Unlike most of my college engineering classmates, I did do higher levels of math in high school. I was bored out of my mind in my basic HS math. I often found ways of making the classes more challenging that did not go over well, such as doing a complex problem entirely in my head and not showing any work, or when I did show work using original methods I created rather than choosing the less challenging way of regurgitating methods listed in the example problem sets. Being able to independently read math textbooks and skip ahead grade levels fit much better for me. The independent study led to a few bad habits since I never heard anyone speaking the terminology. For example, I pronounced the sine operation as sin (like biblical sin) until college. I continued beyond single-variable calculus by taking classes at SUNYA while in HS. I got top grades, so I expected that I’d be able to skip ahead to upperclassmen math courses at Stanford, continuing where I left off. There was quite a difference in the difficulty (for the first time no issues with not being challenged), and I can see why many engineering students chose to repeat the calculus they had done in HS.</p>

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<p>Eightisgreat,</p>

<p>I have heard about Jacobs, but not MUS or Larsen. Actually the word I had been getting is that Saxon was <em>the thing</em> for ambitious students looking at STEM fields, so this is very interesting and helpful. I particularly appreciate giving reasons why Saxon is not a good choice (not enough thoughtful understanding).</p>

<p>I should have added that our extremely rural location makes online anything very difficult… it stalls and hitches and disconnects very frequently. (We have lousy cellphone reception too.)</p>

<p>I will have fun looking up MUS and Larsen. Thank you very much!</p>

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<p>Packmom,</p>

<p>You referred to kids just not being ready for a particular level of math at 16… this is what I am also thinking about for my daughter. She may or may not hit a wall, but if she does I would like to start thinking about other math classes that encourage/teach mathematical thinking but don’t push her past whatever developmental level she is in.</p>

<p>Do you have specific topics that you would recommend? What did your child’s friends take? (And did you think it was a good idea?)</p>

<p>Thanks very much!</p>

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<p>Re acceleration in English:</p>

<p>My daughter was a kid who sort of needed acceleration in English. As a freshman in college, at a college with a strongish core curriculum, she said “My college has six different levels of math entering students place into, so that I am not going to hold back anyone who knows a bunch of math and actually cares about it. I wish there were at least two levels of literature, so that I didn’t have to sit in class with a bunch of perfectly smart kids who have no idea what poetry is or how to read it but feel privileged to take up class time with their utter contempt for the whole project. It’s exactly like high school; I’ve been there, done that.”</p>

<p>She got almost nothing out of her high school English classes. Her work was so far above grade level that her teachers barely bothered to think about it. There was only one teacher, in a 10-week mini-course she had in 10th grade, who really challenged her to think harder and to write more clearly. The others noted that she had a really good command of paragraph structure and style, and she knew how to make an argument, and that’s as far as they went. She actually had trouble when she got to college, because she had completely gotten out of the mindset of doing anything to improve her writing.</p>

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<p>Seems like she would have been better served by being allowed to take actual college English courses at a local college while she was in high school.</p>

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<p>My son was fortunate in his middle school math teacher, who gave the worm math books to study on his own for 2 years. Son was a problem in HS, and it went to district level to let him accelerate. Once they changed the rule, a true math genius in year behind became a close friend. This boy’s dad would drive both boys to a campus 50 minutes away for next math class, then both continued math at local U. </p>

<p>A kid like mine was a pain to the local school, who did not provide the science, language (Latin), econ, and math courses that he wanted. Now they have a program for advanced students to take most of their classes at the local U. It is a win/win solution.</p>

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<p>OP, UCB, Mathmom and others,</p>

<p>I come at this from a unique perspective, perhaps, and I would welcome input.</p>

<p>OP, we’re homeschoolers and my oldest <em>is</em> one of those very mathy kids. He did algebra in 2nd and 3rd grade using Algebra Survival Guide, Honors geometry in 4th with a professor who taught homeschooled kids using Euclid’s elements and his own curriculum, and then in 5th, I didn’t know what to do so I repeated Algebra using Jacob’s Text which we loved. In 6th, I tried to find tutors for my son (my dad) using Foerster’s Alg II/Trig but my dad got ill so my son basically did MathCounts problems. In 7th, he started Calculus with a different tutor who suggested he take it at the local UC. I didn’t want that, so he actually went to the local CC and started with pre-calc in 7th. In 8th he took a semester of Calc I and then just didn’t do math for a semester. Summer after 8th, he did stats at the CC. In 9th, he did calc II and III at the CC. In 10th he did linear Alg. and Dif equations at the CC and then for the rest of high school, he did math competitions and worked with an online tutor on various math topics.</p>

<p>I definitely tried my best to meet his needs but I don’t know that he was that challenged except for math competitions. But, he’s doing great in college at MIT.</p>

<p>He also took one AoPS AIME class, and that was fun for him. </p>

<p>Fast forward to my current high schooler, a rising junior, who has previously struggled with math, even with a diagnosed math disorder.</p>

<p>Even with the struggles in math, I felt he needed a strong curriculum because he had good reasoning skills. He did AoPS Algebra during the summer after 8th grade. It was the hardest, yet most satisfying thing he’d done to date. Two hours of homework each day, 6-7 days a week.</p>

<p>He then took 2 years to complete geometry (sigh) with Teaching Textbooks. (Many things at play there)</p>

<p>We are back to AoPS for Algebra II this summer and just last night, for the first time, he said, “I love math!” Yesssss!</p>

<p>OP, if you have never encountered Art of Problem Solving curriculum, I suggest you check it out. It’s ridiculously hard but so satisfying and thorough. My son feels good when he can solve the problems and understand it. He’s a slow processor but I believe it will help him get quicker. I’m actually thinking about having him take an AMC12 AoPS class and even try a math competition. Never, ever thought I’d say that.</p>

<p>But my question for UCB: As with the OP, if my son jumps out of AoPS, he will reach Calc I at the community college in either fall or spring of senior year, depending on if they let him try to test into pre-calc for this spring.</p>

<p>He took the SAT as a sophomore and got a 690 on the math. I think he can improve. I’m not certain he’ll be applying to selective schools, but we haven’t ruled it out.</p>

<p>Would it be better for him to jump to the CC (and he would need the prerequisite math in order to take physics at the college which is what he wants to do) or keep going with AoPS classes?</p>

<p>And do you really, in all honesty, think having just one semester of Calculus would be enough to apply to selective schools? (Assuming his SAT score will go up during junior year)</p>

<p>He’s faced many health challenges that explain his academic path being a bit rocky, but I’m still not convinced with only Calc I that he would be competitive for selective schools, particularly since he is exploring the idea of engineering as a major.</p>

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<p>It does look like AoPS has precalculus and calculus courses, although it may be easier from a credit and placement perspective to complete the highest level course at an actual college, or perhaps take the AP calculus AB or BC test if he completes calculus through AoPS.</p>

<p>Not sure how selective the colleges are that he is considering, but most colleges do not require high school calculus as a prerequisite for admission or to complete a bachelor’s degree in eight semesters (even majoring in math, physics, or engineering). So completing calculus 1 (or AB) as a high school senior should be more than enough.</p>

<p>Only a few schools like Caltech, Harvey Mudd, WUStL engineering, and Princeton engineering expect frosh to have had calculus in high school. All of the state universities in California (including Berkeley) do not require calculus in high school (even for engineering), though it can certainly be a plus point for admissions and can give some schedule flexibility in college.</p>

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<p>sbjdorlo,</p>

<p>There’s a difference, I know, between big engineering schools and “selective” schools. There are also varying degrees of selective.</p>

<p>UCB is probably better qualified to answer your question in total, but I thought I’d give you this anyway.</p>

<p>USNWR has Texas A&M’s graduate engineering program ranked 6th in the nation for public schools and 11th overall. They’re solid. </p>

<p>Calc I is on the money for the beginning course for the large majority of engineering students at A&M. That is where most students start out. Many have had AP Calculus either/or AB/BC, but most start at Calculus I. So, by those standards, your son would be fine.</p>

<p>It’s not MIT - but still a solid program. And it’s not a complete breeze to get in either, especially if you’re from out of state, your school doesn’t rank, or similar.</p>

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<p>sbjdorlo, I have absolutely no advice to offer you, as I am in awe of how much you know about math textbooks and teachers. My poor son was left on his own, with me providing a car ride at best. I doubt there is any CC poster who could add to your knowledge.</p>

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<p>bookworm,</p>

<p>I learned a lot along the way of trying to find resources for my oldest son. Homeschooling definitely gave us the freedom to pursue what he absolutely loved. (No surprise that he’s a declared math major at MIT) He has always lived and breathed math in one way or another and I’m thankful for all the help along the way. He wasn’t USAMO, IMO, or any of that, but his love of the subject forced me to work with him finding resources.</p>

<p>The reason I would consider guiding my middle son apply to selective schools (possibly, only possibly at this point) would be for two reasons: the student body and the need-based financial aid.</p>

<p>He <em>might</em> make NM semi-finalist as his SAT without the essay was within one point of last year’s California PSAT cutoff. If he somehow does make that, it would open the doors a lot more. Until we know that, I continue to talk college with him and explore ideas.</p>

<p>A large univ. might not be the best thing for him, given his health issues, but I honestly have no clue.</p>

<p>Ironically, even the local state univ., SDSU, is hardly a safety, and he really doesn’t want to go there, but we need to look at it. His SAT scores are well above the average there, so it’s on the list for now. I would love a Harvey Mudd type school for him (Rose Hulman would be awesome but their f. aid makes it a no-go right now)-small student body, great profs, strong support.</p>

<p>Well, we’ll see what the next year and a half brings.</p>