I think what worked best for my son was not the 1/2 year acceleration but the constant reinforcement of material by being on his middle school/high school math teams. There were monthly local competitions and a whole range of topics were covered at each meet: algebra, geometry, trig, pre-calc,calc. His coach made each member do a “qualifer” test before each monthly match, so he was always staying on top of the material and always reinforcing previous concepts for six years. A great foundation.
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I must disagree. For the most part, there really is no such thing as a “math brain.” People who are good at math are not born that way. They become good at math by practice, just like in any other skill. I certainly agree that we shouldn’t force uniformity, but that doesn’t mean that students can be grouped by “talent.” Any given student has the potential to excel at anything, including mathematics. If anything, I would argue that the prevalence of a closed mindset towards math is what is behind the USA’s lackluster mathematical performance.
Take me, for example. By your logic, I was “talented” in social sciences and “untalented” in math in middle school. Math just wasn’t “for me.” However, thanks to an excellent instructor in 9th grade, I went from struggling with algebra to self-studying calculus. Today, I study physics and EE in university. I wasn’t “talented” in middle school and I am not “talented” now, despite what many people have told me. The only thing that changed was my attitude towards math.
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No doubt. SES correlates with a more enriched childhood, better nutrition, all kinds of things that give some an unfair advantage. Overall that is the bigger educational issue to address.
Math skills, like anything, are a doled out on a bell curve. And all along it are people who don’t get what they need to thrive in math. This thread, I think, is focusing on the higher end of the curve, and perhaps people who punch above their weight in the middle through grit. Why is it that people who are advanced struggle and have anxiety over calculus?
Two answers: (1) The people punching above their weight hit a wall and (2) people who are at the far end of the curve haven’t been taught adequately.
The talk about gifted programs addresses #2.
There are plenty of people who are natural academics and test takers, even if it is just .01% of the population, that’s a ton.
I believe in the math brain because I don’t have one, but my mom does, and my husband does and my son’s brain works like his dad’s, not mine. As for my mom, fascinating thing - she had a stroke not long ago, and the main thing it took from her is her math brain. She can talk very articulately about it, as a former math teacher.
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That’s really bizarre. Of course practice is needed, just as it is to get in the NBA. But no one would seriously argue that anyone could become Stephen Curry by simply practicing every day. He has an unusual degree of hand-eye coordination.
What people mean by “math brain” is an unusual ability to hold and manipulate complex abstract concepts in your head. Just like hand-eye coordination, some have more of it than others, but the degree to which people hone that skill will differ. And there’s a very long tail in that ability which is easier to see in math than in say English at an early age. But even in English I can’t imagine many people saying that anyone can become a bestselling author or poet laureate without unusual natural talent.
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You made a general comment about bragging rights and didn’t specify a state. As ucb, data10 point out the standard in CA is pre-calc in 12th, +2 is calc in 10th, no one is bragging about a +2, since many kids are in that track. Honestly the bragging thing was more of a joke since this thread oozes humble bragging.
“that all kids are capable of doing and enjoying math at a high level if presented properly.”
I agree with the labeling comment, but not sure that all kids can enjoy or do well, depending on definition of high level. Even though CA has a good community college system, the majority have issues transferring, maybe even can’t transfer because of the Math 1A (Calc AB) requirement which all transfers need (along with English 1A). About 49% meet that Math 1A requirement (C- or higher).
“This is exactly the type of thinking that makes US the laggard in math education.”
Laggards based on what, the international tests? Most of the countries that do better on the tests are homogeneous (Japan, Finland et al) or small (Singapore).
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I think a big problem that I have observed in US math instruction is math phobic elementary school teachers. In 5th grade one of my kids had a teacher that would give math tests that she herself could not work out the problems of. This was at the height of the transition to common core and she left many students completely dazed and confused about math. I just helped my kid a lot more that year (and some other foundational years also). My 5th and 6th grade teacher was a math major and the foundation he laid for all his students in mathematical reasoning was invaluable. Just a thought!
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Seems like there is another answer:
(3) The people who were pushed ahead by their parents in math further than their interest, ability, maturity, and motivation in math should have placed them are in courses too advanced or difficult for them.
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+2 math track is not the norm, though. Maybe in tiger parent circles, the parents push their kids to that track, whether or not it is appropriate for the kids’ interest, ability, maturity, and motivation in math.
Calculus is not required to transfer to a UC or CSU, unless it is required for one’s major. Precalculus or statistics is accepted as fulfilling the transfer math general education requirement.
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That wasn’t the question posed in the thread title or first post. The fist post instead referred to accelerated students in pre-calc who plan to take calculus next year, as quoted below. Given that they have not taken calculus yet, it is unclear whether they will struggle when they take calc next year. I suspect more often than not, they will do fine in calculus, in spite of having anxiety while taking pre-calc… I expect the anxiety usually involves a combination of lack of self-confidence (may be just in achieving math success, may be generally all academics, or may be more general overall personality), calculus having a reputation for being hard, and strong internal/external pressures to get straight A’s in all classes.
“high school students who are two grades ahead in math (e.g. precalculus in 10th grade) being afraid of the difficulty of calculus that they are looking at for the next year”
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Our CA HS is nationally ranked in STEM in the top 20 (whatever that means). There are three lanes in math: the advanced ends in Calc BC (~20% of students), the middle one ends with calc AB (~50% of students), and the low lane ends with pre-calc. It is very difficult to skip as the only way is to take an exam on all the material for the following grade in either 6th or 7th grade, and pass with a B+. Every year, there are numerous students that try to skip based on online school or summer school but very few succeed. So, accelerating is not the norm in California.
Regarding natural ability - IMO there is natural ability in math but it is not necessary for the level of material in HS, including calculus. My smart but not “math-gifted” daughter worked diligently through the high lane following the natural progression. The only class she found difficult was geometry H. She now studies economics in Oxford U in the UK (a very mathy subject there) and is near the top of her class.
When I went to high school years ago, there were only two formal math lanes:
- +0 standard lane, ending with precalculus in 12th grade, about 90% of the students
- +1 accelerated lane, ending with calculus BC in 12th grade (did not offer AB until later), about 10% of the students (which was probably about 30% of the students who would go to four year colleges immediately after high school graduation).
Once every few years, there would be a +2 math student (recognized by teachers, not because of tiger parent pushing), but such students were rare exceptions.
In theory, either +0 or +1 students could choose regular or honors math courses; in practice, the honors math courses had mostly +1 students and a few +0 students, and most +1 students were in the honors math courses (AP calculus BC was considered honors and was the only calculus option then).
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D tells me she is learning vectors with 3d geometry in her IB HL math class.
There are bell curves for most things in the natural universe including intelligence. You can chose to believe that it is based on parental input (and some of it is). But you cannot explain away people who are two or three sigmas away from the mean in any field( above or below). People are different. Most are around the same but some are not. Math is measurable so it’s easier to quantify. But there are also people who excel wildly in music, the arts, and all the rest.
Do you think Einstein’s parent’s were responsible for his genius? I don’t. In any case, if you have gifted kids why do you think it’s all based on nurture and if you don’t have gifted kids what is the basis for making assumptions regarding “gifted” kids.
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There are many different types of math tracks in CA. The SD Unified paths are pictured in the flowchart at https://sandiegounified.org/UserFiles/Servers/Server_27732394/File/Academics/Curriculum/Common%20Core/Common%20Core%20for%20Parents/math-common-core-pathways.pdf . One of the pictured paths ends in pre-calc in senior year, 2 end in calculus in senior year, and 1 takes calculus in junior year and has opportunity for post-calculus math in senior year.
The nearest public to me supports the latter, so some students at that HS take multivaraiable calc and/or linear algebra in senior year. However, several other district publics do not support post-calculus math. The private and charter schools often do something completely different. For example, one area charter I am familiar with doesn’t support AP classes and instead uses the math track Math 1 (9th grade) → Math 2 (10th grade) → Math 3 (11th grade) → Math 4 (12th grade). The latter class includes calculus. Students take honors or regular versions of the classes instead of being a year ahead/behind.
While there are differences in tracks for different schools, there is probably more opportunity for acceleration in math than any other subject overall.
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That’s very different than a public school in our state, MA. Though in MA, there are many kids who fly through basic algebra and geometry outside of school ( via AoPs or RSM or other). Some accelerate some don’t but they are outside the normal or advanced track and there are no in school options for them. ( Some would attend college level classes).
I don’t think exposure to material or lack of exposure means much at the high school level. There are certainly many thousands of kids (like your daughter) who take whatever track is given and continue to be good or excellent mathematicians down the road. And there are some who tap out.
The thing about math isn’t what level you are at, IMO, but what is your understanding of basic concepts and can you build on them and continue succeeding at a high level. Let’s face it, at some point, most people drop out of math. Even those doing a Phd in math aren’t all doing the same types of math.
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With gifted kids, nurture can still be significant. Otherwise, why would parents of gifted kids spend so much effort and/or money on finding or enhancing educational opportunities for their gifted kids?
Based on this chart, it looks like there are four possible tracks, based on decisions made in 6th grade and 9th grade.
- 6th grade placement in regular track.
a. 9th grade placement in regular track (IM1, IM2, IM3, precalculus or statistics) (+0).
b. 9th grade placement in advanced track (IM1 ADV, IM2 ADV, IM3 ADV, calculus) (+1). - 6th grade placement in accelerated track (IM1 ADV in 8th grade).
a. 9th grade placement in regular track (IM2, IM3, precalculus, calculus) (+1).
b. 9th grade placement in advanced track (IM2 ADV, IM3 ADV, calculus, more advanced math) (+2).
What may be interesting is to know the number of students in each track, particularly 1b (6th grade regular → 9th grade advanced) and 2a (6th grade accelerated → 9th grade regular), which are the situations where students change tracks.
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Blockquote
Yep, some of it is, no doubt.
Sorry meant to quote based on your post
Yep, I don’t think anyone is saying it isn’t. Certainly the reason I stated it in the original post.
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I agree. Some people are head and shoulders above the rest in a specific field. In mathematics today, Terence Tao comes to mind. However, and this is my main point, such people are incredibly rare. I do not believe it would even make sense to say “the top 0.01%.” They are anomalies that pop up every few decades here and there. I do not think it makes much sense to discuss approaches to education while considering the needs to the truly gifted. Rather, their needs ought to be considered on an individual basis without reference to a larger “gifted” group.
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