Gifted Issues Discussion homepage Forums General Discussion Math progression questions

Based on the discussion about the Typical math progressions for high achievers, am I understanding correctly that it doesn't really pay to subject accelerate more than a year in sequence due to forgetting the middle school studies when it comes to college? (That is, unless the person is likely to graduate early and go to college, then it's just shifting the whole process ahead.)

As someone who didn't have Calculus offered at my HS, and didn't need it in college, I'm curious what happens in, say, Calculus (in grade 12, if available, or in college), if a child (of high ability, who needs fewer repetitions) simply went through a normal or one-year-ahead track, vs someone who had a broader/deeper compliment earlier.

And why does the Common Core standard shift Algebra II to earlier a year -- just to give more opportunity for higher math in HS? It seems like if it's not relevant to many college/career paths, and if many kids aren't able to handle Algebra until they are older/more developmentally ready, that it's unnecessarily ambitious.

LOL. I have to disagree, but then my mathy kid is not one of those who needs repetition or easily forgets previous math topics. It may have to do with the way he learns. He is an autodidact and he tends to assimilate concepts rather than memorize procedures. Anyhow, there is no reason or chance to get rusty in his case. DS will take GT Algebra II in 7th, GT Pre-Calculus in 8th, AP Calculus AB in 9th and AP Calculus BC in 10th. Our state requires four years of high school math so DS will be required to study Differential Equations, Linear Algebra and/or AP Statistics in 11th and 12th.

A situation like yours is I was thinking about while I was reading the thread -- hence feeling perplexed. I wonder if is it just a difference between moderately/highly vs profoundly gifted? I find there's a general consensus here of supporting kids moving at their own increased pace, yet it seems like there's also resistance to that when it comes to higher level math and college (though not here as much as in education in general). I'm curious where people draw the line in acceleration.

Perhaps the line needs to be drawn individually for each kid. For us, DS was never accelerated as fast as he was able per testing results - we actually made an affirmative decision to choose a less radical path. The compromise was to accelerate DS enough to prevent harm from destruction of the "spark".

For DD, who is not mathy and who will not study AP Calculus AB until 11th grade, we chose not to accelerate at all. She actually could have handled Pre-Algebra easily in 5th and we knew that by 4th grade. However, she tends to learn everything quickly although not in a deep way. In her case, I can see her mastering the procedures immediately and acing everything but perhaps missing the deeper connections and ultimately vulnerable to potentially forgetting down the road.

Where I went to college I had to have 6 hours of math for a liberal arts degree. The school didn't care what I took in those 6 hours so I went into calculus 2 then 3 and neither was relevant for my major.

It seems to me you could continue to accelerate math right into college if needed regardless of whether it's required for a major or not. At least, it seems to work for liberal arts. Perhaps it wouldn't work so well in other types of majors.

I would think a particularly mathy kid would he able to jump into higher level math in college rather than having to backtrack and go back into college algebra.

I wonder if you realize you just said in the same breath that your daughter is not mathy and could handle pre-algebra in 5th grade. AP Calc in 11th grade is also considered accelerated by most lights, as discussed in the other thread. My child can opt for AB or BC in 11th; both are considered accelerated tracks. This is not, of course, individual acceleration; maybe that is what you meant.

One issue here is what math you need in college very much depends on what major you are interested in. Most schools start accelerating bright math kids at 5th/6th grades. Few kids this age have a solid idea of what they are going to be when they grow up or what major they might take and therefore what is useful. If your child ends up going on to a humanities course in college, the Calculus & or Stats they take in H.S. even if it's 9th grade can be the last math they never need to take.

It also depends on what "higher" math you have available to your student. I think its not necessary good for a student to take Calculus as a freshman (9th) or younger, if they aren't going to take higher math until they get to college 3+ years later. AP Stats, AP Computer Science isn't higher level. BUT there are other options to consider for these students including higher level math at university while still in H.S., going to college early, and some H.S. offer higher level math. What is crazy is if you are playing the get into one of the elite universities game, taking classes at a university don't help in the quest for top SAT's or top GPA's. Taking classes at a local university can hurt your GPA. The best way to play that game is take and get A's in as many AP classes as possible.

But it can work. I just suggest researching a PLAN for what you do if you go too far about the norm. (About 10% of DS's high school class take AP Calculus as a junior.) My husband finished H.S. math in junior high and went on to take math classes at university while in H.S., and went on to get a PhD in a math related field. Yes, it was to his advantage to accelerate that much.


Not sure I understand this question. The way it works in my district is the honors classes, ie the ones that are broader/deeper are taken by the most advanced, accelerated students. The students who take the sequence slower get a more cookie cutter program.

If a student wants to go into higher level math in university. It's more important IMO for the student to have depth. Understand WHY the procedures they are being taught work, be able to prove it and be able to see how to take a non-standard approach to a problem.

This is not my understanding. The "normal" Common Core plan is students take
Commom Core 8 - 8th grade..
Math1/Algebra I - 9th
Math2/Geometry = 10th
Math3/Algebra II -- 11th

This is actually LATER than it was 5 years ago. This is actually pushing things back by around 1/2 year.. 5-10 years ago California was pushing all students take Algebra in 8th grade. (Didn't really work) Common Core 8 has some topics from what used to be Algebra I & Geometry. And all of the above includes topics from Trig/Pre-calc.

Most average kids took either Algebra II in sophmore or junior year. And then a year of pre-calculus if they wanted to. Note my state only requires two years of H.S. math (must pass basic algebra) & most universities only require 3.

College Algebra?

College Algebra isn't really a college level course, it's a remedial college course similar to Algebra II/Trig to get students ready for Calculus and doesn't usually cover math requirements. There are many other options a non-STEM college student to meet college math requirements. Statistics, Linear Algebra, Logic, Discrete Math.

I'm not a mathy person (only went through Alg II in high school) and college algebra definitely counted as college math credit when I was in school. Obviously it's not going to count for some majors, and is not a class that a kid who took calculus in high school is going to take. Remedial math is below college algebra, for students who aren't even ready for that class.

I also had to take calculus for business/social science majors (watered down calculus I guess - it was a really interesting class) and statistics. I aced those classes, which either means that I'm actually decent at math, or that the other students in those classes were just really terrible at math. Maybe a little bit of both.

Appleton, I don't think that's standard. You can get credit in college for taking algebra, but it won't usually fulfill a math distribution requirement. Usually, you would need to continue with stats and/or calc, like you did. That's why there is AP stats and AP Calc, but no AP Algebra. Algebra is high school math (or sometimes even elementary or middle school math for accelerated kids).

A friend of mine had a son who was part of a mathy cohort of kids who took algebra in 6th grade. Most of them finished Calc BC in 11th grade and then took stats in 12th. However, most of the kids chose to repeat some calc in college because they had forgotten things during their year off from calculus.

Yes, I meant that DD is not accelerated in the sense that Pre-Algebra in 6th and AP Calculus AB is the standard GT sequence in our district such that she has tons of classmates and no request/arrangement needed. In our district, AB and BC are distinct and consecutive courses so not interchangeable; BC also covers multi-variate calculus, which is probably beyond the juniors in our standard GT sequence.

By the way, I would not equal being able to handle Pre-Algebra in 5th with mathy. To me, interest/passion is an essential component of mathy; DD has none. Furthermore, a very smart kid could use their general intelligence to rapidly cover materials through Algebra I and perhaps be fine even Geometry or Algebra II, but will likely hit a wall somewhere beyond. I also see something similar going on in Science, where DD averages 97-99%(even in middle school where that is not common) and where her work products have been selected for competition or display despite her not particularly strong grasps of science. I have to sit down and explain deeper connections and sometimes even basic principles to her but she can generate top-notch multi-page lab reports - those exceptional writing & illustrating skills put her over the top.

Being able to handle pre-Algebra in 5th is indeed WAY above the norm for math. Even if in your district it's not that uncommon. Except for outright outliers no one takes pre-Algebra in my district till 6th.. and then about 10% of students take it.

I think you are underestimating your DD's math ability. This is easy to do when we are around a lot of people who are good at math. I think it's particularly easy to do with girls. I graduated with a degree in math & went on to work as a computer programmer for many years. In 5th grade none of my so called interests would have made anyone think I was going to take math in university.. I was not considered "mathy" in 5th grade and refused to do any math that was up and above the regular school work. Mostly I loved to read and be out-of-doors, but I did do very well in math without much effort. I ended up one of the few women in the honors math tracks at school. But I wouldn't never have dreamed in H.S. of joining chess club, or computer science club.

I would like to reiterate a point that was made earlier. It is very very important to keep your gifted child on the honors path in middle school. It's impossible in Common Core states to get off the standard Common Core path for two reasons, 1. Schools push back against it, and 2. It's a whole different methodology. It requires learning math using procedures the adults didn't learn and it's very theoretical and wordy. It's horrible for dyslexic kids who are brilliant at math. Children cannot jump back and forth between curriculums. Children basically have to pick their major in 6th grade, that is math/ science or non math / science degree.

Having to choose path in 6th grade is NOT a requirement for Common Core. It may be how many district are implementing common core but there is nothing in Common Core documents that require this. (At least in CA & MA.). I worked on a committee in my district and we specifically addressed the issue of allowing students to "switch" tracks at key points so that students who took junior high regular placement could still get to Calculus before the end of High School.

Second the terrible methodology is partly because most of the textbooks that call themselves Common Core are horrible. This is the TEXT BOOKS and the text book publishers fault. I'm not in love with Common Core but much of the terrible methodology is implementation problems. My district is going to struggle for a few years with their old textbooks but use them in a slightly different order and supplement with other material since they don't like ANY of the new books that are out.

Yes, I was trying to point out that this could be possible...also, if another child in the family has extreme math talent, or you do yourself, it's all too easy to consider another child with quite a bit of talent not "mathy." And as bluemagic points out, the long game is hard to see sometimes. This is part of why I feel uncertain about my DD. I may be underestimating her or not seeing the long game. Also, she has been at school with some 99.9 kids for sure.


Perhaps this is the fault of teaching.

I just checked and the math requirement for Texas (we have a common core of college classes that are transferable among all of the universities/junior colleges) is one 3 credit hour math class, college algebra or higher and one 3 credit hour math/reasoning course (many math classes meet this requirement as well as programming classes). I don't mean to derail the discussion, but it does occur to me that it is wise to consider which class your child will likely start out in college as result of their high school progression. Many schools seem to have placement tests for math classes now too, which is not something that I remember when I was in college 20 years ago.

I can't speak to five years ago, but that progression looks an awful lot like the normal experience *cough* years ago when I went through school in CA. Select students were placed on the accelerated math track in 7th grade Pre-Algebra, leading to 8th grade Algebra I, and so on. NT students did something else in 7th, did Pre-Algebra in 8th, and Algebra I in 9th, with the rest of the normal progression looking just like your chart.

That is correct above, as with Dude.
I've heard that CC tries to get more kids through Algebra and Geometry but it is bad for gifted kids since they can't accelerate easily. Here is what the "average" kid takes for CC math in our CA public schools.
8th grade- CC 2/3 (used to be Algebra I); now a mix of Algebra I and Geometry.
9th grade- CC 3 (used to be Geometry); now the rest of Algebra I and Geometry.
10th grade- Algebra II or whatever it is called now
11th grade- Pre-Calculus
12th grade- Calculus AB AP.

One more thing on CC. I live in a PARCC state, so the curriculum needs to align with the PARCC questions, which require the weird methodology and wordy trick questions. The math level is so low, I would have to advance my young son three years ahead to learn something new. My state has so many prescriptive requirements, it's impossible to complete the required curriculum and supplement beyond. The children don't even do speed drills. I have lobbied the legislature and districts, a lot. The common defense of CC by our legislators is that it ends tracking and closes the achievement gap. The schools are rated by how well they close the achievement gap, so they are motivated to keep bright students down.

Interesting -- the new math core standards here move Algebra to 8th, Geometry 9th, Algebra II 10th (followed by Trig/Pre-Calc or other, 3 yrs required in HS) -- which is roughly a year ahead of the prior standards for my state (after accounting for shifting some topics). That seems odd considering didn't that work in your area, bluemagic.

I can't remember what the tracks were when I was in HS. I believe I had Advanced Algebra/Trig in 11th, and we didn't have Calculus at the school (had to get special permission and go to the nearby university for it). I took a life skills math class my last year just because I wanted to (I didn't need it), though someone (not sure who, counselor? I was averse to persuasion at that age) questioned it an asked if I was sure I didn't want to take something higher level (pre-Calc, maybe). Considering my college plans, I figured I wouldn't need it. In college, I took a logic class (loved it) and a computer programming class for my math credits, did great, but my heart was in other pursuits.

I think I understand better now, that if a kid is mathy and motivated, having the opportunity to accelerate to some degree and go deeper both have value, but not many negatives for a high-ability learner in the long run. I feel better about the approach I think we should take with the school for my two kids -- finding a balance between a faster pace and a deeper understanding, and needing a way to demonstrate growth (specifically not just individual work without support).

Actually, it is uncommon for students to take Pre-Algebra in 5th grade in our district as well although I believe that more kids could probably handle it if it were readily available. On the other hand, it is also possible that kids who are ready for Pre-Algebra in 5th may not all be ready for Pre-Calculus in 10th grade such that part of the restriction is to address future concerns. It would be fair to also point out that DD has had the benefits of a strong elementary math program, a parent with a math degree and a sibling who can readily rattle off an explanation if she ever gets stuck.

Of course, I do get your point and perhaps I am underestimating DD's math ability a little bit but not her "mathiness" as I have defined it because I am making a judgment based on her today with the understanding that she may change in the future. In fact, that is why I have insisted on her participation in a couple of the national math competitions and why she knows that she is expected to complete AP Calculus BC her senior year. We have had discussions and DD understands the importance of keeping her options open for college. At the same time, having had the opportunity to observe some of the very mathy kids on DS' competitive teams, I have to be realistic. While DD certainly has the ability to earn a degree in STEM and be a competent professional and perhaps even have some of these math geniuses report to her, she is unlikely to pioneer breakthroughs in math. By the way, that is not a put down of DD because she has some incredible abilities in other domains that may take her even farther. Like I said, if she does choose a STEM field, she will probably end up managing/supervising these technical genius types.

Point taken. I don't mean that DD has no math ability as she should be in the top 1%-2% (by grades & standardized test scores) in her class of almost 400 6th graders, only that she is not at the extreme right in ability or passion. DD has enough ability to do whatever she chooses but her chances of achieving the extraordinary is less likely to lie in the math area as in some other domains.

I do hesitate to blame bad teaching in general. It really isn't always the teacher's fault. Sometimes the kid just doesn't get it right away or doesn't bother to think about it and make connections. If a bunch of other kids understands and assimilates the material, then the teacher likely did a decent job. Perhaps it is the cautionary effects of having had twins who were in the same classes throughout elementary and still share some classes and/or teachers in middle school: Sometimes I would have had a complete misunderstanding of a particular teacher if I only had one kid or the other in the class. For example, I might have thought a particular teacher almost never gave homework (DS) or gave way too much homework (DD) at times. DS can squeeze in a ton of work in a short amount of time and does whereas DD sometimes re-does classwork and produces a way more elaborate job than the homework the teacher actually assigned.

Oh, well... I would not equate "mathy" (in my mind, perhaps top 1-2% for math ability) with "likely to pioneer breakthroughs in math"! (What would that be...top .000001%?) Gracious. No, she may not be at the level of the top kids on the math team, but she still might achieve great things in a STEM field--especially if she has great writing skills, which you say she does. (I read a lot of scientific papers...)

Also, remember, she does not have to achieve the extraordinary. Perhaps she could be extraordinary in one area, but will turn out to be more interested in something at which she is less extraordinary.

We are all prisoners of our presumptions! I am thinking maybe 99.99 percentile in math ability and passion (for math breakthrough, not pursuing STEM).

And I agree, she doesn't have to be extraordinary but it would be nice. It just seems that so far her passions tend to be in areas where she has greater talent.