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Math Sequence Past Pre-Calculus for STEM-leaning Kid


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I have a 7th grader who will wrap up in May about 3/4 the way through Derek Owens Algebra 2. We're not rushing any math and making a huge move from Virginia to Hawaii this summer, so we'll likely take off the summer and finish up Algebra 2 in the fall (8th grade) going into pre-cal after that.

After that, what should I do? My guess is he'd finish up pre-cal in fall of his 9th grade year.  He's leaning towards something STEM, so does that mean Calculus BC next? And then what...what do you do after Calculus?

Is there a place where I should stop and do AoPS Intermediate Counting & Probability or is that not necessary? 

 

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Most colleges will prefer 4 years of high school math for a STEM admission, even if calculus is complete.  I’m assuming that’s where you are headed.  Some ideas:

  1. AoPS classes in Counting and probability, or Number theory are excellent, and could be done before or after pre-Calc.  Has your son done the intro levels for these classes?
  2. AoPS intermediate algebra and pre-Calc cover materials not found in most other curriculum.  These could allow you to go “deeper” into the topics if your son is interested, since he has the time.
  3. AP statistics is another option.  My science-loving DD really benefitted from taking this before Calc, too help with understanding data analysis in experiments.
  4. After AP Calculus, there is always DE or online classes in multi variable calculus, differential equations, discrete math.  

Here is an article, explaining far better than I can, the reasons to take other classes before Calculus.  https://artofproblemsolving.com/articles/calculus-trap

 

 

 

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1 hour ago, shburks said:

I have a 7th grader who will wrap up in May about 3/4 the way through Derek Owens Algebra 2. We're not rushing any math and making a huge move from Virginia to Hawaii this summer, so we'll likely take off the summer and finish up Algebra 2 in the fall (8th grade) going into pre-cal after that.

After that, what should I do? My guess is he'd finish up pre-cal in fall of his 9th grade year.  He's leaning towards something STEM, so does that mean Calculus BC next? And then what...what do you do after Calculus?

Is there a place where I should stop and do AoPS Intermediate Counting & Probability or is that not necessary? 

 

My son did pre-calc in 7th and calc in 8th.  Even having a year of calc under his belt, Calc BC in 9th was a big stretch.  We took it through PA Homeschoolers and the teacher had said she had never let a student that young take the class before.  He did okay with the class but he had to really work at it.  I don't think jumping straight from pre-calc to Calc BC in 9th would be a good choice.  I'd spend a year doing regular Calculus or some other math and let him mature a little more before jumping into Calc BC. We ended up doing AP stats in 10th because I couldn't find any other options.  We did Multi-variable calc and diffeential calc in 11th and Complex analysis in 12th (the last 2 years were done through mathandmusicstudio.com - John Rosasco).  He didn't credit for those years but John is such a great teacher and laid such a good foundation that when DS took them "for real" in college, they were very easy for him.  I have no regrets about paying twice for those classes.  

Despite being a math loving kid who self taught himself everything from algebra through calc, he HATED AoPS, the discovery approach was not his thing. I had thought they would be good fillers but it was a complete bomb here.

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14 hours ago, Trabug said:

Most colleges will prefer 4 years of high school math for a STEM admission, even if calculus is complete.  I’m assuming that’s where you are headed.  Some ideas:

  1. AoPS classes in Counting and probability, or Number theory are excellent, and could be done before or after pre-Calc.  Has your son done the intro levels for these classes?
  2. AoPS intermediate algebra and pre-Calc cover materials not found in most other curriculum.  These could allow you to go “deeper” into the topics if your son is interested, since he has the time.
  3. AP statistics is another option.  My science-loving DD really benefitted from taking this before Calc, too help with understanding data analysis in experiments.
  4. After AP Calculus, there is always DE or online classes in multi variable calculus, differential equations, discrete math.  

Here is an article, explaining far better than I can, the reasons to take other classes before Calculus.  https://artofproblemsolving.com/articles/calculus-trap

 

 

 

Trabug--Yes, absolutely! I know I need to have math for him all the way through, so I'm just trying to do a little bit of high school planning to think about how to handle this.

He has not done intro to counting/probability or number theory via AoPS. The series in general isn't a good fit for him, so even though I considered those books to do before Geometry, I ended up not doing them. Would the intro need to be done before the intermediate one? That was also another question--if I did them, would before (or after) pre-Cal be good or does that mess up the flow of math? I.e. is it a disadvantage to do pre-cal and then "break" before calculus?

I thought about statistics, too. So he could do statistics before Calculus as well?

Thanks! I did look at our local CC to see what kind of math options there were and saw classes that looked like those you mentioned! I'll take a look at the article, too.

13 hours ago, cjzimmer1 said:

My son did pre-calc in 7th and calc in 8th.  Even having a year of calc under his belt, Calc BC in 9th was a big stretch.  We took it through PA Homeschoolers and the teacher had said she had never let a student that young take the class before.  He did okay with the class but he had to really work at it.  I don't think jumping straight from pre-calc to Calc BC in 9th would be a good choice.  I'd spend a year doing regular Calculus or some other math and let him mature a little more before jumping into Calc BC. We ended up doing AP stats in 10th because I couldn't find any other options.  We did Multi-variable calc and diffeential calc in 11th and Complex analysis in 12th (the last 2 years were done through mathandmusicstudio.com - John Rosasco).  He didn't credit for those years but John is such a great teacher and laid such a good foundation that when DS took them "for real" in college, they were very easy for him.  I have no regrets about paying twice for those classes.  

Despite being a math loving kid who self taught himself everything from algebra through calc, he HATED AoPS, the discovery approach was not his thing. I had thought they would be good fillers but it was a complete bomb here.

cjzimmer1--Thank you! I really appreciate the "been there, done that" experience. I had that same concern about doing calculus that young as well. Would you consider doing Cal AB first (is that "regular" calculus?) and then Calc BC after just because we have the time to do so OR is doing a different math (statistics or something) a better option before Calc BC? 

I actually have a friend whose son has done most upper level math classes with John Rosasco. What do you mean by he didn't get credit for those last two classes? Just that they were DE level courses but didn't get DE credit?

And YES on AoPS! I discovered in pre-A that discovery method was NOT a good fit for my ds either! We used Jacob's Algebra and Jacob's Geometry (geometry via Derek Owens) and then Derek Owen again this year for Algebra 2. I had concerns that the number theory/counting & probability could be a poor fit still. Did you try those and bombed?

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54 minutes ago, shburks said:

I thought about statistics, too. So he could do statistics before Calculus as well?

Yes he could.  But be aware that AP stats is much more writing/English skills than we had anticipated. I had assumed it was just math (I've never taken stats myself) but there is very precise ways of writing/identifying things.  DS doesn't like to write and was quite annoyed about how detailed things needed to be written.  I don't know if that is true for all stats or just the AP stats.  

Would you consider doing Cal AB first (is that "regular" calculus?) and then Calc BC after just because we have the time to do so OR is doing a different math (statistics or something) a better option before Calc BC? 

Since you said your son wouldn't finish pre-calc till the fall of 9th.  I wouldn't immediately jump into Calc AB.  The reason being the exam is given once a year and you would have to move the material at an accelerated pace to cover it all in time.  You want to lay a good foundation in calculus and rushing through it wouldn't be wise in my opinion.  Now you could choose not to take the exam and then you wouldn't have the time crunch but if it were me, I wouldn't bother taking the AP class if I wasn't going to take the exam.  There wouldn't really be a point.  

So I would spend the rest of 9th laying a good foundation in calc.  Or you could spend time pursuing some of the other maths (but I don't have any good recommendations because I'm just not that versed on what those options might be).  And depending on how comfortable he is at that point, you could try calc AB or BC in 10th or even wait another year.  Calc is needed in so many STEM fields that you really want to make sure they grasp it and some of that comes from maturity.

I actually have a friend whose son has done most upper level math classes with John Rosasco. What do you mean by he didn't get credit for those last two classes? Just that they were DE level courses but didn't get DE credit?

There is no method to test out of those classes and they are not accredited classes so he didn't get any college credit for those classes.  Thus he had to repeat them in college to get the credit even though he already knew the material.  

And YES on AoPS! I discovered in pre-A that discovery method was NOT a good fit for my ds either! We used Jacob's Algebra and Jacob's Geometry (geometry via Derek Owens) and then Derek Owen again this year for Algebra 2. I had concerns that the number theory/counting & probability could be a poor fit still. Did you try those and bombed?

We did Jacob's algebra and geometry as well.  I can't remember what we all used for Alg II and Pre-calc.  I know we used some thinkwell.  My ds was so advanced and I had no clue what I was doing that I made him do every level of math twice with different programs just because I was trying to slow him down while I attempted to figure things out (He self taught himself algebra in 3rd grade so we had plenty of time for repeats and he still ended up in calc in 8th).  The only AoPS we tried was the intro to counting and probability.  We tried it somewhere in the high school years so the maturity was there for him to work through it if the approach had been right for him but it was a no go for us.

 

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4 minutes ago, cjzimmer1 said:

 

You are a wealth of knowledge! Thank you so much! I'm not a math person either--ds clearly got this from my husband--so I never took statistics either. My son sounds very similar to yours--he does not enjoy writing, so perhaps that's not a good fit for him if it's not a class he doesn't really need! 

Excellent point on not jumping into Calculus AB/BC. I hadn't thought about the testing bit, I suppose that's a class he would need to take in a typical school year in order to take the test in the spring. Maybe a regular calculus class for the remainder of the year (whenever he finishes pre-Cal) and then be ready for Calculus BC as a 10th grader or even 11th . 

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My daughter took Calc AB in eighth at home (ChalkDust calculus plus part of one other section that CD's DVD's didn't cover) and BC in ninth at a B&M school.  The school then has a program to do Calc II and III on the high school's campus through DE, so she did those as a sophomore.  After that, she was on the college campus doing DE, starting with differential equations and then a bunch of higher-level math (combinatorics, number theory, other stuff I don't understand).  On-campus DE was the answer for us.  A lot of people take AB and BC in consecutive years in B&M schools.

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My daughter who did Pre-Calc in 9th has done the following sequence via dual enrollment:

10th - Calculus; 11th-Statistics; 12th-Discrete math

She could have done more Calculus any of those subsequent years, but decided that she wants to go into Engineering, and that she wants to start Calc over in whatever Engineering program she does even though she got an A in that first Calc class.

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My older kids both took Calculus 1 and Statistics as dual credit students at a community college in Hawaii.  Both learned a lot, however a couple caveats.  My kids were independent juniors when they started at the CC.  Both had a lot of experience being away from home, doing cross country flights alone, and taking online classes.  They rode the public bus to and from school most days.  

Their Calc class was taught be an older instructor who was very thorough, but old school in grading.  I know that one of my kids had the highest average in the course - with an 85.  

Both retook calculus at university.  This was intentional, in order to give them the firmest foundation for moving forward with other math courses.

FWIW, at the Hawaii state community colleges, pre-calculus is a two course sequence usually taken over two semesters.  My kids took that junior year, then did calculus 1 fall semester and statistics spring semester of senior year.  I would not recommend taking courses below pre-calc at the community colleges here.  The pre-calc classes were hit and miss.  One instructor was quite good and the other was ok, but not great.  

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And as an aside, I would have him do a timed sample math section on the ACT (or SAT if you prefer) to see how he does.  You could have him sit for the exam through a talent search if you wanted..  Is he retaining all that math? Can he do it quickly, efficiently, and accurately?  My oldest kid first hit algebra 1 in 5th grade.  He finished geo and algebra 2 by the end of 8th.   However, his ability to do great on the ACT with it wasn't super amazing.  The pre-algebra skills got rusty.  He was sloppy with it.  Doing some problem solving on the side as we continued math

I agree jumping to Calc BC may be too big of a jump.  A lot of schools use an ACT 28 in math to start at beginning calc.  But a kid that scores higher will do better and be even more comfortable.  I would consider doing a year of stats with continued review and problem solving on the side.  The AoPS sequence is good to look at.  My kids don't love math enough to spend that much time on it.  My kid did do AoPS for a couple year.  Foerester's texts have been a nice compromise of rigor/work load here.  

I would just say don't rush it.  Make sure you're maintaining that old math.  I have a math degree and the pacing is so fast in college, lots of STEM students are lost that way.    Also, college math can require tons of writing in general, so making sure he can "prove" answers in very legible format is important and something we had to work on here.  

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17 hours ago, FuzzyCatz said:

And as an aside, I would have him do a timed sample math section on the ACT (or SAT if you prefer) to see how he does.  You could have him sit for the exam through a talent search if you wanted..  Is he retaining all that math? Can he do it quickly, efficiently, and accurately?  My oldest kid first hit algebra 1 in 5th grade.  He finished geo and algebra 2 by the end of 8th.   However, his ability to do great on the ACT with it wasn't super amazing.  The pre-algebra skills got rusty.  He was sloppy with it.  Doing some problem solving on the side as we continued math

I agree jumping to Calc BC may be too big of a jump.  A lot of schools use an ACT 28 in math to start at beginning calc.  But a kid that scores higher will do better and be even more comfortable.  I would consider doing a year of stats with continued review and problem solving on the side.  The AoPS sequence is good to look at.  My kids don't love math enough to spend that much time on it.  My kid did do AoPS for a couple year.  Foerester's texts have been a nice compromise of rigor/work load here.  

I would just say don't rush it.  Make sure you're maintaining that old math.  I have a math degree and the pacing is so fast in college, lots of STEM students are lost that way.    Also, college math can require tons of writing in general, so making sure he can "prove" answers in very legible format is important and something we had to work on here.  

He actually did the ACT in October this year as a 7th grader as part of the Duke TIP program. His score was pretty high with only having completed Algebra I and Geometry--high enough for entrance into most state universities. My kid doesn't LOVE math, but he's just good at it! I am leaning towards slowing him down a bit and having him do something a little different (Number Theory? Probability?) before pre-cal. 

Regarding pre-algebra skills, what would you recommend "on the side" to make sure those skills aren't forgotten?

Finally, can you give me a little more information on your last statement? Proving answers in a legible format...do you mean following steps, listing all steps, literally handwriting and legibility? Thanks! :) 

On 4/16/2018 at 12:46 AM, Sebastian (a lady) said:

My older kids both took Calculus 1 and Statistics as dual credit students at a community college in Hawaii.  Both learned a lot, however a couple caveats.  My kids were independent juniors when they started at the CC.  Both had a lot of experience being away from home, doing cross country flights alone, and taking online classes.  They rode the public bus to and from school most days.  

Their Calc class was taught be an older instructor who was very thorough, but old school in grading.  I know that one of my kids had the highest average in the course - with an 85.  

Both retook calculus at university.  This was intentional, in order to give them the firmest foundation for moving forward with other math courses.

FWIW, at the Hawaii state community colleges, pre-calculus is a two course sequence usually taken over two semesters.  My kids took that junior year, then did calculus 1 fall semester and statistics spring semester of senior year.  I would not recommend taking courses below pre-calc at the community colleges here.  The pre-calc classes were hit and miss.  One instructor was quite good and the other was ok, but not great.  

Sebastian (a lady)--Thank you for information specific to Hawaii! DS is definitely not ready to go into DE yet. While he has taken science and math classes online, I do still have to follow up to make sure the assignments are being completed for science. I think that's still a few years away. I'd consider it for math as a junior or senior perhaps in a few years! Good information on the pre-cal classes, too. Does it cover two semesters because it moves slower? 

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You might find that now that he is older that switching back to AoPS for the traditional high school sequence might be a good fit.  My ds completed alg 2 early in 8th grade and jumped into AoPS Intermediate as his first AoPS course.  He took their precal in 9th and their cal in 10th (followed by the BC exam where he scored a 5).  He dual enrolled in 11th and 12th at a local university and took multivariable, diffEQ, and linear alg 1 and 2.  

FWIW, he had no problems with that pace and he repeatedly stated during college that he was incredibly thankful for his AoPS courses.  He is a graduating physics/math major this yr and he says that his AoPS courses were extremely beneficial for thinking about physics theory (which is what he will be pursuing in grad school).

I have a dd who refused to consider AoPS after their alg 1 book.  She didn't like the approach at all, so I get some strong math students don't want to go there.  But, if it has been a while, you might want to give it a try again and see. 

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1 hour ago, shburks said:

He actually did the ACT in October this year as a 7th grader as part of the Duke TIP program. His score was pretty high with only having completed Algebra I and Geometry--high enough for entrance into most state universities. My kid doesn't LOVE math, but he's just good at it! I am leaning towards slowing him down a bit and having him do something a little different (Number Theory? Probability?) before pre-cal. 

Regarding pre-algebra skills, what would you recommend "on the side" to make sure those skills aren't forgotten?

Finally, can you give me a little more information on your last statement? Proving answers in a legible format...do you mean following steps, listing all steps, literally handwriting and legibility? Thanks! :) 

Sebastian (a lady)--Thank you for information specific to Hawaii! DS is definitely not ready to go into DE yet. While he has taken science and math classes online, I do still have to follow up to make sure the assignments are being completed for science. I think that's still a few years away. I'd consider it for math as a junior or senior perhaps in a few years! Good information on the pre-cal classes, too. Does it cover two semesters because it moves slower? 

My kids have experience with pre-calc in two different states.  In both cases, the trigonometry was broken out into a separate semester course.  (One school also had a combined 6 credit one semester course.  That was just too big of a bite for a first college class.)

I don't know if it is two courses because of the depth and breadth of the course, because some students only need one or the other (either because that is all their degree requires or because they test out of one course), or because students taking pre-calc in college need a little slower pace than those taking calculus.  

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4 hours ago, shburks said:

He actually did the ACT in October this year as a 7th grader as part of the Duke TIP program. His score was pretty high with only having completed Algebra I and Geometry--high enough for entrance into most state universities. My kid doesn't LOVE math, but he's just good at it! I am leaning towards slowing him down a bit and having him do something a little different (Number Theory? Probability?) before pre-cal. 

Regarding pre-algebra skills, what would you recommend "on the side" to make sure those skills aren't forgotten?

Finally, can you give me a little more information on your last statement? Proving answers in a legible format...do you mean following steps, listing all steps, literally handwriting and legibility? Thanks! :) 

 

That sounds great and that is what has worked well with my really good at math but doesn't LOVE it math kid too.  On the side, we've just worked through some ACT/SAT math prep books that just have bunches of problems.  We'd do 3-5 problems a day.  If he got them all right, great. If he got one wrong, we'd review and might pull a worksheet of those type of problems to review on for a day or 2.  Or go to Khan.  It has been SUPER worthwhile to keep that going and it rarely takes more than 10 minutes a day.  

And yes - I just mean cleanly writing the solution of a problem step by step in such a way that a teacher could say he "proved" his work. That took my kid longer than just getting answers for sure.  

Sounds like you're doing lots of good things.  :)

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