Jump to content

Menu

Beyond Calc and Stats....


Recommended Posts

What If.... your kid had done both Calcs (AB and BC) AND AP Stats AND had to take a "meaningful math course" her senior year to be considered at some of her top choice colleges?

 

She's not interested in moving on to do Linear Algebra or Diff EQ and frankly most colleges balk at accepting credit for those from high schoolers unless she does the class at the uni.....

 

Would you consider maybe Number Probability? Something Else?

Link to comment
Share on other sites

Today she would say Biology. Tomorrow, Music or Something Else. She is cheerfully undecided.

 

ETA - definitely not math though. Math is easy and she tolerates it but her passions are numerous and lie in other areas.

Edited by AK_Mom4
Link to comment
Share on other sites

Cheerfully undecided is a great place to be at that age :)

 

If she doesn't want to go with more calculus-style math, a discrete math or intro to proofs class might be interesting if she did okay with proofs in geometry. Mathematical logic could be another interesting class over here. Of course there's always AOPS NT/CP -- she might find the intro books a little easy going but there's definitely meat in the intermediate book. If the colleges will accept it, a programming class would be another option which provides a useful intro to many things. 

 

There are other highly interesting topics (voting theory, game theory (which has actually been applied to biology, politics, and economics), a second course in statistics), but those would really require a mentor in order to learn them. 

  • Like 2
Link to comment
Share on other sites

Another idea I just thought of:

 

Lial also has a Finite Math textbook. Now, this class is usually taken as an alternative to precalculus or applied calculus, so it is not a post-calculus class, but it is a college-level class that is frequently taken by majors in biology and business. For example, Cornell uses it for one of their freshman-level classes in "finite mathematics for the life and social sciences". Many topics would be familiar, but many topics would be new as well. This would also be a great class to dual enroll in. 

  • Like 1
Link to comment
Share on other sites

How is your requirement worded? Our state requirement is for a math-related class, doesn't have to be math.

 

Economics, several of the sciences, etc count, as long as the course requires a meaningful amount of math.

 

Mathematical programming (e.g. repeating calculus but with MATLAB/Octave) might be another option. Course titles are things like Scientifc Computing, Computational Mathematics, Numerical Modeling, etc.

Link to comment
Share on other sites

We are in Alaska too. My '16 grad did Calc 3 online through Kenai Peninsula College, which was less disruptive than trying to attend regular classes at UAA. On the other hand, you could knock out a Calc 3 5 week intensive during the UAA summer session and be done with math for the year. Those classes are starting very soon, so jump on it immediately if that is her interest.

 

I learned that Comp Sci is actually considered a math class in the Anchorage School District, so that would be a possibility too.

 

Not sure what colleges she is looking at, but if they are selective, it's important that her math is not decreasing in rigor for senior year. If it's just four years of math that you need for the performance scholarship, rigor is less of a concern.

Edited by Gr8lander
  • Like 1
Link to comment
Share on other sites

If she doesn't have much experience in counting and probability, I would take a look at an introductory text like the one published by AoPS.  If she has that covered, then look at the TOC for their advanced c&p book.  

 

AoPS also offers two books on contest math preparation.  You could use one or both of these and call the course "Advanced Problem Solving Techniques" or something similar.  

 

We'll be in a similar boat when my dd is a senior, and I am going to suggest to her that we begin the year with Intermediate C&P and finish the year with volume 2.  

  • Like 1
Link to comment
Share on other sites

What If.... your kid had done both Calcs (AB and BC) AND AP Stats AND had to take a "meaningful math course" her senior year to be considered at some of her top choice colleges?

 

She's not interested in moving on to do Linear Algebra or Diff EQ and frankly most colleges balk at accepting credit for those from high schoolers unless she does the class at the uni.....

 

Would you consider maybe Number Probability? Something Else?

 

This is exactly why I do not ask for acceleration for my 6th grader.  I do not want him forced to take some extreme calculus in the 11th or 12th grade, just because he completed ab or bc early.    i  do not want to force him  to take such math in h.s. unless I am sure he wants to be a math, engineer or science major.  med school, business school, and certainly law school do not require such math. 

Link to comment
Share on other sites

This is exactly why I do not ask for acceleration for my 6th grader.  I do not want him forced to take some extreme calculus in the 11th or 12th grade, just because he completed ab or bc early.    i  do not want to force him  to take such math in h.s. unless I am sure he wants to be a math, engineer or science major.  med school, business school, and certainly law school do not require such math. 

 

Sometimes, there isn't a lot of choice to be had.  It may be a choice between miserable kid or having to scramble for later options.  We've got a 10yo who already knows a bit of calculus, but is nowhere near college-ready.  We can't bring ourselves to make him do 4th grade arithmetic.

 

For the OP, there are still a lot of options available.  I do second the thought of showing increasing rigor.  "Cop out" courses will look exactly like that.  Unfortunately, that means looking for something that is college sophomore level or better.

 

ETA - Additional thought to ponder: at this age, a talent for math may not have turned into a love for it just yet.  I have a math degree, but until my second year of college, I had no interest in pursuing math.  I only did so because my degree required it.  Fortunately, I connected with the right professor, in the right class, and realized that I loved the artistry of the creative genius behind the theory.  If there is *any* chance of this, don't sell her short.  Find a local college, or sign her up for an online remote option, and let her take something more advanced.  Calculus III (multivariate / multivariable calculus) is widely applicable.  If she liked stats, she can take calculus-based prob & stats.  Some colleges have introductory courses for higher math, and many have discrete mathematics (check computer science departments, who occasionally host the course).

 

There will be something both interesting and challenging.

Edited by Mike in SA
  • Like 5
Link to comment
Share on other sites

AoPS counting & probability (both books) along with AoPS number theory would be my suggestion.

 

I would second this. My oldest son has now graduated from Stanford and he told me that the one math he thinks every high schooler who might ever program (and in tomorrow's world that could be most of our kids!) should take is Number Theory. He did AoPS. We just ran out of time to do Counting and Probability. 

 

I know your daughter did not list anything computer related - but last week my oldest ,who is a phD student in Media Studies, sent me a photo of the program she had just written! Yes, in Media Studies! They need to program to do work on the statistical side of things!!!! For the first time she was relieved I insisted she learn to program when she was in middle school.

  • Like 5
Link to comment
Share on other sites

 

 

For the OP, there are still a lot of options available.  I do second the thought of showing increasing rigor.  "Cop out" courses will look exactly like that.  Unfortunately, that means looking for something that is college sophomore level or better.

 

  If she liked stats, she can take calculus-based prob & stats.  Some colleges have introductory courses for higher math, and many have discrete mathematics (check computer science departments, who occasionally host the course).

 

There will be something both interesting and challenging.

 

Agreed.  The appearance of "cop out" is real.  Ridiculous, but real. Discrete math and Multivariable are two good choices.  Apparently, taking Calc early in high school also means you look "weak" if you don't take college calc-based Physics as opposed to college Algebra-based Physics.  Apparently, it doesn't matter (to some) that the student has zero interest in it. 

  • Like 1
Link to comment
Share on other sites

Agreed. The appearance of "cop out" is real. Ridiculous, but real. Discrete math and Multivariable are two good choices. Apparently, taking Calc early in high school also means you look "weak" if you don't take college calc-based Physics as opposed to college Algebra-based Physics. Apparently, it doesn't matter (to some) that the student has zero interest in it.

Lol, I was just reading a bunch of stuff about the top colleges all deciding they don't want students who are so focused on achievement and that they are now more interested in students "who care about others".

 

I also just did a short consultation with a college consultant to come up with an overall plan for my dd and she told me that she should either take Calculus BC in 10th or make Calculus AB her last class. She told me that serious students don't take AB and then BC. It seems ridiculous to me. But her advice that it would be okay if AB was her last math class doesn't seem to mesh with what people are saying here, either.

 

ETA: Oh, and my dd is taking algebra-based physics next year at the local coop because that's what they offer and she has no interest in science. Plus, she wants to take a class with her brother. I never thought of that being an issue and I'm not going to worry about it, but it is interesting to hear.

Edited by OnMyOwn
  • Like 2
Link to comment
Share on other sites

I would second this. My oldest son has now graduated from Stanford and he told me that the one math he thinks every high schooler who might ever program (and in tomorrow's world that could be most of our kids!) should take is Number Theory. He did AoPS. We just ran out of time to do Counting and Probability. 

 

(snip)

I had a similar conversation with my oldest.  He told me that his background in AoPS NT and C&P (he completed both books)has been extremely useful in his computer and business analytics classes. Based on my son's experience, I have made sure that my younger kids complete these books before they graduate from my homeschool, something that may have not happened otherwise.

  • Like 6
Link to comment
Share on other sites

Lol, I was just reading a bunch of stuff about the top colleges all deciding they don't want students who are so focused on achievement and that they are now more interested in students "who care about others".

 

 

 

ETA: Oh, and my dd is taking algebra-based physics next year at the local coop because that's what they offer and she has no interest in science. Plus, she wants to take a class with her brother. I never thought of that being an issue and I'm not going to worry about it, but it is interesting to hear.

 

I wouldn't either. :)  I told my daughter I didn't care what people thought.  She decided to do AP Physics C anyway.  They ditched AP Physics B the year after she took AP chem with AP Calc BC.  She had the choice of taking 5 APs sophomore year to work Physics B in before they switched to Physics 1/2, which she decided was a bad idea. She felt like she need to continue AP science progression, so she took Physics C and finished with Bio. I let her make the call.

  • Like 1
Link to comment
Share on other sites

Sometimes, there isn't a lot of choice to be had.  It may be a choice between miserable kid or having to scramble for later options.  We've got a 10yo who already knows a bit of calculus, but is nowhere near college-ready.  We can't bring ourselves to make him do 4th grade arithmetic.

 

For the OP, there are still a lot of options available.  I do second the thought of showing increasing rigor.  "Cop out" courses will look exactly like that.  Unfortunately, that means looking for something that is college sophomore level or better.

 

ETA - Additional thought to ponder: at this age, a talent for math may not have turned into a love for it just yet.  I have a math degree, but until my second year of college, I had no interest in pursuing math.  I only did so because my degree required it.  Fortunately, I connected with the right professor, in the right class, and realized that I loved the artistry of the creative genius behind the theory.  If there is *any* chance of this, don't sell her short.  Find a local college, or sign her up for an online remote option, and let her take something more advanced.  Calculus III (multivariate / multivariable calculus) is widely applicable.  If she liked stats, she can take calculus-based prob & stats.  Some colleges have introductory courses for higher math, and many have discrete mathematics (check computer science departments, who occasionally host the course).

 

There will be something both interesting and challenging.

 

 

 Our solution for the 6th grader , all advanced math outside of  the school system.  he is wrapping up alg 2 with D.O.  We will deal with appropriate placement when he reaches H.S., and has a better idea of where he is headed. .  

Link to comment
Share on other sites

What If.... your kid had done both Calcs (AB and BC) AND AP Stats AND had to take a "meaningful math course" her senior year to be considered at some of her top choice colleges?

 

She's not interested in moving on to do Linear Algebra or Diff EQ and frankly most colleges balk at accepting credit for those from high schoolers unless she does the class at the uni.....

 

Would you consider maybe Number Probability? Something Else?

I would start by having her spend time looking over 4 yr course plans for various majors. If she says biology, look at the course descriptions and requirements in areas she doesn't like. :) You might find that some majors require a math that you haven't considered. (Or a more advanced stats course, etc.)

 

If you don't find a direction from that, I would look more specifically at the universities she will be applying to. What are her top choices? Not all schools are really going to care. Dd took cal 1 first semester of jr yr. She didn't take any other math until stats spring of sr yr. No school cared that there were 2 semesters with no math. She applied as a foreign lang/international business/ international studies major. I am sure that the multiple upper level foreign language courses were considered equally as when ds applied as a physics/math major with upper level math/science and fewer foreign language credits.

 

Have her call admissions and ask if she takes course X over a math if she has completed BC and stats will negatively impact her application. If there is a course of interest that won't be able to be taken if she takes a math she doesn't want or need, she is the loser if they really don't care.

  • Like 1
Link to comment
Share on other sites

I had a similar conversation with my oldest. He told me that his background in AoPS NT and C&P (he completed both books)has been extremely useful in his computer and business analytics classes. Based on my son's experience, I have made sure that my younger kids complete these books before they graduate from my homeschool, something that may have not happened otherwise.

Did your son use AOPS for all of his math? Could someone who had not used AOPS take these courses after calculus without it being a problem?

Link to comment
Share on other sites

Did your son use AOPS for all of his math? Could someone who had not used AOPS take these courses after calculus without it being a problem?

My kids use AoPS until they hit calc.  You could definitely use the AoPS NT and C&P without having used any of the other books.

  • Like 3
Link to comment
Share on other sites

Could someone who had not used AOPS take these courses after calculus without it being a problem?

 

Yes. The advancement in mathematical maturity would quite probably help them and they might find they can move even faster, but there will be plenty of worthwhile new material and challenging problems. 

  • Like 1
Link to comment
Share on other sites

We are looking at multivariable calculus and/or calculus based statistics for my older boy.

 

 

Could someone who had not used AOPS take these courses after calculus without it being a problem?

Are you referring to the books or online classes?

My oldest did the intro NT book and intermediate C&P books with algebra and it was okay. He didn't take the online class and he skipped the intro C&P book. He will be taking the intermediate NT online class this summer as there is no book.

My younger boy needs deadlines from classes so he is doing intro NT and intro C&P online classes this summer.

 

The NT and C&P books and courses are standalones and doesn't depend on the other aops books or courses.

  • Like 1
Link to comment
Share on other sites

 

 

I also just did a short consultation with a college consultant to come up with an overall plan for my dd and she told me that she should either take Calculus BC in 10th or make Calculus AB her last class. She told me that serious students don't take AB and then BC. It seems ridiculous to me. But her advice that it would be okay if AB was her last math class doesn't seem to mesh with what people are saying here, either.

 

 

 

I disagree with this.  There is overlap between AB and BC.  I believe AB is roughly the first semester or so of BC, so your student would experience some redundancy.  I have heard of students who take one year of Calculus AB, and then follow that with a course called Calculus C, which I see is offered by JHU-CTY and Stanford Online High School.  Maybe that's what she meant?  In any case, I don't think that's an option for a lot of students, who end up taking AB and then BC the following year.  

  • Like 2
Link to comment
Share on other sites

 

 

For the OP, there are still a lot of options available.  I do second the thought of showing increasing rigor.  "Cop out" courses will look exactly like that.  Unfortunately, that means looking for something that is college sophomore level or better.

 

 

 

Could someone explain to me what is meant by "cop out" courses in this context?  

Link to comment
Share on other sites

I also just did a short consultation with a college consultant to come up with an overall plan for my dd and she told me that she should either take Calculus BC in 10th or make Calculus AB her last class. She told me that serious students don't take AB and then BC. It seems ridiculous to me. But her advice that it would be okay if AB was her last math class doesn't seem to mesh with what people are saying here, either.

I have been told to have math every year of high school for my kids so we will have to go the DE route. For my district's public high schools, kids take

1) AP calculus BC (11th) AP statistics (12th) for those who did algebra 1 in 7th and has a good score in Precalculus in 10th grade

2) calculus AB (11th) calculus BC or AP statistics (12th)

3) calculus AB or BC (12th) for those who did algebra 1 in 8th

 

So calculus AB in 12th grade as the last math class is definitely okay but not at 10th grade.

Link to comment
Share on other sites

So something like a business math class?

After calculus? Yes. Before calculus? Business math would be fine.

 

If business math is still desired, I'd suggest mathematical economics (assuming that the stats prerequisite has been met - otherwise, take stats).

  • Like 1
Link to comment
Share on other sites

A bit off-topic, so my apologies, but why don't you use AoPS for calculus?

I love AoPS, but I feel that there are better textbooks out there for calculus.  Another big factor in my decision was that I wanted to use a textbook that was aligned with the AP exam, and the AoPS textbook does not meet this criteria.

 

That being said, I did email AoPS after my oldest completed BC calc to see if he would benefit from taking the AoPS calc class.  I was told that there wouldn't be any benefit if he scored a 5 on the AP exam. 

  • Like 2
Link to comment
Share on other sites

I have been told to have math every year of high school for my kids so we will have to go the DE route. For my district's public high schools, kids take

1) AP calculus BC (11th) AP statistics (12th) for those who did algebra 1 in 7th and has a good score in Precalculus in 10th grade

2) calculus AB (11th) calculus BC or AP statistics (12th)

3) calculus AB or BC (12th) for those who did algebra 1 in 8th

 

So calculus AB in 12th grade as the last math class is definitely okay but not at 10th grade.

I'm actually okay with that since my dd wants to continue with math, but there is so much conflicting advice out there. Recently, there was a thread on here where people were saying stats wasn't acceptable as a solid math course. But, maybe that is just for people who want to major in math or engineering? For years, I've seen people list calculus and then stats in their plans and I always thought we might do that. And maybe we still will.

Link to comment
Share on other sites

I'm actually okay with that since my dd wants to continue with math, but there is so much conflicting advice out there. Recently, there was a thread on here where people were saying stats wasn't acceptable as a solid math course. But, maybe that is just for people who want to major in math or engineering? For years, I've seen people list calculus and then stats in their plans and I always thought we might do that. And maybe we still will.

Fwiw, my oldest did stats after BC calc.  My middle couldn't fit it into his schedule.  My youngest will also do stats.

 

ETA: Oldest is majoring in math

Edited by snowbeltmom
  • Like 1
Link to comment
Share on other sites

Recently, there was a thread on here where people were saying stats wasn't acceptable as a solid math course. But, maybe that is just for people who want to major in math or engineering?

If a public high school student did precalculus in 11th and statistics in 12th, and apply to major in engineering, it would look atypical because calculus after precalculus would be more common for someone applying to engineering school.

I had engineering statistics in engineering school. It was advantageous to have done high school statistics (mine was similar in syllabus to MEP math) as the basic foundation was already laid.

 

Link to MIT OCW is similar to what I had for engineering statistics https://ocw.mit.edu/courses/civil-and-environmental-engineering/1-151-probability-and-statistics-in-engineering-spring-2005/lecture-notes/

  • Like 1
Link to comment
Share on other sites

A bit off-topic, so my apologies, but why don't you use AoPS for calculus?

My ds enjoyed AoPS cal. He did have to prep for the BC exam for a few weeks to get calculator and FRQ practice. He did not like the AP cal class through PAH that he had originally signed up for. He happily ran back to AoPS.

  • Like 2
Link to comment
Share on other sites

I'm actually okay with that since my dd wants to continue with math, but there is so much conflicting advice out there. Recently, there was a thread on here where people were saying stats wasn't acceptable as a solid math course. But, maybe that is just for people who want to major in math or engineering? For years, I've seen people list calculus and then stats in their plans and I always thought we might do that. And maybe we still will.

 

I can't imagine it ever being considered unacceptable.  It is a relatively easy course, though, and won't apply to math, engineering, or most science degrees.  Those will request either specific content (e.g., biology), or a calculus-based probability course.  For both of our kids, we won't do it because it's of low value to them.  They have done/will do AoPS counting and probability, and then calculus-based probability and mathematical statistics.

 

Generally speaking, though, stats is a great course to take in high school, either before or after calculus.

  • Like 1
Link to comment
Share on other sites

Recently, there was a thread on here where people were saying stats wasn't acceptable as a solid math course. But, maybe that is just for people who want to major in math or engineering? For years, I've seen people list calculus and then stats in their plans and I always thought we might do that. And maybe we still will.

 

The advice I have read here is that, if your student is on a STEM path and will need to continue with Calculus in college, that you might not want to take a whole year off of Calculus.  So, if you did BC in 11th, then Stats in 12th, then when you get to college, a lot of the Calculus you learned won't be fresh in your brain.  That makes sense to me.  Might not be an issue for everyone, though.

  • Like 1
Link to comment
Share on other sites

So, if you did BC in 11th, then Stats in 12th, then when you get to college, a lot of the Calculus you learned won't be fresh in your brain. That makes sense to me. Might not be an issue for everyone, though.

Summer is for reviewing or reading ahead with a calculus textbook. I checked the university bookstore of one of my nearest universities while we were there what books are used for calculus and other subjects.

  • Like 1
Link to comment
Share on other sites

FWIW, my engineering daughter did stats senior year, because we couldn't work out the schedule for a math course after Calc 3 for senior year. But the year off from calculus was fine. She earned an A in her first semester math course at Princeton.

 

  • Like 3
Link to comment
Share on other sites

ETA - Additional thought to ponder: at this age, a talent for math may not have turned into a love for it just yet.  I have a math degree, but until my second year of college, I had no interest in pursuing math.  I only did so because my degree required it.  Fortunately, I connected with the right professor, in the right class, and realized that I loved the artistry of the creative genius behind the theory.  If there is *any* chance of this, don't sell her short. 

 

 

 

I completely agree with this.  I took AP chem just to bump up my GPA and my teacher told me I should be a chemistry major and I laughed it off.  I ended up being a pre-med and choosing chemistry because I didn't like biology.  After shadowing a doctor in the ER and attending summer research in chemistry at U of Arizona, I realized that I could never be a MD and loved lab research.  Ended up getting a Ph.D. in chemistry.  Who knew!!!

  • Like 3
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

 Share

×
×
  • Create New...