Rethinking HS school math sequence (AoPS)

[skimomma]

I am looking for opinions and options.

 

Dd is currently in 8th grade and finishing up AoPS Intro to Algebra.  She likes AoPS (she also used it for pre-algebra) and wants to continue using that curriculum but she is not naturally "gifted" in math (meaning that I am helping her a lot more than I think many AoPS students require).  We do not have any idea what direction she may want to take career-wise at the moment but she has expressed some interest in STEM fields.  It is highly likely that she will at least start out any college she might pursue at our local STEM-oriented university even if she is not seeking a STEM path as we get a significant financial discount.

 

My original plan was to have her follow the traditional STEM math path of Geometry in 9th ending with Calculus in 12th.  I would like to avoid outsourcing math as I have a strong math background while there are other subjects we will have to outsource.  I am starting to think a more slow-and-thorough approach might be better for my dd if she indeed does want to stick the course with AoPS.  I teach freshman engineering students and am finding that their math skills are far shakier than their high school transcripts suggest they should be.  I would like to avoid this with dd.  

 

As I was mulling this over, I glanced at the back of dd's math book which happened to be sitting nearby where the AoPS Introduction Series is listed.  It includes Algebra, Counting & Probability, Geometry, and Number Theory.  My understanding is that these can be taken in any order?  I am now considering spending dd's 9th and 10th grade years completing that series in whatever order make the most sense for us then following up with Intermediate Algebra, (maybe) Intermediate Counting and Probability, and Pre-Calc her 11th and 12th grade years.  

 

Anyone do this?  Pros and cons?  If you have done this, what order do you recommend and how much time did each book actually take?

 

[Mike in SA]

Geometry and Intermediate Algebra are clearly full-year courses, but the others can all be done in a half-year, or even in a summer.

[regentrude]

 

As I was mulling this over, I glanced at the back of dd's math book which happened to be sitting nearby where the AoPS Introduction Series is listed.  It includes Algebra, Counting & Probability, Geometry, and Number Theory.  My understanding is that these can be taken in any order?  I am now considering spending dd's 9th and 10th grade years completing that series in whatever order make the most sense for us then following up with Intermediate Algebra, (maybe) Intermediate Counting and Probability, and Pre-Calc her 11th and 12th grade years.  

 

Anyone do this?  Pros and cons?  If you have done this, what order do you recommend and how much time did each book actually take?

 

 

Geometry is a one year course.

Intermediate algebra as well.

C&P and NT are one semester courses each; they are nice, but not part of the typical high school sequence and can be omitted.

Edited May 3, 2017 by regentrude

[wapiti]

Random two cents:  is your question really whether the C&P and NT courses are essential to a non-shaky math foundation? Those are semester-long electives and they even could each be done during a summer.

 

What part of your engineering students' math skills are shaky?  Algebra 1 and 2, calc, or discrete math?  Or problem solving?  Now that she's been through Intro to Alg, I would think you could reliably judge how solid her foundation is.  Is there a particular concern for your dd, or are you comparing apples to oranges (your engineering students' backgrounds vs your dd)?

 

One disadvantage of not doing calc in high school for a competitive STEM student would be seeing it in college for the first time.  Even for those who take calc 1 in college for an engineering path, many may have already been through a first course in high school, yes?  Just thinking out loud.

Edited May 3, 2017 by wapiti

[regentrude]

I teach beginning engineering students too, and those who struggle are lacking a thorough foundation in prealgebra (fractions!) and algebra.

Higher math plays much less a role; any problems they have there can usually traced back to lack of prealgebra and algebra mastery.

 

[skimomma]

To try to address all of the above:

 

I know that Counting and Probability and Number Theory are semester electives.  My theory was to slow things down a little and broaden dd's math background rather than lengthen.  I have noticed that math especially seems to "click" for dd during breaks or when we switch from a math subject then revisit it later.  It is not so much that I think those subjects are essential to a solid math foundation but more that experience working  through different math topics in general could help to strengthen dd's math "grit" which in her case may be more beneficial than progressing further in high school.

 

My freshman students are indeed struggling with foundational aspects of math and I am often perplexed as to how they could have completed the level of math that they have without these basic understandings.  The bigger thing I notice is a complete inability to chip away at a math problem if they do not know the "procedure."  This is why AoPS in general is appealing to me.  And dd likes it.  But I am concerned that dd might not be a good candidate to take a program as challenging as AoPS all the way through Calculus.  

 

Really, I am thinking out loud and trying to weigh what I see as the benefits of the curriculum against the rigor.  And possible ways to reduce the stress while not leaving holes in dd's transcript.  I'm not even sure it is an educational goal of ours for dd to complete calculus in high school although I also agree that seeing it for the first time in college can be challenging for some students.  

[wapiti]

Perhaps take this one year at a time (if she liked Prealgebra, she will love AoPS Geometry :)).  There is more than one way to skin the cat of problem solving grit; you can always switch to a more traditional program later and then add, say, math club/AMCs or Art of Prob Solving Vol 1 or 2.  Using the AoPS core sequence is not the only way to get it.

 

Not to mention, she probably already has a good bit of grit experience.  For example, my 10th grader is in school and her prior AoPS experience resulted in some interesting problem solving results on the board in class and in math club, approaches her teachers hadn't thought of.

[Mike in SA]

Right there with you. I believe breadth adds perspective in math, and can convert a math-tolerant individual into a math lover. "Gifts" may not appear for a while, yet.

 

Personally, I wouldn't artificially slow progress. What you are describing - providing space between learning cycles leading to better comprehension - is a well-known and real phenomenon. However, that doesn't improve by extending the space between cycles beyond a certain point.

 

What we have chosen to do (and it works!) is add additional math threads to our curriculum. At first, it slows things down a little, but within a few months, you start to see acceleration, as concepts begin to tie into one another.

 

So, we haven't done the other books as the only math content. We've used multiple books at all times. It hasn't slowed anything. Younger DS is on his second full year of algebra and third year of geometry, and is quite advanced on both fronts. Older DS did 3 precalculus texts and 2 calculus texts, and is finishing AP calculus as a freshman. Some of that may be talent, but some of it is simply method. We're absolutely certain of that.

[kiana]

I think doing the intro series and then seeing how things shake out would be a great plan. I would be surprised if someone who had gone through the entire intro series couldn't enter directly into a non-AOPS precalculus class and do just fine, if she wants to accelerate later. Or she may start just flying through AOPS as well -- or may start changing her mind about the challenge later. 

[skimomma]

Thanks.  I have some food for thought.  I think we will start with Geometry as planned then figure out if we want to add the electives at the same time or switch to those exclusively afterwards.  

[hsmom08]

Perhaps take this one year at a time (if she liked Prealgebra, she will love AoPS Geometry :)).  

 

Not to go on a rabbit trail but....My dd loved pre-algebra but struggled with algebra.  After 5 chapters, we had to switch to another book, around sept. of last year.  She is finishing up algebra with Lials and she is in 8th grade right now.  I was not planning on using AoPS geometry.  Maybe I should reconsider?????

[wapiti]

Not to go on a rabbit trail but....My dd loved pre-algebra but struggled with algebra.  After 5 chapters, we had to switch to another book, around sept. of last year.  She is finishing up algebra with Lials and she is in 8th grade right now.  I was not planning on using AoPS geometry.  Maybe I should reconsider?????

 

If she loved the Prealgebra text, especially the geometry chapters, then sure, reconsider trying the Geometry text.  Like the other books, some chapters are harder than others (ch 7?); slow down as needed.

 

Some people happen to naturally enjoy geometry better than algebra and others are the opposite.  In particular, for the student talented with visual-spatial skills, AoPS Geometry takes a big-picture approach, which is very different from a traditional geometry text and feels much more efficient (to me LOL).

 

If the challenge problems are too challenging, come back to them later, try a few for review down the road.