Advice: Formal Thought Processing

[sportsmom]

So, based on the advice of another mom of gifted kids, I have intentionally kept DS10 around his typical grade level.  The reasoning is that she has a formal education in these areas and her input is that physiologically, the formal thought process is not fully developed until age 13 and that topics such as algebra are better held off until their brain chemicals are equipped to handle them.

 

I've tried using Abeka (all subjects) and Saxon math and he strongly prefers Saxon.  This year we did Abeka 4 and then Saxon 5/4.  He has requested to never go back to Abeka math again.  And just today, he commented that he would like to complete 3 Saxon math books next year.  My plan had been for him to use Saxon 6/5, and then work our way though 7/6.  Assuming he has no issues with 7/6, then we would forego 8/7 and go directly into Algebra 1/2.

 

My problem is that in general, he's pretty bored, even though he will happily do his work.  The quality of his work is significantly better when he is challenged, unless it's in something like reading comprehension where he struggles with inference.  The more he has to repeat mastered material, the more mistakes he makes.

 

So, I guess I'm looking for a broader input of just how hard should I be pushing?  For those of you with pre-teens who are doing advanced level mathematics, or even older teens who are AL in math, have you seen any struggles as they progress?  Or in hindsight, would you do anything differently?

 

As far as his learning style, he has a nearly photographic memory, and currently "teaches" himself by reading the examples in the book.  If he does not understand a problem, he has to observe it being worked, without it being explained to him.  He has completed Saxon 5/4 in a 10 week period, with no less than 85% on any of the tests - and those are because he made mistakes like labeling and careless errors.

[Pegs]

So, based on the advice of another mom of gifted kids, I have intentionally kept DS10 around his typical grade level. The reasoning is that she has a formal education in these areas and her input is that physiologically, the formal thought process is not fully developed until age 13 and that topics such as algebra are better held off until their brain chemicals are equipped to handle them.

 

Hmm. Do you have enough confidence in this hypothesis to feel justified in intentionally keeping your DS far below the level you believe he could be working at? It sounds like no. The rest of your post shows that you believe he is bored, and would benefit from greater challenge. And really, what's the worst that could happen if you let him finish up a Saxon sequence (maybe with some problem-solving supplements?) and hand him an AoPS pre-algebra textbook?

[wapiti]

I disagree with your friend on delaying algebra until "formal thought processing" has matured.

 

That said, acceleration is not the only answer to the challenge issue.  For a different perspective, try Rusczyk on problem solving (PDF) (video).  (He also gave a nice webinar last night, part of the Well-Trained Mind Conference Series, that should be available in a few days.)

 

Linda Silverman at the Gifted Development Center would also have a very different take.  Here's an old quote though I can no longer find the article on the web:

 

When gifted children are not given opportunities to work at their own level and pace, they settle for less than their best. They learn to slide by without stretching themselves. Patterns of underachievement are subtle and cumulative; they become harder to overcome with each year. Students who attain A’s on their papers with no effort are not prepared to take more challenging classes in high school and college. When work is too easy, self-confidence to attempt difficult tasks is steadily eroded. A student who has the potential to win a scholarship to an Ivy League university settles for a B average at a state college.

 

[sportsmom]

Pegs, I think you really hit the nail on the head.  I've been struggling with it for the past few years (have been homeschooling for 2) and I kind of just followed a lead while finding my footing.  Both years he has completed 2 different programs for most subjects.  This upcoming year is the first time that I'm branching out and hand selecting different curriculum for each subject.

 

Wapiti, the more research I have done the more in line I am with the views that you referenced above, and can personally attest to my PG husband settle for average as a HS student.  He's a network engineer for a prominent company and is the only one of his peers who lacks a college degree.  And had he applied himself in HS, he could have gone anywhere for whatever program he chose - instead he graduated with a C average.  My biggest fear is that our son will learn to "coast" because he knows that he can get better grades than his peers without having to apply himself at all.  Thankfully, at this point, he is highly perfectionistic and he sees himself as his biggest competitor - of course, that's also the downside for other reasons, ha.

 

At his end of year 3rd grade testing (last May) his math and reading scores were conceptually the same as an 11th grader.  If I'm being 100% honest, the thing holding me back most has probably been that in the very near future he will surpass my ability to assist with math.  I struggled all the way though Algebra and Geometry, showing enough work to get myself a passing grade.  Realistically, he essentially self teaches, but if he is doing 2 math studies each year, even just through middle school (so 5th - 8th), at some point he is going to hit a topic that he needs to work through (today we had to talk through a probability question and after working it aloud himself, he understood) and I won't know how to get him through it.

[raptor_dad]

This whole idea is based on Piaget's "Formal Operational" stage which he and Inhelder normed as an 11+ development not 13+... I guess it could depend on beginning to develop versus fully developed. Even if you assume this level of abstract reasoning is required for, not partialy developed by algebra, there is clear research based evidence that the top 2% of students have reached this stage in 5th grade[1].

 

Anecdotally, many kids on this board seem to hit that level earlier than that... enriched population, better teaching, Flynn effect... who knows. Either way, I would follow your DS's lead and not worry about age. I also would consider switching to AoPS or another enriched curriculum.

 

[1] http://www.ascd.org/ASCD/pdf/journals/ed_lead/el_198111_brandt2.pdf

Julian Stanley, the founder of SMPY/CTY/SET, answers this question explicitly in the right-most column of page 3. 

 

[texasmama]

I have a 12 year old self-teaching AoPS Algebra very successfully. He would be bored and miserable in either Saxon or Abeka grade-level math. Not to knock those programs, but there are other choices that probably work better for AL kids.

[quark]

 

 

My problem is that in general, he's pretty bored, even though he will happily do his work.  The quality of his work is significantly better when he is challenged, unless it's in something like reading comprehension where he struggles with inference.  The more he has to repeat mastered material, the more mistakes he makes.

 

So, I guess I'm looking for a broader input of just how hard should I be pushing?  For those of you with pre-teens who are doing advanced level mathematics, or even older teens who are AL in math, have you seen any struggles as they progress?  Or in hindsight, would you do anything differently?

 

As far as his learning style, he has a nearly photographic memory, and currently "teaches" himself by reading the examples in the book.  If he does not understand a problem, he has to observe it being worked, without it being explained to him.  He has completed Saxon 5/4 in a 10 week period, with no less than 85% on any of the tests - and those are because he made mistakes like labeling and careless errors.

 

I am going to address the struggle part a bit. After some tough times dealing with his boredom, we agreed to begin algebra 1 at 8 years old and have not looked back. He loved it. I feel so silly even now about trying to force him to cover gaps until then.

 

Yes, my DS struggles (but mostly only with AoPS, when we use the books as a supplement, and sometimes the classes as a core course). It becomes very clear to me when he is struggling due to boredom vs struggling with a hard problem. With boredom, he will be visibly frustrated, he will be very wiggly and even moved to tears. With hard problems he will be more focused and possibly moved to tears too but there is often also a certain rebellious gleam in his eye where he refuses to let it go (he will let the boring ones go very easily). There are struggles that he still has not overcome. I don't see any reason to make this stop him. We placed a post it note on the page with the hard problem and just moved on but cycled back after a week or few weeks when I felt he was ready to try again. Sometimes, he solves it overnight in his sleep/ upon waking up.

 

There is something so wonderful and meaningful about working on hard problems. The thrill, the challenge, rising to that challenge, watching him work so hard at something that means something to him...no, I wouldn't do anything differently. If at all I would, it would have been to have started him earlier than 8yo.

 

[Arcadia]

As long as it is my boys who set the pace, I have not seen any struggles other than my struggle to chase them to bed. Do not let your child do Alcumus before bedtime.  You might find him asleep at his desk in front of the laptop past midnight.

 

 We placed a post it note on the page with the hard problem and just moved on but cycled back after a week or few weeks when I felt he was ready to try again. Sometimes, he solves it overnight in his sleep/ upon waking up.

 

:iagree:

:lol: I have a stockpile of Staples post it note bought during back to school sales for that purpose.

[sportsmom]

This is such good feedback, thank you all so much.

 

raptor dad - That article is excellent and I look forward to reading it in full.  Thank you so much for explaining the theory, I definitely understand it better now, and feel more confident in my decision to move to more advanced work.

 

texasmama - I appreciate the input.  I only became familiar with AoPS in the past few days.  It's definitely something that I'll be exploring in more depth before we transition into Pre-Algebra.  He loves a challenge, and I never want to encourage him to take the easy path just because it's conventional.

 

quark - Thank you for addressing that part.  What level math was he at before you started him on Algebra 1?  It sounds as though you skipped a few levels and that it's working out well for you.  Honestly, skipping over books has never seriously crossed my mind.  Perhaps testing through them and reviewing material that was missed, but that's as far as I've gotten with the idea.  Actually, I am considering testing through 6/5 to gauge his mastery of material, especially if his goal is to complete 3 levels this upcoming year.  Just yesterday, I told him that he needed to figure out what his goal was, other than simply checking off the books.  I'd be interested in discussing further - our boys sound extremely similar.  

 

Arcadia - That is too funny.  But good advice.  I can see him finding it difficult to disengage for the night as well.

 

Heigh Ho - When I referred to push, it was more along the lines of setting him on a path and helping him succeed, not the lines of dragging him along kicking and screaming.  :)  The only time I have to push is when sometimes he "doesn't want to do" xyz subject today.  But once he begins it, the attitude part goes away and he engages.  DS is very fortunate when it comes to peers.  Most of his good friends are gifted, even if they aren't ALs or taking any advanced classes.  It's that different way of processing the world, and I'm thankful everyday that we are in a place where he has peers.  I imagine as he gets older and into more difficult coursework, the gap will ever widen and his peer base will grow smaller.  He is also the kid who is simply content wherever he is and whomever he is with, he can find a friend.  My DD4 and my son are extremely close, despite their age difference.  Yes they argue and are mean to each other, but they are so close intellectually (even though she presents it differently) that I sometimes wonder if she will be his closest peer.  Asynchronous development....his emotional/social maturity is far closer to her "age" where her emotional/social maturity is (overexcitable, yes) but far more developed in some ways than his.  She is the classic underachiever though, which will probably make him bananas in a few years.  But I have noticed that she has pulled some creativity out of him that I have been unable to do.  They are good for each other.

[Dmmetler]

DD struggles at times, but in many ways that's good. There is nothing at grade level, except for maybe PE, that would challenge her at all. My feeling is that if she needs to go back and revisit algebra later, that's what a College Algebra course, which will start with review of algebra, but then move beyond fairly quickly, is for.  DD decided at age 7 that she was done with "regular math" and wanted to start algebra. We did Pre-algebra twice, once with Key to algebra and LOF, and once with AOPS PA, and are taking 2 years to do AOPS intro Algebra with additional stuff (Counting and Probability, Statistics, LOF Geometry and advanced Algebra).

 

Similarly, she accelerated through science fairly quickly until she got to upper level high school/college level materials-but now has slowed down (so freshman level biology is being spread out over several years with a LOT of time spent on research and independent projects and reading journal articles, technical writing, blogging, and lots more). Chemistry and Physics are likewise being explored a little bit at a time, over several years, using lower level college textbooks plus supplemental materials. Again, I don't expect this to be the last time she does Freshman/lower division/upper high school science-but she's got LOTS of time since I don't even have to start recording high school credits for 3 more years!

 

 

 

 

 

 

[regentrude]

So, based on the advice of another mom of gifted kids, I have intentionally kept DS10 around his typical grade level.  The reasoning is that she has a formal education in these areas and her input is that physiologically, the formal thought process is not fully developed until age 13 and that topics such as algebra are better held off until their brain chemicals are equipped to handle them.

 

This may be a statement about averages, but won't allow conclusion about an individual child. Gifted children are not average. There are plenty of examples of younger children successfully completing algebra and mastering the "thought processes" involved.

It would not occur to me to hold back my student based on such questionable advice.

 

My kids have never been "grade level". At age 13, my DD took her first college physics course, with great success.

[sportsmom]

 Again, I don't expect this to be the last time she does Freshman/lower division/upper high school science-but she's got LOTS of time since I don't even have to start recording high school credits for 3 more years!

 

You and I seem very similar.  I've said this same thing about DS taking Spanish 1 in 4th grade.  Logically, I should apply the same reasoning to math as well as foreign languages.

 

I've done this homeschool thing pretty much on my own for the past 2 years.  Sure, he took an Intro to Spanish and Spanish 1 with my friend (same one as referenced above), and I borrowed the teacher manuals and textbooks from her for the Abeka curriculum from her as well, but other than that, I haven't joined any co-ops and this is the first forum that I've joined.

 

It was intentional - I wanted us to find our footing before I started getting pulled in many different directions.  That and I am really bad at just showing up and taking advantage of things - I have to be all in and volunteering, and with my other commitments, I just didn't have the time to put in what I felt was necessary.  And, I've been in enough groups of moms to know that often there is just too much drama and I couldn't muster the energy to handle it.  Knowing my son's abilities it can be hard to discuss academics with others, especially ones with kids who are struggling.  This was my biggest issue in PS - even his teachers said I shouldn't be concerned because he was "just fine."

[sportsmom]

Heigh Ho - Oh my, that was certainly not my intent at all!  Nudging, or guiding, would be a better term probably.  Thank you so much for your correction on the proper verbiage for the forum.  I'm quite anti-push in the way you interpreted it!  Actually, in that context, it's a huge reason why I am so uneasy about my DD4 entering Kindergarten in the fall.  She is fully capable, but lacks any desire to do the work.  I'm fairly confident that she knows how to read, yet pretends not to be able to do so.  And I know that she intentionally misses her letters.  And other than her (first) name, she refuses to write letters at all.  But I never force her in any way to "perform."  Unfortunately, I'm unsure of how to teach her Kindergarten with her lack of desire, but if I don't send her to PS in the fall, then I *know* she will consider it winning and think she can get away with the same next year (late August birthday and she isn't required to go until next year).  

 

I'm so concerned that she will be forced to conform in order to acclimate that all of the lovely things that make her so special will be squashed out of the necessity of a classroom setting.  She's very compliant, and wants to please, but she has no desire to do the schoolwork.  Her preschool teacher has been lovely and has allowed her creativity to blossom, and knows that DD4 knows much more of the facts than she will give answers to when asked.  She will also use different colors than the ones listed on color by numbers, even though she knows the correct color correspondence, because she thinks that the yellow would be better as purple, and I never want anyone to tell her that's wrong.  DD4 is kind, compassionate, tenderhearted to all around her, shows strong leadership abilities, and is a social butterfly.  She also has many OEs, including an eating disorder and increasing anxiety (we are getting therapy).  The school stuff will fall into place for her one day, or it won't.  But I will never push her or try to break her of her special way of seeing the world.  Just thinking about that happening brings me to tears.