Do You Pause Between Books/Levels in Math?

[elmerRex]

My son is working math levels above his age-grade and he is making good progress in math. Someone told me that we should stop and not let him get too far ahead because he will go to fast and hit the ceiling barrier and not be able to continue after some time. I am not inclined to agree with this because math is not a back-and-forth straight path. I want to keep going for as far as he can and then pause and do something else until he is able to continue some more.

 

What has been the experience of families with kids working far-ahead?

Do you pause between books to avoid kids getting ahead when they CAN go on, or do you pause when your kids are at a point where they can't go ahead and just need more time?

 

[Crimson Wife]

Go until they hit a wall, but I would make sure that I was using a rigorous curriculum like Singapore with IP, Beast Academy/Art of Problem Solving, MEP, etc. Zipping through an easy curriculum does the child no favors.

[go_go_gadget]

The only time we've done something similar is right now, when my DD8 has run out of BA (just a few more weeks until the next one!) and would love to start AoPS Pre-A, but I think she could do with some maturing before AoPS. For the last few months and the next few, we've been/will be doing the BA 4 books are they're released, and using Jacob's Mathematics: A Human Endeavor and other assorted interesting math things (I'm in grad school for pure math, so we have a lot of it about). I wouldn't quite call it ''pausing'', though, because we're still doing math. I would never recommended actually pausing math, because it's too easy to lose ground, but as you said, there are lots of worthwhile detours if the road ahead becomes temporarily too steep.

[MEmama]

No. What would be the point in intentionally holding someone back?

That strikes me as a very public school mindset, existing to ease teachers managing large classes.

When did you as adult actively stop yourself from learning?

[regentrude]

Slowing down progress in anticipation of the hypothetical possibility that the kid may reach a point where he is stuck? Makes no sense to me.

 

We always progressed through math at the kids' speed. DD never hit a "ceiling". DS had gotten halfway through AoPS Intro to algebra in 6th grade and was not ready for some of the more abstract  concepts, so we took a break then and a detour through Counting and Probability before returning to the algebra text.

Both had one spot where they needed additional practice before being able to move on, so I simply created some additional practice problems fro them until they had mastered that particular concept.

 

[Arcadia]

Someone ask me that two days ago what if my boys finish calculus "early" and I told her that's what dual enrollment is for.

My kids set their pace and we don't even cover things in sequence. For example, kid was interested in Fibonacci and binomial in K and we just learn the math for it. Then same kid is interested in fractals and we end up doing polar coordinates and spherical coordinates last year.

 

We did hit the wall with physics not because of my kid but because both hubby and I are not that great at explaining theoretical physics. They both like quantum theory, wormholes, and younger kid has an ongoing interest with hypersonic jets. Now I am on a hunt for an affordable tutor/mentor, maybe a NASA or aeronautical industry retiree.

[elmerRex]

Thank you, just wanted to get others experience and feedback on the thought.

For clarity the woman who said it was an assistant principal at a local middle school who had this thoughth, so I guess that is why she said it. Makes no sense to me instinctively, but I thought maybe it was an American view or tradition.

[go_go_gadget]

For clarity the woman who said it was an assistant principal at a local middle school who had this thoughth, so I guess that is why she said it. Makes no sense to me instinctively, but I thought maybe it was an American view or tradition.

 

Aha. I can see that if a person thinks of the usual school way of doing things as the only possibility, then it would be inadvisable to have a student take, say, algebra in sixth or seventh grade, because then they'd just be cooling their heels until they got to high school and could take geometry. None of that applies to homeschooling.

[wapiti]

No pause in moving forward.  However, as your child matures and becomes able to handle greater depth, I would consider going "backward," supplementally, to add that depth in, for a fuller development of mathematical understanding and talent.

[lewelma]

One of the problems that my older boy has seen in the AoPS classes, is kids who have zoomed ahead in their algorithmic skills but at the expense of developing their problem solving ability.  These kids will ask for all sorts of help on the forum because they can't solve the problems.  Once you give them the hint, they can do the work, but all this has done is allow them to move forward without developing problem solving/insight skills.  He does know that one of these kids has decided to repeat all 4 intermediate classes because of this even though he passed them all already. 

 

So one problem that I do see with zooming forward is that a kid can end up in very advanced classes (AoPS Intermediate Number Theory comes to mind) and have to develop problem solving skills at the advanced level, having never developed them at a lower level. This is very difficult to do based on the experience my ds has had with multiple kids taking AoPS classes at a young age.

 

Clearly, if your kids have the algorithmic *and* the problem solving skills at each level, it does not matter how young they are.  For my ds, however, it took 3 full years to develop them at the lower level, which is why the AoPS Intro Algebra book took so long. He appeared to be moving at a snail's pace when you only considered the algebra content, but when you considered the problem solving skills he learned, he was moving very quickly.  Once those skills were in place, every class he has taken after that was just a reasonable step up in required insight.

 

HTH,

 

Ruth in NZ

[Brad S]

I agree with all or most of the comments above.  I think some of them are hitting on different dimensions of the issue, somewhat depending upon the curriculum and the child.  But pausing seems unnecessary, and you really don't want to pause entirely more than a few weeks.  If your student is using a solid math curriculum and hits a wall, you may need to tweak the approach a bit or the sequence, but I wouldn't stop.

[EndOfOrdinary]

My father has said this about Ds. Dh used to say it. I think it comes from the misguided idea that somehow there is a limit to what there is to learn or people/resources to teach it. As though if a student just is openly allowed to expand themselves how on earth would you ever later contain them without forcefully stopping the learning. After all, if the teacher is the keeper of knowledge, used to impart all own wisdom on the child, what if the student out learns the standard teacher?! Then you would need a teacher who was specialized. If the student keeps learning, more and more specialized teachers would be needed until - gasp - there would no longer be anything out but here and the student would be learning with the teacher!

 

In a society that creates social heirarchy and status symbols around knowledge from the time a child is four years old, openly learning is a truly subversive act.

[kiana]

My son is working math levels above his age-grade and he is making good progress in math. Someone told me that we should stop and not let him get too far ahead because he will go to fast and hit the ceiling barrier and not be able to continue after some time. I am not inclined to agree with this because math is not a back-and-forth straight path. I want to keep going for as far as he can and then pause and do something else until he is able to continue some more.

 

I agree with you absolutely 100% for homeschooled children.

 

For public schooled children it really can create a problem. If a child takes algebra 1 in 5th grade and makes an ok grade, but flounders in geometry or algebra 2 next year, there isn't really a good option to pull them out and say "Hey, let's do probability or informal geometry or number theory or programming for a year, or go through the course at half-speed, while your brain matures"so they're kind of stuck either failing the next math class and then re-taking it (which can cause major issues with self-confidence) or going back to repeat algebra 1 with material they already understood. Both of these are really sub-optimal. 

 

I would not worry about it in any case until you finish arithmetic. After algebra 1 there are so many more options, and if you decide you want to put him in school (for whatever reasons you deem good) you can enrich after algebra 1 so that he won't be too far ahead. 

 

Lewelma's point about problem-solving versus algorithmic skills is also very much worth considering. 

[SparklyUnicorn]

I just keep going.  Why stop because something "might" come up?  You can always deal with that later if need be.  And honestly the only major problems that I can imagine that come up is that upper levels of math take more writing, organization, and attention to detail than some younger kids might be able to handle.  In a homeschool situation it's easy enough to adapt, modify, and work around those sorts of issues.  I had to adapt for a bit until my son caught up with that, but now he is flying again.  I don't anticipate any issues like that anymore.

 

[Runningmom80]

We've been doing a LOF book in between singapore books.  I guess it did "slow him down," but really it was for my own benefit so that I could look over the Singapore books before we started.  *I* needed a breather.  It also broke up the monotony.

 

He welcomed the breaks, and he LOVES LOF, so for us, it worked.

[strawberryjam]

We are doing Singapore Math with IP and we are purposefully going slower then he could go. Reason being is he will go back to being in the school system for Grade 10-12, perhaps Grade 9-12. I also think, for him at least, the extra practice really solidifies his foundation. He isn't bored with going slow yet. He likes getting everything correct. I don't see the point of moving ahead in math unless he's getting 95% or higher. If his scores ever go under 95% I'll know to slow down more. So far we've also been taking breaks to do LOF or math apps, games, etc.

[JDoe]

Some weeks of break over summer if ahead of schedule is on offer. Last year I think a one week break was achieved by one of them, which is on schedule to get more this year.

[Mike in SA]

One of the problems that my older boy has seen in the AoPS classes, is kids who have zoomed ahead in their algorithmic skills but at the expense of developing their problem solving ability.  These kids will ask for all sorts of help on the forum because they can't solve the problems.  Once you give them the hint, they can do the work, but all this has done is allow them to move forward without developing problem solving/insight skills.  He does know that one of these kids has decided to repeat all 4 intermediate classes because of this even though he passed them all already. 

 

So one problem that I do see with zooming forward is that a kid can end up in very advanced classes (AoPS Intermediate Number Theory comes to mind) and have to develop problem solving skills at the advanced level, having never developed them at a lower level. This is very difficult to do based on the experience my ds has had with multiple kids taking AoPS classes at a young age.

 

Clearly, if your kids have the algorithmic *and* the problem solving skills at each level, it does not matter how young they are.  For my ds, however, it took 3 full years to develop them at the lower level, which is why the AoPS Intro Algebra book took so long. He appeared to be moving at a snail's pace when you only considered the algebra content, but when you considered the problem solving skills he learned, he was moving very quickly.  Once those skills were in place, every class he has taken after that was just a reasonable step up in required insight.

 

HTH,

 

Ruth in NZ

 

:iagree: 

 

1000x over.  If the continuation is a race to calculus, you've already lost.  But, we never pause or slow down.  Instead, we add depth, theory, until mastery is evident.  For DS8, we started with theory of arithmetic while he was learning his tables (at 6/7), then went to AoPS Prealgebra, then added content from other programs.  Theory first, before he learns to be afraid of it.  Repetition and drill second, then return to theory for cementing.  We're about to start round two, in geometry, but starting with Kiselev, then moving to AoPS or Jurgensen, depending on his needs.  We didn't exactly slow him down!

[kateingr]

Very much in agreement with lewelma and Mike in SA. I love this article by Richard Rusczyk, from Art of Problem Solving: The Calculus Trap

 

I'm so thankful for the great resources out there (like Beast Academy and Singapore IP) that have helped me to keep my son from getting bored with math and help him develop both problem-solving skills and persistence. No need to pause, but no need to rush either. 

[wendyroo]

:iagree:

 

1000x over.  If the continuation is a race to calculus, you've already lost.  But, we never pause or slow down.  Instead, we add depth, theory, until mastery is evident.  For DS8, we started with theory of arithmetic while he was learning his tables (at 6/7), then went to AoPS Prealgebra, then added content from other programs.  Theory first, before he learns to be afraid of it.  Repetition and drill second, then return to theory for cementing.  We're about to start round two, in geometry, but starting with Kiselev, then moving to AoPS or Jurgensen, depending on his needs.  We didn't exactly slow him down!

 

I agree.  We are still very early in this journey (Peter is a kindergartner working on 2nd grade math), but I am choosing to slow him down not by pausing, but by diving deep into the material he is learning.  We use Singapore's CWP and Zaccaro's books and a lot of interesting (hard, messy) real life math.  

 

The other day Peter was thinking about fractions and how you could cut a square in half.  After discussing the obvious answers, I challenged him to cut a square in half by cutting a smaller square out of the center.  I cut him a square out of cardstock and he figured out the area with Cuisenaire rods and brute force.  Then he figured out what half of the area would be and (lacking square roots) guessed and checked until he approximated what size square would have that much area.  He used the Cuisenaire rods to trace the smaller square and cut it out and then covered the remaining "picture frame" piece with Cuisenaire rods to prove to me that they each had the same area and were therefore each half of the original square.

 

This slows down how fast Peter "gets through" the 2nd grade math book, but it certainly is not slowing down his math education.

 

Wendy

[kiwik]

The American view is the one room schoolhouse view. Dont waste time, learn as much as you can. No need for age/grade lockstep, goal of becoming an independent learner, and mastery expected.

That doesn't seem to agree with what I hear. Mostly I hear people who are told no acceleration at school because of maturity/pregnancy and all sorts of other bizarre reasons. Everybody has to have the same, NCLB.

[kiana]

That doesn't seem to agree with what I hear. Mostly I hear people who are told no acceleration at school because of maturity/pregnancy and all sorts of other bizarre reasons. Everybody has to have the same, NCLB.

 

Yep. And it hasn't been the one-room for a long time, either. Even in my grandmother's day (born during the first world war) the cities were shifting away from it. Her family took her to the country for a year when she had just finished 3rd grade, and the country school put her in 5th. When she came back and they found out, the city school made her go back to 4th grade because she "might have missed" something.

 

[mumto2]

Never a pause in math. I always found something new and interesting for them to do. Duel enrolment doesn't really exist for us because of where we live in the conventional 2hours on campus sense. So they have been working on interesting Coursera classes and going through some older university textbooks.

 

My kids didn't enjoy aops as a first introduction to a topic. They do use it for testing prep. We normally introduced a subject with Lof then did a conventional textbook. Also did Singapore all the way through NEM. Lots of different approaches which greatly aided their abilities to solve problems. We had time because they didn't stop.

[Julie of KY]

No pause.  We celebrate the end of a math book with donuts and then move on. If we need a break from school (or just math) we take a week or a month off, but that has nothing to do with slowing the student down as much as we want to invest out time elsewhere for a bit.

 

I agree with the others. Use a challenging math program. Develop problem solving skills. Once you get a little further on, there are other trails you can take if you want to slow down the typical progression of math. In other words, you can do counting and probability and number theory, etc. rather moving on to geometry or algebra 2. I think this is good for anyone good in math, but especially if you are thinking about putting him back into school with a standard progression in math.

[ritamarj]

I have noticed that every time we had a pause in math ( for different reasons) , it was hard to go back to the same level, and some review was needed !

[Brad S]

One of the problems that my older boy has seen in the AoPS classes, is kids who have zoomed ahead in their algorithmic skills but at the expense of developing their problem solving ability.  These kids will ask for all sorts of help on the forum because they can't solve the problems.  Once you give them the hint, they can do the work, but all this has done is allow them to move forward without developing problem solving/insight skills.  He does know that one of these kids has decided to repeat all 4 intermediate classes because of this even though he passed them all already. 

 

So one problem that I do see with zooming forward is that a kid can end up in very advanced classes (AoPS Intermediate Number Theory comes to mind) and have to develop problem solving skills at the advanced level, having never developed them at a lower level. This is very difficult to do based on the experience my ds has had with multiple kids taking AoPS classes at a young age.

 

Clearly, if your kids have the algorithmic *and* the problem solving skills at each level, it does not matter how young they are.  For my ds, however, it took 3 full years to develop them at the lower level, which is why the AoPS Intro Algebra book took so long. He appeared to be moving at a snail's pace when you only considered the algebra content, but when you considered the problem solving skills he learned, he was moving very quickly.  Once those skills were in place, every class he has taken after that was just a reasonable step up in required insight.

 

HTH,

 

Ruth in NZ

 

I think there's really a lot to this comment and really appreciate your posting this experience.  I wonder what the causes are for the lack of math problem solving skills vs. algorithmic skills.  Is it mostly:

 

(1) a history of giving up too soon before looking at the solution?

(2) using inferior curricula focused on calculation instead of problem-solving skills?

(3) native ability?

(4) lack of maturity when taking the classes?

 

or something else or some combination?  If it's mostly the curriculum, is there a point where it's so late in math that it might make sense to backtrack rather than try to gain the problem solving skills in the next course?