"If your kid is easily mastering the content, then he's not being challenged enough"

[Halcyon]

Someone said this to me, and it made me wonder how many others believe this to be true? DS11 is in the middle of Algebra 1 and is having few problems with it. Yes, it's new material, but he understands it quickly, does the problems and moves on. Does this mean he should be doing Algebra 2? No. Does it mean a this Algebra 1 class is not hard enough for him? My friend feels that a child working at his best level should be getting a B--that means he's being challenged. 

Thoughts?

[texasmama]

This is not a well thought out reply, but my first response is NO!  Some content, such as Algebra 1, just needs to be mastered, you know?  If a student understands it easily, how nice that he/she does not have to struggle to master it.  I think setting the bar such that a student can never earn better than a B- sounds discouraging.  (Keep in mind that I do not currently assign grades...)

 

But that is my off the cuff response.

[sunnyday]

With some caveats, I agree with your friend. Not about grades, I don't feel "getting a B" is either here nor there, but about challenge. I think that all students are done a disservice if they are led to believe that mathematics has anything to do with doing the problems and getting the right answer (but I accept that for some kids, this "school math" is already a stretch). But I think that accelerated students are particularly cheated if any more than a third of the problems they see are the "plug-and-chug" type: http://www.davidsongifted.org/db/Articles_id_10687.aspx

[8filltheheart]

I think it depends on multiple factors. My kids do not find MUS alg and geo at all challenging. If I left their alg and geo instruction there, it would be doing them a disservice. But using it as foundational instruction in order to follow with more challenging material has been a great path for giving my young kids real confidence, (not false confidence), that they are more than capable of mastering high levels of math successfully.

 

But, I also think that sometimes SM makes things far more complicated than they need to be and that simply letting them mature into some concepts is better than making them feel like failures for the way some problems are ambiguously worded. (Especially true with my avg, lacking confidence avg students)

[Dmmetler]

I guess my question is-at what stage and what level of difficulty? I would consider 85% on an AOPS challengers section to be a pretty good sign of mastery-but when DD can get to that stage on the challengers, she's usually at or near 100% on the review section. I wouldn't consider 85% on a Key to Algebra review to be a sign of mastery unless all the mistakes were obviously computational errors (and then it's probably a sign of not mastering something much earlier in the sequence, like, say, multiplication).

 

I think a better way to look at it is to look at different grading scales. I remember being surprised by how wide the range was for the Singapore Science tests in the teacher's guide, until I looked at the test book and realized that the tests were asking for students to use the information and understanding for much more involved applications than had explicitly been taught-so a student who got 80% on that test truly did have a full understanding and ability to use what had been taught, but hadn't demonstrated being able to go beyond and generalize to as great a degree as one who got 90%-and 100% would have been pretty hard on some of those tests!

 

 

 

 

 

 

 

[wapiti]

I think it depends on the type of class.  For example, my dd's algebra 1 class at school seems sufficiently challenging for her; her grades for that class average in the 90s.  On the one hand, she is certainly capable of more challenge (e.g. she used Aops for prealgebra) but on the other hand, I can't say that she hasn't had "enough" challenge - it's not like she's getting 100 on everything - little mistakes and everything is graded, constant quizzes, etc.  There is something to the style - more challenging in this instance might mean more tedious problems, which would simply be irritating.  That is the nature of most school algebra 1 classes, AFAIK.  In this situation, with this style of class, I might be concerned if her average were lower, that she wasn't being careful enough.  If she were using AoPS, it would be a different analysis.  (Now, it's also true that I'd feel better about the whole thing if she were doing mathcounts again this year - that was a hugely important dimension for her last year, but they were without a coach this year.)

 

Part of my sense about how challenging it is for her comes from being there while she does her homework.  I'm the one she asks for help if she didn't totally get something in class.

 

Eta, in this example of my dd and her alg 1 class, there isn't that problem-solving struggle.  That's not to say that there aren't "hard" problems, just that they're not of an aops or competition math style.  What is hard in this class for dd are only things that she didn't understand immediately... hmm... well, with a little luck, she'll be using aops for geometry next year - fingers crossed!

[Embassy]

Yes, I believe it is true.  At the same time, I think it is fine if the challenge isn't in every single subject.  My son has some easy subjects and some that are challenging.  As for your son's case, I guess it would depend on his future goals.  If he is interested in STEM subjects, I might make his math one of the more challenging subjects.  If he is interested in history or english, I would make those more challenging.

[regentrude]

Someone said this to me, and it made me wonder how many others believe this to be true? DS11 is in the middle of Algebra 1 and is having few problems with it. Yes, it's new material, but he understands it quickly, does the problems and moves on. Does this mean he should be doing Algebra 2? No. Does it mean a this Algebra 1 class is not hard enough for him? My friend feels that a child working at his best level should be getting a B--that means he's being challenged. 

Thoughts?

 

If a student consistently gets every problem correct, then yes, he is not adequately challenged.

That does not mean he should skip to algebra 2, but rather that this algebra 1 program is not at a sufficient level for him  to develop problem solving skills and persistence, and that he would benefit from a more challenging Algebra 1 program.

 

It is detrimental for a student to get used to easily getting every answer correct.

Please read Richard Rusczyk's lecture

http://mathprize.atfoundation.org/archive/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf

 

and see what he calls "The tyranny of the 100%" (p 2-3)

 

ETA: More challenging does not mean more or more tedious problems. It also does not mean a harder grading scale.

It means problems where he has to think and apply creatively what he has learned.

[Gil]

It depends on a multitude of factors. There are some things that you just need to get down, and there is nothing wrong with doing them well or mastering them easily.

[raptor_dad]

I think the whole grade thing is a canard. In college my math, biochem, comp sci classes, etc regularly had tests with the highest scores in the 60s... Back in my day, the bar for a 3 or 4 on most AP tests' MC section was ~60%. I think the most important thing here is to delink the concept of grades and raw scores. Once you do that then you can easily up the challenge without threatening anyones ego.

[raptor_dad]

I, also, think you can only work at peak levels in so many areas at one time. Some times a mildly challenging, rigorous curriculum in one area allows for more advanced work in another. I think you can pick 2 or 3 areas in any one year to really push in. Some years math won't be the subject you are pushing in. Depending on the kid, passing algebra, using AOPS, AP courses,  or contest math could be either mildly challenging or pushing. The same range applies in other fields. 

[abba12]

Challenge does not necessarily have to be a higher course.

 

In your example, the child seems to have an aptitude for the content, which is great. That doesn't mean they should skip to Alg 2, they don't know Alg 1 yet! Just because they are learning the concepts easily doesn't mean the concepts don't need to be learned.

 

But in that situation I would be tempted to accelerate or broaden. If it's a simpler course intended to be an introduction I'd pick up the pace. If it's a lot of drill and unneeded practice I'd cut out the unneeded practice and progress through faster in order to get to Alg 2 quicker. If it's a good course without unneeded practice and you don't want to move quicker due to age/maturity/other concepts, I'd see if there was some highly challenging supplement I could add.

 

I do believe kids, especially gifted kids, should always be challenged and should regularly meet a point where they struggle with something. That doesn't mean they should be crying over their schoolbooks being too hard every day! But regular, consistent challenge in each subject area means good, steady progress, and hopefully avoiding many of the issues of being able to coast along (overconfidence, not being able to 'work' at things when they are hard, etc)

[Runningmom80]

And this is why I have already spent a million dollars on math books.

[boscopup]

I would take it to mean that you need to supplement with some challenging questions beyond what you're doing for the regular class. Maybe have him do Alcumus problems on the side?

 

This is the reason I'm using AoPS Prealgebra this year. Dolciani Prealgebra was too easy for my son - he'd get all the problems correct first try. There was nothing challenging enough for him. I get AoPS out, and he is sufficiently challenged. He will usually get the Review problems mostly right, but the Challenge problems at least require him to work hard (I type this as he's five feet away doing the first couple Challenge problems of chapter 4, saying, "Yes! I squashed that Challenge problem!" :lol:). My son isn't ready to move on to Algebra yet. He really isn't. He just needed to use a more challenging course.

 

I think 100% on the regular material is fine, but he also needs material beyond that that will be more at an 80% level, so he's sufficiently challenged.

 

I also agree with a PP that he doesn't need to be challenged ALL the time in EVERY subject. Sometimes I let him work at 100% level in one subject for a time, if I'm just wanting to get him comfortable with that subject and work on automaticity, or if I'm wanting him to focus more energy on another subject where he is being challenged more.

[kiana]

I don't think a kid needs to be getting B's to be challenged. But I do think we could use a different grading scale than this 90/80/70/60 ... I heard at some school districts it's even as high as 96% for an A. Quite honestly, I think that if 96% is an A, there are not enough challenging problems for the better students. I would prefer a kid to be getting 80-90% on more challenging problems.

[8filltheheart]

When I was in high school, the scale was

100-96 a

95-88 b

87-77 c

77-70 d

< 70 f

 

It was hard to earn an A and no one had the same GPA. Only one valedictorian.

[Tanikit]

I do not think that getting 100% on something means that a child was not challenged - could it not be possible that the child was challenged and yet still managed to get it right - a mark is not an indication of challenge at all. I would hope that giving my child a challenging problem she could at some point get it right and that I could say: well done you got those challenging problems right. The time taken to get a challenging problem correct is ALSO NOT an indication of challenge. It has to do with how much effort was required of the child - and that is almost impossible to tell.

 

If challenge implies that you will get it wrong then that is ridiculous. In Math it should be possible to get it right - it may take time or it may take effort or it may even in some cases take some luck - that you managed to think of the correct steps earlier and it went faster. For me challenge means that the child had to think and then possibly think again and again. It means that he/she had to stretch his mind. It has absolutely nothing to do with how many problems the child got right or wrong - if that were the case then many very boring sets of work could be considered challenging simply because the child gave up thinking or working them out and therefore for the required B.

[EndOfOrdinary]

I am going to be totally cynical here and say that it depends on what you want the student to be able to do.  One of the main things I have pulled away from various homeschool groups, is that many parents do not homeschool their children to learn the same things.  This was a brutal realization when I decided to teach a co op class.

 

Some parents want their children to learn how to get along in the world.  If that is the point, sure 100 percent and ease is just fine.  Your kid is learning how to go through this curriculum efficiently.

 

Some parents want their children to learn how to struggle.  If that is the point, nope 100 or even 90 percent and ease isn't going to cut it.  Your kid is being told that effort in general will yield perfection.

 

Some parents want their children to learn how get to the point that they are competent in what is culturally considered appropriate.  If that is the point, sure 100 percent and ease is just great.  They are competent and able to do what is asked of them ideally.

 

Some parents want their children to push personal boundaries.  If that is the point, nope.  No boundaries are being pushed.

 

The point is, none of these answers are more right than any of the others.  It matters what you want your child to get out of it.  Learning how to just do what you are told regardless of whether it is boring might have a place for your child (I say this as an ODD kid who probably could have really done well with a bit of that in my formative years).  Learning how to stretch your perfectionist self image is equally important for some children (I say this with a perfectionist kid and know it is good for him).  Some kids do not do well with struggle and they become easily defeated (that would be my brother; he would have shut down before he learned anything).  If we start producing a system where there is one right answer for every kid, we get public school.  It just doesn't work.

 

The point of homeschooling is for you to be able to find what fits your mission for your child.  The doubts come in when we tend to freak out about what others are doing and who their kids are.  If you have a mission statement that is laid out, it makes it a bit easier.  What do you want for your kid?

[kiwik]

I think if a very bright/gifted kid is honestly trying their hardest and on getting a B then perhaps the teaching isn't very good. If however they are getting A s without having to try their hardest it is too easy. You should have to put in the extra miles to get an A (especially if it requires 96%).

[kroe1]

Yes, I believe that to some extent with DD13. But, it does not mean we skip basics, it just means we do not dwell on them very long. If a math concept is understood easily, then the number of problems I require is every other or every third, and then all of the word problems. B+ to A- is where challenge meets confidence at our house. I am sure that varies greatly with each child.

 

Also, I do not believe how fast a concept is grasped necessarily correlates with how well the concept is retained. We still review quite a bit.

[kohlby]

It depends.  I don't think a child should be getting a B to be at the right challenge level.  A child can get an A - but should be working for that A.  For the early maths, rapid acceleration is sometimes needed to get the basics down quickly.  However, by Algebra I, it is very important to get more depth.  Do not skip to Algebra II, but find more depth for Alg I IF your child needs more of a challenge.  We moved into Art of Problem Solving for Alg I and it's been wonderful!  My child had never been challenged in math before that.  He has worked hard in AoPS, but he does "A" quality work.  He is mastering the material, but it's not instant - he has to work at it.  Some days, there doesn't appear to be much work - he instantly gets it.  But there's other times when he has to really wrestle with the problems.  I look for the learning - as in how much is the child learning overall? 

 

On the flip side, I have another child who is advanced as well but she gets easily stressed.  So she can't handle being challenged as much.  It doesn't mean we go super easy, but we don't go for the hardest curriculums I can find either.  As much as I love AoPS, I doubt it will be the right curriculum for her due to her anxiety and perfectionism issues.  Take in both the challenge level and what that particular child can handle stress-wise. 

[Crimson Wife]

My strived-for challenge range is 80-90% correct. Now are there gifted kids who can achieve greater mastery over a rigorous curriculum? Sure, and that's great. An "A" in a hard course is better than a "B" in a hard course. However, I'd say a "B" in a hard course is better for the child in terms of intellectual growth than an "A" in an easy course.

[idnib]

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