Hi everyone,

I would love to get some advice from all you great people. :*) My DS(7) loves math. He is into algebra and number theory. He does not like practicing any of the concepts very much. For a while he was all excited learning about quadratic equations. Once he learned about it, his enthusiasm for it lasted for 1-2 weeks and he is on to a new concept. I feel he understands the concept, does not like to use the 'normal' way of solving things but tries to use logic as much as possible. Then, we go back to previously learned concepts it appears that he has forgotten how to use them, but will remember them quickly again once someone has shown it to him again.

My question to you - how do I instill in him that the way to solve questions has a benefit and it's not just about finding the answer and yes, there is value to practicing some concepts. He feels he knows a concept when in reality he may understand 'temporarily' but not long-term.

Today we had the first math tutor nearly quit on him as he feels that he cannot teach him anything further but he also felt that DS does not have 100% understanding on all the learned topics either.

If I need to find a new tutor, how would I best describe what I need him/ her be able to do/ what skill sets she/he needs to have?

I am curious if any of you have a similar kid and if a lot of it is also due to maturity or lack thereof given his age.

Thank you!

What is the learning environment in which he is learning these topics?

What you're seeing sounds like very typical 7 year old behavior to me (at least it sounds a lot like my own children at 7 and most of the other 7 year olds I've known). I wouldn't worry about whether or not he sees the value in practicing new concepts at this age - that's something that will come with time, and also perhaps when it's *needed*. Does he have a math tutor because he's begging for more math? If he loves math, I'd let him go with it for now. He might have to come back for more reinforcement later on, but he's got time for that down the road. For now, let him enjoy learning the things he is interested in learning, even if it seems like that changes direction every few days.

Best wishes,

polarbear

ps - another thought that crossed my mind - you mentioned that he was really interested in quadratic equations and then that interest lapsed after 1-2 weeks... I'm not sure that any of the topics my kids cover in math in school really last longer than 1-2 weeks in duration - even quadratic equations. Everything builds on previous topics, but something new is also always being introduced. Even in Algebra and beyond. The thing I remember being repeated over and over again until my kids wanted to bang their collective heads against the wall was math facts

I know there are some more mathy people than myself on this board, so I hope they will chime in. For us, DD9 is similar in not wanting to repeat things over and over. It drove her nuts last year in school when the teachers didn't want to give her new stuff until she had 'perfected' the older topics, so they just kept making her do multiplication and division with more digits and if she got anything wrong they would say, see, she doesn't know it--she needs more practice, and she needs to correct *all* of her mistakes before moving on, so she never got beyond 4 digits--can you imagine doing that all year?? They kept saying they would give her more advanced stuff but never did. (maybe 5 digits? ridiculous) She hated it. We've had more success afterschooling with EPGY, starting when that stuff was happening (although EPGY does have its glitches), and one thing I like is that it keeps cycling the problems back around and if you miss the answers it will give you more of that kind of problem in the future, while if you get them right it will move on more quickly (or at least that is what is supposed to happen, and how it seems, although it varies from course to course). But it's really more about teaching techniques, like (in the algebra course) factoring polynomials for example rather than teaching or even discussing theory. I'm trying to supplement with books but it's difficult because I can't answer any questions that might come up and I feel like maybe DD could go farther if I could, but she seems content at least for now so I haven't pushed it. Since your DS is so advanced, I think it's great that he has a tutor because it seems like that one-on-one instruction from a good teacher is what is really valuable in inspiring a love of math and theory. I think making a kid like that drill until they get everything right first might cause them to lose interest in math altogether--unless he's really not able to understand the next topic because he didn't really grasp the previous one. I guess that might be hard to sort out, but maybe a different tutor would be able to understand this distinction and inspire your kid to go a lot farther. I feel like I can teach my DD the mechanics of math but I don't know enough about theory to either teach or to inspire her, but for her I'm not sure that's where she would be going anyway--it sounds like your DS might be really wanting to go there, so I hope he does. Good luck!

we've noticed this too. since in class they're still counting to 20, my DD5 begged for an online Math programme and she's been flying along with it. each lesson has 10 problems - she generally gets about 4 correct in a row before feeling like she's mastered the concept, and then she invariably wants to switch to something new. when she comes back to the original section, she freaks out because the programme won't let her move on without a) going back and doing the first few over again and b) actually completing the lesson. it's a simple limitation of the online programme, but... ha - it's not like her teachers are any more flexible.

so we've used various tricks to get her to see all of this in a different way, all of which take advantage of her personal currency. she really likes to know her brain is growing - so we've emphasized how much more her brain grows when she's doing something challenging. the repetitive problems themselves aren't challenging, but something about the situation is, or she would just power through it... so we get her to focus on that part - that she's growing her grit/resilience/patience/whatever and as a bonus, she will actually get to move on to the next level, which is what she wanted anyway!

good luck!

DS7 runs about the same way and at a similar place in math. Watching videos on quadratic equations, even some calculus stuff, sometimes doing math stuff through another app, etc. He also stops when he thinks he has the idea. Since he like complex problems, I'll sometimes find him a problem that calls on some subject he's ran through.

My overall thought on this, however, is: Whatever he is doing certainly works for him! Even if not every subject sticks with him, he'll reinforce it later. Traditional approaches and methods may not be applicable. I'll trust that he picks back up on the peripheral skills and structured solving when he is ready to do that. Maybe this style combined with enthusiasm is as significant to the skills of a kid who is functioning four or more standard deviations out in math as is the basic intelligence they bring to bear on it. I don't want to break a good thing.

Hmmm-- well, I don't really see what the OP is describing as problematic in the context of how math curriculum is designed these days. If anything, this touch-and-return method seems IDEALLY suited to the spiraling curriculum.

I wouldn't worry about it. He sounds like he's getting out of it what he can/desires and then moving on, and it actually is a pretty decent match for the way schools approach teaching these days. I wouldn't tweak that too much!!

You'd have more trouble with a kid that takes this attitude and has actual-- real-- mastery that fast, because then when they see the topic again, there is sneering and refusal to do anything at all because they "already know this stuff"(and they really do, see, that's the problem).

Oh, and the answer for mastery kids like my DD?

Give them problems that are hard enough or unique enough that they HAVE to bring the new skill to bear... or at least can see how much more efficient it is to do things that way.

I'm sorry to rain on the parade, but some things don't sound right here. What does it mean to "practice concepts"? It makes sense to "practice methods (or algorithms)" and it makes sense to "understand concepts".

Also it is concerning when you say "we go back to previously learned concepts it appears that he has forgotten how to use them". Why does this happen?

I'm concerned that the approach to mathematics may be wrong, and that there may be too much rushing ahead without a solid foundation.

Not sure if the OP means the same thing, but words I use alternatively with "practice concepts" are "play" and "experiment."

I remember when I learned Pythagoras Theorem. I spent a lot of time practicing with the concept. The school might've wanted me to keep practicing a method of plugging in a side and a hypotenuse and getting the other side. I didn't really need to do that. I needed to play with the concept, and find all sorts of amazing things I can solve using the equation. So I would practice the thought process of applying the formula to various cases like non-right triangles or how about with rectangles and area and.. etc.

DD is like this, too. She begs for new and exciting math concepts and terms, and totally gets them, but doesn't show her teacher she really knows subtracting within 20! She recently got interested in poetry again, which was her obsession last summer/fall, and because she hasn't thought about it since then she was excited all over. She was figuring out how many lines in different forms and rhyme scheme patterns, which she also did last fall. I mostly figure, eh, she's passionate about learning so that'll see her through. I wonder if its just asynchronous behavior, like she relishes these big concepts and patterns but the grind of committing them to automaticity is just not part of her mindset right now.

Though to be fair, this does fit nicely with the apparent "vision" for teaching science and mathematics now in primary and secondary.

(Actually, teaching pretty much everything in K through 12.)

I interpreted this as a reluctance to practice application of concepts.

That is, watch-and-learn = fine, and leads to happiness, a single demonstration or application, fine again, but

do this slightly different application, "I'm bored with this now and I don't want to."

It's probably at least partly a matter of meta-skills being underdeveloped. Kids at this age are not very good at KNOWING when they actually have mastery and when they could use a little more practice/reinforcement. It's a hard target to hit with HG+ kids, though, because they really DON'T need as much repetition as most learners, but they still need (on average) a bit more than they like.

Exactly what 22B says. The way to practise a technique, and reinforce a concept, is to use it in non-routine contexts. Sometimes routine contexts make good warmups, but most children here probably get way too many of them.

Here's a cute problem you can solve using a quadratic. Incidentally, if anyone can solve it without a quadratic, let me know! I saw it elseweb, and the discussion there gave circumstantial evidence that it should be possible,but noone found how. It feels like the kind of problem that might be trivial if you look at it right.

Interesting, ColinsMum. Does "solving it without a quadratic" disqualify you from using Pythagoras?

The same circumstantial evidence - the q was set for 13yos - probably means Pythagoras wasn't intended to be needed, though I'm a bit vague about what gets taught when normally, so I'm not sure. However, I'd be interested to see a solution using Pythagoras!

Actually I'm kind of bluffing. I changed 10 to A, and 24 to B, and equated some ratios, which became a quadratic, and solving that (and dismissing the "-" solution) gives that the police car travels

A+sqrt{A^2+B^2}

This hints that there may be some kind of slick geometric argument that involves a right triangle with sides A, B, C=sqrt{A^2+B^2}, but I did not actually try to find one.

In general, the answer will involve a square root, but it just happens that if A=10 and B=24 then C=26, so you don't see the square root in the given specific problem. So in some sense, "solving a quadratic" is necessary.

I wonder if it was a multiple choice question, in which case one could just check which option works (which is still not totally trivial).

I think Pythagoras is roughly grade 6, and solving quadratics is roughly grade 8.

Right... exactly. Wouldn't the solid foundation come from solving multiple equations/problems using the already understood concepts until they're embedded in memory? But when your 7 year old isn't fond of repetition, this becomes an onerous kill-the-joy task that dissuades the kid from wanting to do more math, and as a parent you don't want that, so you teach him whatever he's curious about, and not worry too much about him remembering because it's way above grade level anyway, but then a year later when he's forgotten you wonder if you did the right thing by not "drilling & killing" ...

(Not that I have any experience with that ) <---sarcasm, in case anyone missed it!!

It's so hard to know what the right thing to do is.

I debate whether to sometime mention to DS to notice when Pyhagoras triples show up in problems as a clue to a solution approach. Or maybe that is something one should have the fun of self-discovering.

By the way in Common Core they have Pythagoras in 8th grade and Quadratics in 9th. Progress, I suppose, I know decades ago I had it in Geometry which I took in 9th grade (which was the only acceleration they offered.)

I just got back to the post and was truly impressed how many people are trying to help me ! Thank you so much for your ideas and thoughts! It also really helps to know that I am not alone. I agree - it is hard to know what the right thing is. Some other math tutor tried to do the "only if you get 95%+ correct can you move on" and it killed his desire right then.

I very much like the idea of trying to apply the concepts. Someone else also mentioned that giving him an answer to a problem and telling him to show me how to get there might work - I tried this today and it surprisingly worked quite well. I am wondering if knowing the answer makes him less answer focused/ stressed and thus allows him to think more clearly about the steps to get there.

For right now, we have decided to let him explore things that he loves and as someone mentioned - given that he is ahead - if he has to get back to things in a while, it should be still ok (or so I tell myself ).

DD is now doing CTY grade 5 math, which has moved off from EPGY. I love the new format.

And it builds quickly. So a mathy kid can listen to the videos, do the exercises, then the test and move on. But the next section builds. I admit we are not far into grade 5 math, but so far it works well for that style of teaching and retention.

What I mean is that a concept should be understood in the context of related topics. It should not be an isolated topic.

Of course it's okay for a kid to explore ahead of their level, but there needs to be a plan to make sure the curriculum is fully covered so there eventually are no gaps.

Working from the answer makes sense. That is an interesting way to engage the top down thinker. I think a lot of the pushing forward is to find the big concept buckets to put other things under. In that way, needed topics being missed isn't relevant, because by their very nature when they hit a topic where they are missing requisite knowledge the drive to backfill to move forward is likely stronger and more effective than trying to teach it in a typical linear and bottom up approach that most people need.

Wren - we used EPGY in the past and so it is interesting to hear that CTY is now different. Zen Scanner - you have beautifully summarized how I feel my son thinks - thank you
Today we bought him a scientific calculator with graphing capabilities. He spent hours looking at it and being very excited about it. I feel this is just like giving him the solutions to make him then work on the steps - having this type of calculator will give him some big picture ideas/ topics and will also make him look at the steps as sometimes I feel that he believes a computer class (like Art of Problem Solving) / calculator more than if mom or dad write it out on paper .

Wren--we're (still) using EPGY, but I had considered CTY and chosen EPGY instead mainly because at the time they were supposed to be similar except that EPGY offered a Stanford transcript, which they have since stopped doing. I'm curious--how has the CTY format changed?

Quite welcome, though I may have skipped to the back of the book a bit as that's my M.O., too.

DS7 got his allowance yesterday and ten minutes later he is giving it back to buy a math reference app on the iPad.

They have this drop down menu. In a topic, there are video lectures. Then they have problem sheets (quizzes) that you do online.

There are worksheets you can print out and practice, but so far there hasn't been the need. Then you do the chapter test on line.

In EPGY, it seemed you did geometry, then multiplication, and it was all mixed up and sometimes the lecture came after.

And I find the curriculum builds on the previous in the new format. Now this is grade 5. I do not know what is still lower. I commented on the new format to the tutor and she said that it was for grade 5 and beyond. But her wording may have indicated that DD would now have this format or it was all changed.

Thanks, Wren! That setup does sound a little better in some ways; it would be great to be able to print out practice sheets, but as far as I know on EPGY there's only a practice test at the end of the course you can really do that with. DD has been bothered by what you mention that sometimes in EPGY the lecture comes after problems that use a new technique that is taught in that lecture. I think that might work to encourage independent thought in a setting with a helpful and positive tutor, but it doesn't work very well the way it is presented in EPGY and DD has been very frustrated by it although now she recognizes it is the way EPGY is sometimes. We might take a look at CTY but there's always an issue switching between curricula of missing subjects or redoing them, I guess. Thanks though for mentioning CTY has changed at least some things; that might make it more useful for some kids.

What is "drilling & killing"? (When I Google I get something about Nigerian oil.)

Drill & kill = drill (practice techniques) and kill the enthusiasm.

Okay, I see. But if this is happening, then something has already gone wrong. Excessive repetitive practice of routine problems based on isolated topics is never going to make up for a lack of understanding of a broad range of topics and their interconnections.

OP is asking about math, and there is a lot of great advice regarding specifically math in this thread - but I'd also worry (which I assume 22B does, above) about a more general problem.

Perfectionism, GT-kind? (Much discussed on this forum. Tasks are often 'too hard' or 'too easy = boring' and nothing in between.)

How does the child handle staying on a task that he is not 'good at (by his own definition)'?

In math everything is founded on other things, if you show your kid that D just takes a combination of A, B, and C, then if they are intimidated by D they have the option to work on A, B, C to push their confidence+skill level.