Jump to content

Menu

x-post: 11 y/o, math and concentration


Recommended Posts

I posted this on the other forum, but maybe will have more luck here since you all have older kids.So forgive me that his is not the typical high school age.

 

My DS 11 is very good at math, has a quick grasp of the concepts and a solid knowledge of prealgebra.

He is currently studying algebra. Today it took us 45 minutes to do two problems (systems of linear equations). Why? Because he makes careless mistakes - not even in doing calculations, but copying the equations from one line to another. He will insert extra signs or forget signs, take the left side of the first equation but the right side of the second etc. Just copying stuff. And then, of course, the simple problems which have nice integer answers become complicated, the (wrong) answers become fractional - and when doing the check in the end he notices that it does not work out (yeah, it is good that he diligently does the check!) But that's twenty wasted minutes.

This is a very new behavior.

 

Does anybody have an idea what I can do? I would like to help him concentrate better on this stuff. It is very frustrating for him because he can do the math and enjoys it - but he does not enjoy having to redo a single problem three times.

Edited by regentrude
Link to comment
Share on other sites

I just posted on the other thread :D In brief, ds17 went through this in Alg 1. He didn't really care about being neat and he didn't want to show all work :rolleyes: I told him that if he was going to act like a third grader, I'd treat him like a third grader. I had him do one problem per side of paper. I also had him turn the paper sideways so that he could use the lines as columns to line up his writing, like kids do when learning long division.

 

It only took a week or two and his work was back to normal :)

Link to comment
Share on other sites

These types of problems require sustained attention to detail. Would a word problem, in an area of science for example, make staying alert through the mechanics any more interesting? Maybe if it had a story to it, it would be easier. This would help the student answer when or why would I need to find a solution to fit three equations?

 

Does everything go well when only two equations are involved? With more than two equations and as a temporary measure, how about "giving away" some facts about the solution like "integers only".

 

Take a break and find some interesting well-crafted true-false concept questions about algebra. (I really like these; sometimes they're harder than typical problem sets.)

Link to comment
Share on other sites

Since it's primarily a copying issue, what about having him use a ruler or index card underneath the line he's copying from? It would help his eyes focus when he's moving back & forth between the text and his paper.

 

For what it's worth, I've worked with lots of high ability math kids of a similar age. It's a common problem, though quite frustrating.

 

~Kathy

Link to comment
Share on other sites

These types of problems require sustained attention to detail. Would a word problem, in an area of science for example, make staying alert through the mechanics any more interesting? Maybe if it had a story to it, it would be easier. This would help the student answer when or why would I need to find a solution to fit three equations?

 

Does everything go well when only two equations are involved? With more than two equations and as a temporary measure, how about "giving away" some facts about the solution like "integers only".

 

Take a break and find some interesting well-crafted true-false concept questions about algebra. (I really like these; sometimes they're harder than typical problem sets.)

 

Thanks, Janice. The problems ARE two equations with two unknowns. He is interested, loves to manipulate them and finds algebra fun. He has no trouble translating word problems into equations, but it does not seem to interest him more if there is a "story".

What kind of questions did you have in mind when you said "true-false concept questions?

Link to comment
Share on other sites

Since it's primarily a copying issue, what about having him use a ruler or index card underneath the line he's copying from? It would help his eyes focus when he's moving back & forth between the text and his paper.

 

For what it's worth, I've worked with lots of high ability math kids of a similar age. It's a common problem, though quite frustrating.

 

Thanks, that is comforting to know.

It is not copying FROM the text, it is on his paper from one line to the next. I'll see if a ruler or something helps.

 

Thinking about it more, I almost suspect that the issue is that with the systems, there are two different equations that alternate - with a single equation, you always refer to just the line immediately above. Hm... I'll see if I can come up with a way for him to organize this better.

Thanks

Link to comment
Share on other sites

BTDT with one of my daughters, also with algebra.

 

In our case it was usually one of two things: carelessness or concentration. If carelessness, it meant that she did not have enough busy work (this child is quite brilliant, frankly, very very quick at understanding things which minimizes the need to practice the pattern). She always tries to get away with it because she's bored with it, obviously, but I try to gently tell her that she can't afford mistakes out of lack of automatism when doing things (ultimately it comes down to that - you don't practice, ergo you lack automatism in doing it), because a single sign or a number can mess up the whole thing, and even if it doesn't matter in algebra, on higher math levels as well as in sciences it will matter a lot. It's quite important to get children interested in scientific careers to understand this point and to really reach this automatism, thus diminishing the possibility of careless mistakes. Focus on being neat in your work is also very important, but mostly, it's about not being careless just because you know how to do it.

If it's pure concentration without the element of carelessness, it's usually on a very physiological level - lack of sleep (or too much of it), not enough rest after eating, consuming sugar (a HUGE one! this same child has some concentration and mood issues that are directly linked to sugar consumption and generally processed foods, so the poor thing can't have any, unfortunately, as it has such side effects on her), stuff like that. Try to see if there's a physiological problem first. What you describe, though, sounds like the carelessness above - the lack of automatism, which is quite common in mathy kids who "get" things and thus don't practice enough for it to become automatic.

Link to comment
Share on other sites

Thanks everybody!

He is aware that it is important to be correct every single time (two physicist parents made sure of that ). We never let him get away with just knowing the concept - we had him practice everything till he could to it automatically (big issue was with distributing factors in front of parentheses expressions and paying attention to all the signs - we worked on that for quite a while).

He also is not rewarded for hurrying- we usually do math for a set time and finish however much we accomplish. So he is not tempted to get done fast in order to do other things.

I'll think about the physiological issue... usually we do math first thing in the morning. he will have slept, woken by himself, been up for 1.5-2 hours (i.e. not sleepy anymore), have eaten breakfast (but not stuffed himself)... hm. Should be prime time for concentration.

 

I will give him quad paper and see if that makes a difference. Today at home, he worked on lined paper and it was bad; yesterday he worked on quad and it was also bad.

 

Thanks for all your suggestions. It also helps a lot to hear that other kids have gone through similar phases.

Link to comment
Share on other sites

My dd was the same age in algebra. Before this, she had just worked the problems directly in the paperback text, so it was the first year that neatness counted. We found using graph paper to make a huge difference and it had the added benefit of having any number lines or graphs drawn where the problem was worked instead of on a separate graph paper. Still, we had errors of the usual kind - I think it's normal. :) She was doing 35 or so problems a day and I expected there to be mistakes. She could usually correct them quickly, but sometimes we'd have that one problem - usually not even one of the more difficult problems - that would take several attempts before finally getting the right answer. I think that's normal too.

Link to comment
Share on other sites

In Algebra Quad paper usually makes issues like these WORSE because you cannot get by with putting one character in each space--like in elementary arithmetic.

 

You could try a whiteboard... often color helps with details.

 

If not a whiteboard then a piece of scrap paper--preferably the back of lightly colored flyer(with some ink showing through to the back is even better!). Have him turn the paper at an angle and work his problem... to work another problem rotate the paper and find another 'empty patch'... this breaks up the forced order of notebook paper--and helps the right side of the brain join the Math party! When the problem checks out it is copied onto notebook paper (copy errors tend to be less here --as it is just wrote copying--no need to think about the next step...).

--

 

This is also a maturity issue. During the puberty years the body shuts down much of the logic/detail parts of the brain--and devotes extra resources to growth... eventually it will come back!

 

I've had moderate success with students who had to work extra problems if they missed some on assignments... they would do almost ANYTHING to reduce their homework load--so they suddenly became extra careful. Others had more success with working the problems on scrap paper then copying them onto notebook paper (or a parent doing this especially if the student was dysgraphic).

Link to comment
Share on other sites

Thanks, that is comforting to know.

It is not copying FROM the text, it is on his paper from one line to the next. I'll see if a ruler or something helps.

 

Thinking about it more, I almost suspect that the issue is that with the systems, there are two different equations that alternate - with a single equation, you always refer to just the line immediately above. Hm... I'll see if I can come up with a way for him to organize this better.

Thanks

 

In solving systems (2x2), I generally work across rather than down when teaching. It seems to help keep the 2x2 system together more.

 

Using substitution, I label equations (1) and (2) and write out what's happening:

 

 

  • Solve eqn (1) for y (do this),

  • Substitute into eqn (2) (do this),

  • Find value of other variable (do this),

  • state answer as ordered pair (do this),

  • and check.

 

I strongly encourage students to write the words above so they are communicating their work. It seems to help with avoiding confusion of substituting into the same equation.

 

For elimination/addition, I still label eqns (1) and (2), but then I generally work horizontally:

(orig system) --> 3(eqn 1) + -2(eqn 2) [writing the step showing the multiplication, then writing the new equations, then work down from there by adding.

 

I also sometimes suggest using unlined paper and taking a LOT of space to work the problems. It seems to help with not feeling cramped with space for the work. (Probably no more than one or two systems per page.)

 

Those are the ideas I have given what I've seen with student errors. Good luck!

Edited by Dana
added comment about unlined paper
Link to comment
Share on other sites

Here is my oddball information:

 

According to John Ratey, a clinical associate professor of psychiatry at Harvard Medical School, anaerobic exercise helps boys to focus fairly well. (Girls can get by with aerobics.) In a nutshell, exercise causes the pituitary gland to produce more human growth hormone (HGH) which has wide-reaching effects. It is complicated to explain everything that is happening, but if you are interested in learning more, I'd suggest reading Ratey's book Spark: The Revolutionary New Science of Exercise and the Brain. Fascinating stuff that is showing good results when put into practice.

 

Amazon link here.

 

Btw, a person has reached the anaerobic stage when he finds the exertion *somewhat hard.* Even though that might seem too simplistic, it is an accurate indicator. Just a few minutes of intense exercise (as little as 30 seconds actually) can boost HGH from two to four hours. My son does jumping jacks before studying something new to help him.

 

I also agree with the maturity issue. All of my kids were like that for awhile. My daughter especially!

 

Good luck. :)

Link to comment
Share on other sites

With mine, it was a matter of convincing them that they really did need to pay careful attention. Somebody here suggested having them write the signs in a different colour. I think we did signs in red and operations in blue and the rest in pencil. I got erasable coloured pencils. We used graph paper (we always have for math). I made them line everything up carefully underneath and I made liberal use of yellow stickies to make sure they were copying the problem right. It was just enough of a bother to switch pencils that they learned to pay more attention to the little details when copying. I also made them use brackets liberally, and made them write diagonally anything they were doing to both sides (not very clear, but you probably know what I mean). I made them write diagonally for every simplifying step and not just do them in their heads. My older one likes, even at 20, to work at a white board if he is doing something hard. That is another option, especially with a younger algebra student. Other people here over the years have said that that solved this problem. It is frustrating, but with gentle encouragement, they outgrow it. More or less. Sigh. My youngest, who is doing pre-calc, spent today making the same sorts of errors because he was doing too many steps in his head. Interestingly, he was solving the same sorts of problems (not sure why - he's been doing this sort for years - we should have skipped this section). There is a lot to keep track of in algebra.

-Nan

Link to comment
Share on other sites

I've read a number of threads commenting on kids going through this stage, particularly with positive/negative numbers when you get things in multiple sets of parentheses and multiple variables. It's a lot to keep track of visually, which is different from mentally/intellectually, as well as sometimes getting so abstract that a child's visual attention will inevitably wander even if they like the puzzle or logic aspect of algebra.

 

At fourteen, dd seems to be coming out of this stage. At least it's been a while since she has consistently run into trouble like she used to.

Edited by Guest
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

 Share

×
×
  • Create New...