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Vida Winter

Need to get dd to slow down and write neatly inst of mental math...

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Math usually comes easy to her but now that she is getting into pre alg. topics (Saxon 7/6) she is relying on mental math too much and making multiple errors. Errors that could easily be avoided. Any ideas on how to get her to slow down and write it out? My advice goes in one ear and out the other.

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What does she say if you let her complete an entire lesson "her way" and then have her go back and re-do each problem that she gets wrong, by writing it out in explicit detail?

 

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What does she say if you let her complete an entire lesson "her way" and then have her go back and re-do each problem that she gets wrong, by writing it out in explicit detail?

 

She does re-do work on her daily homework. Tests are the trouble - she only gets once chance to enter the answer (it's online). I suppose I could sit with her and make her slow down but she needs to learn to slow herself down and take extra care during tests. Maybe a portable white board would help. We also need to brush up on test-taking skills. This semester is her first real experience with taking exams online.

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My son was the same way, as are lots of kids.

 

I had to just enforce it. I had to tell him over and over to show his work.

 

We started that at the beginning of 7th grade and by the end he was writing out his work. He simply had to be trained to do it.

 

You can insist on it being done. If the work isn't written out, then she has to re-do it. Using graph paper is nice sometimes. It's kind of fun to fill in all the boxes with numbers and helps keep everything lined up nicely.

Edited by Garga
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My son was the same way, as are lots of kids.

 

I had to just enforce it. I had to tell him over and over to show his work.

 

We started that at the beginning of 7th grade and by the end he was writing out his work. He simply had to be trained to do it.

 

You can insist on it being done. If the work isn't written out, then she has to re-do it. Using graph paper is nice sometimes. It's kind of fun to fill in all the boxes with numbers and helps keep everything lined up nicely.

 

That's good to know. I've never had one this messy with writing. Maybe by printing out large grid graph paper - she never stays on a line, or in between lines. Her writing is more diagonal, with different sized characters. It's painful to look at.

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Giving more points for writing out then for 'right answer', after all the answer could be a 'guess'

So 5 points for writing out and 1-2 for right answer.

This way dd got a 'fail' on her tests had to redo it.

She quickly learned to write out.

Sometimes she forgets again, and I use the point system again.

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That's good to know. I've never had one this messy with writing. Maybe by printing out large grid graph paper - she never stays on a line, or in between lines. Her writing is more diagonal, with different sized characters. It's painful to look at.

 

Has her vision been checked lately?  FWIW, developmental vision issues, e.g. convergence and tracking problems, can cause these sorts of writing issues.

 

Eta, large graph paper is a good idea.  You might also try a white board.

Edited by wapiti
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Has her vision been checked lately?  Developmental vision issues, e.g. convergence and tracking problems, can cause this sort of writing.

 

You know, that's a good idea. She was checked about 11 mos ago and her vision Rx bumped up. She's due for another exam next month - thanks for thinking of this - I'll make the appt. At least one of the problems missed was due to copying down a number wrong. It's probably still carelessness but the vision angle may be part of it.

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Giving more points for writing out then for 'right answer', after all the answer could be a 'guess'

So 5 points for writing out and 1-2 for right answer.

This way dd got a 'fail' on her tests had to redo it.

She quickly learned to write out.

Sometimes she forgets again, and I use the point system again.

 

The tests are computer-scored so I can't change the grading system. If I gave the tests at home, though, this would be a great idea. Someone else can benefit.

 

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She does re-do work on her daily homework. Tests are the trouble - she only gets once chance to enter the answer (it's online). I suppose I could sit with her and make her slow down but she needs to learn to slow herself down and take extra care during tests. Maybe a portable white board would help. We also need to brush up on test-taking skills. This semester is her first real experience with taking exams online.

What is the worst that could happen if you let her make poor grades on the exams as a result of her stubbornness? This being Math 76, it won't be a part of her high-school transcript. This may be a good grade/age range to began learning that her (in)actions have academic consequences. This is only her first semester, so there is a learning curve to be expected.

 

However, when she does her daily lessons, is she writing out each problem, step by step? How is her working the for corrections, different from her working the problems initially?

 

I would give her whatever resource you think would make it easier to write her work during the tests, (ie, white board) and  remind her to write out her work before she started the exam. Or perhaps, instead of writing out each step, require that she write-out the CHECK her work, prior to entering the problem. If her checking the work does not come out, then she must WRITE OUT the problem, in its entirety and solve it step-by-step on paper.

 

Additionally, I might let her underperform on a couple of tests just so that she can see mom is not being a paranoid, control-freak and so that she can realize that she is ACTUALLY hurting her own grades by not complying with your instructions.

 

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What is the worst that could happen if you let her make poor grades on the exams as a result of her stubbornness? This being Math 76, it won't be a part of her high-school transcript. This may be a good grade/age range to began learning that her (in)actions have academic consequences. This is only her first semester, so there is a learning curve to be expected.

 

However, when she does her daily lessons, is she writing out each problem, step by step? How is her working the for corrections, different from her working the problems initially?

 

I would give her whatever resource you think would make it easier to write her work during the tests, (ie, white board) and  remind her to write out her work before she started the exam. Or perhaps, instead of writing out each step, require that she write-out the CHECK her work, prior to entering the problem. If her checking the work does not come out, then she must WRITE OUT the problem, in its entirety and solve it step-by-step on paper.

 

Additionally, I might let her underperform on a couple of tests just so that she can see mom is not being a paranoid, control-freak and so that she can realize that she is ACTUALLY hurting her own grades by not complying with your instructions.

 

Since it is computer-graded, it is set up to not let her continue with the course until she passes with at least an 80%. She has to go over missed problems with me, and email her teacher who then resets the test and she has another chance to take it (with similar questions but not the same). So the consequences are not drastic, just more work.

 

We went over everything today. She's going to use grid paper and now knows that she is *required* to write down her work neatly or else face rewriting it. Most of the errors on this past test were entirely preventable if she had written down work and not rushed through it.  Only one of the problems (out of 18) was a bit of a challenge.  She has simply got to get in the habit of writing her work neatly, even if she doesn't like the idea.

 

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Big struggle here. 

 

First I defined what a 'careless error' was. It isn't an honest mistake, it is not showing work, not being able to read your own hand writing, writing down problems incorrectly etc.  Then I put down a row of chocolate chips. For every question he got right, he got the chip.  If he got it wrong but made an error in calculation etc then he still got the chip.  If he made a careless error or did not show his work, then I got the chip.

 

It didn't take long before it wasn't an issue and we didn't need the reward.

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Well, isn't that the million dollar question! Currently working on that with ds 11, this is the year I'm making it a priority while still in pre-A he has to learn to do this. I just keep hammering away with the expectation, slowly, very slowly it is becoming the norm. I jump in with various subjects here and there starting it or doing it for him(talking through the how and why of each part/step) so I can give him examples of how to properly label his paper and write out his problems so he doesn't miss anything or make it too sloppy- it is an apprenticeship for organization and neatness, eventually it will sink in.... I think :)

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I'm a maths tutor and I see this a lot.  

 

There are three different issues here that you need to deal with separately.

 

1) Tidiness.  This typically takes about 4 months to remediate.  I just calmly tell the student that their writing is pretty messy and this will haunt them as they continue in mathematics.  Not only will they make more mistakes, they will also lose points for people not being able to read their writing.  I have found that there is a very strange interaction between a good attitude/being focused and tidy work.  If you are focused and working with a good attitude, your writing is typically tidy.  But surprisingly, it works the other way also.  If you can get a kid to be tidy first, it will increase their focus and attitude as a result.  After you get a kid to own the problem, you then ask her what she thinks she should do first.  She needs to decide, not you dictating it to her.  She should be able to come up with something like all letters/numbers on the line, or need to close my 0, or need to make my 5s clearer, etc.  Do one every couple of days, and remind her of her previous goals if you see it sliding. Once things get pretty tidy, you start in on 'mathematical writing'.  This helps continue to focus on tidiness but now with more 'advanced' material so you don't look like you are harping.  So every week I make sure to teach a new thing, in math we hook our t so it does not look like a +.  or cross the z so it doesn't look like a 2, or the square needs to be higher and smaller. etc.  There are plenty of picky things that you can bring up one by one to keep the focus on the tidiness until it becomes a habit.  And finally, you need to tell them that it often happens that you have a push for tidy, and then after a couple of months, you get slack.  Happens to everyone.  Once she notices it, she needs to focus for a week to bring it back up to the level she has achieved, and this will be a lifelong task. So expect it.

 

2) careless errors.  This is such a bad term because it implies that it is no big deal. That they will go away eventually. That everyone does it.  Careless errors need to be defined.  You don't have careless errors, you have a problem with negatives, or a problem with remembering to square a number, or a problem with subtracting accurately in your head.  You need to circle all careless errors in red and then on the outside margin in red write what kind of error it is.  Create a tick chart and tract your errors.  Then you need to focus on reducing that specific kind of error.  They don't just go away on their own, you need to have a plan.  I have been know to put a start in the margin of problems with squares, because I always forget to square things in physics. But do what it takes to quit making that error.  I have found that this process drastically reduces errors and often highlights weak points in the student's math which might require some extra drill.  Errors are happening for a reason.  If the reason is simply lack of attention, then typically, tracking the errors helps the student to attend to that specific problem.  I have never had this method not work.  And I will add that mental math falls into this category.  I tell the students that mental math is absolutely fine for computation as long as they are getting the answer correct.  I tell them that clearly the goal of computation is to get the answer right, so why bother if you have it wrong.  They seem to get it.  So if they are doing the work in their head and missing the problem, they need to do it on paper.  If they are still getting it wrong, they need to track their errors as I described above.  

 

3) test taking.  Test taking skills are not math skills.  Kids need to know this.  I talk to my students about the goal being to learn math as a life skill, but that we also have the reality of taking tests.  The key to test taking is to get practice tests and figure out where your problems are so you can do a better job.  Do you have trouble with time management?  Do you need to learn to skip the hard ones and come back to them?  Do you need to check your work?  Do you need to deal with anxiety?  Do not dictate the answer to a kid, you need to guide them through the process so that she can figure out herself where the problem is.  Also, if a test is done in a different format that the way you do your daily study, the importance of practice tests cannot be overemphasized.  Talk to her teacher, get some no-grade tests that she can do online and grade herself.  The go through and mark up the errors and let her decide what kind of errors they were and how to remediate them.  Usually it takes 5 practice tests to get good at test taking.  However, if it is anxiety, then you need to deal with that separately.  

 

The key point is that kids have to own it.  They cannot be dictated to, as it never works.  Happy to answer any questions you might have.

 

Ruth in NZ

Edited by lewelma
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I'm a maths tutor and I see this a lot.  

 

There are three different issues here that you need to deal with separately.

 

1) Tidiness.  This typically takes about 4 months to remediate.  I just calmly tell the student that their writing is pretty messy and this will haunt them as they continue in mathematics.  Not only will they make more mistakes, they will also lose points for people not being able to read their writing.  I have found that there is a very strange interaction between a good attitude/being focused and tidy work.  If you are focused and working with a good attitude, your writing is typically tidy.  But surprisingly, it works the other way also.  If you can get a kid to be tidy first, it will increase their focus and attitude as a result.  After you get a kid to own the problem, you then ask her what she thinks she should do first.  She needs to decide, not you dictating it to her.  She should be able to come up with something like all letters/numbers on the line, or need to close my 0, or need to make my 5s clearer, etc.  Do one every couple of days, and remind her of her previous goals if you see it sliding. Once things get pretty tidy, you start in on 'mathematical writing'.  This helps continue to focus on tidiness but now with more 'advanced' material so you don't look like you are harping.  So every week I make sure to teach a new thing, in math we hook our t so it does not look like a +.  or cross the z so it doesn't look like a 2, or the square needs to be higher and smaller. etc.  There are plenty of picky things that you can bring up one by one to keep the focus on the tidiness until it becomes a habit.  And finally, you need to tell them that it often happens that you have a push for tidy, and then after a couple of months, you get slack.  Happens to everyone.  Once she notices it, she needs to focus for a week to bring it back up to the level she has achieved, and this will be a lifelong task. So expect it.

 

2) careless errors.  This is such a bad term because it implies that it is no big deal. That they will go away eventually. That everyone does it.  Careless errors need to be defined.  You don't have careless errors, you have a problem with negatives, or a problem with remembering to square a number, or a problem with subtracting accurately in your head.  You need to circle all careless errors in red and then on the outside margin in red write what kind of error it is.  Create a tick chart and tract your errors.  Then you need to focus on reducing that specific kind of error.  They don't just go away on their own, you need to have a plan.  I have been know to put a start in the margin of problems with squares, because I always forget to square things in physics. But do what it takes to quit making that error.  I have found that this process drastically reduces errors and often highlights weak points in the student's math which might require some extra drill.  Errors are happening for a reason.  If the reason is simply lack of attention, then typically, tracking the errors helps the student to attend to that specific problem.  I have never had this method not work.  And I will add that mental math falls into this category.  I tell the students that mental math is absolutely fine for computation as long as they are getting the answer correct.  I tell them that clearly the goal of computation is to get the answer right, so why bother if you have it wrong.  They seem to get it.  So if they are doing the work in their head and missing the problem, they need to do it on paper.  If they are still getting it wrong, they need to track their errors as I described above.  

 

3) test taking.  Test taking skills are not math skills.  Kids need to know this.  I talk to my students about the goal being to learn math as a life skill, but that we also have the reality of taking tests.  The key to test taking is to get practice tests and figure out where your problems are so you can do a better job.  Do you have trouble with time management?  Do you need to learn to skip the hard ones and come back to them?  Do you need to check your work?  Do you need to deal with anxiety?  Do not dictate the answer to a kid, you need to guide them through the process so that she can figure out herself where the problem is.  Also, if a test is done in a different format that the way you do your daily study, the importance of practice tests cannot be overemphasized.  Talk to her teacher, get some no-grade tests that she can do online and grade herself.  The go through and mark up the errors and let her decide what kind of errors they were and how to remediate them.  Usually it takes 5 practice tests to get good at test taking.  However, if it is anxiety, then you need to deal with that separately.  

 

The key point is that kids have to own it.  They cannot be dictated to, as it never works.  Happy to answer any questions you might have.

 

Ruth in NZ

 

It is a pity that the NZ  schools seem to teach them that it is evidence of failure to have to use a pencil to work something out.  When I queried ds8 earlier this year he said "i am in year 4, they expect me to be able to do it {4 digit subtraction with carrying} without using a calculator or a pencil and paper".  His teacher says they are allowed to use scrap paper but there honestly wasn't enough room on the test paper for an average 8 year older writer to write much.  I do like the number sense my kids have but I am not sure how much of that is taught versus natural to them.

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It is a pity that the NZ  schools seem to teach them that it is evidence of failure to have to use a pencil to work something out.  When I queried ds8 earlier this year he said "i am in year 4, they expect me to be able to do it {4 digit subtraction with carrying} without using a calculator or a pencil and paper".  His teacher says they are allowed to use scrap paper but there honestly wasn't enough room on the test paper for an average 8 year older writer to write much.  I do like the number sense my kids have but I am not sure how much of that is taught versus natural to them.

 

It is actually way more serious than that.  Every single kid that I work with has a major disconnect between primary school maths and secondary school maths.  Because they are taught to do everything as mental maths, kids never learn to convert word problems into actual mathematical equations.  For a word problem asking them to subtract 128-32, they will stepping stones, so add a 100 to get up to 132 and then subtract off 4. When you ask them to show their work, they will make some sort of number line.  The problem is they are never taught to differentiate between the mathematical operation they are trying to accomplish and the mental tools they use to solve it. They have no idea they have just subtracted, and it is even worse when it is a two or three step word problem -- they can get the answer correct, but they confound the different mental tools for each mathematical step and have no sense of proper mathematical thinking. So when they get to algebra and have no numbers to work with, they cannot convert a word problem into algebra to solve. The experts mumble in the news about why the NZ Pisa scores for high schoolers dropped so much in mathematics, but no one asked me! (-:  It is a pretty straight forward problem that they have created for themselves, and not easy to fix.

Edited by lewelma
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It is actually way more serious than that.  Every single kid that I work with has a major disconnect between primary school maths and secondary school maths.  Because they are taught to do everything as mental maths, kids never learn to convert word problems into actual mathematical equations.  For a word problem asking them to subtract 128-32, they will stepping stones, so add a 100 to get up to 132 and then subtract off 4. When you ask them to show their work, they will make some sort of number line.  The problem is they are never taught to differentiate between the mathematical operation they are trying to accomplish and the mental tools they use to solve it. They have no idea they have just subtracted, and it is even worse when it is a two or three step word problem -- they can get the answer correct, but they confound the different mental tools for each mathematical step and have no sense of proper mathematical thinking. So when they get to algebra and have no numbers to work with, they cannot convert a word problem into algebra to solve. The experts mumble in the news about why the NZ Pisa scores for high schoolers dropped so much in mathematics, but no one asked me! (-:  It is a pretty straight forward problem that they have created for themselves, and not easy to fix.

Eeek.  Lucky I make him do MM topic books and process skills or CWP.   Still aiming to start AOPS PA in intermediate - especially since the intermediate just did away with their extension class in favour of the MLE much loved by those who have calm, bright, complaint kids.  I actually do think a bit like that despite having been taught plug and chug methods with new maths in the seventies but I can show what i do if i have to.

 

eta.  I am pretty sure my kids would do 128-28-4 and would understand what they were doing.  Both my kids have phenomenal working memories but pens were invented for a reason and it is very hard to work out where you went wrong without having written anything down.  I think it is a bit crazy but i am only their mother after all!  I don't really believe the teachers believe what they preach either - if you had to genuinely do 180 degree turns every five years for 40 years you would be tied in knots.

Edited by kiwik
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I have a pencil-phobic child.  He is quicker than quick with mental math.  This is an issue we work through.

 

I give him time to work it out in his head.  Then I say, "Great! Now, let's show how you did that on paper!" (cheerfully blah blah blah)   I say these things a whole heck of a lot, "Jot that down before you forget." and "Math is communicating with numbers." and "People need to be able to glance at your work and know what you're thinking."  and "It does no good to be right if you cannot communicate the solution."

 

My 3rd child is 9yo and really beginning to dig into Challenging Word Problems.  We spend more time learning how to show his work than any other thing in math at the present. 

 

 

It is actually way more serious than that.  Every single kid that I work with has a major disconnect between primary school maths and secondary school maths.  Because they are taught to do everything as mental maths, kids never learn to convert word problems into actual mathematical equations.  For a word problem asking them to subtract 128-32, they will stepping stones, so add a 100 to get up to 132 and then subtract off 4. When you ask them to show their work, they will make some sort of number line.  The problem is they are never taught to differentiate between the mathematical operation they are trying to accomplish and the mental tools they use to solve it. They have no idea they have just subtracted, and it is even worse when it is a two or three step word problem -- they can get the answer correct, but they confound the different mental tools for each mathematical step and have no sense of proper mathematical thinking. So when they get to algebra and have no numbers to work with, they cannot convert a word problem into algebra to solve. The experts mumble in the news about why the NZ Pisa scores for high schoolers dropped so much in mathematics, but no one asked me! (-:  It is a pretty straight forward problem that they have created for themselves, and not easy to fix.

 

This is confirmation to me to keep at what I'm doing.  Thanks!

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It is actually way more serious than that.  Every single kid that I work with has a major disconnect between primary school maths and secondary school maths.  Because they are taught to do everything as mental maths, kids never learn to convert word problems into actual mathematical equations.  For a word problem asking them to subtract 128-32, they will stepping stones, so add a 100 to get up to 132 and then subtract off 4. When you ask them to show their work, they will make some sort of number line.  The problem is they are never taught to differentiate between the mathematical operation they are trying to accomplish and the mental tools they use to solve it. They have no idea they have just subtracted, and it is even worse when it is a two or three step word problem -- they can get the answer correct, but they confound the different mental tools for each mathematical step and have no sense of proper mathematical thinking. So when they get to algebra and have no numbers to work with, they cannot convert a word problem into algebra to solve. The experts mumble in the news about why the NZ Pisa scores for high schoolers dropped so much in mathematics, but no one asked me! (-:  It is a pretty straight forward problem that they have created for themselves, and not easy to fix.

 

Thank you for putting into words EXACTLY where we are.  We are days from beginning prealgebra with AOPS, and my son doesn't write anything down.  It's obvious to me that the mental math has become so automatic that he doesn't really know how he got from one place to the answer.  

 

Now that we're here, how do we fix this?

 

I try things like 4blessingmom suggested with, "Let's show how you did that on paper," or "jot that down before you forget," but he resists and doesn't do it.  I think it's because we're back to the fact that he may not know how he got there.

 

Do we go back to the simplest letting him know that the whole purpose of the exercise is to write them out and work quickly from there?  I'm not a math person myself so it's difficult for me to work away from curriculum.  I can follow along and figure things out, but he is like lightning compared to me (which frustrates him because I have to go step by step and he's *snap* done).

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Are the tests the same ones that are in the Saxon test book? If so, I would have her do the problems on paper with work written out to your satisfaction and then she can enter her answers online.

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Are the tests the same ones that are in the Saxon test book? If so, I would have her do the problems on paper with work written out to your satisfaction and then she can enter her answers online.

 

Not exactly - questions are pulled from a test bank and are different each time. But the Saxon tests would be good practice. Thanks for the thought.

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I'm a maths tutor and I see this a lot.  

 

There are three different issues here that you need to deal with separately.

 

1) Tidiness.  This typically takes about 4 months to remediate.  I just calmly tell the student that their writing is pretty messy and this will haunt them as they continue in mathematics.  Not only will they make more mistakes, they will also lose points for people not being able to read their writing.  I have found that there is a very strange interaction between a good attitude/being focused and tidy work.  If you are focused and working with a good attitude, your writing is typically tidy.  But surprisingly, it works the other way also.  If you can get a kid to be tidy first, it will increase their focus and attitude as a result.  After you get a kid to own the problem, you then ask her what she thinks she should do first.  She needs to decide, not you dictating it to her.  She should be able to come up with something like all letters/numbers on the line, or need to close my 0, or need to make my 5s clearer, etc.  Do one every couple of days, and remind her of her previous goals if you see it sliding. Once things get pretty tidy, you start in on 'mathematical writing'.  This helps continue to focus on tidiness but now with more 'advanced' material so you don't look like you are harping.  So every week I make sure to teach a new thing, in math we hook our t so it does not look like a +.  or cross the z so it doesn't look like a 2, or the square needs to be higher and smaller. etc.  There are plenty of picky things that you can bring up one by one to keep the focus on the tidiness until it becomes a habit.  And finally, you need to tell them that it often happens that you have a push for tidy, and then after a couple of months, you get slack.  Happens to everyone.  Once she notices it, she needs to focus for a week to bring it back up to the level she has achieved, and this will be a lifelong task. So expect it.

 

2) careless errors.  This is such a bad term because it implies that it is no big deal. That they will go away eventually. That everyone does it.  Careless errors need to be defined.  You don't have careless errors, you have a problem with negatives, or a problem with remembering to square a number, or a problem with subtracting accurately in your head.  You need to circle all careless errors in red and then on the outside margin in red write what kind of error it is.  Create a tick chart and tract your errors.  Then you need to focus on reducing that specific kind of error.  They don't just go away on their own, you need to have a plan.  I have been know to put a start in the margin of problems with squares, because I always forget to square things in physics. But do what it takes to quit making that error.  I have found that this process drastically reduces errors and often highlights weak points in the student's math which might require some extra drill.  Errors are happening for a reason.  If the reason is simply lack of attention, then typically, tracking the errors helps the student to attend to that specific problem.  I have never had this method not work.  And I will add that mental math falls into this category.  I tell the students that mental math is absolutely fine for computation as long as they are getting the answer correct.  I tell them that clearly the goal of computation is to get the answer right, so why bother if you have it wrong.  They seem to get it.  So if they are doing the work in their head and missing the problem, they need to do it on paper.  If they are still getting it wrong, they need to track their errors as I described above.  

 

3) test taking.  Test taking skills are not math skills.  Kids need to know this.  I talk to my students about the goal being to learn math as a life skill, but that we also have the reality of taking tests.  The key to test taking is to get practice tests and figure out where your problems are so you can do a better job.  Do you have trouble with time management?  Do you need to learn to skip the hard ones and come back to them?  Do you need to check your work?  Do you need to deal with anxiety?  Do not dictate the answer to a kid, you need to guide them through the process so that she can figure out herself where the problem is.  Also, if a test is done in a different format that the way you do your daily study, the importance of practice tests cannot be overemphasized.  Talk to her teacher, get some no-grade tests that she can do online and grade herself.  The go through and mark up the errors and let her decide what kind of errors they were and how to remediate them.  Usually it takes 5 practice tests to get good at test taking.  However, if it is anxiety, then you need to deal with that separately.  

 

The key point is that kids have to own it.  They cannot be dictated to, as it never works.  Happy to answer any questions you might have.

 

Ruth in NZ

 

Ruth, thank you so much for these tips. These are exactly the types of things we need to be doing.

 

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Thank you for putting into words EXACTLY where we are.  We are days from beginning prealgebra with AOPS, and my son doesn't write anything down.  It's obvious to me that the mental math has become so automatic that he doesn't really know how he got from one place to the answer.  

 

Now that we're here, how do we fix this?

 

I try things like 4blessingmom suggested with, "Let's show how you did that on paper," or "jot that down before you forget," but he resists and doesn't do it.  I think it's because we're back to the fact that he may not know how he got there.

 

Do we go back to the simplest letting him know that the whole purpose of the exercise is to write them out and work quickly from there?  I'm not a math person myself so it's difficult for me to work away from curriculum.  I can follow along and figure things out, but he is like lightning compared to me (which frustrates him because I have to go step by step and he's *snap* done).

 

First of all, prealgebra is a fine place to start. So don't panic.  Second, you need to put it in your head that you will NOT harp.  Your child needs to own it if you expect it to happen, so you need to put on your benevolent manipulation hat and secretly get your kids to want to do it.  This is the key skill of a good maths tutor/teacher/homeschooler. 

 

So I would take the approach with your child of you are entering a new stage in mathematics and only now are you ready to learn mathematical thinking (so kind of a lie, but also not as your kid clearly couldn't do it before).  I would talk about moving from primary school computation to proper mathematical thinking. Something like "Mathematical thinking is about converting words/ideas into symbols written down in a standardized way, and I will teach you how to do this.  No longer will you be showing 'your' work, now you will be showing 'the' work.  All primary school computations you do (+ - x /) will be done in the computation box in your notebook, we will set aside 1/4 of your notebook for these computations.  Computations can be done any way you like, with an algorithm, in your head, with a calculator (well probably not for your kid, but I have some who have dyscalculia).  I don't care how you do them or if you write them down, but they *must* be correct.  If I see that you are getting them wrong, then we will work together to find a way to make sure they are right.  But this is all primary school stuff that you already know.  What we are going to focus on is secondary school work, and this is mathematical thinking.  Every maths problem from now on has proper workings, and I will show them to you.   Workings that all people everywhere expect, this is from trig to algebra to calculus.  It is no longer *your* workings, just stuff out of your head, but rather *the* workings which are done in a certain way.  We will keep a little flashcard with the stuff I show you so you can understand what is expected for each problem in showing your mathematical thinking."

 

"Now in the beginning you will find that mathematical thinking is tricky.  And why shouldn't it be? Mathematical symbols need to be written into words and sentences.  This process will take all year to get good at, and then you will continue to add on new mathematical symbols, words, and sentences every year.  So be patient with yourself.  You might get frustrated because you will be doing things differently than you have in the past, but that is only because you are ready.  This is preAlgebra; not 5th grade math.  And you are ready.  So the first thing we need to do is set up your notebook with the computation boxes, and we need to make a notecard."

 

*****

 

This little talk I have to re-emphasize almost every time I see a kid.  NO Nagging!  They must own it.  

 

So what are proper workings?  Well, probably what you were taught.  So make it sound like it is something new to master so that you leave behind the angst.  Also, at first a *single* line of proper workings with all mental maths behind it is all you can expect.  But slowly over the period of the year, you will say 'now this problem has 2 lines of proper workings. Let me show you what they look like.'  Over time, once a kid sees how hard the proper workings are to write, they will come to realize that it actually is a skill to master and not just a waste of time.  As they get further along they will also see the need for it.

 

So what are the 'proper' workings that you will show them?  I'm looking through a prealgebra book that my ds uses

 

Lets say you are finding the area of a quarter of a circle with r of 3: you must write A=PI 3^2 / 4  (don't have an equation editor, sorry) The key is A=, and all the numbers plugged in unchanged.  Then the next line is A= with the answer and units.  Tell them you get a point for the proper working line, a point for the answer, and a point for then unit.  As they get further along, you tell them that actually the first line of proper workings is the formula line, then you do the plug in line, and then the answer.  For advanced kids if you need to find the area of the circle with a smaller semicircle cut out of it, the more advanced workings is to put both formulas in one line so A=pi r^2 - pi r^2 / 2. and then do the plug in line.  At this point you talk to them about the order of operations are discuss whether they need a parentheses or not.  Putting everything in one line can be quite tricky at times.

 

For algebra, you need to distinguish between an expression and an equation, and make sure they know the difference.  You must work DOWN.  No equal signs allowed unless it is an equation. I can go into the details of this if needed.

 

So for word problems like, and object travels 247 miles in 4 hours and 20 minutes.  Calculate the average speed in miles/hr.  I only need one line of work  Speed=247/260 x 60 . All calculations are done in the calculation box anyway they want.  If a student cannot put it all in one step it is fine to do Speed = 247/260 then answer with miles/min as the units.  Then the second line of work is Speed = answerx60, with units miles/hour.  1 point for proper workings line, 1 point for answer, 1 point for units (or 6 ticks total if they make it 2 steps) Be very careful with your ticks.  They are for very specific lines of work.  Make sure your kid knows exactly what you are ticking and why. 

 

Some problems have no proper workings.  And you need to make sure to tell your kid this.  So if it is just a straight computation problem like 8^3, there is only an answer (unless they get it wrong a lot, and then you need to discuss how to improve computation, just make sure to separate primary school computation from secondary school mathematical thinking.  Its a pride thing).  If it is a word problem with a straight computation, the proper workings are like the average question above.  Make sure that 10%-20% of the work they do requires no proper workings, so they take you seriously about the other stuff.

 

So for every new bit of material, you go about it like this:

1) teach the proper working line (1 line at first) for everything new. (If you are not sure of the proper working line, ask your kid. 'what do you think is the proper workings here?'  don't do this for the first 2 months or more, but later on it is both ok and helpful.  So make sure that you PREP for the first 2 months or more so you know what the proper working line is.  Of course it is not an exact science, but I wouldn't tell the kid that until he fully owns it.  At first there is a *proper* working line!

2) put the line on the card (this is just a stop gap until the kid starts to get it, so like 3 months)

3) have the kid do 1, and correct the working line if needed.  remind that all computation goes in the computation box.  There needs to be clarity between computation and mathematical thinking

4) have the kid do a couple independently and make sure to come back and check right away that it is going well.

5) mark his paper in front of him with a red tick for the working line, a red tick for the answer, and a red tick for the unit if required.  Don't look at the computation box unless there is a problem. This reinforces the difference between the two types of working.  Proper workings look a certain way and represent mathematical thinking using mathematical symbols; whereas computations can be done on paper, in your head, or on a calculator.

6) Let him do the rest of his work independently, but remind him of the multiple tick idea and that you are really working on the next level of mathematics. Remind him to check his note card if he has forgotten what the proper workings look like. 

 

Slow and steady wins the race.  This takes time, but is worth it.

 

Ruth in NZ

Edited by lewelma
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I've just finished my post, so go back up and read the rest because I think I answered your question.

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I've just finished my post, so go back up and read the rest because I think I answered your question.

 

Yes, mostly. For the notebook, do they do one problem per page, or divide the page into sections? And then cards would be in an index card box just like other flash cards. I love these ideas - so very helpful.

 

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Notebook:  I used graph paper notebooks with biggish boxes.  I rule every page in red down the middle. The half width double column approach helps kids to work *down* rather than across which will soon be a requirement.  For a kid who does written computations, the left side is for the mathematical workings, and the right side is for computations.  Usually you can get about 5 problems per page, but we just keep using the page until either the left or right side is full. So it could be 1 very long problem or 10 short ones.  We skip lines between every mathematical workings line.  The computation side can be used in anyway the student desires.  My way on the mathematical workings side, their way on the computation side (as long as they are getting it right).

 

For a kid who does mostly mental computations, I rule the notebook down the middle, and then cut the right hand side in half and they use the bottom right hand box for computations. The other 3/4 of the page is for mathematical workings.  Even kids who do 100% mental computations, I still require the small 1/4 page box for scrap, and remind them that sometimes it is worth writing down a single number from an earlier computation so you don't have to hold it in your head.  It also allows me to have a place to work with them if their mental computation is wrong.  We will redo the incorrect computation in the box, even if we do it in a mental maths notation rather than an algorithm. (so stepping stones on a number line or whatever tool their mental calculation used)

 

The computation box can be messy (as long as they are getting the answers correct), it can also be used for scrap paper, brainstorming, sloppy diagrams, etc.  I don't look at the computation box unless they are getting the computation wrong, and then we sit down and brainstorm a plan (no harping, no arguing, just matter of fact working together to see how they can get it right using their technique or a new one, etc).  But the mathematical workings area is to be very tidy -- labelled in red with the topic across the top, ruled in red, checked in red.  The rest is in pencil (or pen but then crossing out must be a single line through).  As I said before, a tidy notebook can actually cause a kid to be more focused and pay more attention to detail.  So I require it.  This lay out reinforces the importance of the mathematical working, by underplaying the computation.  Basically the message is: computation in primary school work, do it as you want as long as you get it right. This encourages them to focus more diligently on the mathematical workings/thinking, and also helps them to own the accuracy of the computation.

 

Note cards:  I use the big ones and skip lines. I ask the kid how they want to write it so that they can replicate it in the future (they need to own it.  The card is for them, not me).  Some kids want a generalized statement, others like an example with units.  Some like both.  I always put a short note like 'averages:' or 'Trig:' These cards are just a temporary stop gap until they can understand what is required.  Typically younger kids need to use them for about 6 months, older kids 2 months.  Really depends on the kid.  And you might need 5 cards total.  10 if you are using the little ones.  It is easier for a kid to find what they are looking for if you have a geometry card, algebra card, numeracy card, etc.  I find that kids will ask me a year later when they are doing something as review and have long since gotten rid of the cards, "now, what was the workings that I need to write out?"  This is a very good sign.  Yes, they have forgotten, but yet they know that there are proper statements that are required to organize and show their thinking.  They relearn very very quickly.

Edited by lewelma
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I just found a worksheet in the end of year stuff brought home. Dividing 4 digit numbers by 8 mentally by halving 3 times. He has scribbled interim results. Between the questions but got a lot wrong in the last step. I feel really sorry for the year 9 teachers.

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Notebook:  I used graph paper notebooks with biggish boxes.  I rule every page in red down the middle. The half width double column approach helps kids to work *down* rather than across which will soon be a requirement.  For a kid who does written computations, the left side is for the mathematical workings, and the right side is for computations.  Usually you can get about 5 problems per page, but we just keep using the page until either the left or right side is full. So it could be 1 very long problem or 10 short ones.  We skip lines between every mathematical workings line.  The computation side can be used in anyway the student desires.  My way on the mathematical workings side, their way on the computation side (as long as they are getting it right).

 

For a kid who does mostly mental computations, I rule the notebook down the middle, and then cut the right hand side in half and they use the bottom right hand box for computations. The other 3/4 of the page is for mathematical workings.  Even kids who do 100% mental computations, I still require the small 1/4 page box for scrap, and remind them that sometimes it is worth writing down a single number from an earlier computation so you don't have to hold it in your head.  It also allows me to have a place to work with them if their mental computation is wrong.  We will redo the incorrect computation in the box, even if we do it in a mental maths notation rather than an algorithm. (so stepping stones on a number line or whatever tool their mental calculation used)

 

The computation box can be messy (as long as they are getting the answers correct), it can also be used for scrap paper, brainstorming, sloppy diagrams, etc.  I don't look at the computation box unless they are getting the computation wrong, and then we sit down and brainstorm a plan (no harping, no arguing, just matter of fact working together to see how they can get it right using their technique or a new one, etc).  But the mathematical workings area is to be very tidy -- labelled in red with the topic across the top, ruled in red, checked in red.  The rest is in pencil (or pen but then crossing out must be a single line through).  As I said before, a tidy notebook can actually cause a kid to be more focused and pay more attention to detail.  So I require it.  This lay out reinforces the importance of the mathematical working, by underplaying the computation.  Basically the message is: computation in primary school work, do it as you want as long as you get it right. This encourages them to focus more diligently on the mathematical workings/thinking, and also helps them to own the accuracy of the computation.

 

Note cards:  I use the big ones and skip lines. I ask the kid how they want to write it so that they can replicate it in the future (they need to own it.  The card is for them, not me).  Some kids want a generalized statement, others like an example with units.  Some like both.  I always put a short note like 'averages:' or 'Trig:' These cards are just a temporary stop gap until they can understand what is required.  Typically younger kids need to use them for about 6 months, older kids 2 months.  Really depends on the kid.  And you might need 5 cards total.  10 if you are using the little ones.  It is easier for a kid to find what they are looking for if you have a geometry card, algebra card, numeracy card, etc.  I find that kids will ask me a year later when they are doing something as review and have long since gotten rid of the cards, "now, what was the workings that I need to write out?"  This is a very good sign.  Yes, they have forgotten, but yet they know that there are proper statements that are required to organize and show their thinking.  They relearn very very quickly.

 

Ruth, this is EXACTLY what we need to be doing. Thank you so much for the detailed information. We are on break after today for a couple of weeks but when we come back I'll be raring to go. In fact I will make cards for some of the things we've done so far so she can start using them right away.

 

 

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Notebook: I used graph paper notebooks with biggish boxes. I rule every page in red down the middle. The half width double column approach helps kids to work *down* rather than across which will soon be a requirement. For a kid who does written computations, the left side is for the mathematical workings, and the right side is for computations. Usually you can get about 5 problems per page, but we just keep using the page until either the left or right side is full. So it could be 1 very long problem or 10 short ones. We skip lines between every mathematical workings line. The computation side can be used in anyway the student desires. My way on the mathematical workings side, their way on the computation side (as long as they are getting it right).

 

For a kid who does mostly mental computations, I rule the notebook down the middle, and then cut the right hand side in half and they use the bottom right hand box for computations. The other 3/4 of the page is for mathematical workings. Even kids who do 100% mental computations, I still require the small 1/4 page box for scrap, and remind them that sometimes it is worth writing down a single number from an earlier computation so you don't have to hold it in your head. It also allows me to have a place to work with them if their mental computation is wrong. We will redo the incorrect computation in the box, even if we do it in a mental maths notation rather than an algorithm. (so stepping stones on a number line or whatever tool their mental calculation used)

 

The computation box can be messy (as long as they are getting the answers correct), it can also be used for scrap paper, brainstorming, sloppy diagrams, etc. I don't look at the computation box unless they are getting the computation wrong, and then we sit down and brainstorm a plan (no harping, no arguing, just matter of fact working together to see how they can get it right using their technique or a new one, etc). But the mathematical workings area is to be very tidy -- labelled in red with the topic across the top, ruled in red, checked in red. The rest is in pencil (or pen but then crossing out must be a single line through). As I said before, a tidy notebook can actually cause a kid to be more focused and pay more attention to detail. So I require it. This lay out reinforces the importance of the mathematical working, by underplaying the computation. Basically the message is: computation in primary school work, do it as you want as long as you get it right. This encourages them to focus more diligently on the mathematical workings/thinking, and also helps them to own the accuracy of the computation.

 

Note cards: I use the big ones and skip lines. I ask the kid how they want to write it so that they can replicate it in the future (they need to own it. The card is for them, not me). Some kids want a generalized statement, others like an example with units. Some like both. I always put a short note like 'averages:' or 'Trig:' These cards are just a temporary stop gap until they can understand what is required. Typically younger kids need to use them for about 6 months, older kids 2 months. Really depends on the kid. And you might need 5 cards total. 10 if you are using the little ones. It is easier for a kid to find what they are looking for if you have a geometry card, algebra card, numeracy card, etc. I find that kids will ask me a year later when they are doing something as review and have long since gotten rid of the cards, "now, what was the workings that I need to write out?" This is a very good sign. Yes, they have forgotten, but yet they know that there are proper statements that are required to organize and show their thinking. They relearn very very quickly.

Ruth, thank you for this! In preparation for beginning it with my daughter (and refreshing my own skills), I spent the weekend completing the first chapter of Foerster's Algebra 1 according to these instructions. It worked brilliantly! I can't wait to introduce this method to her. It will be the perfect scaffolding to help her transition from workbook-based arithmetic (math mammoth) to textbook-based higher math. I modified the notecards slightly by using small ones (which was all I had) and writing on them the definitions/essential info from each section of the chapter. Before taking the chapter test, I quickly reviewed the cards and found them very helpful! I feel much more prepared to teach Algebra, or really, to facilitate her self-teaching. This text is so clear and she is so independent that I anticipate she'll prefer to just work through it alone. Anyway, thanks OP for bringing this up and thanks Ruth for offering such specific, helpful advice.
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