Math People: Why does my daughter want to do her Algebra from left to right?

[...................]

So basically, she's using TT Geometry.  Last year she did all her math and mathnasium and I constantly heard "your daughter is very smart but she doesn't show her work..."

Now she is doing Algebra within her TT Geometry and after a big huge to-do here about her showing her work I am looking it over and she does all the Algebra from left to right. Since she does it all in her head, she's really just writing three random steps so that she can say "I showed my work"  

If I ask her to show me every single step that went on in her brain, she starts crying.  She literally tears up and gets frustrated.  If I say ok, show me how you would show your work, she does a problem that would take me (granted I am very sequential and slow) about 7 steps, in two, the first and the answer.  That's it.  Everything else was in her head.  The subtraction, the canceling, the combining, the division- all in her head.

So I said you have to show as much work as you can, and she said "If I do I get completely lost and have no idea where I was" 

So I'm like ok, well I like it that you showed three steps here when you really preferred to show only one, so I appreciate that you are writing down at least one intermediary step.  BUT I need you to do them from TOP TO BOTTOM and she was rather upset again- crying -very frustrated...

I explained and explained and explained that when she gets to ALg 2 and pre-calc she will absolutely need more steps and they cannot be done  in her head and that they'd run off the side of the paper and then she wouldn't know where she was. She finally agreed only because I threatened to have her use a different math program where a person of authority would be grading it and reminding her of these things because I am not going to have a fight all the time.

BUT what on God's green earth would make someone be so insistent about working left to right when they do all the darn problems in their head anyway?  Seems to me if you're doing it all in your head it doesn't even matter!

Edited October 23, 2018 by Calming Tea

[regentrude]

what do you mean by "left to right"???

ETA: Is she writing several equations on one line?

Is she connecting statements with equal signs that are not, in fact, equal? (A common issue with students who write run-on "equations" but do operations that cause the end not to be equal to the front)

Edited October 23, 2018 by regentrude

[...................]

nope, she just writes the "steps" from left to right

[regentrude]

2 minutes ago, Calming Tea said:

nope, she just writes the "steps" from left to right

can you be more specific? how exactly does she write them? as separate equations, but on a single line?

[...................]

my work looked like this:

90+B=2B-6

+B            +B

    90=3B+6

96=3B 

(a this step I would draw a divide line and divide on both sides but don't know how to type that in here)

B=32

 

Hers is

90+B=2B+6     90=3B+6  32=B  (and that second step would most likely be missing if it wasn't for her trying to show at least something in the middle for me)

It's just that she prefers to work from left to right as she's solving things...rather than top to bottom.  She Is able to do it and showed all her work really well after I came back to check, and did it from top to bottom but it's still very frustrating to her and I just don't know why.  

[...................]

I mean I get why it's frustrating to show more work.  It takes time and she is so fast, it actually trips her up to have to write it out neatly.  So that, I get.  Even though I'm sticking to my guns about it ?

What I don't get is why someone would really want to work from left to right, and be so very frustrated by changing that.

[Arcadia]

12 minutes ago, Calming Tea said:

If I ask her to show me every single step that went on in her brain, she starts crying.  She literally tears up and gets extremely angry.  If I say ok, show me how you would show your work, she does a problem that would take me (granted I am very sequential and slow) about 7 steps, in two, the first and the answer.  That's it.  Everything else was in her head.  The subtraction, the canceling, the combining, the division- all in her head.

So I said you have to show as much work as you can, and she said "If I do I get completely lost and have no idea where I was" 

 

For DS12, he can’t think and write at the same time very well until recently. Physics actually helped him write down his working for math. Chemistry too but not as much as physics. Writing down breaks his train of thought so he cries. If you ask him to explain, he is basically redoing the question. Now he can remember most of what he was thinking so he can “regurgitate” the steps on paper after working the problem out mostly in his head. DS13 can’t write as fast as he thinks but has the benefit of a good memory so he can regurgitate the working after writing down the answer. 

What happens if you ask your daughter to do the work verbally because the bottleneck seems to be putting the steps down on paper. She is writing math the way people write essays. How does she write her poetry? Or how does she read sonnets? Wondering if it is a vision tracking issue.

[regentrude]

7 minutes ago, Calming Tea said:

my work looked like this:

90+B=2B-6

+B            +B

    90=3B+6

96=3B 

(a this step I would draw a divide line and divide on both sides but don't know how to type that in here)

B=32

 

Hers is

90+B=2B+6     90=3B+6  32=B  (and that second step would most likely be missing if it wasn't for her trying to show at least something in the middle for me)

It's just that she prefers to work from left to right as she's solving things...rather than top to bottom.  She Is able to do it and showed all her work really well after I came back to check, and did it from top to bottom but it's still very frustrating to her and I just don't know why.  

Honestly, I don't think writing it like this is  a big issue. It will resolve itself once the math gets hard enough that each side of the equation is long, or if she gets an outside teacher who mercilessly deducts points.

As for skipping the middle step: a student who is advanced in algebra would not need the intermediate step; it is something I would require of a beginner, but not of a student who is already proficient in algebra.

[...................]

I think Arcadia’s questions about poetry helped! 

 

I asked dd how she writes poetry and she said each line in poetry is a NEW THOUGHT so it makes sense to give it a new line.

each step in math is the same

thought and that’s why she says she really has a hard time giving it a new line and it makes it even harder for her to write it down because she’s already slowing herself down by writing it in the frost place. 

 

 

[regentrude]

6 minutes ago, Calming Tea said:

 

What I don't get is why someone would really want to work from left to right, and be so very frustrated by changing that.

I have a lot of students who do that. They squeeze all their homework onto a single sheet of paper. Usually they mend their ways when they run into problems and see that taking more space will improve accuracy. But as long as they get everything correct, they won't change.

[...................]

So Reg, should I tell her never mind write it how she wants? 

I did just convince her to write top to bottom. And she’s doing it though it’s hard. 

[...................]

Thanks so much guys at least now we understand why and also I won’t worry too much. 

 

 

 

[forty-two]

5 minutes ago, Calming Tea said:

I mean I get why it's frustrating to show more work.  It takes time and she is so fast, it actually trips her up to have to write it out neatly.  So that, I get.  Even though I'm sticking to my guns about it ?

What I don't get is why someone would really want to work from left to right, and be so very frustrated by changing that.

My oldest finds shows her work to be really hard. It was a year of hard, frustrating work on both our parts for her to learn how to show her work in arithmetic (by which I mean writing out the equations in word problems, not showing all the procedural steps in calculating).  And today we just started learning how to write equations with letters and solving them algebraically, and there were horrible tears and cries of frustration.  At least for her, fussing about format would just be one more dang pointless thing in a whole series of pointless (and hard) things.  Could she just put semi-colons (and some white space) between the equations to separate them?

One thing I thought of wrt her frustration with showing her work was lewelma's discussion about showing *the* work instead of showing *your* work.  She said, wrt teaching her younger son, that *his* actual work was in fact unshowable - that his actual thinking was so non-linear that there was no way to express it in the usual, linear step-by-step way.  So learning to show *the* work actually involved learning a whole new way of thinking.  It wasn't just that he couldn't put his thoughts down on paper, but that his thoughts weren't *capable* of being shown logically on paper.  That really resonated with me, wrt teaching my oldest - that learning to show step-by-step work is learning a whole new kind of thinking.

[regentrude]

25 minutes ago, Calming Tea said:

So Reg, should I tell her never mind write it how she wants? 

I did just convince her to write top to bottom. And she’s doing it though it’s hard. 

If you can get her to write underneath, then that would be preferable (although I would no longer require her to show all steps in a simple algebra problem that is part of a geometry problem - just like we no longer require students to show work for their arithmetic once they moved past that stage).

The main thing with her way is that she needs to make sure there is enough white space so that the equations are clearly identified as separate. And eventually this will no longer work because one single equation will take up the whole line ? Then she will have to write underneath. 

I am curious how she writes out geometry problems. Proofs are a sequence of distinct thoughts. How does she write out a geometric proof that covers a page?

[...................]

Good question.  She does write her proofs the same way anybody would, line by line, from top to bottom 

[RootAnn]

1 hour ago, Calming Tea said:

my work looked like this:

90+B=2B-6

+B            +B

    90=3B+6

96=3B 

(a this step I would draw a divide line and divide on both sides but don't know how to type that in here)

B=32

 

Hers is

90+B=2B+6     90=3B+6  32=B  (and that second step would most likely be missing if it wasn't for her trying to show at least something in the middle for me)

It's just that she prefers to work from left to right as she's solving things...rather than top to bottom.  She Is able to do it and showed all her work really well after I came back to check, and did it from top to bottom but it's still very frustrating to her and I just don't know why.  

Am I the only one who can't get over the fact that this example starts out wrong (adding B to both sides instead of subtracting it) and thus is wrong?

I was going to say that I have a kid who insists on subtracting from left to right because he worked so hard on reading that way that he finds it difficult to start on the right and move left. (He usually does all his regrouping before he starts, so it works at this stage.

I actually have a kid who writes her math very similar to CT's example, but we are working on showing work, writing down the page, and circling her answer when she's done.

[...................]

I'm sure we did it right on paper, lol...we got hte right answer, I just was hurrying while copying it...it was about complementary angles so the original problem was probably 90-B ?

Edited October 23, 2018 by Calming Tea

[forty-two]

1 minute ago, RootAnn said:

Am I the only one who can't get over the fact that this example starts out wrong (adding B to both sides instead of subtracting it) and thus is wrong?

Oh, good catch!  My dd actually did the exact same thing today, and flipped out when I pointed it out to her.  She's pre-algebra, not geometry, but she just didn't understand how to write the work, although she already had the correct answer before we ever started figuring out how to show it.  I really think lewelma is on to something, that kids who jump straight to the answer and have a hard time showing or explaining it are using thought processes that aren't explainable in the usual linear, step-by-step method.  When I was teaching dd to write equations for word problems, she'd already have the answer, and then backfill the intermediate work.  She'd often make mistakes in those intermediate steps in the beginning, because she didn't understand what they were or why they mattered - correct or incorrect, they had nothing to do with how she actually solved the problem.  It took a lot of work for me to connect her intuitive understanding of the problem to the linear steps.  We did a lot of manipulative work, where she did the next step with the manipulatives and I wrote it down, because she could see with her eyes that the manipulative step was true, and she could see that the equation I wrote accurately reflected that step, and it helped give meaning to the otherwise meaningless steps.

[regentrude]

41 minutes ago, RootAnn said:

Am I the only one who can't get over the fact that this example starts out wrong (adding B to both sides instead of subtracting it) and thus is wrong?

I was going to say that I have a kid who insists on subtracting from left to right because he worked so hard on reading that way that he finds it difficult to start on the right and move left. (He usually does all his regrouping before he starts, so it works at this stage.

I actually have a kid who writes her math very similar to CT's example, but we are working on showing work, writing down the page, and circling her answer when she's done.

I noticed but I figured she was just slapping an example together to illustrate what she was talking about, so didn't feel the need to point that out.

[aprilleigh]

1 hour ago, Calming Tea said:

Good question.  She does write her proofs the same way anybody would, line by line, from top to bottom 

Your best bet, both for the vertical alignment and showing the work, would probably be to teach her to look at each problem as a proof. She has to show WHY it works that way. However, I agree with everyone else here that, once she's proven that she CAN show the work, insisting she show work for skills she's mastered it just a recipe for frustration.

[...................]

Hey I’ll tell her that! That makes sense.

[BusyMom5]

For my DD that does well, I accept a second line that has variables on one side, known numbers on the other.  So in your example I made her write the original problem on the first line, regrouped into Bs on one side and numbers on the other side on the second line.  After you get a few variables she automatically started writing each step, but she would do more than one on the same line.    

 

I also had the thought that moving horizontal across the page may be her way of expressing moving chunks og numbers. Think back to 3rd grade or so, when they have kids moving ones or tens in chunks.  

I think you might be worrying a little too much.  

[almondbutterandjelly]

I did want to mention that in way upper level math, it can be perfectly acceptable to write your work left to right, but you do have to put an arrow between each step.  It means "if that, then this."  Also, college level proofs in analysis are written in paragraph form, so left to right isn't such a terrible habit, IMO.