Jump to content

Menu

solving math problems on paper


Recommended Posts

DS11 (today is his birthday!) is working through AoPS pre-algebra. Back in the fall, he would write out pages and pages of beautiful work to solve out problems. (I used to text pictures to my BFF, who is a college math professor, because they were so nice!) At the time, my only complaint is that he would write across the page, rather than down the page. Fast-forward to lately, and it is an absolute battle every single day to get him to write down anything at all besides the answers. (If and when he does write things out, steps are still horizontally across the page, rather than down, but this is now the least of my concerns.) Usually, he will sit for a while, talking math calculations out loud to himself, and then he writes down the answer. When he goes back to check the answers, it is impossible for him to figure out where any mistakes were made, because he has no written work to consult. (FWIW, he doesn't get many wrong, so this doesn't seem to be a problem to him.) 

I am frustrated that he won't write out his work.  We worked really hard last year, when finishing up Beast Academy, to write out solutions in full. We've talked over and over about how mathematics is a language, and he needs to be able to communicate his thoughts and solutions to other people, clearly and logically, on paper. But, he JUST WILL NOT DO IT.  Add into all of this the physical growth he's had in the last year, and the long periods of cloudy-hormone-growth-spurt-brain, and I don't know how to handle this. (He's grown several clothing and shoe sizes over the last year; as my husband says, 'He's going to be a big dude.") If I had the disposable income, I would just enroll him in AoPS pre-algrebra 2 and have him be required by someone else to write out some of the work. DH is home during this time, but he's no help on school work. 

Any ideas on how to approach this? Or, should I just let it go for pre-algebra, and start the fight anew when we start the algebra book? 

Link to comment
Share on other sites

I'm chuckling a bit because we had the same hiccup with our oldest at that point with the same book.  I'm so sorry.  Don't each chocolate chips like I did, daily. I'm still working to lose that weight. 🙂 Writing the solution IS solving the problem. Coming to the correct answer is only part of the solution.   

We ended up switching away from AOPS pre-algebra. It wasn't a great fit personality wise for Oldest, and the battle was seen in writing the proofs.  We went to Aufmann instead (which is used in Chalkdust). The algebra book from AOPS is written in a different style, and you can probably go back to it, but Oldest decided to stick with Chalkdust and did all the way through.  His first day of college calculus was spent with the professor lecturing about formatting writing solutions.  I felt a bit validated....8 years later.

  • Like 1
Link to comment
Share on other sites

Ooooh, that's hard. I'm a stickler for written, logical work. But since he's able to do a large portion of the problems in his head accurately, and he's demonstrated in BA and PreA that he knows how to write solutions, what would happen if--just for the rest of PreA-- you made the rule that when he misses a problem done mentally, he must write out the full solution on his 2nd attempt before trying again?

 

Or if you looked over the work ahead of time, designated 2-3 problems as MUST SHOW FULL SOLUTION and then let him solve the remainder of the problems however he liked?

Edited by mathmarm
another suggestion.
  • Like 2
Link to comment
Share on other sites

54 minutes ago, mathmarm said:

Ooooh, that's hard. I'm a stickler for written, logical work. But since he's able to do a large portion of the problems in his head accurately, and he's demonstrated in BA and PreA that he knows how to write solutions, what would happen if--just for the rest of PreA-- you made the rule that when he misses a problem done mentally, he must write out the full solution on his 2nd attempt before trying again?

 

Or if you looked over the work ahead of time, designated 2-3 problems as MUST SHOW FULL SOLUTION and then let him solve the remainder of the problems however he liked?

Both of these are great ideas. Thank you very much!

  • Like 1
Link to comment
Share on other sites

2 hours ago, prairiewindmomma said:

I'm chuckling a bit because we had the same hiccup with our oldest at that point with the same book.  I'm so sorry.  Don't each chocolate chips like I did, daily. I'm still working to lose that weight. 🙂 Writing the solution IS solving the problem. Coming to the correct answer is only part of the solution.   

We ended up switching away from AOPS pre-algebra. It wasn't a great fit personality wise for Oldest, and the battle was seen in writing the proofs.  We went to Aufmann instead (which is used in Chalkdust). The algebra book from AOPS is written in a different style, and you can probably go back to it, but Oldest decided to stick with Chalkdust and did all the way through.  His first day of college calculus was spent with the professor lecturing about formatting writing solutions.  I felt a bit validated....8 years later.

So. Many. Chocolate chips! 😉

I like the statement that is in bold above. I'am going to use that, thanks!

Edited by Noreen Claire
Link to comment
Share on other sites

Maybe the amount of writing has increased and he finds it tiring to do? Has the level of math increased so that he needs to give more energy towards understanding it? Or, especially if it has appeared very recently, is he absorbing the stress of the situation worldwide? He may have enjoyed the act of writing before and it is no longer novel and interesting? Think about what may have changed since the "good old days" of beautiful solutions. It may very well be the growth spurt.

Mathematical understanding and the ability to communicate a solution in writing are separate skills. I am no expert, but I hesitate to prioritize writing solutions over love of math/mathematical understanding and knowledge. He has time to develop the skill of writing every solution fully. I like mathmarm's suggestion to designate problems (although I would choose 1 problem per day) in which he needs to write a full solution and allow him to explain orally how he did other problems. Continue to talk about how mathematics is communication so he doesn't forget in the interim.

Hope that helps!

  • Like 2
Link to comment
Share on other sites

Noreen, if it makes you feel better, Sacha is also 11 and this has been an ongoing battle for us. I have made the decision to take him out of the AoPS Academy classes and put him entirely into the AoPS online classes (we had been doing a mixture of both) to force him to do the writing problem once per week. There were no writing problems in the Academy classes and it was becoming a problem for us because he would consistently get green/blue in his problem sets each week and in Alcumus only to bomb his exams, in part, because he wouldn't write out his solutions so his professor could never award him partial credit if he made small errors on his exams (he also has ADHD and some fine motor issues, and the time pressure on the written exams is also an issue, but we never ask for any accommodations). Anyway, I agree with the other suggestions in just doing a small amount of writing to develop the logical communication/proof writing skill apart from the problem solving skills.

Edited by SeaConquest
  • Like 2
Link to comment
Share on other sites

On 4/11/2020 at 8:40 AM, square_25 said:

And what is the purpose of doing that all the time for questions that are obviously already easy for him?

Honestly, once he stopped writing out his solutions his work got *much* slower, which I think is partly because the problems are more complex and partly because he is trying so hard to hold all the numbers/calculations in his head. When he does write things down, he just works faster! He's got a perfectionism streak, and I think he believes that has should be able to continue to do all the work in his head, like he used to when it was easier. 

When he starts the next chapter next week, we will put in place the practice of writing out on one or two problems in each section, chosen by me in advance, and see how that goes for a few weeks. We weren't planning to take an April vacation this week but, with DS7's concussion, everyone will have an easy week this week...including me!

Link to comment
Share on other sites

15 minutes ago, SeaConquest said:

because he wouldn't write out his solutions so his professor could never award him partial credit if he made small errors on his exams

This is my point that I make to him - if he doesn't write the work down then, when he gets a problem wrong, we cannot easily identify if he made a simple calculation error or if he didn't understand the problem or whatever the issue was.

We might alternate some chapters where he only works out one or two problems that I pick in advance and some chapters where he only has to write out full solutions for the problems that he gets wrong on the first try.

Link to comment
Share on other sites

On 4/13/2020 at 12:59 PM, Noreen Claire said:

Honestly, once he stopped writing out his solutions his work got *much* slower, which I think is partly because the problems are more complex and partly because he is trying so hard to hold all the numbers/calculations in his head. When he does write things down, he just works faster! He's got a perfectionism streak, and I think he believes that has should be able to continue to do all the work in his head...”


Yup. I’m already dealing with this from DS7... I’d guess we have a long road of head-desking ahead of us. 🙃

  • Like 1
Link to comment
Share on other sites

On 4/13/2020 at 10:59 AM, Noreen Claire said:

Honestly, once he stopped writing out his solutions his work got *much* slower, which I think is partly because the problems are more complex and partly because he is trying so hard to hold all the numbers/calculations in his head. When he does write things down, he just works faster!

I have a 17yo bonus student who does this in Algebra 2.  He takes *absolutely forever* to do things that would be fairly quick if he would just write everything down.

I actually wrote up a 1500 word dissertation explaining all of the reasons he needed to write out his work beyond "because I said so."  I haven't given it to him yet because I'm pretty sure it would go in one eye and out the other.  

  • Haha 1
Link to comment
Share on other sites

1 hour ago, square_25 said:

Ah, hmmm. Can you give me an example of a problem like this? And how much writing would you want him to do? 

The problem that he got wrong today was: (abbreviated) A train travels 324 mi at 50mph and makes the return trip at 40mph. To the nearest tenth of a mile, what was the train's average speed for the 648 mi trip? 

So, you have to calculate the time (first part), calculate the time (second part), calculate the time (total), and divide the distance (total) by the time (total) to the nearest tenth of a mile. He attempted the solution without writing any numbers down, trying to keep them all straight in his head. He got the answer wrong, but I'm not sure if he made a conceptual mistake or if he made a computational mistake, because he wrote only the answer! It also took much longer than it should have, because he had to keep revisiting the numbers he was trying to remember so he wouldn't forget them before he got to the point where he needed to use them (I think?).

Anyway, we will start our work tomorrow by working that problem again. 

  • Like 1
Link to comment
Share on other sites

40 minutes ago, square_25 said:

Hmmmmm. Would you be OK if he just jotted some notes to himself or do you want him to write out a full solution?

I would be thrilled if he would jot some numbers down while he solved the problem - it would make his thinking go so much faster.

I do also want him to practice writing out a full solution every once in a while, and to recognize the importance of being able to logically communicate your solution on paper to another person. 

Link to comment
Share on other sites

  • 2 weeks later...

In our case, I'm finding this is sort of working itself out on its own. I used to work really hard to get him to write out something (ANYTHING!! lol) in BA, all to no avail, and I worked on it a lot the first 2-3 months of preA before finally throwing in the towel and letting him off without writing out full solutions (he is dysgraphic, so there is more to his not writing things down than the "normal" refusal, and I have three younger kids who are also 2E that needed my attention during the day). While my ds10 can do an amazing amount of work in his head, by the end of the AoPS prealgebra book, he was increasingly getting problems wrong. He primarily works on alcumus, and he started to just get really frustrated with getting so many wrong. After a few weeks/months of gentle prodding on my part, he was able to see the value himself in writing things down to help him keep track. Increasingly, I find him starting to write things down (varying from chicken scratches to full solutions), especially on the more complicated problems, so I'm hopeful we'll keep going in that direction! I have a degree in math, and hope to turn him into a proof writer one of these days, yet. 😄 

  • Like 3
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...