How to help teenager fix silly mistakes in math?

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n00b_to_investing
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How to help teenager fix silly mistakes in math?

Post by n00b_to_investing » Thu Sep 13, 2018 3:52 pm

an unusual topic for this esteemed forum but hoping to get some advice on how to support and help my teenager improve math skills. She continues to make silly mistakes like missing the "-" sign, occasionally copy original questions incorrectly, skipping a question in test etc. I tell her to review her work, write legibly, go slow ... she gets frustrated and dejected when I ask her to go back and find her mistakes. I see the occasional brilliance where she would solve complex computations in her head even before I finish reading the question, and then sometimes she is sloppy and will not add numbers correctly. She had vision issues (seeing double etc) in the past, which has largely been addressed with vision therapy/prisms.

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Re: How to help teenager fix silly mistakes in math?

Post by Alexa9 » Thu Sep 13, 2018 3:55 pm

Computer Programs
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Get tested to see if it is a medical issue

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Re: How to help teenager fix silly mistakes in math?

Post by Thesaints » Thu Sep 13, 2018 3:57 pm

This is the cause
n00b_to_investing wrote:
Thu Sep 13, 2018 3:52 pm
I see the occasional brilliance where she would solve complex computations in her head even before I finish reading the question,
and this is a consequence
and then sometimes she is sloppy and will not add numbers correctly.
Last edited by Thesaints on Thu Sep 13, 2018 4:01 pm, edited 1 time in total.

student
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Re: How to help teenager fix silly mistakes in math?

Post by student » Thu Sep 13, 2018 4:00 pm

I would say that she should not skip steps until the sloppiness is gone.

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Re: How to help teenager fix silly mistakes in math?

Post by delamer » Thu Sep 13, 2018 4:05 pm

I used to work with a guy who had a PhD in statistics who always said he was lousy at math. In other words, he made stupid reading and transposition errors.

You could try having her put her answer back into the original equation to see if it works, as a check.

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Re: How to help teenager fix silly mistakes in math?

Post by sport » Thu Sep 13, 2018 4:09 pm

DW works in the schools. Her advice is to ask the school for advice. There may be a guidance counselor, psychologist, or specialist who can provide professional advice.

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Re: How to help teenager fix silly mistakes in math?

Post by nisiprius » Thu Sep 13, 2018 4:09 pm

I don't have any answer.

When I was a substitute teacher I would always tell students "Unless your teacher has told you to do it mentally, write it out. Write every single step, one step at a time. Don't try to combine steps in your head. You don't get extra points for doing it in your head. If you write out all the steps, you are giving your teacher the opportunity to give you partial credit. More important, if you do have something wrong, showing all the steps will give your teacher a better chance of seeing where you went wrong and helping you."

In the case of your kid, I would separate two issues. First, praise her for understanding the math. Second, suggest that learning how to avoid mistakes is actually a skill in itself, to be learned separately. Avoiding errors and checking for errors is actually a creative task. And, unfortunately, it is extra work, because, in one form or another, it always amounts to working the problem twice.

I'm tempted to say "introduce her to computer programming!"
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Re: How to help teenager fix silly mistakes in math?

Post by lotusflower » Thu Sep 13, 2018 4:14 pm

Here's what I tell my kids: Nobody likes to proofread their own writing or their own math, but you have to put your big kid pants on and do it. Also if you want to do music (or any skill-based activity) it more effective to go slowly and get rid of mistakes and then speed up after you have control, than it is to max out our your speed before starting to reduce mistakes. Math is not really any different.

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Re: How to help teenager fix silly mistakes in math?

Post by daveydoo » Thu Sep 13, 2018 4:21 pm

Time.

Especially if it's a younger "teenager."
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Re: How to help teenager fix silly mistakes in math?

Post by Fallible » Thu Sep 13, 2018 4:37 pm

sport wrote:
Thu Sep 13, 2018 4:09 pm
DW works in the schools. Her advice is to ask the school for advice. There may be a guidance counselor, psychologist, or specialist who can provide professional advice.
This would also be the advice of my relatives who were teachers, especially considering some of the mistakes described and the vision issue.

OP, what is your daughter's age? Have you talked with her teachers? Does she have problems with other subjects?
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Re: How to help teenager fix silly mistakes in math?

Post by Abe » Thu Sep 13, 2018 4:45 pm

Have you ever considered the possibility that she may have dyslexia. The reason I say this is because I am dyslexic, and I see what appears to be symptoms of dyslexia in your daughter.

Edited to add: I experienced most everything you described about your daughter. Even this, " I see the occasional brilliance where she would solve complex computations in her head even before I finish reading the question". Many times I would know the correct answer to a problem, but I couldn't arrive at the answer the way the teacher taught it, I had to do it my own way.
Last edited by Abe on Thu Sep 13, 2018 5:04 pm, edited 1 time in total.
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grayfox
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Re: How to help teenager fix silly mistakes in math?

Post by grayfox » Thu Sep 13, 2018 4:50 pm

The best way to expose errors is to find a solution two different ways. They should agree. If not, there is something wrong with one or both.

A variation on this is to make a rough calculation as a sanity check. For example, what the sign should be? What order of magnitude are you expecting?

Also, dimensional analysis. What unit are you expecting? kg * m^2 /s^2 ?

Or plug the solution into the original equation and show that it works.

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Re: How to help teenager fix silly mistakes in math?

Post by livesoft » Thu Sep 13, 2018 4:54 pm

My sister recounted the discovery that my 3rd grade nephew didn't know how to read. He had been in an excellent school mostly because his sisters were outstanding students. I'm just writing this is because sometimes teachers (and parents) don't see what's in front of their face.

Other advice in the thread is excellent.
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Re: How to help teenager fix silly mistakes in math?

Post by kaneohe » Thu Sep 13, 2018 4:57 pm

Agree w/ the advice to get a 3rd party in the school involved. Even if they do exactly the same thing that you
would do, it's kind of like hiring somebody to teach them how to drive. Removes the family element which tends
in many cases to cause more friction for some reason.

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Re: How to help teenager fix silly mistakes in math?

Post by jayk238 » Thu Sep 13, 2018 4:58 pm

Sometimes these types of issues can be due to underlying learning issues-dyslexia, thyroid, etc. no harm in getting tested so she can be treated instead of struggling all her life.

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Re: How to help teenager fix silly mistakes in math?

Post by Grt2bOutdoors » Thu Sep 13, 2018 5:02 pm

It’s a consequence of social media. In social media driven world, everything is quickly done and final. Your daughter is not alone in that regard. May I suggest approaching the homework in sections, one question at a time. One equation at a time, break each part of the solution into parts, review for accuracy then compile and present complete solution. This coming from someone who is not fond of math.
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Re: How to help teenager fix silly mistakes in math?

Post by Mjar » Thu Sep 13, 2018 5:07 pm

n00b_to_investing wrote:
Thu Sep 13, 2018 3:52 pm
an unusual topic for this esteemed forum but hoping to get some advice on how to support and help my teenager improve math skills. She continues to make silly mistakes like missing the "-" sign, occasionally copy original questions incorrectly, skipping a question in test etc. I tell her to review her work, write legibly, go slow ... she gets frustrated and dejected when I ask her to go back and find her mistakes. I see the occasional brilliance where she would solve complex computations in her head even before I finish reading the question, and then sometimes she is sloppy and will not add numbers correctly. She had vision issues (seeing double etc) in the past, which has largely been addressed with vision therapy/prisms.
tell them to slow down and recheck their work before they submit. My daughter does the same thing. When she is done and wants me to look it over I ask her go back and check it then I will review it. Most times she catches her own mistakes.

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Re: How to help teenager fix silly mistakes in math?

Post by downshiftme » Thu Sep 13, 2018 5:22 pm

Agree w/ the advice to get a 3rd party in the school involved.
Maybe you will get lucky and run into the rare caring and competent school who can diagnose and help fix student math issues. We tried numerous times and we never did. We got lots of blame and defensiveness, but ultimately we were on our own to find the right combination of focus and actual math knowledge that got us unstuck. Some math teachers are not all that competent in math themselves, and those that are are sometimes unable to explain it to students, or only able to explain it one way that doesn't connect and are unable to give any alternate explanations or understand student questions about the explanation that they do give. It's even worse in elementary school. We found tutors and outside math classes solved the issues, but it took some trial and error to find one that worked well.

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Re: How to help teenager fix silly mistakes in math?

Post by kaneohe » Thu Sep 13, 2018 5:30 pm

downshiftme wrote:
Thu Sep 13, 2018 5:22 pm
Agree w/ the advice to get a 3rd party in the school involved.
Maybe you will get lucky and run into the rare caring and competent school who can diagnose and help fix student math issues. We tried numerous times and we never did. We got lots of blame and defensiveness, but ultimately we were on our own to find the right combination of focus and actual math knowledge that got us unstuck. Some math teachers are not all that competent in math themselves, and those that are are sometimes unable to explain it to students, or only able to explain it one way that doesn't connect and are unable to give any alternate explanations or understand student questions about the explanation that they do give. It's even worse in elementary school. We found tutors and outside math classes solved the issues, but it took some trial and error to find one that worked well.
Completely agree........was mainly trying to get 3rd party involved to eliminate the family friction element.
Should not have restricted it to school.

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Re: How to help teenager fix silly mistakes in math?

Post by jj45 » Thu Sep 13, 2018 5:35 pm

Often, these kind of mistakes fall into a rather narrow range of the kinds of manipulations that a student gets wrong. But different people make different kinds of mistakes. If you learn the kind of mistakes you tend to make, you can make a point of being slow and careful when doing those particular kinds of steps, without having to be tediously slow the entire time. It's like in spelling, you don't look every word up in the dictionary, that would be terrible. You look up the ones you tend to misspell, and everyone has their own bugbears. So if you can work with your kid to help them identify which mistakes they tend to make, they can focus in on those steps in the math.

It is also important to help them realize that these kind of mistakes have nothing to do with someone's mathematical ability. Unfortunately high school is particularly bad in making people feel like they are bad at math because they make minus sign errors. Try to emphasize to them that this is as silly as thinking someone is a bad writer because they make spelling mistakes. It is so common as to be a stereotype, many excellent mathematicians did terrible in high school math because they made these kinds of mistakes.

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Re: How to help teenager fix silly mistakes in math?

Post by investor4life » Thu Sep 13, 2018 5:40 pm

Have her articulate (speak out loud) the problem and each step of the solution. That will help eliminate at least a few mistakes.

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Re: How to help teenager fix silly mistakes in math?

Post by jabberwockOG » Thu Sep 13, 2018 5:44 pm

Intelligence and learning can be quite high in a person but sometime it may not coincide perfectly with high end testing results. What may be missing is the personal desire and discipline to sweat the details in tests as well as in related intensive detail work. This should not be framed or implied to be a personal failing. Sometimes is just a person's nature and the way they are wired that they have no real interest in working in a manner required to achieve high scores in laborious multi step detail oriented tests.

Lots of good suggestions already posted, but I would also suggest being careful not to push too hard and to avoid framing a young person's potential success in life with being detail oriented and producing high math test scores. There is still a lot of room in the world to do quite well in areas that do not require high end scores in subjects like math and science. I used to tell my kids, the world has plenty of smart people, but what we need more than anything is more creative people and more good people.

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Re: How to help teenager fix silly mistakes in math?

Post by lightheir » Thu Sep 13, 2018 6:00 pm

Honestly, it's probably genetic for the most part.

They can likely 'improve' it with care and attention, but it will never truly go away.

I was the same way - I would make really stupid 'careless' seeming errors in complex mathematical work, but have the right algorithm for solving problems that peers in my top ivy league college couldn't even solve - even some of the best ones.

I'd commonly get 'you'd be brilliant at math if you didn't make stupid mistakes!' And believe me, I tried SOOO hard. This was a recurring theme throughout my life, as my mom clearly never, ever suffered this problem, and literally thought I was not trying hard enough or intentionally making errors since her brain would do nothing of the sort.

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Re: How to help teenager fix silly mistakes in math?

Post by Irisheyes » Thu Sep 13, 2018 6:11 pm

This is very reminiscent of my daughter when she was a middle schooler.

She starting getting low Bs and even a C in her math tests because she did sloppy work, made mistakes in her multiplication, wrote numbers down illegibly and then misread them on second step calculations, etc, etc. Conceptually, it was a breeze for her but the implementation of what she understood was awful.

We started going over together every single math assignment together at night. It made for a very painful couple months as we made her redo her work. It "helped" that her teacher was a stickler and marked her down ferociously every time these silly mistakes happened. Painstakingly, over the course of a few months, her work started improving as she learned to be more careful.

She's now a sophomore in the advanced math track at high school and at the top of her class. Those careful habits, which we hammered into her, have persisted and she is flying now in math. I remember how stressful those months were though. Good luck!

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Re: How to help teenager fix silly mistakes in math?

Post by dodecahedron » Thu Sep 13, 2018 6:14 pm

This is a very common phenomenon. I have two suggestions for reading:

Sanjoy Mahajanś classic book Street Fighting Mathematics, published by MIT Press. Paperback copies are relatively inexpensive on Amazon etc. but there is also a free ebook version that can be had if you enroll in MIT´s free OpenCourseware class, which is also titled Street Fighting Mathematics. It was originally offered as a one-month intensive class during MIT´s January Independent Activities Period. The idea is to cultivate the skill and habit of intelligently guessing results so that you can easily recognize a wildly wrong answer, which is often what results from a silly mistake.

Along somewhat similar lines, but specifically focused on calculus in particular, another classic book is Misteaks and how to find them before the teacher does.

Edited to add: she has plenty of distinguished company in making careless mistakes. In fact Nobel Laureate economist Joe Stiglitz was so famous for making sign errors that the term ¨Stiglitz transformation¨ was coined to refer to the phenomenon of flipping a sign downstream of the original error when you realize you must have made a sign error in an upstream step. His final results were generally correct (because he had a strong intuition of how things SHOULD come out) but his proclivity to make multiple (self-cancelling) sign errors in the exposition of the intermediate steps along the way has been legendary for decades.

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Re: How to help teenager fix silly mistakes in math?

Post by adamthesmythe » Thu Sep 13, 2018 6:37 pm

Ask her if she would be confident enough in her answers if a bridge would fall down if she were wrong.

And if that doesn't make a difference- don't let her major in engineering.

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Re: How to help teenager fix silly mistakes in math?

Post by rgs92 » Thu Sep 13, 2018 6:48 pm

I did this all the time but ended up majoring in math in college (and getting an M.S. later). I still do things like that.

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Re: How to help teenager fix silly mistakes in math?

Post by cheese_breath » Thu Sep 13, 2018 6:58 pm

Abe wrote:
Thu Sep 13, 2018 4:45 pm
Have you ever considered the possibility that she may have dyslexia. The reason I say this is because I am dyslexic, and I see what appears to be symptoms of dyslexia in your daughter.

Edited to add: I experienced most everything you described about your daughter. Even this, " I see the occasional brilliance where she would solve complex computations in her head even before I finish reading the question". Many times I would know the correct answer to a problem, but I couldn't arrive at the answer the way the teacher taught it, I had to do it my own way.
Since this isn't a medical forum we can't mention things like dyslexia or attention deficit disorder. But if we could I'd suggest you have her see a medical professional to eliminate these or other possibilities.
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Re: How to help teenager fix silly mistakes in math?

Post by Jags4186 » Thu Sep 13, 2018 7:03 pm

Unpopular opinion:

Perhaps your daughter isn’t as good in math as you think she is? Some people make lazy mistakes because they aren’t challenged. Others make lazy mistakes because they’re lazy. Others make mistakes because they are getting it wrong. Make sure you know which this is.

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Re: How to help teenager fix silly mistakes in math?

Post by Boglegrappler » Thu Sep 13, 2018 7:17 pm

Years ago, I was pretty decent at math on things like the SAT and other such tests.

I had good competency in the "multiplication tables", which, regrettably, I think very few kids today have. They are ignored by instructors.

When I took tests, I cared about getting the right answer, so I was concentrating hard and "trying". I also worked very quickly and usually did each problem twice to confirm that I had the right answer and hadn't made an error.

If doing the problem twice gives the wrong answer twice, then you are beginning to hone in on the source of her problem. A mistake caused by sloppiness will be found quickly. A mistake caused by conceptual problems will be made again. If its the latter, that's a longer fix.

Good luck. In the end, it depends on caring about getting the correct answer.

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Re: How to help teenager fix silly mistakes in math?

Post by whodidntante » Thu Sep 13, 2018 7:30 pm

I also tend to quickly assess things and react, and occasionally I miss the point. Anyway, don't pay off your mortgage.

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Re: How to help teenager fix silly mistakes in math?

Post by MSchleicher » Thu Sep 13, 2018 8:09 pm

Can you share an actual sample problem and her work? As a former teacher, I’m curious and want to take a closer look at her work. There may be an underlying reason for the mistake that may be mistaken for rushing or an oversight.

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Re: How to help teenager fix silly mistakes in math?

Post by Totrep » Thu Sep 13, 2018 8:59 pm

I tutor teenagers in math. Broadly speaking, you can reduce "silly" errors in a few ways:
(1) Slow down, do fewer mental computations and show more steps
(2) Check your work effectively (plug answers back in, evaluate your answer in the context of the problem)
(3) Get better at doing fast arithmetic and algebra

You have received some good suggestions in each of these areas. A major benefit of (1) is that it generates more opportunities for partial credit. But if your daughter is copying down questions incorrectly, she may copy down intermediate steps incorrectly as well, thus creating additional opportunities for things to go wrong.

If you have time to help and your daughter has a competitive spirit, you could work on (3) by racing her through each problem. The goal is simulate the stress and adrenaline of an exam and improve her ability to do quick calculations under these conditions. After the race, you would then discuss the key steps that a teacher needs to see to follow her train of thought.

Of course, one of the best tools for reducing simple math errors is ... a calculator. People worry about over-reliance on technology, but keep in mind that you are allowed to use calculators on some portions of the PSAT, SAT, ACT, SAT II Math, and AP Calculus exams. In all of those except the ACT, you can even use a calculator such as the TI-89 Titanium with a CAS (computer algebra system; it will symbolically solve equations, factor, etc). If you get in the habit of checking homework problems you did by hand with your calculator, you will not only detect errors but hopefully become more effective at using the calculator as well.

You can also use technology to help with (2). For example, if you solve a system of equations by hand with substitution, you can check the answer by solving graphically with desmos.com. Ideally, this will also deepen your understanding of the problem.
jj45 wrote:
Thu Sep 13, 2018 5:35 pm
Unfortunately high school is particularly bad in making people feel like they are bad at math because they make minus sign errors. Try to emphasize to them that this is as silly as thinking someone is a bad writer because they make spelling mistakes. It is so common as to be a stereotype, many excellent mathematicians did terrible in high school math because they made these kinds of mistakes.
+1. As someone who spent many years in college and grad school studying theoretical math, I can't tell you how frustrated this makes me. Hopefully, this problem will diminish as we grow more comfortable outsourcing basic algebraic manipulations to technology. In the meantime, I agree with nisiprius: remind her that while error avoidance is not math, it is a useful skill, and try to keep her upbeat while she practices it.

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Re: How to help teenager fix silly mistakes in math?

Post by livesoft » Thu Sep 13, 2018 9:06 pm

Another silly mistake is not looking both ways when trying to cross the road or when pulling out into a busy any road when driving
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Re: How to help teenager fix silly mistakes in math?

Post by brandy » Thu Sep 13, 2018 9:39 pm

This might be a perceptual processing disorder. Consider Irlen Syndrome https://irlen.com/what-is-irlen-syndrome/# . It is a problem with the brain’s ability to process visual information and affects many areas, including academic performance, reading/comprehension, math computation, etc, and there are possible remedies.
I used to teach, and several students were helped. My dd also has the problem, and uses an overlay.
Best wishes

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Re: How to help teenager fix silly mistakes in math?

Post by stan1 » Thu Sep 13, 2018 9:58 pm

Many different answers because people learn differently. There's a percentage of people who do well on traditional lectures, homework sets, and tests but that's not how everyone learns. I'd encourage her to try different techniques. One I used in math was to do the problem twice. If I came up with the same answer I was pretty confident it was right. If I came up with a different answer I knew I had done something wrong. I found this more useful and actionable than "checking my work".

I'll offer another option since you mention she often is a few steps ahead and might have some talent that isn't being developed. Computer programming is different than math but would help her develop complementary analytic and problem solving skills. Programming does enforce working through a process to solve a problem and it also allows for some creativity.
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Socrates28
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what grade?

Post by Socrates28 » Thu Sep 13, 2018 10:44 pm

what level math? does she like math or have other educational interests....e.g., science, history, English?

I am an Licensed Educational Psychologist and now work at a college, but was a school psychologist for 15 years

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Re: How to help teenager fix silly mistakes in math?

Post by MathWizard » Thu Sep 13, 2018 11:37 pm

grayfox wrote:
Thu Sep 13, 2018 4:50 pm
The best way to expose errors is to find a solution two different ways. They should agree. If not, there is something wrong with one or both.

A variation on this is to make a rough calculation as a sanity check. For example, what the sign should be? What order of magnitude are you expecting?

Also, dimensional analysis. What unit are you expecting? kg * m^2 /s^2 ?

Or plug the solution into the original equation and show that it works.
I am a mathematician. This is exactly the way I do things.

I don't consider that I know how to solve a problem unless I can solve it 2 completely different ways.

A trick bookkeepers used to do when adding a lagecoln of numbers by hand is to add from the top down, then add from the bottom up, and chech that the answer was the same.

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Re: How to help teenager fix silly mistakes in math?

Post by n00b_to_investing » Fri Sep 14, 2018 12:39 am

Thank you, everyone, for the suggestions.

We tried a few today during practice.
And in fact, I asked her to check her answers by plugging the result back in the original equation, which worked well and she was able to self-correct.
After a break, we went over the practice problems again ... this time I asked her to orally solve the problems.
Will continue to try different things and reinforce the need to show her work, don't do multiple steps at once etc.
Requested an appointment with the teacher too.

On a separate note, I can't say enough how thankful we are for the overwhelming response and support we are getting on this forum; its difficult to express our gratitude in words. I found courage from this forum to manage my investment, and today as a Dad getting help on personal matters brought tears of joy!!!

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Re: How to help teenager fix silly mistakes in math?

Post by criticalmass » Fri Sep 14, 2018 5:05 am

A really fast way to check math equations is to use Casting Nines or casting out nines. I’ve done this since elementary school to catch stupid errors.

Ex.
578
+123
———

Add digits, but whenever there is a 9 or digits add to 9, omit them. You can keep adding individual digits to speed things along. Keep doing this until your check digit is a single digit.

578 5+7=12...(1+2= 3) ……3 + 8 = 11...1+1= [2] <——- check digit for 578

123 1+2+3 = [6]

Now let’s add 578 and 123, we get 701. To check, we also add the check digits from casting nines.....

578. [2]
+123 [6]
——————

2+6= [8] ........Remember this number [8].

578 [2]
+123 [6]
—————-
701 7+0+1= [8]. That matches our check digit from before, so our addition work is correct.

It actually gets much faster in practice, and you can use various combinations when adding digits and casting all nines. It works because of our base 10 number system. Just use the same operation (+,-,x, etc) on the check digits as you do on the actual figures you are working with.

There are other examples and videos on the internet that are better than I can do on a BH forum, but you should get the idea. It’s been a fast math checker (great for exam situations) and stupid mistake checker for centuries. It’s not infallible because you have a one in ten chance that your wrong check digit could be the same as a correct one, but I’ll take those odds. And actually it’s even better than 1 in 10 because your mistakes are likely to be off by one, which casting nines will catch.

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Re: How to help teenager fix silly mistakes in math?

Post by oldcomputerguy » Fri Sep 14, 2018 7:09 am

I have a nephew who in his middle and high school days had constant struggles with, shall we say, less-than-pleasing grades. He is intelligent and has a quick mind, but couldn't do the work. They finally had him tested, turned out he was dyslexic. Once the condition was diagnosed, he, his parents, and his teachers were able to deal with it.
It’s taken me a lot of years, but I’ve come around to this: If you’re dumb, surround yourself with smart people. And if you’re smart, surround yourself with smart people who disagree with you.

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Re: How to help teenager fix silly mistakes in math?

Post by kaneohe » Fri Sep 14, 2018 7:56 am

criticalmass wrote:
Fri Sep 14, 2018 5:05 am
A really fast way to check math equations is to use Casting Nines or casting out nines. I’ve done this since elementary school to catch stupid errors.

....................................
interesting idea.....never heard of it before.........in simple words,why the heck does it work?
Might help me half the time. The other times, the error is writing the number down correctly from telephone input.

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Re: How to help teenager fix silly mistakes in math?

Post by nisiprius » Fri Sep 14, 2018 8:08 am

MathWizard wrote:
Thu Sep 13, 2018 11:37 pm
grayfox wrote:
Thu Sep 13, 2018 4:50 pm
The best way to expose errors is to find a solution two different ways. They should agree. If not, there is something wrong with one or both.

A variation on this is to make a rough calculation as a sanity check. For example, what the sign should be? What order of magnitude are you expecting?

Also, dimensional analysis. What unit are you expecting? kg * m^2 /s^2 ?

Or plug the solution into the original equation and show that it works.
I am a mathematician. This is exactly the way I do things.

I don't consider that I know how to solve a problem unless I can solve it 2 completely different ways.

A trick bookkeepers used to do when adding a large column of numbers by hand is to add from the top down, then add from the bottom up, and chech that the answer was the same.
Indeed. I suspect that the root problem is one I had myself as a kid: the amount of work. All strategies for preventing silly mistakes require roughly twice the work of just getting through it, because most of them really amount to doing the problem twice. And many of them require creative work (e.g. realizing that dimensional analysis can be used).
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

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Re: How to help teenager fix silly mistakes in math?

Post by investingdad » Fri Sep 14, 2018 9:04 am

Grt2bOutdoors wrote:
Thu Sep 13, 2018 5:02 pm
It’s a consequence of social media. In social media driven world, everything is quickly done and final. Your daughter is not alone in that regard.
No it isn't.

It's a product of personality.

My daughter is 13, is in Honors math, and is not prone to silly mistakes.

My son is 11, is in Honors math, and is prone to silly mistakes.

Both have minor, but similar, exposure to social media. My daughter a bit more than my son.

My son takes after me and my daughter after my wife. I was prone to silly mistakes back in the 80s until I finally broke the habit late in high school.

Both of us have/had a tendency to rush to be done with it.

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Re: How to help teenager fix silly mistakes in math?

Post by sport » Fri Sep 14, 2018 10:02 am

criticalmass wrote:
Fri Sep 14, 2018 5:05 am
A really fast way to check math equations is to use Casting Nines or casting out nines. I’ve done this since elementary school to catch stupid errors.

Ex.
578
+123
———

Add digits, but whenever there is a 9 or digits add to 9, omit them. You can keep adding individual digits to speed things along. Keep doing this until your check digit is a single digit.

578 5+7=12...(1+2= 3) ……3 + 8 = 11...1+1= [2] <——- check digit for 578

123 1+2+3 = [6]

Now let’s add 578 and 123, we get 701. To check, we also add the check digits from casting nines.....

578. [2]
+123 [6]
——————

2+6= [8] ........Remember this number [8].

578 [2]
+123 [6]
—————-
701 7+0+1= [8]. That matches our check digit from before, so our addition work is correct.

It actually gets much faster in practice, and you can use various combinations when adding digits and casting all nines. It works because of our base 10 number system. Just use the same operation (+,-,x, etc) on the check digits as you do on the actual figures you are working with.

There are other examples and videos on the internet that are better than I can do on a BH forum, but you should get the idea. It’s been a fast math checker (great for exam situations) and stupid mistake checker for centuries. It’s not infallible because you have a one in ten chance that your wrong check digit could be the same as a correct one, but I’ll take those odds. And actually it’s even better than 1 in 10 because your mistakes are likely to be off by one, which casting nines will catch.
While this is all true, it applies to arithmetic, not math. An analogy I like to use is that arithmetic is to math as spelling is to literature. If you are working on a problem In trigonometry, analytic geometry, or calculus, etc., "casting out nines" will not be useful.

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Re: How to help teenager fix silly mistakes in math?

Post by criticalmass » Fri Sep 14, 2018 1:14 pm

sport wrote:
Fri Sep 14, 2018 10:02 am
criticalmass wrote:
Fri Sep 14, 2018 5:05 am
A really fast way to check math equations is to use Casting Nines or casting out nines. I’ve done this since elementary school to catch stupid errors.

Ex.
578
+123
———

Add digits, but whenever there is a 9 or digits add to 9, omit them. You can keep adding individual digits to speed things along. Keep doing this until your check digit is a single digit.

578 5+7=12...(1+2= 3) ……3 + 8 = 11...1+1= [2] <——- check digit for 578

123 1+2+3 = [6]

Now let’s add 578 and 123, we get 701. To check, we also add the check digits from casting nines.....

578. [2]
+123 [6]
——————

2+6= [8] ........Remember this number [8].

578 [2]
+123 [6]
—————-
701 7+0+1= [8]. That matches our check digit from before, so our addition work is correct.

It actually gets much faster in practice, and you can use various combinations when adding digits and casting all nines. It works because of our base 10 number system. Just use the same operation (+,-,x, etc) on the check digits as you do on the actual figures you are working with.

There are other examples and videos on the internet that are better than I can do on a BH forum, but you should get the idea. It’s been a fast math checker (great for exam situations) and stupid mistake checker for centuries. It’s not infallible because you have a one in ten chance that your wrong check digit could be the same as a correct one, but I’ll take those odds. And actually it’s even better than 1 in 10 because your mistakes are likely to be off by one, which casting nines will catch.
While this is all true, it applies to arithmetic, not math. An analogy I like to use is that arithmetic is to math as spelling is to literature. If you are working on a problem In trigonometry, analytic geometry, or calculus, etc., "casting out nines" will not be useful.

Of course, casting nines doesn’t solve calculus integration and the like. Nobody has claimed it will. However arithmetic is a component in other types of math too, and mistakes in arithmetic used there can be quickly caught too.

You other comment is incorrect. Arithmetic is a subset of mathematics, just as calculus and trigonometry are. Here is a definition to help you: https://www.merriam-webster.com/dictionary/mathematics

:idea: Arithmetic is to math like the Earth is to our solar system, or like mammals are to animals.

See also:
http://www.chicagotribune.com/lifestyle ... story.html

At any rate, I offer casting nines here as a useful method to quickly catch simple math errors. It has helped me many times, as well as my students. Unfortunately it will not help you with differentiation, geometry, or word definition/ analogy errors. :)

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Re: How to help teenager fix silly mistakes in math?

Post by alfaspider » Fri Sep 14, 2018 1:48 pm

Good luck to her. I suffered through high school math, eventually scoring a 5 on the AP Calculus exam, but the frustration of silly mistakes caused me not to take any math beyond that. It's easy to stay "go slow", but high school exams are typically taken under significant time pressure. Often, I would get halfway through a problem, know there was a mistake, but not have time to find and correct it.

In retrospect, I think a big problem was that I was chronically sleep deprived in high school. That might be something worth looking into.

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Re: How to help teenager fix silly mistakes in math?

Post by sailaway » Fri Sep 14, 2018 1:55 pm

This sounds like boredom. If so, making the process more meticulous is not going to help. Try more challenging types of math, with real world applications and therefore real world consequences. Cooking, chemistry sets, drawing, CAD drawing...it all depends on the current focus.

Also, am I to understand that you are reading the problems to a teenager? Or are you reading along with her?

I would look at how this person is processing the numbers themselves. Numbers just don't make any sense to me at all. The best I can describe it is that they dance around in my head like children each listening to a different song. I made it through advanced calculus and through all of the standardized tests thanks to what is now called new math, but was the only way I could consistently process numbers and I had to figure it out for myself. Pen and paper also help; I call it making the dancing kids sit down for a minute. On the other hand, my husband can do just about anything in his head, to the awe even of his computer geek colleagues when he has an answer before they have set up the problem. But he struggles if he has to write it all down and he skips steps if he tries to explain it to me. In the end, I sometimes make silly mistakes because the actual math is so overwhelming, he sometimes makes silly mistakes because articulating the step by step process is so overwhelming. We both do better when we are conscious of our weaknesses.

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Re: How to help teenager fix silly mistakes in math?

Post by criticalmass » Fri Sep 14, 2018 3:27 pm

I will add another angle. Eventually I figured out that I took different approaches to math problems, whether factoring equations or solving proof problems. In computer science, I developed algorithms that were often quite different from the other students and instructor yet (often) accomplished the same thing, sometimes even more efficiently. (Efficient (least “expensive”) algorithms are highly prized in C.S.)

Different people think in different ways and this can be extremely frustrating in an environment where all students are expected to take the same approach. You might try to see if this is part of the issue....Creativity should be embraced, even in problem solving.

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Re: How to help teenager fix silly mistakes in math?

Post by frankmorris » Fri Sep 14, 2018 3:49 pm

Haven't read all the responses so apologize if this has been said, but if the issue is that she gets the answer correct when she self-checks, but doesn't self-check and often makes careless answers, a simple strategy is just to have her place a check mark next to the number of the problem indicating that she has checked her work. Then, before turning in the assignment, she should review to be sure she has check marks next to each problem number, then put a check mark at the top right of the first page. Also have her tell her teacher(s) so they get what's up.

Even at my age, I constantly make spelling mistakes, etc. and even errors with numbers. None of us are perfect, and re-checking work is just part of being a non-flawless human ;). Some of us remember to do it, some of us have to have checklists, like grocery lists.

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