Encouraging patience in problem solving

[musicianmom]

How does a parent instill a desire in a child to put in the effort to solve real math problems?

 

Dd8 is doing much better in math since we switched to Beast Academy. However, for any problem that requires her to think about how to solve it, or *gasp* try various things to see what works, her first reaction is "help!" I feel like when I help her, the learning opportunity is lost. But she doesn't have the drive to persist and push through to the solution herself.

 

I see her being like I was: good at mathematical operations, terrible at any sort of problem solving. Every year my school would send me to the city-wide math competition, because I was the top student in my class, but my performance in the contest was embarrassing because I had no idea how to apply my knowledge to the contest-level problems.

 

I realize now that problem solving is essential to doing well in higher level science courses, so I want my kids to be better at it than I was!

[Lilaclady]

I think this is an essential skill but needs to be developed step by step. If your child is not used to doing tough problems then you need to help by setting her up for success. At first you may show her how to do it, then you may giver her your own example but with some numbers changed so she can practice it. Later when she comes to you, you ask her if she has applied what you showed her earlier, then later you tell her she may need to read the questions again and see exactly what she is being asked to find.

I think it is an ongoing thing but the more you work on it, the more adept she will be at solving hard problems. HTH

[Arcadia]

Take your time to cultivate her patience and willingness to put in the effort.  Rome was not built in one day :)

Out of every 10 questions, I would be willing to help for 1 or 2 after due effort on their part.

My kids take turns to sulk through their math. My 8 year old won't give up and just plough through, my 7 year old would sleep on it.

[acurtis75]

I shared some problem solving techniques with dd8 from her mus honors lessons and we just worked a little at a time at building stamina. Fwiw she is 8 1/2 and I've seen an improvement in the last month or so after working on this for over a year. She is starting to understand having to try more than one way to solve the problem is not a sign of failure and that persistence is more valuable than knowing answers right away.

[texasmama]

My experience has been that learning to tolerate struggling with math problems is somewhat of a developmental skill that most 8 year olds just do not have yet.  My 10 and 12 year olds are developing the skill at this point, but my almost 8 year old does not have it.  So when she asks for help, I give her help or guidance or a hint of some type.  My 10 and 12 year olds will let me know when they are done, done, done with wrestling with math problems and need me to work it out on the whiteboard. 

[mom2bee]

As far as I can tell, it is something that is developed/taught incrementally and I think that the "Buddy System" would be an excellent approach for anyone who is willing, but especially a young child. I have actually been thinking about this a lot lately, in my quest to develop my own problem solving abilities (which aren't all that great, I feel) I have began to wonder a lot about this.

 

I get flustered and feel "trapped" quickly on my own, to the point where I often can't see the obvious. However I love and enjoy working on a problem with someone. In my experience as a math tutor, many people feel this way. They'd rather work tricky problems with a buddy, someone to bounce ideas off of. The trick is to guide and not lead them to the answer, which I haven't really mastered yet myself, but that is the gist. For elementary age, you'll probably know the answer quite often without a whole lot of work, but this can be hard when you yourself don't know the answer or approach to a question in Geometry or Calculus.

 

I suggest setting aside some time especially for problem solving everyday or a few times a week. Get a couple of problems and work them together, it will take a while to find your rhythm, but it will be worthwhile. Here are a few steps that I find helpful for many students, regardless of age.

 

1) Write things out in words that you understand.

What are we trying to find out? What do we know? What can we measure, compare, compute...

 

2) Draw a picture/diagram where appropriate

 

3) Use a dry-erase surface (don't ask me why this works so often for so many, it just does...)

 

4) Break it into small problems

 

5) Write an action plan

1st we'll calculate the perimeter, 2nd subtract any parts that have gaps, 3) check our answer

 

6) Jot down some basic ideas that you both have about the problem

 

7) Write neatly! (You will probably have to be scribe early on, but model neat and orderly writing and gradually require that she do the same!

[sunnyday]

My son and I spent some time talking about this today. He was home sick, but not feeling too ill, and I didn't want it to seem like he could get a vacation from school just by having a morning tummyache. So we did a full day of learning. DS got frustrated several times over math and handwriting.
 
We talked about it a bit...he told me it is uncomfortable to make a mistake...I made my pitch for a "growth mindset" and brains being like muscles...he countered with Hermione from Harry Potter. I assured him that Hermione only gets things right so much because she works REALLY hard studying, and also, her strength is memorizing from books. When it comes to things you *have* to do--try--fail--try again to accomplish, like riding a broom, she's not as naturally gifted but has to work harder.
 
This evening out of the blue he told me, "That thing about Hermione and riding the broom? It's like in Ninjago. The sensei says, 'Spinjitsu can be learned, but Spinjitsu cannot be taught.' That means that someone can tell them how to do the moves, but until they do them and practice them, they will not really understand and they won't really be good."
 
My jaw dropped. By Jove, I think he got it!
 
So that would be my answer, to encourage a growth mindset by continually reiterating that it's only learning if the student is working at it, not if it comes easily. If you don't like Sensei Wu's formulation of the idea, try John Holt's. "Learning is not the product of teaching. Learning is the product of the activity of learners."

 

I also agree with the "buddy system". A few weeks ago DS and I worked through one of the sample problems from 3A, and it was certainly a challenge and he got frustrated a few times, but I let him be frustrated and calm down again before I'd gently start prodding him in a direction I thought would be useful. When he got the answer, it felt to him like it was his own discovery from his own hard work and he was so thrilled! Nothing can replace that intrinsic motivation of true success. :)

[musicianmom]

Thank you all! I was feeling guilty about giving her hints, but maybe that's just where she is maturity-wise. I'll keep encouraging her.

[mom2bee]

Thank you all! I was feeling guilty about giving her hints, but maybe that's just where she is maturity-wise. I'll keep encouraging her.

 

Yeah, just keep encouraging and guiding her. Also, try and redefine (or offer an alternate view) or the idea of a problem. That is something I have been doing lately with my students and for some of them it is working. There is a difference between a problem and a challenge, both of which can be very good things. No one moans about a "problem" to which they have mastered the answer and become fluent at executing the solution.

 

a "problem" isn't bad, it just something we deal with. Opening a door is a "problem", making a sandwich is a "problem", getting dressed, walking across the room, brushing our teeth, playing an instrument, decoding unfamiliar words and using a tool are all "problems" but by the time we're 8yos, most of they aren't really challenging problems.

 

We know how to solve them, and they are commonplace enough that we have practice solving them. But sometimes something happens that makes the problems a little harder to solve--a slipper knob or a missing key, missing sandwich ingredients, dirty laundry, no toothpaste, no sheet music, an obscure phonics patter or rule, not knowing how to use a tool--all of these situations present a new layer of complexity to a problem but we don't always go screaming for help when we encounter, we use what we DO know to figure them out.

 

I find that redefining the parameters of what a "problem" is is slowly helping for some of my students and me, relax about having a "problem" problems are like colors or feelings, they aren't bad--we enjoy some more than others, but they are natural and can be fun and enriching to experience in new ways.

[boscopup]

I use socratic questions that lead my son in the general direction of the right answer, but he still has to come up with it himself. It's tricky sometimes. I have to really think about what question to ask that won't just give away how to solve the problem. But usually I can think of something. :) We aren't to the point of letting him figure it out over the course of an hour on his own. He's just not there yet. He'll look at a problem, then if he can't do it, he'll be in tears and say, "I don't know what to do!" And at that point, he's lost. So I try to not let him get to that point. I have him look at it as long as he can without crying, then I start the socratic questioning to get him to really think about the problem. I don't just show him how to do it though.

[musicianmom]

Argh! Some of these problems are beyond me! I wouldn't even call them math problems, they're more like riddles or puzzles.

 

I just skipped the birthday problem with dd:

 

The little monster says, "The day before yesterday I was 6. Next year I'll turn 9." How is this possible?

 

Yes, once I looked up the answer it made total sense. So did the solution to an Agatha Christie mystery once Hercule Poirot explained everything. But there was no way I would have figured it out, even back in the days when I was scoring 32 in math on the ACT. And I can't even see how to reverse-engineer a set of Socratic questions that would lead dd to the answer.

 

Maybe a math tutor is needed to unlock that part of her brain, because how can I unlock it when obviously that part of MY brain has never been unlocked?

[maize]

Here's an idea: we're used to being rewarded for correct answers, and punished (even if only by personal disappointment) for wrong ones. To learn problem solving, we need to begin seeing every attempt at a solution as positive. You might try rewarding your daughter for every attempted solution, say put a star by the problem for every way she can think of approaching it, with the idea that the more stars she gets the better. Even if she has solved a problem, let her take another look and see if she can think up a different way to get to the solution.

[mathmarm]

Argh! Some of these problems are beyond me! I wouldn't even call them math problems, they're more like riddles or puzzles.

 

I just skipped the birthday problem with dd:

 

The little monster says, "The day before yesterday I was 6. Next year I'll turn 9." How is this possible?

 

Yes, once I looked up the answer it made total sense. So did the solution to an Agatha Christie mystery once Hercule Poirot explained everything. But there was no way I would have figured it out, even back in the days when I was scoring 32 in math on the ACT. And I can't even see how to reverse-engineer a set of Socratic questions that would lead dd to the answer.

 

Maybe a math tutor is needed to unlock that part of her brain, because how can I unlock it when obviously that part of MY brain has never been unlocked?

 

What is wrong with previewing the material before she begins it? Both the text and the solutions are materials that should be previewed by the teacher before hand if it will help you to help your student. I've not known many math teachers who don't come to class with their notes.

 

I always studied the solutions to problems my first couple of years teaching--it's not that I couldn't solve the problems, but sometimes it helped to know where students might stumble, where a conceptual leap would be required or where we would need to make use of something the students probably hadn't seen in a semester or two. Also, having the solutions worked out and fresh in my mind was very helpful to me so that I'd know what sort of leading questions I could ask the students to help them discover the answer for themselves.

 

Remember: It's not your job to know all the answers, its your job to guide them through the solutions and teach them the process, so that they will know how to find the solution themselves!

 

You're more than equipped to teach your child--and well, you just need to do your homework :)

 

 

(See? That was a funny!)

[LMD]

Here's an idea: we're used to being rewarded for correct answers, and punished (even if only by personal disappointment) for wrong ones. To learn problem solving, we need to begin seeing every attempt at a solution as positive. You might try rewarding your daughter for every attempted solution, say put a star by the problem for every way she can think of approaching it, with the idea that the more stars she gets the better. Even if she has solved a problem, let her take another look and see if she can think up a different way to get to the solution.

 

Oooh, I really like this - and I think DD would too.  I do try to encourage her to not think of her answers as 'wrong' - but just a step closer to the solution.  I'm often saying, 'Great, so now we know one way that didn't work, let's try another one...'

 

For my DD (also 8) she often goes to the *sigh* need help just because it's a bit hard.  Once she gets going, with some gentle encouragement and leading questions, she gets a kick out of solving it.

 

 

And yes, some of the BA questions are occasionally hard for me too...  :blushing:

[tabinfl]

I'm in the very early stages of this, 1st grade word problems. I call them math "puzzles" because it sounds like much more fun than a "problem" or a "question".

 

I do a lot of socratic type questioning, and even after I give them hints or even a step towards the answer, I always ask another question and have them repeat whatever answer I just gave them. If they head down a wrong path, we back up and try again -- when working on multi-step problems I don't let them get all the way to the end (at this age) before correcting course. I use a lot of drawings and manipulatives to illustrate concepts too -- watching me draw on the whiteboard is always more entertaining than looking at pictures in the book, especially when I make numbers backwards and other silly mistakes because I'm trying to write sideways or upside-down. ;)

 

Ironically, my best math puzzler is the one who gets most easily frustrated when she doesn't understand something, or when the answer isn't obvious to her right away. She loves doing math, even when it takes some effort, but hates feeling like she doesn't know the answer. Sometimes I just have to insist that she follow along, break it down into tiny steps, and feed them to her one by one to build up some confidence -- one or two like that and then she's ready to tackle a little more on her own.

[daijobu]

I lead a couple of math olympiad teams.  After they take the exams, I have the students tell me how they solved each problem.  Sometimes their solutions are elegant, and sometimes they are more like guess and check.  ("Well, I figure a shirt probably costs $15, but that was too high so then I tried $12...")

 

But I think it helped for students to see how other students puzzle through their solutions, trying different approaches and hitting roadblocks.  

 

If you can pull it together, math olympiad teams can be a great adjuct for learning this skill.

[mom2bee]

I lead a couple of math olympiad teams.  After they take the exams, I have the students tell me how they solved each problem.  Sometimes their solutions are elegant, and sometimes they are more like guess and check.  ("Well, I figure a shirt probably costs $15, but that was too high so then I tried $12...")

 

But I think it helped for students to see how other students puzzle through their solutions, trying different approaches and hitting roadblocks.  

 

If you can pull it together, math olympiad teams can be a great adjuct for learning this skill.

Yes, but how do you teach or model problem solving techniques to your teams? Seeing as how they're on the olympiad team, they probably have some interest or motivation to be on the team and perform well in mathematics.

 

Are there any techniques you use to get the kids problem solving in particular though?

[8filltheheart]

Not a direct approach answer, but my kids that spend the most time playing strategy games are my best problem solvers. Chicken or the egg? I'm not sure. Are they attracted to complex strategy games bc they are problem solvers or vs. vice versa?

 

Either way, games that make them think ahead multiple moves in order to determine the consequences of a single choice means that are puzzling through multiple options and discerning the outcomes. It makes a child move beyond simple linear thinking because "branches" exist off the straight line path and those "branches" have branches.

 

Simple games like Mancala, Othello, Qwirkle, etc are great for young kids to start to see how to think ahead to see how a choice impacts outcome. Others that have more rules......chess, Stratego, Risk, Axis and Allies, Settlers of Catan, certain card games, etc. Advanced Mastermind is a great game for thinking through probability of pattern selection.

 

I am a huge advocate for playing games. They are a fun way to learn how to mentally think ahead while making lots of mistakes in the process.

 

And just like others have suggested, Socratic questioning while they are learning helps them learn how to see the bigger picture. When they are first learning, I'll even physically show them how different choices lead them down paths to different outcomes.