Problem-solving math for student that struggles in math

[Catherine]

So I've been reading the thread about 8Filltheheart's disappointing college visit with her son, which devolved into a conversation about math and physics taught as problem-solving exercises. A number of users of AoPS have chimed in about its value. I espouse this point of view, but my dilemma is that my child has struggled a lot in math. We've used RightStart and are finishing up the last level. The conceptual approach of RS, along with its use of multiple different kinds of drill, have worked beautifully for my 12 yo ds. He has a deep understanding of math concepts, and this is reflected in his test scores. Not to be too focused on testing, but I'm using it as a guide to "what we need to work more on."

 

This kid finds it very difficult to do anything with multiple steps. Some LDs here I won't describe in excruciating detail. He can't keep it all in his head at once. Also has poor reading comprehension, I think for the same reason-can't keep the content of a long sentence, or a series of sentences, in his head long enough. So for obvious reasons, he struggles mightily with math problems. Here's a for instance: I've hauled out our old Singapore CWP and Intensive Practice books. Yesterday and today, I gave him ONE problem to do from the level 3A book, and he is in tears asking for mercy after 10 minutes.

 

After a stern lecture about persistence, he's put in a good deal more time, with no progress. Eventually, I worked with him to help him see how to apply trial and error to narrow the possibilities. With that, he made progress. But I'm looking for a good problem-solving book that I can use here and there to develop his patience, persistence, and skill. Would Kitchen Table Math be too babyish for a 12 yo 7th grader? Can anyone recommend another similar book? For now I'll keep on the CWP which I have several levels of. TIA.

[wapiti]

I think your inclination is good, to use the lower levels of CWP and IP first, and as he's successful, gradually move to higher levels.  First I would think about ways to help him around his LD issues though, with explicit training.  I would not throw problems at him to sweat over until he has more strategies to help him around his LDs.  I'm not sure what those ways should be, but one that comes to mind would be having him read a problem and then together make a list of all the pieces of info in the problem so that he's not trying to keep all that in his head at once.  (Maybe on a white board?)  Then together look at the list and try to draw a picture of relationships between items on the list (maybe that would take the form of a bar diagram, but whatever seems to make the most sense to him) and so on.  I would do quite a lot of work together at the beginning of a level/topic and then gradually get him solving problems more independently.

 

just my two cents :)

[redsquirrel]

Yes, I think using the CWP specifically as a way into working on coping mechanisms is key. A meta discussion with him about 'this question is challenging for you because it requires XX skill. What can you do when you are faced with this type of a challenge?" If you can work with him on the challenges in an explicit manner it might be very helpful to him.

 

The book 'The Myth of Laziness' comes to mind. In it the author talks about different challenges kids face and different ways they can approach it. I think for kids who have a difficult time remembering steps in a process it was keeping notes on those steps in a notebook and reviewing them...? I can't remember exactly.

 

But at his age and with those challenges I think 'coping, coping, coping' needs to be a mantra. I think that is actually more important than the skill of problem solving at age 11.

[Emerald Stoker]

Catherine, I wonder if he would enjoy some recreational math books? I'm thinking of things like Martin Gardner's collections of puzzles. It's a similar sort of problem solving, I would say, but with the added advantage of humour and/or whimsy, and the further advantage of having no grade level marked on the front cover.

 

Just a thought...

[8filltheheart]

I'll offer a counter approach.   Maybe an algebraic approach vs. the bar diagram approach would be a better fit for how he thinks.   Hands on Equations takes the same sort of problems and has kids solve them algebraically.    Maybe the visual, hands on approach would help him keep everything clear in his mind as works through the steps.   The other advantage is that 3 levels are included and students can work their way up through them in difficulty.   My 6th grader has been doing MIF and HOE since late 3rd grade.   She has difficulty setting up bar diagrams, but she solves the problems w/o difficulty by setting them up via HOE's approach.   I have no problem with her doing it that way since it is obviously the way her brain thinks.   

 

FWIW.....I dont think the conversation devolved.  :)   It is actually the core of what occurred.   ;)

[Catherine]

I'll offer a counter approach.   Maybe an algebraic approach vs. the bar diagram approach would be a better fit for how he thinks.   Hands on Equations takes the same sort of problems and has kids solve them algebraically.    Maybe the visual, hands on approach would help him keep everything clear in his mind as works through the steps.   The other advantage is that 3 levels are included and students can work their way up through them in difficulty.   My 6th grader has been doing MIF and HOE since late 3rd grade.   She has difficulty setting up bar diagrams, but she solves the problems w/o difficulty by setting them up via HOE's approach.   I have no problem with her doing it that way since it is obviously the way her brain thinks.   

 

FWIW.....I dont think the conversation devolved.  :)   It is actually the core of what occurred.   ;)

Thank you for the suggestions, not just you, 8, but everyone else too.

 

What is MIF?

[8filltheheart]

MiF is Math in Focus.   It is similar to SM.

[Momling]

Weird... I thought I'd responded to this post...

 

Anyway, my girls are not math lovers. We've had success doing just 1 or 2 word problems consistently every day in addition to our regular math. We've used CWP, HOE verbal problems and Zaccaro "Become a problem solving genius". This slow-and-steady approach has really helped their attitude and willingness to persevere.

 

Another thing that helps is that I don't just hand the book to the girls to do by themselves. I do the problems with them. I show enthusiasm for the process and talk about how much I love puzzling out the problems. I think it's good for them to see me also struggle and falter and persevere and succeed (usually). We often then compare strategies. I also keep close track of their frustration level and before it gets too much, I'll give hints and, if necessary, guide them to the answer -- but we never quit after a failed attempt at solving a problem. I will always then give them an identical problem with different numbers so they can apply the strategy and feel good about solving it. We regularly return to difficult problems. Sometimes I also have them write their own similar problems to stump each other and me. We keep it light and fun and they've really improved in their ability to solve tricky problems.

[Catherine]

OK, did some research here. It HOE looks very relevant for my son, as he really benefits from the use of manipulatives and strategies that make the math visible. But it looks like it isn't so much a problem-solving book as a math concept book-still very useful, but I'm just clarifying. I couldn't be sure from the HOE website and the reviews only talk about the program's usefulness in teaching algebraic concepts and solving equations. Can anyone speak to this?

 

Also, the Zaccaro books. All of them look great, but I am picturing a scenario of ds reading a section on a problem-solving strategy, using it, then moving on to another strategy, but not retaining the first or being able to access or use the it again later. He does best when the learning is made explicit somehow-he doesn't necessarily understand or retain things that he's read from a page. Can anyone comment more on how you've applied the lessons in Challenge Math and Become a Problem-Solving Genius?

[8filltheheart]

I'm not sure what you are looking for. Did you see the sample problems from the verbal book?

http://www.borenson.com/AboutHandsOnEquations/VerbalProblemsBook/tabid/843/Default.aspx

[Jaybee]

This isn't a longterm program or anything, but my son loved this book:

 

http://www.amazon.com/Book-Perfectly-Perilous-Math-Mathematicians/dp/0761163743/ref=sr_1_1?ie=UTF8&qid=1385180521&sr=8-1&keywords=perilous+math

 

The day I brought it home, he sat down with it and was engaged. I like to think it started him thinking about math in a different way, and I have since added other problem-solving type books in our work.

[Crimson Wife]

There is a Singapore book called Process Skills that is supposed to be similar to CWP only with more guidance for each step: http://www.singaporemath.com/Heuristic_and_Model_Approach_s/143.htm

[Alte Veste Academy]

These thoughts might not be especially helpful, or maybe even relevant, so feel free to ignore me, but... :D

 

Does a problem-solving mindset have to be engendered through math? For every child, regardless of strengths and weaknesses? I read the thread in question (I think, LOL), and found myself nodding and agreeing. Naturally, it made me think I want my kids to be able to think! But, at the same time, wasn't the discussion about kids who seemed advanced and exceptional but were so only on paper? Kids who presumably knew the material but could not think deeply about that material? You said your son has "a deep understanding of math concepts." That is wonderful!

 

When I read your OP, I thought to myself why can't it sometimes be good enough for this or that particular kid with a particular set of circumstances to master the mechanics of a subject without being expected to take on the same mindset of kids who excel in that subject to the point that they are going to major in it.

 

I have two kids who are natural puzzlers. They have a great deal of drive and patience for stewing on math problems while contemplating various solutions. They also ask a lot of questions about math, good questions that most of the time I can't even answer. AoPS is a good fit for them. I have another who is quite good at math, accelerated even, but couldn't care less about digging deeper. But, in other subjects, look out! Even in science (math's BFF?), this child asks amazing questions, and the drive to dig deeper is there. I often wonder if and when it will spark a drive to develop more patience with problem solving in math. But I don't push it. I do CWP/IP and other supplements with this child, but more buddy style than have-at-it style. Maybe it ends in something greater than rote learning and maybe it doesn't, but I am not particularly concerned because it is one of many subjects and, quite frankly, this child's gifts seem to lie (a very worthwhile and impressive) elsewhere.

 

Anyway, I don't think there is anything wrong with working to cultivate a stronger problem-solving mindset in math, but I think it is infinitely more important for a problem-solving mindset to be cultivated in any subject or, to some degree, in a variety of subjects than in one particular subject. (I mean, seriously, just look at how often Sheldon seeks Penny's advice! :D) What are your son's strengths? You can have a problem-solving mindset in history, art, current events... Personally, I think it is OK for the knowledge gained in some subjects to serve as mere tools for some while being the big project for others.

[Elisabet1]

I hated Challenging Word Problems. I do not think that a child's ability to do CWP reflects his ability to do math overall. I also think that for some kids, it will cause a hate for math in kids who otherwise would like it.

[Heathermomster]

Have you read the book How the Brain Learns Mathematics by Sousa?

 

In the back of that book, the author briefly mentions solving word problems using the RIDD procedure and word problem maps for individuals with maths and reading disabilities.

[sbgrace]

We use the process skills books by Singapore linked above. This has really helped my son with weaknesses in this area. It scaffolds much better than CWP. It does have difficult problems like the CWP book. But it teaches methods and leads the child to the point where he can solve those types. We've made a lot of progress. If my son struggles with a problem or type of problem we work through it/them together on the white board. Then he tries again on his own the next day.

[Catherine]

When I read your OP, I thought to myself why can't it sometimes be good enough for this or that particular kid with a particular set of circumstances to master the mechanics of a subject without being expected to take on the same mindset of kids who excel in that subject to the point that they are going to major in it.

 

Anyway, I don't think there is anything wrong with working to cultivate a stronger problem-solving mindset in math, but I think it is infinitely more important for a problem-solving mindset to be cultivated in any subject or, to some degree, in a variety of subjects than in one particular subject. (I mean, seriously, just look at how often Sheldon seeks Penny's advice! :D) What are your son's strengths? You can have a problem-solving mindset in history, art, current events... Personally, I think it is OK for the knowledge gained in some subjects to serve as mere tools for some while being the big project for others.

Oh, believe me, there is no question of this child majoring in math. : ) And I hope I am not giving the impression that my goal is to change him into something he is not. Really, my hope is just to get him close to grade level in concepts and in word problem solving by the time he leaves my tutelage, possibly for high school in 2 years. Right now, he cannot begin to do word problems in the basic operations consistently correctly. We're talking adding, subtracting and fractions. OTOH, he doesn't really grasp books like Lial's BCM that well-he does much better with manipulatives and "conceptual" math like Rightstart. His retention of concepts he learns from Lial's is not good. He understands math far beyond what he can DO, if that makes sense. So advancing his conceptual grasp is not my goal, it is moving his calculating and problem-solving up closer to grade level. Thus far, our time has been devoted to drilling facts in various ways, continual review of fractions, decimals, basic operations, etc. Because of his LDs, keeping multiple steps straight, doing them in the correct order, avoiding calculation errors, not mixing up digits or transposing them, is a big challenge for him. So I'm hoping to find materials that give problems to solve for practice. We haven't done much problem-solving yet. I hope to start that now.