# resources for developing problem solving ability at the elementary level

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s/o of the other thread that talked about algorithmic knowledge vs. problem solving ability:

DS7 is good at elementary level math (very accurate and rapid mental calculations, arithmetic and can handle most word problems well).

I am looking for ways to develop his problem solving ability in academic subjects (mainly math for now and science in the future)- I mostly try to use the "discovery method" of teaching - I ask a lot of leading questions instead of giving out a direct answer and I try to setup a problem with appropriate clues instead of teaching how to solve it (Socratic reasoning methods). I am sure that there is more to developing the problem solving ability of a student than just this. I would love to spend this summer just working on developing his problem solving ability. Looking for resources, expertise, suggestions etc. TIA.

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The most essential problem-solving strategies are ones you probably already model and teach him to employ: draw a picture, find a pattern, solve a simpler (related problem), work backwards, and so on. It's easiest to do this with the types of problems uncommon to most elementary curricula but common to all the usual suspects on this board: Zaccaro, BA, MEP, contest math, etc. The most important thing is the amount of experience he gets with the sort of problem that isn't just immediately solvable by application of an algorithm, but those that really require the use of the strategies. Productive struggle is hard for Hermione-type parents (like me) to watch, but probably the most valuable time they can spend. Contest math is probably best suited to acquiring that experience, because it's designed for that purpose and isn't also trying to teach concepts at the same time.

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Oh, good question. I wish I had a really good answer, the "no, I don't know this, I won't even try it!" complaint is so frustrating.

One nifty thing was the Algebra Readiness Made Easy series. They present a list of "clues" and then asks questions like "what clue should you use first?" "Now what information do you know?" "How did you know that?"

It help my kid a little to break out information into parts he could work with. But it's still a struggle to get him to think through things in BA. I don't think it's a logic problem really though, he usually gets the logic puzzles in Building Thinking Skills in superman speed.

:bigear:

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Somewhere on this board, from a long time ago, there was a very long list of resources.  Might have been quark post.  I'll see if I can find it.  Maybe it's this one http://forums.welltrainedmind.com/topic/320275-designing-a-non-traditional-math-course-for-a-math-loving-structure-hating-child/?do=findComment&comment=3272174

In addition to the obvious ones mentioned (BA, Zaccaro, MOEMS, etc), there's also the Borac books (check Amazon for Cleo Borac), and Hard Math for Elementary.

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We love strategy games. Games which require multiple mental step strategies definitely build logical ordered thinking and problem solving skills.

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Mathematics: A Human Endeavour by Jacobs is also good for investigation style learning.  There are lots of topics in that book that are outside of primary school math but still before Algebra.  Unfortunately, the book is in my library or I would give you a few examples.

Ruth in NZ

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the most famous book to me is "How to solve it" by George Polya.

One thing he said that I liked was something like: "Solutions are like grapes, they come in bunches.  So when you have an idea that works on one problem, look around for another one that it will work on."

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The most essential problem-solving strategies are ones you probably already model and teach him to employ: draw a picture, find a pattern, solve a simpler (related problem), work backwards, and so on. It's easiest to do this with the types of problems uncommon to most elementary curricula but common to all the usual suspects on this board: Zaccaro, BA, MEP, contest math, etc. The most important thing is the amount of experience he gets with the sort of problem that isn't just immediately solvable by application of an algorithm, but those that really require the use of the strategies. Productive struggle is hard for Hermione-type parents (like me) to watch, but probably the most valuable time they can spend. Contest math is probably best suited to acquiring that experience, because it's designed for that purpose and isn't also trying to teach concepts at the same time.

I'm SO a Hermione.  I need to remember this.  We do challenging stuff, but I think I step in too early sometimes.

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At a recent FOL sale I picked up book 2 of a series called Figure it Out: Thinking Like a Math Problem Solver by Sandra Cohen. It does the whole present a problem and asks questions thing, but also teaches the Make a Picture and Use a Pattern strategies. You can see samples of them here.

I think it looks interesting, especially since I was never taught problem solving strategies, and need to be taught them myself.

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Thank you for all the wonderful resources, I think that I can find most of the recommended books in my library. And we do have the zaccaro, borac etc. problem solving books and we use them on occasion. My DS is learning chess, so that might count as a board game that involves strategy, I guess, but we really don't play any other strategy games (must pull out all the unused board games in the summer).

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Hermione-type parents

What are Hermione-type parents? (I have not read Harry Potter, which I assume this is referring to?)

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What are Hermione-type parents? (I have not read Harry Potter, which I assume this is referring to?)

Hermione is a real overachiever. She read all her schoolbooks the summer before, she gets 127 on all her tests, she starts studying (that is, more than usual) for her end-of-year tests in, like, December, her biggest fear is being told she failed everything, she routinely does work well above grade level, and she spends her free time (such as it is) haranguing her friends to study more. One year she bought them study planners for Christmas and made them color coded schedules of what to study when. Another year she actually spends the whole year traveling through time so she can take more classes than possible every day, including an optional class on "Muggle Studies", despite having grown up among Muggles, aka "non-magical humans".

Productive struggle isn't really her thing, and the one teacher who really hates her (the Mean Teacher, Snape) has, imo, a valid point when he accuses her of being an insufferable know-it-all who simply regurgitates from the textbook.

I assume, of course, that "Hermione-type parents" means the poster is like Hermione and not like Hermione's parents, who don't seem very concerned with their daughter at all. She goes away to boarding school, and after the first few years she barely even goes home for vacations. Can you imagine your 14 year old is away at school all year, and then you're okay letting her spend Christmas and summer with another family? In the books she erases their memory for their own good (legit for their own good) and it's not even made clear whether or not she bothered to get their consent first (I believe in the movie she clearly didn't, but....) Anyway, her parents could never have understood her subjects to begin with.

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Hermione is a real overachiever. She read all her schoolbooks the summer before, she gets 127 on all her tests, she starts studying (that is, more than usual) for her end-of-year tests in, like, December, her biggest fear is being told she failed everything, she routinely does work well above grade level, and she spends her free time (such as it is) haranguing her friends to study more. One year she bought them study planners for Christmas and made them color coded schedules of what to study when. Another year she actually spends the whole year traveling through time so she can take more classes than possible every day, including an optional class on "Muggle Studies", despite having grown up among Muggles, aka "non-magical humans".

Productive struggle isn't really her thing, and the one teacher who really hates her (the Mean Teacher, Snape) has, imo, a valid point when he accuses her of being an insufferable know-it-all who simply regurgitates from the textbook.

I assume, of course, that "Hermione-type parents" means the poster is like Hermione and not like Hermione's parents, who don't seem very concerned with their daughter at all. She goes away to boarding school, and after the first few years she barely even goes home for vacations. Can you imagine your 14 year old is away at school all year, and then you're okay letting her spend Christmas and summer with another family? In the books she erases their memory for their own good (legit for their own good) and it's not even made clear whether or not she bothered to get their consent first (I believe in the movie she clearly didn't, but....) Anyway, her parents could never have understood her subjects to begin with.

Yes, I was referring to Hermione herself, and not so much the overachieving but the near-total inability to not answer every question the moment that it's asked.

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Yes, I was referring to Hermione herself, and not so much the overachieving but the near-total inability to not answer every question the moment that it's asked.

It's an affliction, really. Oughta go form a support group....

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It's an affliction, really. Oughta go form a support group....

Thanks for the elaborate answer. I Googled Hermione parents and obviously got pretty confused.

I think it's a real problem in our culture (and most cultures, from what I can tell). The school system seems to try to encourage it, with multiple choice tests etc.

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Yes, I was referring to Hermione herself, and not so much the overachieving but the near-total inability to not answer every question the moment that it's asked.

And not knowing anything is too terrible. But to be fair she knows it she just can't help it. And is very insecure about being a muggle.

Eta the boarding school and visiting friends in the holidays was quite common I think with poorer kids attending wealthy schools maybe it just translates to non magical attending magical schools.

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The Math Kangaroo material's are a great intro to problem solving and contest math. You could find a book like the MOEMS Creative Problem Solving Book or even better you could just dive in together and figure it out.

The Canadian site has many more free samples than the US. https://kangaroo.math.ca/index.php?kn_mod=samples&year=NO

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