Gunakan Fungsi Search Untuk Mencari Nota

Loading...

Saturday, June 20, 2009

Eight Problem Solving Strategies

EIGHT PROBLEM SOLVING STRATEGIES.

1. WORK BACKWARDS
To solve some problems, you may need to undo the key actions in the problem. This strategy is called Work Backward.
Working backwards is a standard strategy that only seems to have restricted use. However, it’s a powerful tool when it can be used. In the kind of problems we will be using in this web-site, it will be most often of value when we are looking at games. It frequently turns out to be worth looking at what happens at the end of a game and then work backward to the beginning, in order to see what moves are best.

2. GUESS AND CHECK
Some problems cannot be solved directly. You need to use a strategy called Guess and Check.
Guess and check is one of the simplest strategies. Anyone can guess an answer. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check. This is a strategy that would certainly work on the Farmyard problem but it could take a lot of time and a lot of computation.
Guess and improve is slightly more sophisticated than guess and check. The idea is that you use your first incorrect guess to make an improved next guess. You can see it in action in the Farmyard problem. In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. In some problems though, where there are more variables, it may not be clear at first which way to change the guessing.

3. LOOK FOR A PATTERN
In many ways looking for patterns is what mathematics is all about. We want to know how things are connected and how things work and this is made easier if we can find patterns. Patterns make things easier because they tell us how a group of objects acts in the same way. Once we see a pattern we have much more control over what we are doing.

4. DRAW A PICTURE
It is fairly clear that a picture has to be used in the strategy Draw a Picture. But the picture need not be too elaborate. It should only contain enough detail to solve the problem. Hence a rough circle with two marks is quite sufficient for chickens and a blob plus four marks will do for pigs. There is no need for elaborate drawings showing beak, feathers, curly tails, etc., in full colour. Children should be encouraged to use this strategy at some point because it helps children ‘see’ the problem and it can develop into quite a sophisticated strategy later.

5. MAKE A TABLE

There are a number of ways of using Make a Table. These range from tables of numbers to help solve problems like the Farmyard, to the sort of tables with ticks and crosses that are often used in logic problems. Tables can also be an efficient way of finding number patterns.


6. MAKE A LIST

Making Organised Lists and Tables are two aspects of working systematically. Most children start off recording their problem solving efforts in a very haphazard way. Often there is a little calculation or whatever in this corner, and another one over there, and another one just here. It helps children to bring a logical and systematic development to their mathematics if they begin to organize things systematically as they go. This even applies to their explorations.
When an Organised List is being used, it should be arranged in such a way that there is some natural order implicit in its construction. For example, shopping lists are generally not organised. They usually grow haphazardly as you think of each item. A little thought might make them organised. Putting all the meat together, all the vegetables together, and all the drinks together, could do this for you. Even more organisation could be forced by putting all the meat items in alphabetical order, and so on.

7. ACT IT OUT
Meaning that two strategies combine together because they are closely related.
Young children especially, enjoy using Act it Out. Children themselves take the role of things in the problem. In the FARMYARD problem, the children might take the role of the animals though it is unlikely that you would have 87 children in your class. But if there are not enough children you might be able to press gang the odd teddy or two.
There are pros and cons for this strategy. It is an effective strategy for demonstration purposes in front of the whole class. On the other hand, it can also be cumbersome when used by groups, especially if a largish number of students are involved. We have, however, found it a useful strategy when students have had trouble coming to grips with a problem.
The on-looking children may be more interested in acting it out because other children are involved. Sometimes, though, the children acting out the problem may get less out of the exercise than the children watching. This is because the participants are so engrossed in the mechanics of what they are doing that they don’t see through to the underlying mathematics. However, because these children are concentrating on what they are doing, they may in fact get more out of it and remember it longer than the others, so there are pros and cons here.

8. USING SYMMETRY
It helps us to reduce the difficulty level of a problem. Playing Noughts and crosses, for instance, you will have realized that there are three and not nine ways to put the first symbol down. This immediately reduces the number of possibilities for the game and makes it easier to analyze. This sort of argument comes up all the time and should be grabbed with glee when you see it.

48 comments:

Professor said...

Can you please help me to solve this problem. Thank you!

Amy and Judy sold 12 show tickets altogether. Amy sold 2 more tickets than Judy. How many tickets did each girl sell?

and

Justin : Hey Yutaka, a total of 350
students voted on whether a
tiger or a dolphin should be
the new school’s mascot. I
heard that 70% of the
students voted for the tiger.
Yutaka : Well Justin, I’m glad the
tiger won! I wonder how many
students voted for the tiger.

Can anyone help to solve using different strategy. Thank you!

Anonymous said...

Would you be fascinated about exchanging links?
My web page :: www.spaingolf.us

Anonymous said...

Somebody essentially help to make seriously posts I'd state. That is the very first time I

frequented your web page and thus far? I surprised with the

analysis you made to create this particular submit

amazing. Excellent process!
My page: costablancaspain.us

Anonymous said...

Keep functioning ,remarkable job!
Feel free to visit my weblog : www.elcheproperty.net

Anonymous said...

You can certainly see your expertise within the paintings
you

write. The arena hopes for even more passionate writers such as you
who

are not afraid to mention how they believe. At
all times go after your heart.
My blog : http://www.thespainforum.com/classifieds/showcat.php?cat=21

Anonymous said...

Great post. I used to be checking continuously this blog and I
am

inspired! Very helpful information particularly the

last phase :) I maintain such

information a lot. I was seeking this particular information


for a very lengthy time. Thank you and best of luck.
Feel free to visit my page - www.fishingspain.net

Anonymous said...

Somebody necessarily assist to make critically posts I would state.
This is the very first time I

frequented your website page and thus far? I surprised with the


research you made to create this particular post

amazing. Wonderful process!
Feel free to surf my site ; http://www.golfpropertyspain.info/

Anonymous said...

That is the proper blog for anybody who desires to find out about this topic.
You

understand a lot its virtually exhausting to

argue with you (not that I truly would need…HaHa).

You definitely put a

new spin on a subject thats been written about for years.
Great stuff, simply

nice!
Take a look at my page : mouse click the following webpage

Anonymous said...

Hey there! I could have sworn I've been to this site

before but after checking through some of the post I realized it's new to me.


Anyhow, I'm definitely glad I found it and I'll be bookmarking and checking back

frequently!
Also visit my website http://www.jobsinspain.org/

Anonymous said...

I'm often to blogging and i actually recognize your content. The article has really peaks my interest. I'm going to bookmark your site and preserve checking for
new information.
Stop by my website - Coplaner.info

Anonymous said...

I take pleasure in, result

in I found exactly what I used to be having a look for.
You have ended my four day lengthy hunt! God Bless you man.
Have a great day. Bye
Here is my web site :: just click the next article

Anonymous said...

Hello there! Do you know if they make any plugins to help
with

Search Engine Optimization? I'm trying to get my blog to rank for some targeted keywords but I'm not seeing very good

results. If you know of any please share.
Cheers!
Feel free to surf my web-site :: http://murciaproperty.net

Anonymous said...

I am constantly looking online for

ideas that can assist me. Thank you!
My website > costablancaspain.us

Anonymous said...

You made some nice points there. I looked on the internet
for the subject matter and found most guys will go
along with with

your site.
My web site: inma.blog.24heures.ch

Anonymous said...

Hey there! I'm at work browsing your blog from my new iphone

4! Just wanted to say I love reading through your blog and look forward to all your

posts! Carry on the outstanding work!
Feel free to surf my blog post ; thespainforum.com

Anonymous said...

Thank you for the good writeup. It in fact was a amusement account it.

Look advanced to more added

agreeable from you! However, how could we communicate?
Review my blog post ... edu.ua

Anonymous said...

Do you have a spam issue on this site; I also am a blogger, and I was wondering your situation;
we have developed some nice procedures and we

are looking to trade techniques with other folks, please shoot me an e-mail if interested.
Here is my web blog ; http://www.villasspainproperty.com/page4.html

Anonymous said...

There are certainly a number of details like that to take into consideration.
That could

be a great level to convey up. I provide the ideas above as

general inspiration however clearly there are
questions just like the one you

deliver up the place crucial thing

shall be working in trustworthy good faith. I

don?t know if best practices have emerged round things like that, but I am positive that your job is clearly recognized as a good
game. Each boys

and girls feel the impression of just a moment’s

pleasure, for the remainder of their lives.
Look into my web-site diysolarheatingspain.com

Anonymous said...

Great goods from you, man. I've understand your stuff previous to and

you are just extremely magnificent. I actually like what

you've acquired here, really like what you're stating and the way in which you

say it. You make it enjoyable and you still take care of to keep it smart. I

can not wait to read far more from you. This is actually a

tremendous website.
my web page: cambrilssolar.livejournal.com

Anonymous said...

As I site possessor I believe the content matter here is rattling excellent , appreciate it for your
efforts. You should keep it up forever! Good Luck.
my site > http://www.thespainforum.com/f339/

Anonymous said...

Hello, i think that i saw you visited my blog so i came to “return the favor”.
I

am trying to find things to enhance my website!I suppose its ok to use some

of your ideas!!
My webpage ; spain vs netherlands world cup final 2010 highlights

Anonymous said...

Usually I do not learn post on blogs, however I would like to

say that this write-up very compelled me to take a look at and do it!
Your

writing style has been amazed me. Thanks, very great post.
Feel free to visit my weblog ; Http://revctrl.org

Anonymous said...

Heya i am for the first time here. I came across this board and I
find It really useful & it helped

me out a lot. I hope to give something back and help others
like you aided me.
Here is my page ... caulicle

Anonymous said...

Excellent post. I was checking continuously this
blog and I am impressed! Very

helpful info specifically the last part :) I care for such

information a lot. I was looking for this certain info for a
long time. Thank you and good luck.
Feel free to visit my web-site ; http://woodhull.tv/

Anonymous said...

wonderful post, very informative. I wonder why the other specialists
of

this sector do not notice this. You must continue your writing.
I'm confident,

you've a great readers' base already!
Also visit my webpage ... http://tlm.tudelft.nl/

Anonymous said...

Thank you for the auspicious writeup. It in fact was a amusement account it.
Look advanced to more added

agreeable from you! By the way, how can we communicate?
Visit my weblog - http://www.radardirectory.com/index.php?site=8646

Anonymous said...

Hi there! Do you use Twitter? I'd like to follow you if that would be

okay. I'm undoubtedly enjoying your blog and look forward to new posts.
My page : gummier

Anonymous said...

excellent points altogether, you just received a

brand new reader. What may you suggest about your

put up that you simply made some days ago? Any

positive?
My web page :: aortae

Anonymous said...

Today, while I was at work, my sister stole my apple ipad and tested
to

see if it can survive a 25 foot drop, just so she can be a
youtube sensation. My iPad is now broken and she has 83 views.

I know this is entirely off topic but I

had to share it with someone!
Feel free to visit my blog ; anatomy

Anonymous said...

hi!,I like your writing very much! share we communicate more about your article
on AOL? I need a specialist on this area to solve my problem.

May be that's you! Looking forward to see you.
Feel free to visit my website - www.culturame.it

Anonymous said...

I used to be very happy to search out this

internet-site.I wished to thanks for your time for this glorious learn!
! I definitely enjoying each

little little bit of it and I've you bookmarked to take a look at new stuff you

weblog post.
Also visit my weblog endarch

Anonymous said...

Hey! Someone in my Myspace group shared this site with us so I

came to give it a look. I'm definitely enjoying the information. I'm

bookmarking and will be tweeting this to my followers! Superb blog and
superb

design.
Here is my homepage : http://social.internetcairo.com/latest-seo-news/www-baileymusicco-com

Anonymous said...

Hi there! I just wanted to ask if you ever have
any problems with hackers?

My last blog (wordpress) was hacked and I ended up losing months of hard work due

to no back up. Do you have any methods to stop hackers?
Feel free to visit my web page nilghau

Anonymous said...

I really appreciate this post. I have been looking everywhere for this!
Thank goodness I found it

on Bing. You've made my day! Thanks again
Here is my website : Salivate

Anonymous said...

Hey There. I discovered your weblog the usage of msn.
That is a

very neatly written article. I will be sure to bookmark it and

come back to read extra of your helpful info. Thank you
for the

post. I will certainly return.
Feel free to surf my weblog : Torredembarra,

Anonymous said...

advertising
Here is my web blog : http://xaviii.buenblog.com/2012/01/31/curiosidades-de-la-Vida-sabias-q/

Anonymous said...

Hey just wanted to give you a quick heads up. The words in your post seem to be
running off the screen in Chrome. I'm not sure if this is a

format issue or something to do with browser compatibility but I

figured I'd post to let you know. The style and design look great though!
Hope you get

the issue resolved soon. Thanks
Here is my blog post : ww41.prestige-autosports.com

Anonymous said...

Valuable info. Lucky me I found your website by accident, and I am shocked why this

accident did not happened earlier! I bookmarked it.
Here is my website devein

Anonymous said...

You actually make it appear so easy together with your

presentation but I find this matter to be actually something

that I feel I'd by no means understand. It sort of

feels too complicated and very vast for me. I am

taking a look forward to your subsequent

publish, I’ll attempt to get the cling of it!
Also visit my site ... koreanewsonline.Blogspot.com.es/2012/10/ancient-philippine-treasures-set-to.html

Anonymous said...

Hi there, simply became aware of your weblog via Google,
and located that it is truly informative. I am gonna

be careful for brussels. I will appreciate when you continue this in future.

A lot of folks might be benefited from your writing. Cheers!
My site > ktosexy

Anonymous said...

whoah this weblog is great i like

studying your articles. Stay up the good work!
You

recognize, many persons are looking

around for this information, you can aid them greatly.
Here is my website ; superman doomsday

Anonymous said...

Thanks for your own hard work on this site. My mom

enjoys carrying out

internet research and it is obvious why. Almost all know all of the
dynamic manner you

create useful guides on

the blog and as well as

improve

response from website visitors on the idea so our own girl is undoubtedly studying so much.
Have fun with the remaining portion of the year. Your conducting a very
good job.
Also see my webpage > http://peccavi.com/

Anonymous said...

great submit, very informative. I'm wondering why the other experts of this sector do not understand this.

You should proceed your writing. I'm confident, you've a huge readers'

base already!
Also visit my webpage ... http://www.oahuislandnews.com

Anonymous said...

I was just searching for this information for a while.
After 6 hours of

continuous Googleing, finally I got it in your site. I wonder what's the lack of

Google strategy that do not rank this type of informative websites in top of the list.

Usually the top web sites are full of garbage.
Here is my webpage - http://nokia.satiro.es/user/BebeVdz/history

Anonymous said...

What i do not understood is actually how you're not actually much more well-liked than

you might be now. You are very intelligent. You realize thus

significantly relating to this subject, produced me personally consider it from so many varied angles. Its like men and women aren't fascinated unless it is one
thing to

accomplish with Lady gaga! Your own stuffs great.
Always maintain it up!
Also visit my webpage : car loan rates

Anonymous said...

An fascinating dialogue is worth comment. I

believe that you need to write extra on this topic, it may not be a taboo subject but generally persons are not
enough to talk on such topics. To the next. Cheers
Feel free to visit my web page :: http://dancallis.blogspot.ru/2011/12/dslr-video-w-canon-5dmk2.html

Anonymous said...

I truly appreciate this post. I have been looking all over for this!
Thank goodness I found it

on Bing. You have made my day! Thank you again
Also see my page: lovinghugs.com

Anonymous said...

My programmer is trying to convince me to move to .

net from PHP. I have always disliked the

idea because of the costs. But he's tryiong none the less. I've been using WordPress on
a variety of websites for about a year and am nervous about

switching to another platform. I have heard excellent things about
blogengine.net. Is

there a way I can import all my wordpress posts into it?

Any kind of help would be

greatly appreciated!
My web-site : ireadthatsomewhere.blogspot.ru

LinkWithin

Related Posts Plugin for WordPress, Blogger...