Edudeaf: Math Strategies

Key words: Instructional Strategies/Math/K-12

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Date: Thu, 8 Aug 1996 22:31:56 EDT

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From: Cathy Brandt

Subject: Strategies

To: Multiple recipients of list EDUDEAF

Me AGAIN! :)

One of the other concepts that I am going to particularly stress this year is the development of strategies. We will use these in areas such as math. But, also in dealing with various personal situations, communication needs situations as well as general problem solving.

Anyone done specific Strategy Development in the past? Any resources you care to share? Any ways to implement and develop this thinking with kids?

I'd thought about having a specific area in the room (like our Reading corner, Computer center, Make a Mess) where we would have a large write on area. Kids could put various problems or situations there and we could as a group discuss strategies we could use to solve them. I also thought about keeping resources, examples, games etc there.

Now I need those resources, examples and games. :) In the training I've been giving this summer on Math Software we have talked a lot about strategies we use to solve various math situations. So, I have some of those in mind. But, I need a wide variety of other types of things.

Your 2 cents?

Cathy - who has learned how very FEW strategies she actually employs and how much she does randomly

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Date: Fri, 9 Aug 1996 06:58:00 -0400

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From: Randey

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

Hi Cathy,

Have you ever seen "the UNgame"?? I found one in a christian book store though I'm sure they're available elsewhere since its not really a religious game, but more like you're looking for. You draw a card, and answer the questions... no one can interrupt the person answering. Its for people of all ages. We have a travel size one and use it in the car on long trips. Makes for some interesting conversations.

Randey

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Date: Fri, 9 Aug 1996 09:08:01 -0400

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From: jean wright

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

In-Reply-To: <1.5.4.32.19960809105800.00674520@tir.com>

First, I should introduce myself - I'm new to EDUDEAF. My name is Jean Wright, and I'm a pre-school teacher turned interpreter/tutor (currently going into tenth grade). I have three kids in high school and middle school, (none are deaf). Our foster kids were what got me into signing, one was hard of hearing, several were speech delayed and signing was a great way to help them express themselves. They've all gone on into adoptive homes, but I learned to love signing, so here I am. We enjoyed the Ungame as well - I hope they are still making them. We also have a "What would you do if..." game that the kids made up when they were going through that 'what if...?' stage. The rules are fairly simple, someone poses a problem, real or ridiculous, and we round-robin to solve that problem, sometimes spinning into others along the way. The 'moderator' decides when the discussion gets ridiculous. We did a lot of safety training this way, at home and in my Head Start classroom. e.g.: What would you do if you saw a fire? What would you do if your brother was sick, and your parents weren't home? How would you know when to get help? Who would you call? The kids often took the game home to their own families, and drove them nuts with it, too. (It can get a little crazy, but that's the fun of it) -and, Cathy, IMHO, sometimes the best teaching is done without a visible strategy - it's just a little scarier that way. JSW*

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Date: Sat, 10 Aug 1996 22:09:18 -0400

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From: "G.Jane Harmon"

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

Cathy, I fail to see how mathematics can have any strategy. One either knows the rote method of solving the problem or they don't. There aren't any two ways to do a problem, IMO; whereas, with a real life problem, there are multiple ways of solving a problem. Solving life problems boil down to the objective(s) and what is or is not acceptable to the individual needing a solution.

Just my 2 cents worth.

gjane
Beaufort, SC -- soon to be Bel Air, MD (civilization, again!!)

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Date: Sat, 10 Aug 1996 22:46:03 -0400

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From: Linda Semesky

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

Dear gjane,

There are numerous ways to solve a problem. One small example, I used on my son Alex..5-1/2 and HOH....today was this. He had to find out how many pounds this guy had gained if each of his 6 pieces of clothing weighed 15 pounds. Well, the math software was pretty sophisticated so it was expecting multiplication of 15X6. Because Alex is turning 6 in October, he does not understand multiplication. He does understand addition and this software let you input the data into a calculator and let it do the calculations. So, I showed him that he could get his answer by adding the 15 pounds, 6 times. He did it on the calculator and got 90...he was right and thrilled and accomplished the same task of solving the problem that a third grader might. He just used simpler tools.

Also, you can find the height of a tower many different ways. Depending on what you chose to measure you can use the sine, cosine, tangent, cotangent to determine the height of the tower. It all depends on what is easiest to measure. The angle that the top of the tower makes with the ground. The distance you are from the tower when you measure the Angle. The distance from the top of the pole at an angle to where you are standing. Etc.

There are different ways of proving Geometry theorems and on and on. Yes, so what you must teach is strategies how possible ways to look at the problem.

Even if you're faced with a problem that you can't do, if you can break it down into another problem you understand, you can solve it. Just like with Alex, he used addition instead of multiplication because he didn't know what 15X6 was. This strategy needs to be taught to anyone. It helps them learn what multiplication really is....really multiple additions and how to get around things they may not know by breaking them down into simpler components. This is one of the fundamentals of succeeding both in math and in life...

My two cents,

Linda S.
from Towson, Maryland.....too much civilization to be civilized anymore

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Date: Sat, 10 Aug 1996 23:07:57 -0400

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From: "Barbara K. Strassman"

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

Cathy-

I'd like to recommend a wonderful article on cognitive strategy instruction:

Harris, K. & Pressley, M. (1991). The nature of cognitive strategy instruction: Interactive strategy instruction. Exceptional Children, 57(5), 393-404.

Basically, they recommend that you think aloud and that you explain to children when, where, why, and how to use a strategy. Then, the kids need LOTS of practice with increasingly difficult materials.

If you can't get a copy of this, I could mail you one.

Barbara Strassman
Trenton State College

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Date: Mon, 12 Aug 1996 00:59:56 EDT

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From: Cathy Brandt

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

In-Reply-To: Message of Sat, 10 Aug 1996 22:09:18 -0400 from

Thanks for your thoughts. I appreciate hearing from all perspectives. But, I happen to strongly disagree on this one. I do believe that it is essential that kids do know things rotely such as math facts. But, I don't believe that is the only end or goal in math.

Kentucky is in the midst of major education reform. One of the areas of this is the development of critical thinking skills. Story problems in math is one of the hardest areas for both hearing children and those who don't hear. A child can read the problem over and over - knowing all of the basic math facts by heart - and NEVER be able to solve the problem.

The development of strategies are crucial. We all use them every day when we deal with numbers. But, most of us use them so subconsciously that we don't realize HOW we think. This is so important for children to understand.

There are key words to use, there are steps to organizing the data so that one can solve the problem. We use a lot of "open ended" questions here. To most of you that simply means essay questions. These require more than just a factual answer. We go through various "strategies" as we organize our thoughts to answer such questions.

Even when the answer is strictly right or wrong there can be more than one way to arrive at the solution. The example about multiple addition when a child doesn't know multiplication yet is excellent. There are many other situations like this. It is amazing to me when we do math problems in class and I ask HOW did you arrive at that answer to see the variety of ways kids have used to find the RIGHT answer.

I'm not discounting the importance of rote knowledge. But, I am saying that it is CRITICAL that children be able to think about how they think so that they can attack areas of new information where rote knowledge isn't possible.

Cathy - who often finds this area one of the most challenging and most rewarding when students are learning HOW to arrive at solutions

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Date: Mon, 12 Aug 1996 06:30:53 -0400

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From: randey

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

< have you ever seen "the UNgame"?? i found one in a christian book

i thought maybe you could go thru the deck, pick out certain questions that you think they could answer such as "name three things you like about yourself". use them for journal questions if you have them keep journals. i don't know what age you mean by "elementary aged" though. maybe if they're younger, they could draw the 3 things they like. perhaps something like would show them the difference between the tangible and intangible... just a thought...

randey

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Date: Mon, 12 Aug 1996 19:36:42 -0400

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From: Linda Semesky

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

One of the things that I've been working on tonight with Alex is that if you see the word more in a word problem it means add (+), if you see the word less or take away then it means subtract (-). So he is learning the strategy of translating the word problem into a straight calculation. And, he's almost got it down consistently. Another ex., of strategy in math.

Linda S

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Date: Mon, 12 Aug 1996 23:41:35 EDT

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From: Cathy Brandt

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

In-Reply-To: Message of Mon, 12 Aug 1996 19:36:42 -0400 from

On Mon, 12 Aug 1996 19:36:42 -0400 Linda Semesky said:

>One of the things that I've been working on tonight with Alex is that if you see the word more in a word problem it means add (+), if you see the word

Actually, this is a faulty strategy. In a word problem where one is asked "how many more oranges than apples do I have" the child must subtract, not add. Be careful when using the Key Word strategy. While it may be a beginning it can ultimately lead to confusion.

It's important that you use the complete context or determine what specific information is the question asking.

Cathy - who's had way too many kid learn this in their earlier math training only to come to my room where there are more complex problems and struggle

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Date: Tue, 13 Aug 1996 11:41:37 -0400

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From: Mcfdyn@AOL.COM

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

Way back when ... when I was in elementary school, we were taught to do word or story problems by making an outline.
What I know
what I need to know
operation (or what i need to do)
then work it out

e.g. problem I mentioned

Mom has 15 apples; Alex has 9 apples how many more apples does Mom have?

WHAT I KNOW (I'm not shouting, just using headers)
Mom has 15 apples
Alex has 9 apples

WHAT I NEED TO KNOW
How many more apples Mom has (the difference between Mom and Alex)

OPERATION
subtraction

PROBLEM
15
- 9
--------
6

Back then I thought it was a boring waste of time for easy stuff, but when I became a teacher I saw the benefit of the method for those who didn't get how to do word problems. After a while, it begins to be automatic and the kids don't need to write everything out. HTH

kathy
mcfdyn@aol.com

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Date: Tue, 13 Aug 1996 11:42:21 -0400

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From: Birgit Woelker

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

When I was in school, I was one of the few girls who actually liked math. Why? I think because I had a teacher who could reach me. This teacher thought about what are the subjects kids or youngsters like to talk or to laugh about. And then he transferred a story that could get the child's interest into a math problem.

E.g.:

(4-7 years) Your new puppy ate one of your socks, hid one in the garden and pooped on the third one. You have three pairs of socks, how many are left for you to wear.

(youngsters) You bring home two cute bunnies from a fair. One boy and one girl bunny........They proliferate at a rate of 20 days and usually have 5 kids. The kids mature in 50 days. Your parents are away for the summer. They will be back in 3 months. How many bunnies will you have by then.

(young adults) You like to see your girlfriend who lives in the second floor. Her parents are not allowing her to see you. You like to climb up to her room. If her window is at 12ft height and right in front of the house is a bush which is 3 ft wide how long does the ladder have to be?

You get 2 pimples every day. After 10 days a friend gives you this magic cream that makes 4 pimples disappear in 24 hours. You do not like your boyfriend see the pimples. How soon can you invite him over?

Did you understand the concept? Math can be really fun. I know that I bore my 6 year old daughter to death with apples and oranges. But if I talk about horses or cats or pink hairbows I can get her to do math.

Every once in a while I am facing a group of highly unmotivated students which is a tough task. To teach them adaptation to the environment I use a game which is simple and powerful. Each two students get a piece of colorful paper (wallpaper for instance with prints) and 60 to 100 pieces of small plastic chips in different colors (M&M's might do too). The chips all go onto the paper. With a stopwatch I let them pick as many chips as possible in 10 sec. They have to count the pieces and the remaining pieces on the paper. By comparing the data with data from the other groups they will find that the red chips are less likely to be picked on patterns with red, the green chips remain on the paper that has green print on it etc.

Good luck, Birgit

____________________________________________________________________________

Dr. Birgit Woelker
State University of New York
Department of Molecular Genetics and Microbiology
Stony Brook, NY 11794-5222
phone: (516) 632-8798
Fax: (516) 632-8891
e-mail: birgit@asterix.bio.sunysb.edu

____________________________________________________________________________

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Date: Tue, 13 Aug 1996 16:12:08 GMT

Reply-To: Cheryl_Christian@nynet.nybe.north-york.on.ca

Sender: A Practical Discussion List Regarding Deaf Education

From: Cheryl Christian

Organization: North York Board of Education

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

I really loved the ideas that Birgit put in and am going to copy them to share with my staff when we go back to school next month. The first one really caught my eye because this could come up an interesting solution....

(4-7 years) Your new puppy ate one of your socks, hid one in the garden and pooped on the third one. You have three pairs of socks, how many are left for you to wear.

If all the socks are the same you'd still only have one pair to wear since it takes two but if all the pairs were different and the puppy took one from each pair you'd have none......lots of language ideas could come from this one also.

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Date: Tue, 13 Aug 1996 11:18:08 CST

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From: Malinda Eccarius

Subject: strategies

To: Multiple recipients of list EDUDEAF

Hi,

On the subject of math strategies, I have had a lot of luck having kids create their own story problems from number sentences, and working with them on the language required.

1. I write a number sentence (e.g. 2+3=5).
2. I use stamps, or student artwork if we have time, or their instructions for my artwork if we don't, to create a reasonable story. If the farm set is out, for example, we might put a fence down the middle of the paper and stamp 2 horses on one side of the fence and three cows on the other side of the fence.
3. We work together to decide some background information about the farm (who owns it, etc) so that we can do more problems about this same farm. (optional step, but fun in creating math workbooks for other kids).
4. We make sure that all needed information is stated in clear English (making it a pragmatically appropriate written language lesson--I have done the instruction in ASL with some kids, but the English is written).
e.g. On Mr. Brown's farm, two horses are in one pasture and three cows are in another pasture.
5. We create a question (on early problems, this takes more direction than on later problems) such as "How many ________ does Mr. Brown have in his two pastures?" The cognitive issues here are: What do you call the category that contains both cows and horses, and why not say "on the farm" instead of "in the two pastures?" (because he may have other animals in other places, of course.) A lot of cognitive discussion skills get covered here.
6. The student writes the problem down on the picture page, or dictates, depending on the student's skills and goals.
7. I present a constrasting number sentence (e.g. 3-2=1) to show the impact of the sign. We go through the steps again. Because subtraction is rarely visualized well in workbooks, I insist on two pictures for a subtraction problem. If something is removed, we show before and after. If something is compared, we show them mixed up, and then organized into one on one matching rows.
8. Gradually, the number sentences become more complex, the numbers larger, and the pictures less exact (just a referent or a graph, etc) rather than all of the animals for 27+39, and so forth.

The discussion of what we know, what we need to know, etc., leads naturally from this activity, because we need to provide the information to others. The kids love making math workbooks for each other!

Malinda (who is moving to the University of Nebraska this Friday and hit a deer on the highway this morning and will be moving in a rental car!!)

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Date: Wed, 14 Aug 1996 00:59:13 -0600

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From: jmsimes@STTHOMAS.EDU

Subject: Re: Strategies

To: Multiple recipients of list EDUDEAF

In-Reply-To: <1.5.4.32.19960811030757.006871e8@pop.trenton.edu>

Another GREAT article I found is:

Ellis, E. S. (1993). Teaching strategy sameness using integrated formats. Journal of Learning Disabilities, 26(7), 448-481.

Even though this article is written with LD kids in mind, the strategies and explicit examples of graphic organizers are applicable to all kinds of students. Basically the author contends that "learning strategies need to be taught in a more unified manner so that problem-solving domains are more readily crossed."

Another great book I recently got from ASCD is called _Visual Tools For Constructing Knowledge_, by David Hyerle. It's full of ideas and visual representations for helping kids and teachers develop whole to part and part to whole thinking strategies....... gives good explanations on what visual tools are, why we should use them and how to maximize their potential.

Both of these works really emphasize making connections across disciplines and focus a lot on thinking skills as well as some easy to remember classification systems and "rote" strategies to draw from.

Jolinda
jmsimes@sstthomas.edu

(If you're not a member of ASCD you can find out more about the organization at http://www.ascd.org. I think you can order books and catalogues through that web site too. I found the Journal of Learning Disabilities in the public library.)

Uploaded by: Melissa Close/Kent State University/Deaf Education Major