amanda ed 492 senior research paper

8/2/2019 Amanda ED 492 Senior Research Paper

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Manipulatives for math in Elementary school

Amanda Lewandowski

ED 492

Alverno College

Fall 2010


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Abstract

This paper shows my research and understanding of the role of manipulatives in math

instruction and the effects those manipulatives can have on students learning. I have always

enjoyed using manipulatives for math because I am hands-on learner. When I would use

manipulatives for math, I would get a better understanding of the math concepts because I

could see and touch the problem instead of just reading it out of a book. I thought that it would

be interesting to research if others feel the same about this topic. My research question was

Does using manipulatives for math in elementary school affect students learning? Through

the literature I read I formed four themes that I would base my findings on. Those themes

included, the pros/cons of using manipulatives, how are manipulatives used, who benefits from

using manipulatives and what is the teachers role? I conducted my interviews and observations

off of my four themes that fit my findings.

My first theme, pros/cons of using manipulatives, gave me an insight to how

manipulatives can affect students learning. From my literature review I learned that using

manipulatives during math lessons help the students get a better understanding of math

because manipulatives can be moved around to show a math concept. I also learned that using

manipulatives is a better approach for non-traditional learners and that a hands-on approach is

an effective learning technique for all learners. Using manipulatives during math can cut down

on math anxiety and help improve childrens long-term and short-term retention of math.

Experiences with manipulatives for any period of time can give the students a well- needed

deeper understanding of math concepts.


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The people I interviewed talked about students not needing a background with

manipulatives in order to use them correctly. They also talked about how students can use

manipulatives for short term and still get the same learning benefits as if they used them for

long term. Teachers can use items that are easily found in a household for manipulatives. My

observations allowed me to see that students can use manipulatives for a short term and still

get the same understanding just like if they were using them long term.

My next theme, how are manipulatives used, helped me understand the different math

concepts teachers use manipulatives for and how manipulatives can enhance students

learning. The literature that I read said that teachers must make connections between the math

concepts and solving the problems using manipulatives. My interviewees talked about the

different math concepts that manipulatives work best for and the concepts that dont work well

with manipulatives.

Who benefits from using manipulatives helped me understand the different types of

learners that learn best with manipulatives and the learners that dont learn well with

manipulatives. The literature that I read said that manipulatives are especially useful for

teaching low-achievers, students with learning disabilities, and English-language learners. My

interviews talked about all types of learners can benefit from using manipulatives.

My last theme, what is the teachers role, allowed me to understand how teachers use

manipulatives in the classroom during math instruction. The literature that I read said that

teachers who use manipulatives with young learners help them to explore mathematical

concepts by converting abstract math ideas to concrete models. Math concepts are abstract


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and using manipulatives can help students because they can touch and move the items. My

interviewees talked about a teachers background with using manipulatives, setting rules for

using manipulatives, and math concepts and manipulatives that will be used to get the most

learning of those concepts. My research and findings will inform my reader about the affect

manipulatives have on students learning.


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Table of Contents

IntroductionPage 6

MethodsPage 8

FindingsPage 11

Conclusion.Page 19

References.Page 20

AppendixPage 21


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Introduction

When I was in grade school I can remember my teachers during math instruction would

explain the mathematics concept and then would send the class off to work. I hated math

because the examples that were in the textbook were too hard to understand if you didn t

understand the concept. My own experiences with math in elementary school lead me to find a

different approach to teaching mathematics in primary grades since I would like to be an

elementary school teacher. A different approach to teaching mathematics is using

manipulatives during the math lesson to help the students get a visual picture of the concept

being taught. This led me to ask does using manipulatives for math in elementary school affect

students learning? From this, I have found in my research that manipulatives used correctly

during a lesson can help many different types of learners, help the teacher get a better insight

into the students mathematic understanding, and can help the students form a better

understanding of mathematic concepts.

When organizing my research for this paper I thought about how I could group all of my

information. I decided that from the literature my themes that were reoccurring were

pros/cons how to are manipulatives used who benefits from using manipulatives what is the teachers role


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From my themes I was able to create my questions that I would ask during my interviews. I also

used my themes to direct what I observed during my observations.


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Methods

I started my research by first finding something that I found interesting to use in a

classroom. Since I want to be an elementary teacher I wanted to look at the effects of

manipulatives being used in elementary classrooms to teach math. My research question was

does using manipulatives for math in elementary school affect students learning? Once I

formed my question I started doing my observations at the school I was doing my field work at.

The class was a third grade class with eleven girls and eight boys. This class was also the only

class in the whole school district to work with manipulatives in math. During their math lessons

I would take notes on the math concept they were using manipulatives with and how they were

using the manipulatives to figure out the math problems. By doing my observations this way I

was able to see if the concept was able to be learned with manipulatives and if the students

were learning by using manipulatives.

During this time I was also doing research by searching articles online to develop

findings in which I would base my paper upon. I used keys words such as manipulatives for

math, students learning, effective teaching methods, and elementary school. I wanted to see

what teachers thought about using manipulatives in a classroom for math. Once I would find

articles, I would read each article to see to see what was similar and different between them.

From this I based my research on four findings that I felt related to the area of manipulatives I

was researching and they were pros/cons, how are manipulatives used, who benefits from

using manipulatives, and what is the teachers role.


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For this research project I also interviewed four people about using manipulatives for

math. I interviewed three third grade teachers and one second grade teacher. For all of my

interviews I asked the same set of questions. The questions I asked were

What is your background with using manipulatives? Do you believe the students need a background with using manipulatives in order to use

them correctly?

Do you believe that students get the same learning experience if they use themanipulatives for short term? Or long term?

What concepts do you believe students learn best with manipulatives? What concepts do you believe dont work with manipulatives? What materials work best for manipulatives? What materials dont work for manipulatives? What type of learners do you believe learns best with manipulatives? What type of learners do you believe dont learn with manipulatives? How you ever dealt with parents that believe manipulatives were toys? How do you set rules for the students to work with manipulatives? Where do you store the manipulatives? Do students have access?

I created these interview questions from my findings from my reading. Once I had my

questions I sent them to the four teachers through email because their schedules didnt

work with my class schedule.


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After I found my articles, did my classroom observations, and interviewed the four

teachers I organized all of the information I gathered. Then I assigned a color to each of the four

findings I made and went through all of my papers and highlighted where I saw a theme. This

helped me visually see where all the information would fit into my paper. This method also

helped me see everything I learned because I only had to look at the areas I highlighted in each

article.


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Findings

Teachers can use many different materials for manipulatives. Manipulatives are

important tools to use during math instruction and many researchers have started to see the

benefits of using manipulatives in math. This literature describes the pros and cons, how the

manipulatives are used, who benefits from them, and what the teachers role is when talking

about manipulative use in math. These themes are evident throughout different pieces of

literature. Teachers who are in the classrooms and working with students have their own

thoughts about the use of manipulatives with their students. The themes mentioned in the

literature can also be seen throughout interviews with teachers. Teachers have to figure out

when it is appropriate to use manipulatives during their own math instruction. Observations of

students using manipulatives also give an insight into some of the themes mentioned. This

shows how the manipulatives affect student learning in math. The following findings are based

off of the four themes that were evident throughout the literature, interviews and

observations. The observations take what was seen in the classroom and makes connections to

what was said in the literature read and interviews conducted for this research project.

Pros/Cons

Literature

Learning becomes interactive and engaging as students become comfortable with their unique

learning styles throughout (DeGeorge, 2004) the activities they are involved in. This is an

important connection for students to make because it allows them to take what they are


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learning and become responsible for their own learning. While reading articles about

manipulatives in math I came across some pros and cons about using manipulatives in the

classroom. DeGeorge says that students are better able to visualize math concepts and gain

insight into necessary fundamentals when they use rods, cubes, and other tools. These tools

are used as manipulatives to help students better understand the math concepts being taught.

When children are learning math they have to go through a period of transition from concrete

to abstract ideas that may be difficult to understand. Manipulatives are particularly useful in

helping children move from the concrete to the abstract levels. (Hartshorn, 2003) All of these

articles mentioned benefits of using manipulatives but Boggan mentions that there are ways in

which a teacher can teach use manipulatives incorrectly that will result in the students not

learning the experience. In order for the students to get full benefits from using manipulatives

the teachers and students need to be aware of how to properly use them during math.

Interviews

During the interviews conducted there were lots of opinions about whether

manipulatives had the same effect if used for short or long term use. Debra, a third grade

teacher, said that she hasnt had enough experience with long term usage. In the short term

they are very effective. Lisa, also a third grade teacher, said that I think learning can be

enhanced by using them regardless of how long. she went on to talk about how she uses

manipulatives with her students who have never had experience with them before and it was a

beneficial experience for them. With the four teachers interviewed, none of them have ever


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come across a math concept that couldnt be taught using manipulatives. All of the teachers

talked about the pros of using manipulatives and didnt mention any cons.

Observations

While observing a 3rd

grade student using coin cards to make combinations of how to

make a dollar, you could see the benefits of using manipulatives during math instruction. This

student was not only able to figure out what card coins make a dollar together but also what

the total amount of money on each card was that he didnt at that time to make the dollar.

Looking back at the literature and what it had to say about the benefits of using manipulatives,

Tichenor said that By providing various manipulatives, teachers encourage students to think

about math concepts in multiple ways. This is exactly what was observed with the third grader

learning about money.

How are Manipulatives used?

Literature

Manipulative materials are concrete models that involve mathematic concepts, appealing to

several senses that can be touched and moved around by students. (Heddens, 2000) Having

those concrete models allows the students to move the materials around and visualize the

problem given. It would be easier for students to do a multiplication problem using

manipulatives instead of reading a problem out of a book and asking them to solve the problem


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just using paper and pencil. With a simpler example DeGeorges says that mixing paint colors

brings the concept of ratio alive. For example, one part yellow to two parts blue makes a

different green than one part blue to two parts yellow.

Interviews

While interviewing teachers they all gave examples of how manipulatives can be used

with students. Debra said that manipulatives can be used for all concepts if it is going to be

beneficial to the students learning. She gave examples such as place value, fractions, graphing,

and geography. She also talked about the materials used for manipulatives and she included

characteristics about them that included being well made, colorful and visually appealing.

Angelia, a third grade teacher, gave examples of the types of manipulatives that correspond to

the different math concepts. She noted that clocks are good for telling time, plastic money

helps students understand the amounts of money, cubes can be used for place value/number

sense, and rulers are used for measurement. These are all important math concepts for

elementary students to understand and can be related to real life situations in which

manipulatives would be useful.

Observations

During observations there were students in a third grade class using cubes to help them

with place value. The teacher modeled place value on the board and then showed the students

how to use the cubes to create different three digit numbers. Each student was given a set of


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cubes and had to figure out different combinations to make 100 out of ten cubes. For example

the students figured that each of the ten cubes had to be 10 in order for all of them to equal

100. Then the students were given a worksheet with three digit numbers on them and had to

use the cubes to show the number given. Each student worked with the cubes and figured out

how to use the cubes to show hundreds, tens and ones. This is one example of how

manipulatives can guide student learning and create a learning experience the students will

remember.

Who benefits from using manipulatives?

Literature

Boggan says that studies have shown that students who use manipulatives in specific

mathematical subjects are more likely to achieve success than students who dont have the

opportunity to work with manipulatives. Some children need to use manipulatives to learn to

count while other students understanding of place value increases with the use of

manipulatives. Research also indicates that using manipulatives is especially useful for teaching

low achievers, students with learning disabilities, and English Language learners. This is saying

that all students can benefit from the use of manipulatives no matter who the student is.

Interviews

Jenny, a second grade teacher, said that all students can benefit from manipulatives.

ELL students, students with learning/cognitive disabilities, children with small motor trouble,


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and visual learners can benefit from manipulatives. Jenny also talked about the students who

would have difficulty using manipulatives. She said that students with attention problems or

organizational issues may need one-on-one assistance in order to get the most from an activity

using manipulatives. Lisa talked about kinesthetic learners and how they enjoy the movement

while using manipulatives. She also mentioned that visual learners are able to see concepts

differently when using manipulatives during math. She continued by saying just about

everyone enjoys using manipulatives and can learn from them. She did mention that some

students may have a difficulty using manipulatives to understand math. She talked about

students who are extreme auditory learners sometimes dont get as much out of using

manipulatives as others would during exercises using manipulatives.

Observations

While observing in a third classroom there were many students that benefited from

using manipulatives during their math instruction. The students in this class had a wide range of

abilities and during math all of the students were able to use manipulatives, no matter what the

manipulative were, to help better understand the specific math concept. One child who had

attention issues was more concentrated on the work he was doing while using manipulatives.


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What is the teachers role?

Literature

Elementary teachers who use manipulatives to help teach math can positively affect

students learning. Students at all levels and of all abilities can benefit from manipulatives.

(Boggan, 2009) Teachers have the responsibility of deciding what manipulatives to use and

when to use them with students during math. The teacher has to decide what will be

appropriate for the students in the specific class. Hartshorn says that teachers must choose

activities and manipulatives carefully to support the introduction of math concepts.This also

connects to Boggan who says that teachers need support making decisions regarding

manipulative use including when and how to use manipulatives to help them and their students

think about mathematical ideas more closely. He continues to say that teachers need to know

when, why and how to use manipulatives affectively in the classroom as well as opportunities

to observe firsthand the impact of allowing learning through exploration with concrete

objects. The teachers role is very important and should be the reason that manipulatives are

effective in the classroom.

Interviews

While interviewing teachers, they focused on how they set rules/context for the

students before using manipulatives. These teachers set up success for the students before

having them learn using the manipulatives. Debra mentioned that students should respect the

materials and if they are not being used correctly they are removed from the lesson. If

necessary the student is only allowed to use them with teacher supervision. This does not


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happen very often. Debras role in her classroom is to make sure that all of the students are

using the manipulatives in a way that is beneficial to their own unique learning styles. Jenny

said that the teacher should set clear and high expectations for each student. she also said if

students know what to do and know your expectations they will need fewer extra rules during

instruction.

Observations

During observations in a third grade classroom, the teacher would always demonstrate

how to use the manipulatives properly for each math concept she was teaching. This allowed

the students to visually see what she was asking them to do. Then the manipulatives were

handed out to the students to be used with the specific math concept in mind. The teacher was

able to assist students work with the manipulatives during their work time.


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Conclusion

All of the literature, interviews, and observations that I have gathered and used in my

research paper give my readers the information needed to understand how important

manipulatives are in a classroom. There is a wide variety of manipulatives and it is important to

understand the different types in order to use them for the most effective learning for the

students.

What is learned through using manipulatives is more than what a student can get out of

just reading a problem from a textbook and trying to do it. Manipulatives, if used correctly,

allow the students to understand math concepts that are abstract by moving concrete

materials. This allows the students to construct their own understanding of the math concepts

and they can apply their understanding to other math related concepts.

Does using manipulatives for math in elementary school affect students learning? is

the question that my research paper is about. Through the literature I read I formed four

themes that I would base my findings on. Those themes included the pros/cons of using

manipulatives, how manipulatives are used, who benefits from using manipulatives, and what is

the teachers role? I conducted my interviews and observations off of my four themes that fit

my findings. From the literature and observations that are mentioned, the importance that

manipulatives have on students learning is evident. Manipulatives do affect students learning

in a positive way and should be used doing math lessons to help students get a better

understanding of the different math concepts.


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References

B o g g a n , M a t t h e w , H a r p e r , S a l l i e , & W h i t m i r e , A n n a . ( 2 0 0 9 ) . U s i n g

m a n i p u l a t i v e s t o t e a c h e l e m e n t a r y m a t h e m a t i c s . J o u r n a l o f I n s t r u c t i o n a l P e d a g o g i e s , 1 - 6 .

D e G e o r g e , B a r b a r a , & S a n t o r o , A n n e M a r i e . ( 2 0 0 4 ) . M a n i p u l a t i v e s : a h a n ds - o n

a p p r o a c h t o m a t h . P r i n c i p a l , 8 4 ( 2 ) , 2 8 .

H a r t s h o r n , R o b e r t , & B o r e n , S u e . ( 2 0 0 3 ) . E x p e r i e n t i a l l e a r n i n g o f

m a t h e m a t i c s : u s i n g m a n i p u l a t i v e s . R u r a l E d u c a t i o n a n d S m a l l S c h o o l s .

H e d d e n s , J a m e s . ( 2 0 0 0 ) . I m p r o v i n g m a t h e m a t ic s t e a c h i n g b y u s i n g

m a n i p u l a t i v e s. U n p u b l i s h e d m a n u s c r i p t , D e p a r t m e n t o f E d u c a t i o n , K e n t S t a t e

U n i v e r s i t y , K e n t , O h i o . R e t r i e v e d f r o m h t t p : / / w w w . f e d . c u h k . e d u

R o s e n , D i n a , & H o f f m a n , J o . ( 2 0 0 9 ) . I n t e g r a t i n g c o n c r e t e a n d v i r t u a l

m a n i p u l a t i v e s i n e a r l y c h i l d h o o d m a t h e m a t i c s . Y o u n g C h i l d r e n , M a y 2 0 0 9 , 2 6 -

3 2 .

T i c h e n o r , M e r c e d e s . ( 2 0 0 8 ) . M a t h m a n i p u l a t i v e s . N e w T e a c h e r A d v o c a t e ,

1 5 ( 3 ) , 4 - 5 .
http://www.fed.cuhk.edu/http://www.fed.cuhk.edu/http://www.fed.cuhk.edu/


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Appendix

Here are the questions that I used for my interviews

1. What is your background with using manipulatives?2. Do you believe the students need a background with using manipulatives in order to use them

correctly?

3. Do you believe that students get the same learning experience if they use the manipulativesfor short term? Or long term?

4. What concepts do you believe students learn best with manipulatives?5. What concepts do you believe dont work with manipulatives?6. What materials work best for manipulatives?7. What materials dont work for manipulatives?8. What type of learners do you believe learns best with manipulatives?9. What type of learners do you believe dont learn with manipulatives?10.How you ever dealt with parents that believed manipulatives were toys?11.How do you set rules for the students to work with manipulatives?12.Where do you store the manipulatives? Do students have access?


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Here are the answers from my interview questions

Questions Agree Disagree

1 All have used manipulatives in their

teaching positions.2 All believe that students do not need a

background with manipulatives in order to

use them.

3 All believe that students can use them for a

short term and still get the same benefit.

4 Addition, subtraction, patterns, geometry,

division, multiplication, measurement,

time, money

5 Angelia, Lisa, and Deborah said they

havent come across any.

Jenny- Basic facts memorization

6 Wood, heavy plastic, foam manipulatives,cardstock, materials that are colorful, visual

and easy to use, clocks, cubes, rulers,

thermometers, cereal such as Fruit Loops,

marshmallows, pretzel sticks, M&Ms, Q-

tips, toothpicks, magnets, seeds, spaghetti,

flashcards, measuring cups, tangrams,

money, faction strips, dry erase boards

7 Regular weight paper, construction paper,

materials that are cheap and dont fit well

together.

8 Special Needs, ELL, Visual, Hands-on/Kinestic, small motor trouble, students

with learning/ cognitive disabilities

9 Closed mind, Extreme auditory learners,

and students with tactile issues, students

with attention problems or organizational

problems.

Angelia believes that all types of learners will

benefit.

10 Lisa, Angelia, and Jenny have never come

across any parents that dont agree.

Deborah- has come across parents that dont

think upper grades should use them.

11 Clear explanations and high expectations,

model, allow exploring and playing first.

12 Students have access to manipulatives that

they are currently working with. Others

manipulatives can be used if asked for.


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A chart of the four themes used in this research paper and the

interview questions that the theme connected to.

Themes- Question #s

What is the teachers role 1, 2,3,11,12

How are manipulatives used 4,5

Who benefits from using manipulatives 8,9

pros/cons 3,8,6,7

amanda ed 492 senior research paper

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