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					                                                           Elementary Math Enrichment 1

Running Head:       Elementary Math Enrichment

                               Action Research Study

   How do you enrich math instruction for children with a rapid rate of acquisition?

                              Does it make a difference?

                                 Heather M. Balsamo

                              Slippery Rock University

                                                            Elementary Math Enrichment 2

       The question for this study was developed based on a pattern I was seeing in my

math class. A few of my fifth grade students were always finished with their regular

work a long time before their peers. Initially I addressed this issue by either giving them

additional work or having them peer tutor. At first, they enjoyed the extra work, but over

time they began to resent it and were not at all enthusiastic about receiving it. I also

discovered that they would rather be working than tutoring their peers. I began pre-

testing each lesson to determine if these students had already grasped the concepts before

the lessons. I quickly learned that the vast majority of the time these students did not

know the content prior to the lesson being taught. However, after the lesson was taught,

they were ready for more challenging work than were most of their classmates. This led

me to the question of how to enrich students with an accelerated rate of acquisition while

still meeting the needs of the regular learners in the classroom.

       My cooperating teacher and I have 17 students in our fifth grade math classroom

in the PR School District. We have an interesting mix of students in this class. The

“gifted” students were identified in previous years and are receiving enrichment through

a pull out program during our math time. This leaves all the students who did not qualify

for the program, including students with IEP‟s. Although we do not have the highest

achieving students in the classroom, there is still a wide variety of ability among the

students who remain. I have several students who need to go through each lesson, but

who are ready for more challenging material once the lesson is taught. Many of these

students get through the practice material given after the lesson in half the time of the

other students. These students have very little trouble with the concepts we address and

                                                           Elementary Math Enrichment 3

often become bored during the last 20 minutes of class because they are finished with the

work and their classmates are still working. I am concerned with reaching all students,

but with this study I focused on making sure I could challenge the students who have an

accelerated rate of acquisition so they would not become bored.

        In doing my research, I observed students for several weeks to see which students

seemed to need more of a challenge on a regular basis. I noticed that some students

worked very quickly and were able to accurately complete the regular problems in about

half the time as the other students. I also noticed that I had several students who did not

work as quickly, but did work as accurately as the faster students. I determined that part

of the reason for this was that the two fastest students almost always worked

independently and competed with each other to see who could finish first. The other

students who were doing well but working more slowly were more apt to be working

cooperatively with their other classmates with no interest in seeing who could get

finished first.

        After determining which students were ready to receive the more challenging

work, I set up the study to determine the effectiveness of enriching the more advanced


Background Research/Survey of Literature

        Research in this area strongly suggests that teachers need to find a way to reach

all learners in the classroom. Teachers need to make sure that they are not leaving behind

the students who are at a lower level but at the same time they must make sure they are

                                                             Elementary Math Enrichment 4

challenging those students who do not need as much repetition and are ready to move

more deeply into the concept at hand.

       For too long, the abilities of higher achieving students have been ignored because

they did not test into the group that is pulled out for enrichment and were therefore placed

in the regular classroom to learn at the same pace as the students who do not learn as

quickly or have learning disabilities. Standardized testing has also placed more of a

focus on the students at the low end of the achieving spectrum because of accountability.

However, equity in the classroom can only happen when teachers are able to

acknowledge that their students possess individual differences. Teachers also need to

realize that their more able students deserve accommodations as much as their students

with learning disabilities and challenges (Thorson, 2000).

       One key aspect of this is to set high goals for all students. “When you have high

goals, the kids tend to do better” (Lumsden, 1996). If the expectations are set too low,

especially for your higher achieving students, “kids will often adjust their performance

downward to meet your low expectations” (Lumsden, 1996). Teachers must recognize

that all students of every level of ability have a right to an appropriate education that

challenges them. Too many of our children with higher ability are receiving an education

that is boring and unfulfilling (McClure, 2001). If we fail to provide an environment that

challenges all students, we are encouraging the children to underachieve (Reed, 2004).

       The research shows a variety of ways to deal with these issues from challenging

the students to go deeper into the concept to compacting the curriculum to allow the more

able students to cover the material more quickly.        Teachers need to find ways to

                                                               Elementary Math Enrichment 5

challenge their higher achieving students while still meeting the needs of the others in the

classroom. The research supports the need for teachers to take students of higher ability

deeper into the content and encourage them to use higher order thinking skills. “Many

lessons in mathematics … focus on activities which emphasize what Bloom denoted as

„lower order thinking skills‟… Able pupils are often very efficient at these kinds of

activities and quickly become bored by doing „more of the same‟… They can benefit

from extending … into activities which promote higher order thinking skills” (McClure,


         The research shows that differentiating to meet the needs of all learners in the

classroom helps struggling students get what they need to be successful and helps more

advanced students get what they need to be engaged and challenged so they do not

become bored and uninterested. Encouraging students of higher ability to use higher

order thinking skills is an excellent way to keep them challenged and engaged in the

mathematics classroom and having them keep pace with the rest of the class. Teachers

just need to plan work that challenges all students at a level that is suitable to their ability.

Action Research Design (Pseudonyms have been used to protect student identities)

         My study follows what the research has shown to be effective in working with

students with more advanced abilities. Because it was determined that all students

needed the actual lesson, instead of modifying and differentiating the instruction, I chose

to differentiate the product. I did this by assigning more challenging work on the same

concept to my students receiving enrichment. Compacting the curriculum would not

                                                          Elementary Math Enrichment 6

work in this classroom because the students all need each lesson and are not at a level of

ability that would allow them to move ahead in the curriculum.

       Before my study, I was providing extra challenge work for three of the students in

my classroom. Two of the students, “Katherine” and “Carter”, were students who were

always finished with the in-class work in a short period of time and were becoming

bored. They sat next to each other and often competed to see who could finish first. The

third student, “Vincent”, was given this extra work by request of his parents. At first,

these students were excited to be receiving “enrichment”. However, after a while their

enthusiasm turned to dissent at having to complete more work than their peers. I agreed

that this arrangement was not very fair and designed this study to attempt to remedy the

situation. I wanted to make sure they were challenged without having to do twice as

much work as their peers.

       “Katherine” is a very energetic, enthusiastic and competitive student. She always

participates in class and has been working on her ability to explain her problems. She has

been very successful in math this school year and she enjoys the opportunity to accept a


       “Carter” is also very energetic and competitive. He enjoys being challenged and

particularly enjoys working on brain teaser activities. “Carter” has been very successful

in math this year although he tends to make simple errors because he tends to rush

through his work. This comes from his competitive spirit and the fact that he likes to

finish before “Katherine”.

                                                             Elementary Math Enrichment 7

       “Vincent” is also an energetic and competitive student. However, “Vincent” is a

unique case. I have gotten the impression from “Vincent” that he would rather not

receive enrichment. “Vincent” is receiving enrichment because his parents want him to

receive it. “Vincent” is an average math student who has struggled, to some degree, with

many of the concepts we have covered.             He does not complain about receiving

enrichment, but he is not anxious to seek it out either. My main reason for choosing to

place “Vincent” in the enrichment group was the persistence of his parents.                  If

“Vincent‟s” parents were not pushing for him to be enriched, I would not have chosen

him for this study. His work habits, ability and attitude were not consistent with what I

looked for in the other students chosen for this study.

       The remaining four students in this study were chosen based on test grades and

accuracy of completing assignments. These students, “Cynthia”, “Brittany”, “Samantha”

and “Margaret”, do not always work quickly, but they usually work accurately and

understand the concepts quickly without too much difficulty.

       “Cynthia” is a very pleasant and cheerful student who is always a willing

participant in class. She does not always have the right answer, but she is willing to take

risks and learn from her mistakes. Overall, “Cynthia” has performed well in math this

year. When she struggles or misunderstands a concept, she is very willing to discuss her

mistakes and do what she needs to improve and learn from them. “Cynthia” is usually

able to do the regular class work with little trouble. I felt that her attitude and her ability

made her a good fit for this enrichment study.

                                                           Elementary Math Enrichment 8

       “Brittany” is also a very pleasant and cheerful student. She is not as vocal in class

and volunteers to give answers only occasionally. However, it became apparent through

observing her work that “Brittany” is a very capable student. Although she works

somewhat slowly, her work is accurate and she is able to do the regular class work with

little trouble. She will ask questions if she is confused and she is very helpful to other

students when working in cooperative groups.

       “Samantha” is an energetic and pleasant student who always has a positive

attitude. She does well in math and is very invested in getting good grades. She enjoys

being challenged and likes to try to keep up with the most advanced students in the class.

She works efficiently and quickly in math. She is willing to correct and learn from her

mistakes. Her grades and diligence made her a good candidate for this enrichment


       “Margaret” was a questionable addition to this study. Overall, “Margaret” has

done well in math. She has struggled at times, but overall has done very well. She has an

extremely helpful attitude. The main reason I chose her to be part of this study was due

to her success with multiplication and the concepts we were studying over the course of

the action research study. “Margaret” would definitely be a student I would have to

monitor on a regular basis to be sure enrichment was appropriate depending on the


       The research I found suggested that a way to differentiate for more advanced

students was to take them deeper into the concept the entire class is studying. I felt this

was the best method for this class due to the fact that the students who were being

                                                          Elementary Math Enrichment 9

enriched still needed the lesson in order to be successful. I decided that to properly

challenge these students, but keep on the same lesson as the rest of the class, I would

assign them more challenging problems in class while the other students worked on the

less challenging practice problems in the book. For some lessons, I assigned the more

challenging problems in the book to the enriched students and the less challenging

problems to the other students. Other times I would give the enriched students the

practice page to work on in class. This page is what the other students receive for

homework. I did this because the practice page problems were more challenging than the

problems in the book. For homework, I would assign a problem solving page to the

enriched students and the regular practice page to the other students. This method

provided an on-going challenge to the enriched students on a daily basis. For review

activities, I gave the enriched students a Marcy Cook activity in which they were required

to fill in the blanks of various decimal multiplication problems using tiles numbered 0-9.

Each tile was used once on each page. They had to use problem solving strategies and

their knowledge of multiplying decimal numbers to figure out where to place the number

tiles for these problems. After completing a page they would self check using an answer

sheet. The students were challenged and thoroughly enjoyed this activity. The other

students in the class worked in small groups on a product pinwheel game in which they

had to multiply decimal numbers to find products. This activity allowed the students to

further explore the concept of multiplying decimals without challenging them beyond

their capabilities.

                                                        Elementary Math Enrichment 10


       For collecting data, I chose to let the students tell me how they felt about the

enrichment by way of a questionnaire at the conclusion of the study. I felt this was the

best way to determine if the students were more challenged than they had been before the

study. I also included questions to ascertain if the enrichment impacted their attitude

about math and learning.

       My first question was open ended to get a feel for how the students viewed math

enrichment. To follow are the responses the students gave to the prompt: “To me, math

enrichment means…”

        “…to think more. It helps me get smarter in math” (“Katherine”).

        “…not math you already know. Its math that gets you working. Not just
         sitting around bored because you know the answers” (“Carter”).

        “…more challenging math. Also funner math” (“Vincent”).

        “…to think harder and more challenging” (“Cynthia”).

        “…that I‟m doing well in math, and I need harder things to help my grades do
         good” (“Samantha”).

        “…receiving challenges and harder math for smarter kids” (“Brittany”).

        “…it‟s the same lesson as everybody else in the class. It‟s just a little harder
         problems. That it doesn‟t mean you‟re a better person than other people”

   The second question was also in the form of an open ended statement. Many of the

answers were similar, but I did get an unexpected response from “Samantha”. To follow

are the responses to the prompt, “Receiving math enrichment made me feel…”

        “…smart. It made me feel good” (“Katherine”).

                                                           Elementary Math Enrichment 11

        “…like I am smarter” (“Carter”).

        “…better because it was funnier. It also made me happy” (“Vincent”).

        “…a little bit smarter and excited for more challenges” (“Cynthia”).

        “…unique and smart” (“Brittany”).

        “…great because “Katherine” would always say „I got an enrichment page.‟ I
         always would feel really bad and not as smart. Now I feel really good because
         we‟re even smart” (“Samantha”).

        “…more confident in math. I don‟t feel any more special than other people”

       “Samantha‟s” response caught me off guard because I had not realized that the

enrichment I was giving to “Carter” and “Katherine” was having an impact on the other

students. It taught me that differentiation is a topic that needs to be addressed with all

students. When I have my own classroom it will be my goal to ensure that all students

understand that they will receive the materials and instruction they need to make them

successful. Because all students have different abilities, their work will not be identical.

       The remaining questions on the survey asked students to give a rating of 1

through 4 to express their answers. This was followed by an open ended response for the

students to explain the reason for their answers.

       Question three asked the students to rate how much they liked receiving math

enrichment. Their choices were: (1) not at all; (2) not very much; (3) a little bit; and (4)

very much. All students circled 4, which indicated that they all liked math enrichment

very much. Their reasons for why they liked math enrichment varied as follows:

            “Because you get to do something other people don‟t. You also get to
             sometimes go apart from the class” (“Katherine”).

                                                          Elementary Math Enrichment 12

            “Because it challenges me to work harder” (“Carter”).

            “Because I like it. It is also fun and challenging” (“Vincent”).

            “I like challenges and I like improving my grades” (“Cynthia”).

            “Challenges are fun! I like hard because if it was easy it‟s boring and
             makes my brain turn on. Besides, regular is pretty easy” (“Brittany”).

            “Because it will help me in math and get better grades. I love challenges
             very much” (“Samantha”).

            “It made me start to like math a little be better. I never really liked math”

       The next question asked the students how they felt about the level of the work

they received. The results were as follows:

                      Student View of Enrichment Difficulty Level

              Too Hard


              At my level

              Too easy

                                  0           1       2       3        4        5

                                                  Number of Students

       As a follow-up to this question, the students were asked to tell what they think

they learned at a higher level because of the enrichment. Their responses follow:

                                                          Elementary Math Enrichment 13

            “I think it made me understand more and it made me smarter”


            “Carter” did not respond to this question.

            “Not that much because I did it before” (“Vincent”).

            “[I learned] more challenging multiplication problems” (“Cynthia”).

            “A lot! Regular math teaches me the most, but [I learned more by] putting
             a challenging twist on math” (“Brittany”).

            “I learned so much more and when I learn harder things it will be easy for
             the tests and quizzes” (“Samantha”).

            “I learned just about the same thing of 5th grade math. It was just a little
             harder” (“Margaret”).

       It became apparent after seeing the results to this question that the majority of

these students did not find the enrichment work very challenging. This tells me that I

could have given them more challenging work. It also shows me that I will need to

monitor student perceptions on a regular basis to be sure the students are being

appropriately challenged.

       The next question asked the students how receiving enrichment has changed their

attitude about math. The results follow:

                                                       Elementary Math Enrichment 14

                  How Enrichment has Changed Student Attitudes
                                  About Math

              Do not like math as
              Attitude has not
              Like math a little bit
              Love math a lot more

                                           0           1           2           3

                                                   Number of Students

       When asked to explain the reason for their answers, the students responded as


            “Katherine” responded that she likes math a little bit more “because they
             make me do math more, so I‟m liking it more.”

            “Carter” responded that he loves math a lot more “because I get to
             challenge myself.”

            “Vincent” responded that he likes math a little bit more “because it‟s not
             as easy.”

            “Cynthia” responded that her attitude about math has not changed
             “because sometimes challenges aren‟t hard.”

            “Brittany” responded that she loves math a lot more because “I love
             changes and challenges. Math keeps your brain going and helps a lot in

            “Samantha” responded that she loves math a lot more “because I always
             think I wasn‟t very smart before, but knowing I have enrichment pages I
             am pretty smart.”

                                                         Elementary Math Enrichment 15

           “Margaret” responded that she likes math a little bit more because “it‟s
            more fun doing harder math. You‟re always up for the challenge.”

       I feel that the final prompt gave me the best feel for which students belong in

enrichment math on a regular basis. The final prompt asked the students if given the

choice, how often they would want to receive enrichment. The results follow:

                  If Given a Choice the Students Would:

       No longer receive math
       Receive enrichment
       once in a while
       Receive enrichment half
       of the time
       Receive enrichment

                                      0            2            4          6

                                               Number of Students

       The student responses to why they felt this was are as follows:

           “Katherine” would like to receive enrichment everyday “because I like
            doing things other people aren‟t and I like the challenge.”

           “Carter” would like to receive enrichment everyday “because I like math

           “Vincent” would choose to receive math enrichment only half of the time
            “because I sometimes get tired of it.”

           “Cynthia” would choose to receive math enrichment everyday because “I
            like doing enrichment pages.”

                                                          Elementary Math Enrichment 16

            “Brittany” would choose to receive math enrichment everyday because
             “enrichment math makes me feel unique and smart and I love that feeling.
             Life would be boring if there were no challenges.”

            “Samantha” would choose to receive math enrichment everyday because
             “I like challenges. I think that doing enrichment everyday would make it
             easy for the tests and quizzes.”

            “Margaret” would choose to receive enrichment math only half of the time
             because “I like enrichment math. I just don‟t want it every single day.”

       The results from this question reinforced my thoughts about “Margaret” needing

to be monitored to be sure enrichment is appropriate. I believe “Vincent” enjoys being

challenged but he likes to do the regular work sometimes too. “Vincent” knows what his

parents expect of him, but he is not always enthusiastic about doing it.

Implications and Recommendations for Other Elementary Teachers

       This study took a look at differentiating the products of students with an

accelerated rate of acquisition in mathematics.       It showed that the students in the

enrichment group enjoyed the experience because they became challenged beyond the

level of the text.   As teachers we need to reach the levels of all students in our

classrooms. We cannot allow our more advanced students to become bored while we

attend to our students who do not grasp the concepts as quickly.            With a few

modifications, these students can be challenged and their enthusiasm either maintained or

strengthened through enrichment work and activities.

       Looking at student work and attitudes from the beginning of the year provides a

teacher with a good look at how each of the students handles problems in mathematics.

My cooperating teacher and I noticed early on that “Katherine” and “Carter” had more

                                                          Elementary Math Enrichment 17

advanced ability in math but we were not sure how to challenge them to keep their

interest. These students stood out because they were always the first two finished with

class work and they had very little trouble with the content. After watching the rest of the

class over the course of several weeks, I was able to see other students who would benefit

from more advanced work as well.

       When teachers are looking to enrich students, they need to be careful about the

students they choose for enrichment. There were a few students in this study who

enjoyed the enrichment, but were not enthusiastic about being enriched on a regular

basis. As teachers we need to know where to draw the line with students so they do not

burn out and begin to resent the subject.

       Teachers also need to monitor the level of work they are giving the students to be

sure they are being challenged at the appropriate level. I found through my study that

most of the students felt that the enrichment work was at their level. It is my goal to

make sure these students are being challenged beyond what they already know.

       When I have my own classroom I will utilize what I have learned about student

attitudes toward math and the need to challenge the students who grasp the concepts more

rapidly. It is my desire and commitment to make sure all students receive what they need

to be successful at their level of ability. While working to help all students grasp the

concepts, we cannot expect the more advanced students to continue to do the problems

they already know how to do without getting bored and disenchanted with math. It is our

duty as teachers to make sure these students continue to be challenged.

                                                          Elementary Math Enrichment 18

       I am anxious to go beyond what I learned in this study to look at progressing more

deeply into full differentiation. In this study I looked solely at the product students put

forth after the lesson. I would like to next look at how I can differentiate the instruction

in the mathematics classroom.

                                                         Elementary Math Enrichment 19


Kettler, T., & Curliss, M. (2003). Mathematical acceleration in a mixed-ability
        classroom. Gifted Child Today Magazine, 26(1), 52-57.

Lumsden, L. (1996). Motivating today's students: the same old stuff just doesn't work.
      Portraits of Success, 1(2), 1-8.

McClure, L. (2001). Supporting the able mathematician. Support for Learning, 16(1), 41

Reed, C. F. (2004). Mathematically gifted in the heterogeneously grouped mathematics
       classroom: what is a teacher to do?. The Journal of Secondary Gifted Education,
       (3), 89-95.

Thorson, Ed., A. (2000). Making schools work for every child. ENC Focus: A Magazine
      for Classroom Innovators, 7(4), 34-36.


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