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
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
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
“…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
“…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
At my level
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
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
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
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
“Vincent” responded that he likes math a little bit more “because it‟s not
“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
once in a while
Receive enrichment half
of the time
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,
Thorson, Ed., A. (2000). Making schools work for every child. ENC Focus: A Magazine
for Classroom Innovators, 7(4), 34-36.