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ACTION RESEARCH PROSPECTUS 1
Action Research Prospectus
Amy Day
Kennesaw State University
ACTION RESEARCH PROSPECTUS 2
TABLE OF CONTENTS
Abstract………………………………………………………………………………….…...1
Introduction……… ………..……………………………………………………………......4
Literature Review……………………………………………………………………………7
Methodology……………………………………………………………………………..…17
Results…………………………………………………………….………………………...20
Limitations…………………………………………………………………………….…....26
Conclusion………………………………………………………………………………….30
References……………………………………………………………………………….….32
Appendix…………..…………………………………………………………………….….32
ACTION RESEARCH PROSPECTUS 3
AbstractSchool systems across the United States are adopting programs to encourage math
discussion. Many schools are requiring teachers to use Number Talks as part of their daily math curriculum. This action research investigates the effectiveness of Number Talks as a strategy to increase number sense within children and a means to explain their thinking. The study took place over a five week period in a second grade mathematics classroom. Six students were involved in the study and data was collected on how often they participated in Number Talks, the percent of time the students had a correct answer, and the percent of time they were able to explain their thinking. A student survey was also given to all students in the class as part of the end of unit assessment. The results indicated that Number Talks may have a positive effects on all students as a means to increase number sense.
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INTRODUCTION
Context of the Research
Each student is unique and comes to school with a varied level of number sense. The
overall deficiency with students’ foundational skills in number sense and numerical reasoning is
being exposed more with the Common Core State Standards (CCSS). The CCSS has eight
Mathematical Practices and calls for instruction grounded in conceptual understanding and
mathematical reasoning in which students are expected to be able to explain their thinking in
mathematics instead of a collection of rules and procedures memorized (CCSSI, 2010). How can
educators build upon a student’s existing number sense in order to help them develop more
numerical reasoning?
Purpose and Importance of the Study
Why has there been such a push for students to have opportunities to talk and discuss
with peers in mathematics? This ideas of “math talk” has been around since the early 1990s
when the NCTM called attention to classroom dialogue. Leaders in the educational community
began pressing for teachers to analyze how they currently used conversation in mathematics
classrooms and to consider how they could use it more effectively (Ball, 1991). Each student
that arrives in the classroom has a different experience with the type and frequency of exposure
to number discussions in which they have received. Exposure to “math talk” begins before a
child is even of age to go to school. Research shows that this “math talk”, experienced at home,
builds number sense. Number sense is a strong predictor of further success in school
mathematics (Dyson, Jordan, Glutting, 2013). If discussion about math build a strong foundation
for number sense, which in turn leads to future success in mathematics, what strategy should
educators use to insure students are given the opportunity to have daily math discussions? One
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strategy that is suggested, which many counties across the United states have adopted and the
Georgia Department of Education includes as part of their unit tasks, is Number Talks. The
purpose of this study is to see if Number Talks are an effective strategy for all students.
Thesis: Statement of the Problem and Research Questions
I was inspired to do my action research on the effects of Number Talks because I have
discovered students do not have a foundation for numbers, also known as number sense. Also, in
my seven years as a teacher, I have experienced many students that fear math. With Georgia
Standards of Excellence, students are required to explain or justify their reasoning. Since I have
been teaching second grade math for the past three years, I see students struggling with
explaining their thinking and justifying their answer when solving math problem. Many times
students will leave the open ended parts of an assessment blank which require them to explain or
justify their answer. Often times I will see students write “I just know”. One instructional
strategy listed on the Georgia Department of Education Website as an effective way of teaching
students to explain their thinking is Number Talks. According to the Georgia Department of
Education website, classroom number talks should be five- to 15-minute conversations around
purposefully crafted computation problems. They are a productive tool that can be incorporated
into classroom instruction to combine the essential processes and habits of mind of doing math
(Georgia Department of Education, 2015). During Number Talks, students are asked to
communicate their thinking when presenting and justifying information they solve (Parrish,
2011). For this reason, I would like to research the instructional strategy Number Talks in my
classroom to see to see its effectiveness as a tool for teaching children how to explain their
thinking. My driving question for this action research is: Are Number Talks an effective
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strategy for educators to use to build number sense within students? If so, are they effective for
all students?
Definition of Terms
Terms central to this study are defined as follows:
Number Talks are defined as a short, ongoing daily routine that provides students with
meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping
students develop computational fluency because the expectation is they will use number
relationships and the structures of number to add, subtract, multiple and divide (Math
Perspectives, 2011).
Number Sense essentially refers to a student’s “fluidity and flexibility with numbers,” (Gersten
& Chard, 1999). Students have a sense of what a number mean, understand their relations to one
another, able to perform mental math, understand s symbolic representation, an can use those
numbers in real world situations.
REVIEW OF LITERATURE
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Introduction
What does the literature say about the importance of math discussion? All of the studies
and literature reviewed documented the importance of students taking part in regular math
discussions to promote number sense. The studies show there is a strong correlation between a
child’s success in higher mathematics and a child’s exposure to number sense at an early age.
Having a strong foundation in mathematics is essential for young children’s success in school.
Children’s early mathematical abilities predict their growth in mathematics (Aunola, Leskinen,
Lerkkanen, & Nurmi, 2007).
For this review of literature, I will begin by presenting research that defines number sense
and the important role it plays with children. Next I will discuss strategies that can be used to
build number sense. After that I discuss what literature says about a specific strategy called
Number Talks and how it can be used effectively to promote number sense within the classroom.
It is important to note that all the “well-known” mathematical specific publications like
the Georgia Department of Education (GDOE), National Council for Teaching Mathematics
(NCTM), Math Perspectives, Teaching Children Mathematics, and Math Solutions have
numerous articles and write-ups that support math discussions as an integral part of the math
curriculum. Their research supports that math discussions leads to math fluency.
Importance of Number Sense
This section presents research which supports the overwhelming significance of number
sense in relation to a child’s success in mathematics. First number sense is defined and all of the
components are listed. Next, literature is reviewed which discusses the negative impacts that can
be imposed on students if they are not exposed to number sense strategies early in childhood.
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This is followed by research that shows the positive impact that interventions can have on
students that show a weakness in number sense at an early age.
What literature says about number sense
As defined earlier, number sense essentially refers to a student’s fluidity and flexibility with
numbers, (Gersten & Chard, 1999). The National Council of Teachers (2000) identified the
following five components that characterize number sense:
Number meaning
Number relationships
Number magnitude
Operations involving numbers and referents for number
Referents for numbers and quantities
Recently there has been a big push for number sense within the classroom. Why is number
sense important? Number sense requires students to think logically. A classic example is
described by Parrish (2011).
Parrish states:
Mary, a third grader, solves 12 minus five on her paper by crossing out the 12 and
recording a zero above the ten and a twelve above the two. When she was asked to share
why she solved the problem that way Mary quickly replies “Because you have to do it
that way when the bottom number is bigger than the top number.” We would like to
believe that this is a unique situation; however, our classrooms are filled with students
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like Mary who view mathematics as a collection of rules and procedures to memorize
instead of a system of relationships to investigate and understand (p. 3).
Simply stated, number sense is referred to as “make friends with numbers” (Carlyle & Mercado,
2012).
So the question is, how do educators help build the foundation of number sense within
students? Burns (2007) highlights the following key research-based teaching strategies to build
numbers sense:
Model different methods for computing
Ask students regularly to calculate mentally
Have class discussions about strategies for computing
Make estimation an integral part of computing
Question students about how they reason numerically
Pose numerical problems that have more than one possible answer
Websites, newsletters, publications, workshops, and literature all around are discussing the
importance of number sense.
Impacts on Students who are not Exposed to Number Sense at an Early Age
Research has been done on the impact of students who were not exposed to number sense
at an early age. In the research I reviewed, the studies targeted students that were of a low social
economic status. A disproportionate number of children from low-income families come to first
grade with weak number competencies, leaving them at risk for a cycle of failure (Dyson,
Jordan, Glutting, 2013). Much research has been done to identify specific number activities that
can improve numerical understanding in preschoolers from low-income families.
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In a study by Ramani, Rowe, Eason, & Leech (2015) titled Math talk during informal
learning activities in Head Start families researches how the increased frequency of engaging
children in number-related activities at home predicted a child’s foundational number skills, such
as counting. Findings suggest that the quantity and quality of number-related experiences that
occur at home can contribute to the variability found in low-income preschooler’ numerical
knowledge (Ramani, Rowe, Eason, & Leech, 2015).
As stated in an article from Yahoo News, “scientists are unraveling the earliest building
blocks of math — and what children know about numbers as they begin first grade seems to play
a big role in how well they do everyday calculations later on” (Neergaard, 2013, para. 2). This is
an impactful statement but is supported by continued research. Just as suggested in the research
of Ramani, Rowe, Eason, & Leech (2015), Neergaard (2013) suggests that children need to be
exposed to conversations at home that involve math and mathematical thinking. Examples
include talking about shapes that are seen around, counting objects and stating a number with the
object, talking about distance, measuring using cooking, etc. It is becoming more and more
apparent that children need a strong foundation of number sense in order to be successful in more
advance math and life skills. If students do not come to school with these foundation then
interventions need to be put in place to help ensure a child’s future success.
Interventions to build number sense
In the study conducted by Dyson, Jordan and Glutting (2013), a universal screener was
used to see if students showed a weakness along with the use of an achievement test. Students
who showed a deficiency were given specific interventions that were researched to help students
with a weakness in number sense. The intervention was carried out in a small group, 30 session,
three days per week for a total of 24 sessions. The specific interventions that were used include
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number comparisons, number board games, number sequencing activities, addition and
subtraction strategies, regular use of manipulatives, etc. Unlike Number Talks, these activities
had students working hands on with math materials. Students were not just using mental math
strategies to explain their reasoning. The results of the study indicated the intervention students
showed a significant growth in the areas of number knowledge, story problems, and number
combinations compared to the “control group”. This study is an example that proves that
Number Talks are not the only proven strategy that could be used to help students build number
sense. Within all the literature reviewed, the overwhelming results showed that students benefit
from discussions in mathematics. This discussion can be focused on mental math questioning or
in some examples, like above it, it can involve the use of math manipulatives in addition to
discussions.
Another example of a math discussion intervention that teachers can use with students
struggling is called revoicing. Revoicing is an intervention used that allows students the ability
to verbalize their mathematical thinking (Chapin, O’Connor, & Anderson, 2003). Below is an
explanation of why revoicing might be an effective intervention to facilitate math discussions
within the classroom.
Chapin, O’Connor, & Anderson (2003) state the following:
When students talk about mathematics, it’s often very difficult to understand what they
say. Even if their reasoning is sound it may not appear sound when they try to put their
thoughts into words. Sometimes it is impossible to tell whether what they have said
makes sense at all. And if you as the teacher have trouble understanding it, there’s not
much hope that the student’s classmates will do any better. Yet given you goals to
improve mathematical thinking and reasoning of all students, you cannot give up on an
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especially unclear students. If the only students who’s contributions are taken seriously
art hos who are easy to understand, few students will ever improve. Deep thinking and
powerful reasoning do not always correlate with clear verbal expression (p. 4).
This is a common scene in the mathematics classroom even if the teacher is comfortable
leading classroom discussion when teaching literature. Chapin, O’Connor, & Anderson (2003)
suggest that due to this uncertainty with math discussions, educators can use revoicing as a talk
mover that can help students deal with the inevitable lack of clarity of student’s contributions to
discussion. In a revoicing move, the teacher essentially tries to repeat some of all of what the
student has said and then asks the student to respond and verify whether or not the teacher’s
revoicing is correct (Chapin, O’Connor, & Anderson, 2003).
This idea of encouraging and giving students the opportunity to talk and have discussions
in math is simplistically stated by Reinhart (2000) when he says “my definition of a good teacher
has change from “one who explains thing so well that students understand” (p. 3) to “one who
gets students to explain things so well that thy can be understood” (p.3). Educators nationwide
are finding that they can help children become confident problem solvers by focusing on getting
them to talk and communicate in partnerships, small groups, whole groups, and in writing. In
addition, English Language Learners are flourishing as they experience focused opportunities for
talking and trying on new mathematical vocabulary (Garcia, 2005).
Number Talks as a way to build number sense
As mention before, there are numerous researched based ways that educators can use to
promote and build upon number sense. One of these strategies is called Number Talks. Many
school district are implementing this strategy as part of their daily math routine. Number Talks
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are an organized way to implement math discussion into the classroom and is intended to be non-
threating for students. They encourage students to think about numbers and how they work
which, as research suggests, will lead to number sense. In the Georgia Department of
Education’s curriculum information, Number Talks are presented as part of the daily curriculum
and align with the standards.
Number Talks Defined
It is important to note, just because there is talk in math that does not mean that it is
effective and will lead to students developing number sense. Knowing this, I choose to focus on
Number Talks after reading an article that compared math talk in the U.S. and Chinese
Classroom (Sims, 2008). Past research suggest that student achievement and engagement are
enhanced when students receive opportunities to explain and justify answers, compare multiple
solution strategies, and accept and learn from errors (Kazemi & Stipek, 2001). Sims (2008)
watches hours of film from a Chinese and U.S. mathematics classroom and finds that compared
to the U.S. classroom, in the Chinese classroom the star attraction was the mathematics and the
core ideas most often featured student talk. In contrast, the U.S. classroom the walls were
decorated, tables were set up with mathematics games, numerous manipulatives and creative
activities were presents. The Chinese teachers did not appear to talk as much as the U.S.
teachers (p. 120). The talk was coming from the students and it was a structured environment
that welcomed discussion amongst students.
In my professional opinion, a teacher must ensure that meaningful and impactful
conversations are occurring in the classroom. An organized plan needs to be established to
ensure this is occurring daily within the classroom. The research presented proves there are
several effective strategies educators can use to promote number sense using math discussions.
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One meaningful strategy that was presented throughout the literature was Number Talks.
Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing
practice with computation. Number talks should be structured as short sessions alongside the
ongoing math curriculum. They are not intended to replace the current curriculum or take up the
majority of the time spent on mathematics. Teachers need to spend only five to 15 minutes on
Number Talks daily (Math Perspectives, 2007).
The goal for Number Talks is for students to become fluent with math which will lead to
number sense. A Number Talk is a powerful tool for helping students develop computational
fluency because the expectation is that students will use number relationships and the structures
of numbers to add, subtract, multiply, and divide (Math Perspective, 2007).
The National Council for Teachers of Mathematics (2000) states:
Computational fluency refers to having efficient and accurate methods for computing.
Students exhibit computational fluency when they demonstrate flexibility in the
computational methods they choose, understand and can explain these methods, and
produce accurate answers efficiently. The computational methods that a student uses
should be based on mathematical ideas that the student understands well, including the
structure of the base-ten number system, properties of multiplication and division, and
number relationships (para. 6).
Research shows that using communication in the classroom to represent, explain, justify,
agree, and disagree mathematically molds the way students learn numerical reasoning.
Classroom dialogue engages students, encourages them to learn more, and allows for the
exploration of ideas, strategies, procedures, facts, and more (Math Solutions, 2015). Number
Talks gives students the opportunity to think about numbers and how numbers work in a safe and
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nonthreatening environment. As noted Richardson (2011), “Number Talks comes from inspiring
each child to think and make sense of the mathematics they are presented. Students are never
trying to figure out what the teacher want. Rather they are totally engaged in their own sense
making process (p. 1). She goes on to say, too much of school, as experienced by children, is
learning what they are supposed to be learning. But a Number Talk is an opportunity for
children to learn that they can figure things out for themselves in the way that makes sense to
them. Math Solutions states it simply by saying Number Talks provide the students an
opportunity for deeper understanding through communication. Individually or in groups,
students articulate and defend their ideas and analyze the reasoning of others (Math Solutions,
2015)
What do Number Talks look like in the classroom?
Plummer (2011) says “For Number Talks to be effective there are several elements that must be
in place to ensure students get the most out of the experience” (p. 3). These include:
Encourage sharing and clarify students thinking by asking questions Teach intentionally Create a safe and supportive environment Name and label the strategies students use when scripting (as a visual for others to learn
from) Vary the number talk to meet the range of student needs
Faye Nguyen (2014) offers some suggestions on what she says during her daily Number Talks to
keep the conversations going.
Thank you for sharing I am not worried about the correct answer right now, I am just interested in what you
were thinking. Did you change your mind or question your strategy when you talked to your partner? I know it is tough to articulate your thinking, take your time.
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Math teachers sometimes get the wrong answer too.
These prompts by the teacher encourage students to think mathematically and allows for a
non-threating learning environment. Students are encouraged to practice and take risks. It is
intended that with this environment students will flourish.
Summary
In conclusion, the research overwhelming proves that students need to be exposed to math
discussions. These math discussions help students develop number sense which is a critical
building block for future success in mathematics. As mentioned in the review of literature,
Number Talks is not the only strategy that is researched based. Knowing that many counties are
adopting this strategy for the use of building a strong number sense in children I want to research
its effectiveness for all students.
METHODOLOGY
Purpose
The purpose of the study was to examine the effectiveness of Number Talks as an
instructional strategy to help students explain their thinking in mathematics. According to the
Georgia Department of Education, “Number Talks are an effective strategy that prepare students
to think critically and assist them in explaining their thinking when solving problems
mathematically” (p.4). The following question will drive my action research. Are Number
Talks an effective strategy for educators to use to build number sense within students? If so, are
they effective for all student? The unit test that was given to students was titled: Applying Base
Ten Understanding. This unit required students to have strong number sense in order to be
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successful. Students had demonstrate a strong understanding of the Base Ten system and use
strategies to solve problems. The standards covered included:
1. MGSE2.NBT.6 Add up to four two-digit numbers using strategies based on place
value and properties of operations.
2. MGSE2.NBT.7 Add and subtract within 1000, using concrete models or drawings
and strategies based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy to a written
method.
3. MGSE2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally
subtract 10 or 100 from a given number 100–900.
4. MGSE2.NBT.9 Explain why addition and subtraction strategies work, using place
value and the properties of operations.
Setting
The study took place over a five week period in the months of February and March in the
2015-2016 school year at a suburban elementary school in Roswell Georgia. The school has
approximately 840 students in a K-5 setting. The county which the school is a part of created
common end of unit assessments that are a requirement for the learning community PLC. The
development of the unit tests is based off of the Georgia Standards of Excellence. Prior years’
data analysis of these assessments has brought awareness within the school and learning
community that students are having a difficult time justifying or explaining their thinking. Due
to this weakness, my action research is designed to analyze effective strategies that could be used
to help students with explaining their thinking mathematically.
Participants
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There were 24 participants that participated in my action research. These students were
all of the students in my math block. Of the 24 students there are 13 boys and 11 girls. The
population of the class is made up of 11 Caucasian students, 9 Hispanic students, two African
American students, and one Indian student. There are seven students that receive services in
ESOL and three students that have an IEP. The students come from a variety of backgrounds.
Thirteen of the students qualify for free or reduced lunch while the other 11 come from a middle
class socioeconomic background. To my knowledge, there are eight students that live in a single
parent home. These 24 students all participated in daily Number Talks. They were all given a
pre and posttest for the math unit used in this study. Of those 24 students, I collected more in
depth data for six students. These six students were the main focus of my study. This group was
made up of four boys and two girls. There were four Hispanic and two Caucasian students.
Two of the students were in the English Language Learner program and two others had and IEP.
These six students were in the lowest performing students on the unit pretest that was presented.
Procedure
The use of Number Talks as a strategy for promoting number sense within student took
place daily as part of the math instruction. The strategy was used in whole group and within
math small groups. The majority of problems selected for the daily Number Talk came from
Sherry Parris’s book Number Talks. One of the standards for this unit required students to use
mental math. If the focus for the day was based around that specific standard then I had students
complete the Number Talk in a whole group setting since it was not going to be differentiated.
There were other times throughout the study in which I felt that using Number Talks whole
group was more effective then small groups. The rest of the time I used Number Talk in the
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small group setting. This allowed me to differentiate the numbers for the group of students. The
six students that were a part of my action research were in the same small group.
How the Number Talk lessons worked each day in a whole group setting:
1. Question was projected for students to see as they walk into the classroom
2. A timer is set for 1 to 3 minutes, depending on the question.
3. Students estimated the answer using mental math-no calculators, dry erase boards, or
talking. As the students came up with an answer they would hold up a finger on their
chest to indicate they have a possible solution.
4. When timer went off it was set for additional minute. Students talked with their
neighbors about the problem and their solution.
5. I randomly called on three students, using Popsicle sticks, to share their thinking about
the problem. I scribed the students’ strategy as they were explaining it on the
ActiveBoard.
6. I then asked if there were any additional strategies that were used.
7.
The small group setting followed the same routine but were done within small groups during
math rotations. This setting allowed for a more intimate setting and, in theory, helped ensure all
students participated. The small group setting also allowed me to hear more student responses
because I was not having to keep a large group quiet on the carpet while students were
explaining their strategy they used.
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Materials
This action research required few materials. The only expense that was encountered was
the Number Talks book by Sherry Parrish. Consumable materials were the data collection sheets
and the pre/posttest which were created using Microsoft Office. Microsoft Excel was used to
make graphs to analyze the data collected.
In order to conduct this action research I used a mix method research design.
Quantitative and qualitative data were necessary to find out if Number Talks were an effective
strategy to promote number sense. In addition the mix method design was used to find out if
Number Talks were effective for all students.
The quantitative data was used to analyze the pre and posttest for the six students, to
show the percentage of times those six students participated in Number Talks, to show the
percent of correct answers, and the amount of times those students were able to explain the
strategy they used to solve the mental math problem. Quantitative data was also used for all 24
students to show their opinions about the effectiveness of Number Talks. This information was
collected using the unit posttest survey.
I also collected qualitative data in small groups on the focus group of six students by
taking anecdotal notes to support the quantitative data. As the students were explaining the
strategy used, I wrote down the key words to the students stated. These key words are an
indication of the strategies students used to solve the problems. In addition to using this
qualitative data, I took notes anytime I heard someone mention Number Talks in relation to the
unit being taught.
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Procedures for analyzing and interpreting data
I first analyzed the quantitative data since it will drive the qualitative data. The
quantitative data collected was transferred on to Excel spread sheets and graphs created. To
analyze the qualitative data, I started by reducing the volume of the information I gathered on
anecdotal notes by organizing the data into important patterns and themes in order to construct
some sort of framework. The noted patterns were entered into a word cloud generator. After
analyzing both sets of data a conclusion was drawn to determine the effectiveness of Number
wereTalks.
Results
To recap, Number Talks were conducted in the classroom for 5 weeks. Data was
collected on six students, two students that are English Language Learners, two students with
special needs and two students that are considered general education. Data collected included:
pre/post test scores, questionnaires on each test, accuracy and participation during Number
Talks, and anecdotal notes taken as the students explained their thinking. The results indicate
there was student growth from the pre to posttest but it was not substantial. None of results from
the data collected were substantial. The average score for the posttest was 63% students
participated in number talks 74% of the time getting 57% of the answers correct. In my action
research students were only able to explain their thinking 39% of the time and indicated that
Number Talks helped them 50% of the time. The average test score (63) was close to the
average percentage of solving the Number Talk problem correctly (57). When I interpret this
data I conclude that the Number Talks were effective but not as impactful as an educator would
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hope. The data suggests that this strategy may not have been effective for the population of
students tested.
Figure 1 shows the pre and post test score results:
Student Pre –Test Score Post-Test Score DifferenceStudent A-ESOL 24 53 29Student B-Gen Ed 42 70 28Student C-IEP 42 70 28Student D-Gen Ed 0 70 70Student E-ESOL 18 42 24Student F-IEP 36 72 36Mean Score 27 63 36
This data shows that overall this group of students did not do well on the unit test. The
average score for the post test was a 63. When I analyzed this data for my PLC meeting I used a
cut score of 70 or above and an indication that the students mastered the material. Using the
same standards for my action research, four of the six students show mastery. Of the four
students that show mastery, three of them scored a 70 which is the lowest score possible to
indicate mastery. Student A and E scored well below the level of mastery.
On the posttest there was a student survey for each problem I felt could have been solved
using problems and strategies we used during our Number Talk sessions.
Figure 2 shows the student survey on the posttest:
Did Number Talks help me solve this problem
Yes Somewhat No
ACTION RESEARCH PROSPECTUS 23
Figure 3 shows the results of the student survey for the six students in the focus group:
50%
27%
23%
Student survey results: Did number talks help me? 6 students in focus group
YesMaybeNo
This pie chart shows that the students felt the strategy was effective or possible effective
at least 77% of the time which is a large amount. This indicates that the students found value in
the strategy used.
Figure 4 shows the results of the student survey for other 18 students:
39%
44%
17%
Student survey results: Did number talks help me? 18 students nonfocus group
YesMaybeNo
ACTION RESEARCH PROSPECTUS 24
This pie chart shows that the other 18 students felt the strategy was effective or possible
effective at least 83% of the time which is a substantial. This sampling of students found the
strategy to be more effective and outperformed the focus group on the pretest.
As the students were solving the problem mentally during whole and small group I
observed if they were following the Number Talk protocol. If I saw the student holding up a
finger I placed a check by their name to note participation. When I rotated around the room to
ask for the correct answer, if they had the correct answer I would turn the check into an X to
indicate they had the correct answer. Also on that recording sheet I noted if the student had a
chance to explain their strategy and if so, were they able to explain it correctly. The data
collected using this method is displayed below.
Figure 5 shows the percentage of times each student attempted to participate in Number
Talks when given the opportunity
Student A Student B Student C Student D Student E Student F
87100
7055
30
92
Percent of times focus group participated in Number Talks
Figure 6 shows the percentage of correct answers for each student
Student Percentage of Correct Answers
Student A-ESOL 55.8
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Student B-Gen Ed 70.8Student C-IEP 44.8Student D-Gen Ed 60Student E-ESOL 42.6Student F-IEP 70.8
Mean 57.4The mean score for correct answers using the Number Talk strategy is very similar to the
mean score for the posttest.
Figure 7 shows the percentage of time each student was able to explain their strategy used
during the Number Talk
I have also included the information from Figure 6 that shows the percent of time the student had
the correct answer.
Student Percentage of Correct Answers
Percent of time student was able to explain answer
Student A-ESOL 55.8 46Student B-Gen Ed 70.8 53Student C-IEP 44.8 29Student D-Gen Ed 60 82Student E-ESOL 52.6 46Student F-IEP 70.8 39
When analyzing the data showing the percent of correct answers compared to the student’s
ability to explain their thinking I did not see a correlation. What I am able to see as their teacher
is a correlation with their ability to explain their thinking in all subject areas and the written
expressive ability. Student C receives IEP services in reading a writing. Student D is in my high
level reading group and chooses to write when given choice boards.
Figure 8 is a word could from big ideas that were used while students were explaining their
answer
ACTION RESEARCH PROSPECTUS 26
For three of the students, on from each sub group, anecdotal notes were taken on the
students as they were explaining their thinking. This information was organized and key phrases
were placed in a cloud generator to show how often they were used. The larger the word the
more often it was used during the Number Talk. Base Ten was use the most by students who
were explaining their thinking.
CONCLUSION
Limitations
This research study had several limitations which must be acknowledged at this point.
First, there were only six students in the focus group. With such a limited sample general
implications were made. In addition these six students scored the lowest on the pretest. In my
professional opinion, I would say that if there was a larger, more diverse sampling there would
be indication that Number Talks are more effective.
Another difficult was capturing what the students were saying when they were explaining
their thinking. I first tried recording the conversations but I realized that the students were self-
conscious and they were hesitant to explain their strategy or how they arrived at their answer.
Once again, I am going to suggest this is impacted by the group that I was collecting data on.
The group of students that participated in the study only choose to participate in the Number
Talk strategy 72.3% of the time. During whole group Number Talk lessons I consistently
ACTION RESEARCH PROSPECTUS 27
noticed other students participating 100% of the time. Sometimes I was not able to hear what the
students were saying because they were speaking so softly.
Another limitation of the study was the student survey which all 24 students took. I saw
students participating and filling out the survey for the first three or four questions but after that I
had to remind the students to make sure to answer the survey. As I was monitoring the room I
noticed that students completed the questions on the test but did not fill out the survey. When I
would point to the questionnaire often times they would just bubble in one of the faces. I am not
confident that they were choosing their response based on the effectiveness of the Number Talk
strategy.
Time was an additional limitation. I only had a five weeks to compile the data. I feel
that the students needed more time with the Number Talk strategy to show if it is effective for all
students. Four of the six students that participated in my study receive additional time as an
instructional accommodation. With my experience working with them, they take additional time
to become familiar with a strategy and need constant practice. As I first introduced the strategy I
noticed it took all 24 of my students practice to become familiar with explaining their answer. I
would say it took two full weeks of practice to become familiar with the strategy. The students
involved in my focus group continued to struggle as the data suggests. I feel that if I had more
time to collect data on those students I would see that the data would be a stronger indication that
Number Talks is an effective strategy for all students as a means to build number sense. The
Georgia Standards of Excellence has the use of Number Talks as a daily intervention to build
number sense. In addition, the book published by Sherry Perrish has a set of Number Talks that
will last an entire school year. This seems to show that Number Talks is meant to be a strategy
that is used daily and requires time for students to show success and to be effective.
ACTION RESEARCH PROSPECTUS 28
I feel another limitation of the study is that it was hard to collect data to measure the
amount of number sense a student has. The driving questions was to see if Number Talks was an
effective strategy for students to build number sense. The assessment I used required students to
have number sense but it does not measure their actual level of number sense.
Discussion
Overall I would say that the students responded well to Number Talks. As they became familiar
with the intervention they became excited to see the problem that was going to be presented each
day. I saw students’ confidence rise and their ability to explain their thinking increase. Through
my research I wanted to see the effects of Number Talks in building students’ number sense and
their ability to explain their thinking. I surmise that Number Talks was more effective in
building number sense compared to helping students explain their thinking. I had several
teachers comment on my students’ ability to use mental math to solve problems. Each morning
we see a different set of students on the grade level and teachers would complement me on my
students’ ability to use mental math and solve problems with invented algorithms. The literature
reviewed makes it clear that students need to be exposed to math discussions on a daily base and
Number Talks would be a good strategy to use with students in a small group setting throughout
the school year, not just a five week period. Of the six students in the focus group the students
that English was their second language were the most timid to discuss how they arrived at an
answer. The data seems to show that ELL learners and students with IEPs may take longer to
adapt the intervention but according to their student survey they feel that the intervention was
effective at least 50 percent of the time.
Implications for Future Research for Educators
ACTION RESEARCH PROSPECTUS 29
This research is important to bring awareness to the importance of daily math
discussions. As presented in the review of literature, many teachers have a difficult time leading
a discussion in math. It is my hope that this research will inspire others to begin math discussion
in class that promote number sense and provide multiple opportunities for students to explain
their thinking. I also hope that my research reminds educators to look at each individual student
and determine what that student needs to be successful. As my research implied, Number Talks
may not be the most effective strategy for every student. Just because it is Georgia frameworks,
it does not mean that it is the most effective strategy for all students. Some students may benefit
more from working with concrete models as a means for building number sense.
Implications for Future Research for Researchers
One suggestion for future research would be to see if Number Talks are more effective in
small group or large group setting. From my limited research I found that students were more
apt to explain their thinking and try multiple strategies in a small group setting. Another
suggestion would be to research other strategies which claim to build number sense to see if they
are more effective for lower performing students. As part of my master’s program I am working
with another strategy called CGI which requires students to use word problems to increase
number sense. Research could be conducted to see if this strategy would be as effective as
Number Talks. I would strongly recommend future researchers spend at least six months
collecting data on a larger student sampling to see the effectiveness of the intervention.
ACTION RESEARCH PROSPECTUS 30
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APPENDIX
Data Collection Sheet
Monday Tuesday Wednesday Thursday FridayY N Y N Y N Y N Y N
Student A-ESOLStudent B-Gen EdStudent C-IEPStudent D-Gen EdStudent E-ESOLStudent F-IEP