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ACTION RESEARCH PROSPECTUS 1

Action Research Prospectus

Amy Day

Kennesaw State University


TABLE OF CONTENTS

Abstract………………………………………………………………………………….…...1

Introduction……… ………..……………………………………………………………......4

Literature Review……………………………………………………………………………7

Methodology……………………………………………………………………………..…17

Results…………………………………………………………….………………………...20

Limitations…………………………………………………………………………….…....26

Conclusion………………………………………………………………………………….30

References……………………………………………………………………………….….32

Appendix…………..…………………………………………………………………….….32


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.


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


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


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


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.


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


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.


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


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


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


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.


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


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.


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


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


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


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.


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.


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


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


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


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


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


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


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.


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


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.


References

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http://mathsolutions.com/common-core-support/math-talk/

http://mathsolutions.com/common-core-support/math-talk/


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

Documents

amydaymasterprogram.weebly.com€¦ · Web viewEach student is unique and comes to school with a varied level of number sense. The overall deficiency with students’ foundational