Cross Age Peer Tutoring Focused on Multiplication Fluency€¦ · Web viewFurther, findings...

Running head: CROSS AGE PEER TUTORING FOCUSED ON MULTIPLICATION FLUENCY 1

Cross Age Peer Tutoring Focused on Multiplication Fluency

Inez Aispuro, Amanda Burk, Brooke Shapter

California State University, San Bernardino

CROSS AGE PEER TUTORING FOCUSED ON MULTIPLICATION FLUENCY 2

Abstract

A quantitative research study was conducted at local elementary school in Victorville, California.

The research investigated Effects of Peer Tutoring on Student Performance. There was a total of

six third grade students being tutor by sixth grade students for four weeks. The research team

aimed to answer how does cross age peer tutoring influences a third-grade student’s

multiplication fact fluency? As well as Why does using flashcards and cross age peer

tutoring affect student’s fluency on multiplication facts? Observation notes on student

behavior and interactions were taken as well as written down by classroom teacher. Results

showed improvement of peer tutoring on student performance and interesting findings from

observational notes taken. Research also showed and motivational influence and better scores for

students being tutor by their peers than those who were not tutored.

Keywords

Cross-age peer tutoring multiplication facts fluency Amazing Classroom flashcards


Introduction

Mathematic proficiency is important not only for success in school but also for success in

life (Greene, Tiernan, & Halloway, 2018).

Mathematical competence was a major factor in accounting for higher levels of

employment, work productivity, and income…Mathematical ability can be likened to

basic literacy in that it is a vital component for independent functioning within society

(Greene et al, 2018)

Even with the emphasis on mathematical fluency, 18% of fourth grade students in the US are

performing below grade level, while 15% of fourth grade students in Ireland were performing

below the basic level (Greene et al, 2018).

One factor in the impact on mathematical proficiency is a lower socioeconomic status

(Greene et al, 2018). The fact that a lower socioeconomic status can lead to low grades and low-

test scores are important to note can lead to failure in schools and even dropping out tells us that

research focusing on this subgroup is incredibly important (Greene et al, 2018).

Fluency in math facts is an incredibly important skill for students to master. Greene et al

(2018) found in their study that students who were both “accurate and fluent when performing

basic arithmetic have been found to perform better on assessments of overall mathematical

ability.” Multiplication facts, in particular, are very important for students to master as they

continue their mathematics education. If one does not know their multiplication facts it will

impact a student’s ability to be successful as they move further in their mathematics education.

“Fluency is defined as quick and accurate responding to selected stimulus, with minimal effort,

that enables an individual to function efficiently and effectively in their natural environment:

(Greene et al, 2018). Basically, this means that students are able to correctly solve mathematical


problems quickly, with not a lot of hardship on their part. This becomes important as students

move on with their mathematical concepts. Use of the digital practice and testing site Amazing

Classroom allows students to individually practice their multiplication facts and participate in

timed tests which can influence their fluency.

Cross age peer tutoring is defined as an “instructional method that has the benefits of

individualizing content based on students’ needs, while allowing for extensive feedback and

maintaining high levels of task engagement” (Greene et al, 2018). We decided to focus on cross

age tutoring instead of straight peer tutoring. By using older students who were already fluent in

their multiplication facts, they provided a role model for the third-grade students who were

already struggling. Peer tutoring is a “method of structured collaboration that encourages

children to learn from each other. Peer tutoring is widely reported to have beneficial effects on

student learning in mathematics” (Tsuei, 2011). The use of visuals to increase participation is an

important part of cross age peer tutoring which allows students a motivational feedback process

(Tsuei, 2011). In our study we decided to use flashcards to provide instant feedback to the

students as well as engaging them in their own tutoring.

Children are adept at explaining and teaching concepts to one another. They give and

receive help, share knowledge, build on each other’s ideas and recognize and resolve

conflicts between their own perspectives and those of other students that emerge during

peer learning (Tsuei, 2011).

Since students tend to help their peers when working one on one or even small group, cross age

peer tutoring can be a successful strategy to help students succeed, especially in mathematics.


Purpose of the Action Research Study

The purpose of our study is to monitor the effects of cross age peer tutoring on

mathematical fluency.

Action Research Questions

The researchers involved in the study have all be active in education in one facet or

another. Three of the researchers have been classroom teachers while the fourth is a special

education para-educator. We decided to focus on mathematical fluency, specifically

multiplication facts, in the third grade. Multiplication facts are very important for students to

master as they continue their mathematics education. If one does not know their multiplication

facts, it can impact the introduction and use of division as well as concepts pertaining to

fractions, decimals, and even algebra and geometry. The decision to use third grade students was

made because they were the students the researchers had access to. Our main action research

question was How does cross age peer tutoring affect a third-grade student’s multiplication

fact fluency? We also decided to look at Why does using flashcards and cross age peer

tutoring affect student’s fluency on multiplication facts?

Literature Review

Tutoring most of the time is an extra expense, whether the case is an individual out of

school tutor, or a tutor provided by the school. Unfortunately, tutoring is an expense that most

school’s budget cannot afford. Tutoring reviews the material and can provide support for the

student receiving it. Peer-tutoring is a more cost-effective solution. Peer-tutoring, the majority of

the time, uses students within the same school, which would not be an expense for the school.

Huang (2013), showed in his research that after-school tutoring does bring up the national

average, especially in mathematics and science; therefore, it is likely that peer tutoring will affect


student performance, using quantitative research. Another study that showed a positive impact of

tutoring was by Ritter (2009). The study found that tutoring inside the classroom increased the

level of the students’ mathematical performance. The effects of cross-age peer-tutoring will

likely influence a third-grade multiplication fact fluency.

According to Cheng (2009), tutoring not only affects student achievement, but also their

motivation, and attitude. This was shown in their study titled, “Investigation of the Effects of

Reciprocal Peer Tutoring.” The participants were tutored by other classmates, in order to support

each other. This gave the students getting tutored to give feedback and have an interaction about

the material. Since the classmates were all the same age they did not add any extra knowledge or

methods, besides what was taught by the teacher. All of the areas that the researcher was

studying increased, but the academic achievement was the lowest area improved.

Cheng (2009), showed how peer tutoring is an effective way to help students, but it did

not address if adding older classmates to peer tutor could be beneficial. Adding an older student

could show the younger students more ways of manipulating the material, and the older students

a sense of responsibility.

Another research study that did not only focus on academic performance, but the

retention of the students is by Reinheimer. This study compared sets of data from students that

did and did not receive tutoring. They used descriptive and inferential procedures to analyze the

data. After analyzing the data, the study concluded that tutoring affects the student’s academic

performance in a positive way but did not increase their grade point average. This could mean

that tutoring does not increase the students' retention of the information, but there are other

variables that could contribute to this.


Our research is limited to a four-week period, so we are unable to know if the

information being taught from the tutors is being memorized for longer than this period. In order

to know how long the information is being memorized for, we would need to conduct a

longitudinal study.

From a third-grade teacher’s perspective, multiplication is one of the hardest concepts for

students to learn quickly. Baker (2003), studied tutoring with using an elementary school and a

university. This method is potentially a more costly option. University students could be paid in

college credits, if the university agrees, which would be the best option for the school district.

The methods done in Baker (2003) research was tutoring students for 90 minutes, once a week,

for twenty weeks. The university tutors would help their students with their homework first, then

continue with a more interactive approach to tutoring. They used math manipulative, like board

games that included math and flashcards. The students were more engaged in the tutoring when

using math manipulatives. Overall, there was a 86% increase in student performance.

Similarly, Mathes (2003) used university students to tutor their students for a month-long

period. The researchers found that peer-assisted instruction enhanced students reading

performance. The younger students enjoyed getting tutored by adult college students.

Although university students are shown to be a good way to bring up the students

academic performance, they are not the most convenient way of tutoring students. For our

research, an older grade student is a more convenient way to conduct our tutoring. Baker (2003)

bought in the idea of using math manipulatives into the research. Flashcards are a simple, yet

educational way to teach the students mathematics. Students will need to get used to the fast

passed way of flashcards and will hopefully retain the information easier.


Yang (2016), used a program named Sketch Zone in their research to examine the

student's mathematical performance. This research used Sketch Zone with tutoring to try to

improve the student's performance. Students who had tutored, along with Sketch Zone, were

compared to students who were taught in small groups from the teacher. The results of this study

found that the students being taught in a small groups performance increased more than the

students who have been tutored and used Sketch Zone.

Seeing how this research found that tutoring while using a program does not increase

performance, we decided to not use any online instruction with our tutoring group. In our

research, Amazing Classroom, an online mathematics instruction, is used to compare with our

tutored students. We did this to see if the problem with Yang’s research was that the study

combined tutoring with online instruction, and not separating the two instructions.

A study that was both cost effective and improved students’ academic performance was

one that included older elementary students tutoring younger grades in mathematics

(subtraction/addition) is in the article titled, “Cross-Age Peer Tutoring and Fluency-Based

Instruction to Achieve Fluency with Mathematics Computation Skills: A Randomized Controlled

Trial.” The study used random assignment with 41 female students. The students getting tutored

were second and third graders, the tutors were fourth and fifth graders. The tutoring sessions

were 30 minutes a day, three times a week, using two different types of flashcards, using

mathematical material. The study showed both sets of students had an increase in proficiency in

their addition and subtraction skills. Another study that showed a positive impact of tutoring was

by Ritter (2009). The study found that tutoring inside the classroom increased the level of the

students’ mathematical performance.


These studies confirm our thought of using older grade students to peer tutor younger

grade students. With Greene (2018) study, it is brought into question that if the sex of the student

had anything to do with their performance. Both studies found that using tutors from the

students’ current school increases the students' academic performance.

Moreover, a study conducted by researcher Tsuei (2011) proved positive effects found

that synchronous peer learning on students’ mathematics. The longer the period of time spent in

online peer learning the more the learner benefited. It was found that the student who needed

help showed a higher growth rate in mathematics learning when paired with peers who have

different abilities. The study confirms an impact in mathematics reasoning skills. Although our

research study was only for a short period of time, we were able to find positives results. A

longitudinal study would need to be conducted to continue monitoring outcomes. Additionally,

Yang, Chang, Cheng, and Chan (2016) further described the benefits of mathematical

communication abilities through computer-supported reciprocal peer tutoring. Findings showed

students' math creations were more clearly as well as more efficient. Learners mathematical

representations and solution reasoning became accurate after the learning activity. Further,

findings confirmed that the experimental group outperformed the control group in the

assessment. Overall, both studies concluded with positive peer tutoring outcomes.

To study the effect of cross-age peer-tutoring influence a third-grade multiplication fact

fluency, six 6th grade students peer tutored six 3rd grade students. The tutoring is done four days

a week, for twenty minutes, in a four-week time period. Flashcards will be used as the

mathematical manipulative. The students will also be timed to show their improvement over the

weeks. To compare to the other students, Amazing Classroom is used. The students not being

tutored will work on Amazing Classroom, doing only multiplication studying with online


instruction. The tutored students then use Amazing Classroom to see if there is a significant

difference in results.

Methodology

Research team has six sixth-grade students going to a third-grade classroom Tuesday

through Friday. Peer tutoring begins at exactly 12:20 pm and end at 12:40pm, four days a week

for a total of four weeks. Student come in and work with the same six third grade students for

twenty minutes. During the twenty minutes students are working on multiplication flash cards in

a quiet area inside the classroom or outside the classroom in the hallway. During this time the

rest of the student not being tutored are working on multiplication facts on a website called

Amazing Classroom. Amazing Classroom is a digital website that allows the students to work at

their own pace on a timed multiplication facts. The students cannot move forward to the next

level until they pass their current level of 100 problem in eight minutes. For example, if a student

is on multiplication threes they must pass 100 multiplication facts levels one - twelve in eight

minutes on the computer. (for example, 3 x 5) Scores were taken every Monday for these six

students to see if there is improvement. Online scores reflected how far a student advanced in

eight minutes. If the student is able to get 100 percent, then they will advance to the next level.

Moreover, Amazing Classroom is a website available to teachers. The cost is $29.95 per

school year. The website has preset templates that allow the teacher to choose a background, add

pictures and edit parent information. Preset tabs include: Contact Info, Weekly Updates,

Homework Info, Math, ELA, Spelling. Science. Social Studies, Class Rules, Class Schedule,

Class Pictures. The website also offers Math Facts Testing, Standardized Testing, White Board

Resources, Worksheets and Activities, Classroom Forms, Parent Newsletters, and Grade books.

It does require web maintenance, but it is extremely user friendly. It is required that students


have a secure login that keeps the website safe. However, the website Amazing Classroom was

used exclusively in this study to keep track and updates of student progress, levels, provide

multiplication practice for the students, and use it to assess students on their math facts fluency.

The six tutored third-graders were also given the opportunity to work on Amazing Classroom

during other times throughout the week.

Furthermore, for these six "test students", researchers recorded their Amazing Classroom

levels each Monday along with taking paper assessments that will come from a 100 math facts

worksheet. (Appendix E) Written assessments were given on 10-22-18, 10-29-18, 11-05-18, 11-

13-18, and 11-26-18. Written assessments were not completed on 11-13-18 due to the Veteran’s

Day Recess and neither written or online assessments on 11-19-18 due to the Thanksgiving

holiday. (Appendix A) This is an activity they worked on daily, and their scores fluctuated.

However, for the assessments, a print out their scores was done every Monday to see results.

These scores will reflect how far a student will advance in eight minutes. If they get 100% they

will advance to the next level. The scores will be determined by how many correct out of 100 in

the eight minutes. For example: (78/100). Classroom teacher also had a mini discussion with the

students involved in the research after the conclusion of the four weeks. Pre and Post tests were

used to determine the third-graders feelings about multiplication both before and after the

tutoring period.

Data Analysis

Data was collected on six third-graders that were tutored by six sixth-graders. These

students were chosen based on their performance of a written multiplication test that gave

students 100 problems to complete in eight minutes. The study group was chosen due to their

low performance on the test.


Both quantitative data (Amazing Classroom Level scores and scores on the paper tests)

and qualitative data (Student survey before and after tutoring) were collected. The majority of

data analysis looked at the progress of individual students in both the Amazing Classroom tests

and the written test. A spreadsheet was created with the student’s scores in both Amazing

Classroom and the paper/pencil test in Excel. The focus was the range between the first quiz and

the last quiz. We also looked at the mean for each student and the complete focus group. Test

scores were compared over the entirety of the tutoring period to see if the tutoring improved the

fluency of multiplication facts. Information from the student surveys was also collected and

then analyzed using a spreadsheet for the mean scores on the specific words. Students circled the

answers they felt, but none added any extra information.

Results

Overall the results of the study were positive. When comparing students starting point on

the written tests to their ending point, there was an average of 57.46 points growth for the

students. The quantitative data collected on the students was easy to interpret with it being

numbers. It was easy to determine whether scores went up or down.

Figure 1: Sample of growth on Written Test

22-Oct 29-Oct 5-Nov 12-Nov 19-Nov 26-Nov0

102030405060708090

100

Sebastian N.

Growth in Written Test Out of 100


For this student you can see he began at about 33 and after the four weeks of tutoring he scored a

99. All the students showed growth throughout the tutoring period (See Appendix A and

Appendix B).

The qualitative was much harder to determine due to student’s answers to the surveys. A

comparison was made between opposite types of words with the scores representing the student’s

feelings about multiplication both before and after tutoring. (Appendix C and Appendix D)

Figure 2: Students progression on feelings about Multiplication gathered from Surveys

Scar

ed/G

ood

Ner

vous

/Impr

ovem

ent

Frus

trate

d

Anx

iety

/Eas

ier

Mix

ed F

eelin

gs/H

elpf

ul

Con

fiden

t/Aw

esom

e

Ove

rthin

king

/Lea

rned

a lo

t

Con

fusi

on

Mad

/Pla

yed

Aro

und

Too

Muc

h0

1

2

3

4

5

Survey Answers Pre and Post Tutoring

Feelings about Multiplication Before Tutoring Feelings about Multiplication after Tutoring

Students demonstrated both growth in the written tests as well as the digital tests. Students also

showed a change in attitude towards multiplication as the tutoring progressed.

Summary and Conclusions

We the researchers learned much about the effects of peer tutoring. The data shows that

these students showed growth over the period of four weeks.


Lesson 1: The relationship between the third-grade students and the sixth-grade students

was important. The younger students seemed to enjoy their time with the older students. It

became apparent that students who tended to goof off during the tutoring time did not score as

well that week on the assessments. The students that used the time to actually practice their

multiplication facts showed growth on the weekly assessments.

Lesson 2: Using flashcards helped students internalize the multiplication facts as well as

increasing their quickness with answering the problem. Students seemed to take the flashcards

as a challenge. As long as they were not busy playing around they stayed focused. It almost

became a competition between the different tutoring pairs. They were overheard comparing how

many flashcards they had gone through and how many were answered correctly. The sixth-grade

students seemed to take it as a point of pride when their tutorees succeeded. (Appendix F)

Lesson 3: Students can be successful with the use of cross age peer tutoring. By bringing

in the older student, the younger seemed to view them in a position of power that we do not

believe would have happened if the third-grade students tutored each other. The sixth-graders

were “big kids” and therefore knew more than the third-graders. It created an environment

where the third-graders looked up to the sixth-graders and almost put the younger students in a

position where they wanted to please the older students. It was fascination to see the interaction

between the two different groups.

Further Action and Directions

Our tutoring project ended after the four weeks that we had available. However, since the

project was so successful it should be extended and continue, as long as it keeps enriching the

students and offering the skills needed to succeed on the different tasks. It would be prudent to

shake up the tutoring students both in the third-grade as well as the sixth-grade. Students may be


successful in one task, but not so much in others. As the class transitions to division, the focus

students will possibly change and should be offered the opportunity to be successful through the

use of cross age peer tutoring.

As the tutoring continues, data will be collected to study the efficacy of cross age peer

tutoring in a different mathematical setting, not just multiplication. The hope is that students will

continue to show growth in their fluency of the different tasks.

The potential for data collection and research is practically boundless due to the changing

nature of mathematics in the third-grade. Data should continue to be collected to determine if

the success was due to such a small tutoring window or if cross age peer tutoring will continue to

be successful as it is used for longer and longer periods. It would be intriguing to also see if a

longitudinal study could be completed to study the effect the tutoring has on different years of

students. Granted there will not be students who are exactly the same year to year, but the basic

conditions can be replicated. Students who participate in the tutoring can be matched to previous

years participants through their scores on the multiplication assessments. The possibilities for

continued research seem to be endless.

Reflection

Having completed this research project has furthered our knowledge to better support

findings using facts and examples. Gathering facts gives work more credibility. The Effects of

Peer Tutoring on Student Performance research project was a group work. The study began with

four team members but, unfortunately ended with three. Each team member was assigned to a

section. In this assignment we created a research paper that looked at the outcomes of peer

tutoring. Finding showed various benefits not only for the tutor but for the tutee as well. Some of

the benefits included staying on task, focus, engaged, increase scores/levels, boost motivation,


ability to learn at their own pace, collaboration, building relationships, and most importantly

academic growth. After our finding we know that setting up purposeful and meaningful

connections between students in a loosely structured academic settings has numerous positive

outcomes. We have observed peer-tutors emerge as leaders, become better students as a result of

their engagement in the project, and develop meaningful connections with their peers. It was

amazing to see tutors gained confidence in their own abilities as students. Overall, we all

enjoyed conducting this research project and gained such incredible knowledge to incorporate in

our future classrooms as well as share study findings with colleagues.

This action research project has provided the researchers with data to support our

hypothesis that cross age peer tutoring would be beneficial for multiplication fact fluency. We

believe that any educator could implement this strategy in their own classroom and see similar

results. As long as there are upper grade tutors volunteering to help the lower grade students,

this process will hopefully be successful. The use of the flashcards also helped with keeping

students engaged in the tutoring process. Overall this research was a success.

As we move on, we hope to continue this research with our focus students for

multiplication and alternative focus students as the class moves in to division. We also hope to

complete latitudinal studies looking for trends from year to year.


References

Baker, J. D., Rieg, S. A., Clendaniel T. R., (2003). An investigation of an after-school math

tutoring program: university tutors + elementary students = a successful partnership.

University of Pennsylvania Education, 127(2) 287-293. Retrieved from

http://libproxy.lib.csusb.edu/login?url=http://search.ebscohost.com/login.aspx?

direct=true&db=eric&AN=EJ765828&site=ehost-live

Cheng, & Ku. (2009). An investigation of the effects of reciprocal peer tutoring. Computers in

Human Behavior, 25(1), 40-49.

Greene, I., Tiernan, A.M., & Holloway, J.J. (2018) Cross-age peer tutoring and fluency-based

instruction to achieve fluency with mathematics computation skills: A randomized

controlled trial. Journal of Behavioral Education 27(154). https://doi-

org.libproxy.lib.csusb.edu/10.1007/s10864-018-9291-1

Huang, M. (2013). After-school tutoring and the distribution of student performance.

Comparative Education Review, 57(4), 689-710. doi:10.1086/671346

Mathes, P., Torgesen, J., Clancy-Menchetti, J., Santi, K., Nicholas, K., Robinson, C., & Grek, M.

(2003). A comparison of teacher-directed versus peer-assisted instruction to struggling

first-grade readers. The Elementary School Journal, 103(5), 459-479.

Menesses, K. F., & Gresham, F. M. (2009). Relative efficacy of reciprocal and nonreciprocal

peer tutoring for students at-risk for academic failure. School Psychology

Quarterly, 24(4), 266–275. https://doi-org.libproxy.lib.csusb.edu/10.1037/a0018174

Reinheimer, D., & McKenzie, K. (2011). The impact of tutoring on the academic success of

undeclared Students. Journal of College Reading and Learning, 41(2), 22–36.

https://doi-org.libproxy.lib.csusb.edu/10.1007/s10864-018-9291-1

https://doi-org.libproxy.lib.csusb.edu/10.1007/s10864-018-9291-1


Ritter, G. W., Barnett, J. H., Denny, G. S., & Albin, G. R. (2009). The effectiveness of volunteer

tutoring programs for elementary and middle school students: a meta-analysis. Review of

Educational Research,79(1), 3-38. https://doi:10.3102/0034654308325690

Tsuei, M. (2011). Using synchronous peer tutoring system to promote elementary students’

learning in mathematics. Computers and Education 58(4), 1171-1182.

https://doi.org/10.1016/j.compedu.2011.11.025

Yang, E. F. Y., Chang, B., Cheng, H. N. H., & Chan, T. W. (2016). Improving pupils’

mathematical communication abilities through computer-supported reciprocal peer

tutoring. Educational Technology & Society, 19 (3), 157–169.

https://doi.org/10.1016/j.compedu.2011.11.025


Appendix A

Student Raw Data on Both Amazing Classroom and Written Assessment

Gentrie Noah Taleah Jocelyn Kaleb Sebastian N.Online Level

10-22 1 1 1 1 1 110-29 3 2 2 2 3 211-5 3 2 2 2 3 311-13 4 2 3 2 3 311-29 4 3 3 3 3 3

Written/10010-22 56 43 28 30 68 3310/29 63 47 21 39 15 4011-5 73 56 59 49 57 4611-29 100 93 79 85 100 99

Gentrie Noah Taleah

Jocelyn Kaleb Sebastian N. Whole Class

Range: 44 50 51 55 32 66 --

Mean 73 59.75 46.75 50.75 60 54.5 57.46


Appendix B

Student Charts demonstrating Growth Broken Down by Student


0.5

1

1.5

2

2.5

3

3.5

4

4.5

Gentrie

Multiplication levels in Amazing Classroom


10

20

30

40

50

60

70

80

90

100

Gentrie




0.5

1

1.5

2

2.5

3

3.5

4

4.5

Noah

Multiplication Levels in Amazing Classroom


10

20

30

40

50

60

70

80

90

100

Noah




0.5

1

1.5

2

2.5

3

3.5

4

4.5

Taleah

Multiplication Levels in Amazing Classroom


10

20

30

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50

60

70

80

90

100

Taleah




0.5

1

1.5

2

2.5

3

3.5

4

4.5 Jocelyn



10

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50

60

70

80

90

100

Jocelyn




0.5

1

1.5

2

2.5

3

3.5

4

4.5

Kaleb



10

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50

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70

80

90

100

Kaleb




0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sebastian N.



10

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90

100

Sebastian N.



Gentrie Noah Taleah Jocelyn Kaleb Sebastian N. Class Mean0

10

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80

90

100

Mean of Written Test

Mean of Written Test


Appendix C

Raw Data on Student Survey Answers

Students Feelings About Multiplication

# of Students who chose the word

Before TutoringScared 4Nervous 4Frustrated 4Anxiety 1Mixed Feelings 1Confident 1Overthinking 2Mad 4Confusion 3

After TutoringGood 5Improvement 3Easier 3Helpful 3Awesome 2Learned a lot 1Confusion 1Frustrated 2Played Around Too Much 3


Appendix D

Charts demonstrating Student’s Feelings About Multiplication

Scared

Nervou

s

Frustra

ted

Anxiet

y

Mixed F

eeling

s

Confid

ent

Overth

inking Mad

Confus

ion0

1

2

3

4

5

Student's Feelings About Multiplication Before Tutoring Begins

Number of Students who expressed the feeling

Good

Impro

vemen

tEasi

er

Helpful

Awesome

Learne

d a lo

t

Confus

ion

Frustra

ted

Played

Arou

nd0

0.51

1.52

2.53

3.54

4.55

Student's Feelings About Multiplication After Tu-toring

Number of Students who expressed the feeling


Scared

/Goo

d

Nervou

s/Impro

vemen

t

Frustra

ted

Anxiet

y/Easi

er

Mixed F

eeling

s/Help

ful

Confid

ent/A

wesome

Overth

inking

/Learne

d a lo

t

Confus

ion

Mad/Play

ed A

round

Too M

uch

0

1

2

3

4

5

Survey Answers Pre and Post Tutoring

Feelings about Multiplication Before Tutoring Feelings about Multiplication after Tutoring


Appendix E

Samples of Student Assessment and Survey Document


Appendix F

Images of Students Participating in Cross Age Peer Tutoring

Cross Age Peer Tutoring Focused on Multiplication Fluency€¦ · Web viewFurther, findings...

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