Final Using Peer Tutoring Strategies to Increase Mathematic Achievement

Using Peer TUToring sTraTegies To increase
MaTheMaTic achieveMenT
Beth Csiszer
February 9, 2011
Using Data to Improve Teaching and Learning
EDCI 635
Dr. Linda Pickett

Using Peer Strategies to Increase Mathematic Achievement Csiszer
Introduction
Purpose
The goal of this study is to identify whether the use of peer tutoring will positively impact
students mathematic achievement on the MAP test and the students’ attitudes towards working
with a peer.
Justification of Study
With limited people and resources to differentiate instruction, teachers are seeking ways
to reach the needs of all of their students. One way to differentiate is through peer tutoring.
Studies have shown that if can be effective for many different groups of students. Peer tutoring
allows teachers to accommodate the diversity of learning styles and levels in a classroom. At the
same time, it gives students time to interact with one another, and promotes better attitudes
towards school and towards each other, according to studies conducted.
There have been several studies that suggest that peer tutees benefit from peer tutoring.
Studies also show that tutoring benefits the tutor. In a study by Dinenn, Clark and Risely (1977),
tutees gained 59% correct words in a list they were tutored by a peer to learn while the tutor
gained 47% correct works in a spelling task. In a reading program, called PALS, a study was
done to determine its effectiveness. The results were that there was a statistically significant gain
in words read per minute and a decrease over all of words missed. In a study by Kamps,
Greenword, Arreaga,-Mayer, Veerkamp, Utley, Tapia, Bowman-Perrot, and Bannister (2008),
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they found that there was a significant increase in test scores of weekly quizzes with the use of
peer tutoring. There was also significant support from a study by Golding, Facey-Shaw and
Tennant (2006) to suggest that it increases students’ attitudes when in a peer tutoring
environment towards classroom content. One other study, by Mathes, Torgesen, Clancy-
Menchetti, Santi Nicholas, Robinson and Grek (2010) shows that when using a peer tutoring
program, there is virtually the same amount of gains in a student’s reading progress as there is
when a student is in a small, teacher directed group.
There is now a higher demand for being able to do complex math problems in the
workplace; therefore we must be sure students are able to perform these problems in the school
setting. However, in a 1997 study, it was found that American eighth graders performed
approximately 2 years behind other students in mathematics (Fuchs, Fuchs, and Karns 2010).
Therefore, it is important that we find ways to increase students’ mathematical achievement.
According to the article, “Difficulties with Mathematics” on the website hosted
through pbs.org, Misunderstood Minds, students may exhibit poor math skills as they rise to
older grades because they have computational weaknesses, and difficulty transferring
knowledge. They also have difficulty understanding the language of mathematics. This is
especially true for ELL students. Students also have difficulties comprehending the visual and
spatial aspects of math as well as other language difficulties, again, as with ELL students.
Background
Hunter Street Elementary is one of 4 Elementary schools in York, South Carolina. It is a
Title One School which houses PK-4th
grades. The school currently has 662 students enrolled.
The population of the school consists of 52% male and 48% female. The racial demographics are
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1% Asian, 15% African American, 13% Hispanic, 4 % Biracial, 64% White, and .01%
unclassified. Fifty-three percent of students qualify for free lunch, 3 % for reduced lunch and
44% pay full price for their lunch.
This action research plan takes place within one 4th
grade classroom of twenty students.
The room has 10 males and 10 females. The participates are 70% white, 20% African American,
5% Biracial and 5% Hispanic.
Within this classroom, one student qualifies for ELL services; five students have IEPs
and are being served within the area of Language Arts. Five students qualify as gifted. One
student qualifies as gifted and resource. There are two speech students in the room and six who
do not qualify for special services.
The MAP scores of students in this classroom were compared for both reading and math
in the fall and winter. There was a larger gain in students’ scores in the reading portion of this
test than the math portion. For this reason, it was decided that a strategy would be implemented
to increase students’ achievement in math. (See reading and math MAP Scores-Appendices C &
D).
Students’ grades from quarters 1 and 2 also suggest that there is not as much growth in
math as there is in other areas of the curriculum. (See Quarter 1 & 2 Grades for Reading and
Math –Appendices E & F)
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Definitions of Key Terms
MAP-Measures of Academic Progress; a nationally normed, computer-based test used to
determine child’s ranking among other students in the same grade in core subjects as well as
growth throughout the year. Administered two or three times a year
Peer Tutoring- Pair students up to teach a lower student skills that the higher student already
comprehends and can explain to another student
Tutor- Student who helps another student, student has already comprehended material and can
explain it to another student
Tutee- student who is receiving additional instruction in an area he or she is having difficulty in
Differentiate- to differ instruction according to a child’s needs; can be done individually or in
groups.
DRA- Directive Reading Assessment (used to determine students’ reading levels by measuring
their fluency, comprehension, and rate)
PALS- Peer Assisted Learning Strategies
ELL- a student who is an English Language Learner; English is not his first language
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.
Limitations
The students in this study will complete a MAP test in the fall, winter and spring of the
academic year. Students are expected to make growth, so maturation will be a limitation. I will
have to compare students’ growths from fall to winter, and winter to spring. Another limitation is
the fact that some students are not good at multiple choice tests. This will affect the outcome. A
third factor that could be a limitation in this study will be mortality of subjects. Throughout the
year, I am likely to have students move in and out of the classroom. I will have to use only those
students’ results that are there for the entire year. Furthermore, since I am relying on peer
tutoring for my results, the effectiveness of each tutor will pay an important part in the results of
this study. Some students will be better tutors. In conjunction with the fact some students will be
better tutors, I will also have some students who are better tutees. That is, they will be more
receptive of the instruction given to them by their peers. Also, some students may not complete
questionnaires truthfully when I distribute them. Therefore, I may not have a true measure of
attitudes to compare. Lastly, not all parents may agree to have their child to participate in this
study. I will have to take all of these factors into consideration.
Review of Literature
The effects of implementing a class wide peer tutoring model on social approvals and
disapprovals during unstructured free time.
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Lawson and Trapenberg (2007) conducted a study to observe the number of social
approvals and disapprovals when using peer tutoring. In this study, three students were chosen
from a self contained classroom to be tutored because they had emitted high rates of disapprovals
and low rates of approvals during baseline testing. All eight students in the classroom
participated in the Classroom Peer Tutoring model. Data supported their hypothesis that peer
tutoring would be effective the number of social approvals delivered by peers during both
instructional and unstructured free time settings and decreased social disapprovals. There were
social improvements in other areas, as well as a result of the peer tutoring.
Enhancing mathematical development: effects of peer-assisted learning strategies
The researchers of the effects of peer-assisted learning strategies on mathematical
development (Fuchs, Fuchs and Karns 2001) found there was a positive correlation between the
use of a peer-assisted learning model and achievement in math. Within this study, 168 students
were tested (84 per condition, which is the instruction students receive). Eighty-four students did
not take place in peer tutoring. Eighty-four students did take place in a peer tutoring model. For
the group that was taking part in peer tutoring, they were taking part in the condition twice a
week for 15 weeks. The findings show that the growth of the PALS group exceeded the non-
PALS group’s growth by 24%.
Total class peer tutoring and interdependent group oriented contingency: improving the
academic and task related behaviors of fourth-grade urban students
In a study conducted by Lo (2004), he found that by implementing at total class peer
tutoring program that targeted eight students, seven increased their total social studies
performance as well as their time on task. Of the eight target students, one was identified as
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learning disabled and was mainstreamed into the regular classroom. Students were selected to
study based on teacher nomination, indicating they performed lower than average in social
studies and had high off tasks behaviors
Within the classroom, thirteen of the fourteen students said that they liked peer tutoring.
There was significant support for the use of peer tutoring in the classroom.
The results showed that all of the students achieved a higher mean quiz score than their
baseline. Six of the eight students made noticeably progressive improvements in their test scores.
Seven of the eight exhibited less off task behaviors.
A comparison of teacher-directed versus peer-assisted instruction to struggling first
grade readers
In a study by Mathes, Torgesen, Clancy-Menchetti and Santi, (2003), it was determined
that both peer tutoring and teacher directed small groups yield similar results in student
achievement. There was, however a large difference in scores of students who received no peer
tutoring or small group instruction for the teacher.
The efficacy of class wide peer tutoring in middle schools.
Kamps, Greenwood, Arreaga-Mayer, Veerkamp, Utley, Tapai, Bowman-Perrott and
Mannister (2008) conducted a study on the effectiveness of class wide peer tutoring in a middle
school setting. The study was conducted with nine-hundred seventy –five middle school
students in grades six through eight within fifty-two classrooms within a three-year time period.
There were moderate to large effects noted in the study of peer tutoring on achievement.
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Quizzes were given one to two times a week per subject. Classroom behavior and on task
behavior was observed and recorded as it occurred when classrooms were being observed.
Overall, the use of peer tutoring and the strategies to improve student behaviors changed the
students’ behaviors improved and there were academic gains. On task data showed similar
improvements. There were statistically significant gains in both reading and social studies scores.
The results for science were mixed.
Effects of a peer-mediated program on reading skill acquisition for two-way bilingual
first-grade classrooms.
Calhoon, Al Otaiba, Cihak, King and Avalos studied the effect of peer tutoring on
reading skill acquisitions for two-way bilingual first grade classroom (2007). In their study, they
found that students who participated in PALS had significant gains in all areas of reading with
the exception of letter identification. Peer tutoring was more beneficial for English proficient
students than the ELLs in this study.
Students who participated were surveyed. Overall, they had a positive experience and
perception of the peer tutoring experience.
Project Overview
Design
This intervention study will be conducted in a fourth grade classroom within a small
suburban school district in the southeastern United States. The study will take place over a six
week time period. It will be based on a convenience sampling. Students will be compared to
themselves for the results.
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Students will all take the MAP test in the winter to determine their percentile rank
nationally in Mathematics. Test results will be recorded for later comparison. Students’ math
grades will also be compared. A pretest and post test in mathematics will also be distributed, for
students to complete before and after the study. Students will also complete a rating scale about
peer tutoring and how they feel about working with other students in group settings. A survey
about students’ mathematics will also be distributed before and after this study. These tests will
act as the pretests and the post tests of this study.
All students will then be assigned a student to tutor similar to the way peers are assigned
to one another in the PALS reading program. Students will be ranked one through twenty based
on their math MAP scores. Students will then be paired with the top Math MAP student being
paired with the eleventh top Math MAP student; the second top Math MAP student will be
paired with the twelfth top Math MAP student, etc. Students are being paired this way to keep
the very top students from working with the very bottom students as that kind of pairing can be
frustrating for both the high and the low students.
Action Research
Prior to week one, all necessary permissions will be obtained from administration to
collect data and perform this action research project. A photo release letter was also sent home,
although a blanket district one had been sent home. The principal wanted to be sure the parents
understood that it was possible their children may be videoed or have pictures taken during this
project.
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Week One
During week one, administration will be informed that research will be conducted.
Administration will be briefed as to what the research will entail, and how it may benefit the
students.
Week 2
During week two, parents will be sent home a permission slip to sign. The
students will also be given the Assent to Participate form. Students will also be trained as to how
peer tutoring will work. This will be a five day process. During this time, students will be given
explicit instructions, observe modeling of tutoring, and practice peer tutoring.
Week 3
During Week 3, students will perform a pretest about their attitudes towards working
with a partner (Appendix G), their attitudes towards mathematics (Appendix F) and will take a
mathematics pretest (Appendix H). Upon completion of these tests, the researcher will review
what the students’ attitudes are, as well as the students’ strengths’ and weaknesses from the
mathematics pretest.
Weeks 4-6
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For weeks four through six, students will participate in Peer Assisted Learning Strategies
on Tuesday and Thursday of each week for 20 minutes each day in mathematics. During this
time, students will keep the same tutor and tutee unless there is a significant problem that cannot
be rectified or if a student moves. Students will be given Math material to work on based on
what the lower student of the pair needs. The top student will teach the lower student how to do a
problem. The lower student will then have a turn to teach. Finally, the higher student teaches the
skill again. As skills are mastered in the pair, new material will be introduced. This material will
be scripted so that both students in the pair can read what to say to one another when teaching
each other the lesson. The teacher will keep this work filed so that there is a record of what
material each pair has completed
Week 7
Students will perform post tests on both their attitudes towards working with a group
(Appendix G), and their attitudes about mathematics (Appendix F). Students will also complete
the Post-Test assessment of mathematics (Appendix H).
Week 8-9
The researcher will chart results of the surveys, as well as the pre/post mathematics tests.
Students’ third quarter grades will also be analyzed and charted. If time allows, MAP will also be
given to students as an addition post assessment. After the researcher reviews and charts her
findings, they will be shared with team members, administration and collegues.
Treatment
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The teacher involved in this study has received training in the PALS reading program.
Since this program will be run similarly to that of the PALS reading program, the training will be
beneficial. All students will participate in this study, given that proper permission is obtained to
do so from the parents.
The peer tutoring in math will include manipulatives (appendix I) and handouts to
reinforce what is being taught in the lesson the peers will be completing. During the peer tutoring
sessions, the teacher will monitor the groups to make sure they are all in task. She will also
reward the students with a “points system.” The points system entails groups receiving points if
they are on task when she observes their group. The group or the groups with the highest points
may receive some sort of a token as a reward. The teacher will also take anadotical notes while
students are tutoring one another to determine if a lot of students still do not understand concepts
that were taught.
Experimental Groups
Independent Variable
The independent variable is the peer tutoring program that will be implemented.
Dependent Variables
The dependent variables will include students’ test scores on the MAP test before and
after peer tutoring has been implemented, the pre and post tests of math, students’1st,
2nd
and 3rd
quarter grades and the attitude surveys of both math and working in groups.
Selection and Assignment of the Subjects
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This study’s participants will be a convenience sampling. It will include all students from
one fourth grade classroom under one teacher. The classroom will include an ELL student, six
learning disabled students, six gifted students and a high level of free and reduced lunch
students. Since all students will be participating in both conditions, there will be no need for
assignment to conditions.
Instruction and Data Collection
The students will be given a pre and post test in mathematics. The scores of the pre and
post tests will be compared to determine if there is growth in their knowledge of math. Students’
third nine week math grades will also be compared to those of the first and second nine weeks to
see if their grades increase due to the peer tutoring.
The students’ performance on MAP will be tracked from the fall to spring. Should this
data be available on time, the results of the winter and spring tests will be compared to determine
growth. The growth will be compared to previous growth of the student and typical growth of the
students based on the data MAP provides to determine if maturation or peer tutoring is a cause of
students’ gains in their MAP scores. Students’ percentile ranks for both the fall and the winter
will also be compared to get a more true measure of student’s growth; since, again, maturation
will be an issue in this experiment, should this data be available by the close of this experiment.
Students’ first, second and third quarter grades will also be compared to see if grade
improve after they participate in peer tutoring.
The rating scale of students’ attitudes towards math will be administered before and after
the peer tutoring sessions to determine if peer tutoring has had a positive effect on students’
attitudes towards peer tutoring. Each of ten questions regarding group work and peer tutoring
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will be ranked from one through three. One will be to represent that the student disagrees, two is
for unsure, and three is to demonstrate the student agrees. There will be two open ended
questions to gather qualitative data. (See Appendices F & G).
The rating scale for working with a peer will have eight questions that will be rated from
one through three. Two open ended questions will be included in order to gather qualitative data.
One will be to represent that the student disagrees, two is for unsure, and three is to demonstrate
the student agrees.
Ethical Considerations
The researcher will share her proposal with administration and seek approval to conduct
this study within her classroom. Upon approval, she will send home a detailed letter outlining
why she intends to use peer tutoring in her classroom. She will seek to obtain permission for the
students to participate in the study from the parents. Students who do not receive permission to
participate in a peer tutoring model will be allowed to use a computer based learning program to
reinforce math skills so that they are still receiving math instruction.
This study will only take place for the time period between the second and third MAP test
to determine if peer tutoring is beneficial to all students. If there is not a significant gain, then
peer tutoring will be discontinued and students will once again be taught with traditional
methods.
Procedures
The collection of data will be by the use of five instruments; the MAP assessment (if
available on time), students first, second and third quarter grades, and students’ scores on the pre
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and post tests on the math assessment as well as the rating scale survey students will be
administered about their attitudes towards math and working in a group. All five instruments will
serve for the pre and post test data. All students will participate in a peer tutoring program for 4
weeks. The students’ scores on the pre and post tests, third quarter math grades and the
students’ percentile growth will be used to determine the method’s effectiveness on math
achievement. The surveys will be used to determine if students’ attitudes towards math or group
work changes. Students will take the math assessment and will complete the attitude surveys
prior to beginning the tutoring program. After training in peer tutoring, students will participate
in the program for four weeks. At the end of the four weeks, students will take both post
assessments. The results of both the pre and post tests will be analyzed using a t-test. The results
of this study will be published and shared with colleagues.
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References
Calhoun, M. B., Otaiba, S. A., Cihak, D., King, A., & Avalos, A. (2007). Effects of a peer-
mediated program on reading skill acquisition for two-way bilingual first-grade
classrooms. Learning Disability Quarterly, 30(summer), 169-184. Retrieved July 23,
2010, from the Educator Reference Complete database.
Dineen, J., Clark, H., & Risley, T. (1977). Peer tutoring among elementary students educational
benefits to the tutor. Journal of Applied Behavior Analysis, 10(2), 231-238. Retrieved
July 23, 2010, from the JSTOR database.
Fuchs, L., Fuchs, D., & Karns, K. (2001). Enhancing mathematical development: effects of peer-
assisted learning strategies. The Elementary School Journal, 101(5), 495-510. Retrieved
July 24, 2010, from the JSTOR database.
Kamps, D., Greenwood, C., Arreaga-Mayer, C., Veerkamp, M. B., Utley, C., Tapia, Y., et al.
(2008). The efficacy of class wide peer tutoring in middle schools. Education &
Treatment of Children, 31(2), 119-156. Retrieved July 23, 2010, from the Educator
Reference Complete database.
Lauren, Nathan V., and Sarah Lee. "Misunderstood Minds. Math Difficulties | PBS." PBS:
Public Broadcasting Service. Web. 29 Jan. 2011.
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<http://www.pbs.org/wgbh/misunderstoodminds/mathdiffs.html>.
Lawson, t., & Trapenberg, g. (2007). The effects of implementing a class wide peer tutoring
model on social approvals and disapprovals during unstructured free time. Journal of
early and intensive behavior interventions, 4(2), 471-482.
Lo, Y. (2004). Total class peer tutoring and interdependent group oriented contingency:
improving the academic and task related behaviors of fourth-grade urban students.
Educational and Treatment of children, 27(3), 235-262. Retrieved July 24, 2010, from
the ERIC database.
Mathes, p., Torgesen, J., Clancy-Menchetti, J., Santi, K., Nicholas, k., Robinson, C., et al.
(2003). A comparison of teacher-directed versus peer-assisted instruction to struggling
first grade readers. The Elementary School Journal, 103(5), 459-479.
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Appendix A
Timeline
Dates Action to be Conducted
January 31-February 4 Gain approval from the school’s administration
to conduct study
February 7-11 -Seek permission from parents allowing them
to participate in the study.
-Selection of appropriate software for
computer-based learning for students who are
unable to participate
February 14-18 -Perform pre-assessment of students’ attitudes
-Perform pretest in Mathematics
Train students in peer tutoring, modeling and
allowing them to practice.
February 21-March 18 Implement Peer Assisted Learning strategies in
the classroom
March 21-25 Perform post tests on mathematics, students’
attitudes toward mathematics and students’
attitudes towards group work
-Perform post-assessment of rating scale of
attitudes of students towards peer tutoring.
March 28-April 1 .
-The researcher will chart results and analyze
findings
- Researcher will decide if finding support
hypothesis
-Students’ third quarter grades will be analyzed
-Perform MAP assessment as a post-
assessment if available
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April 4-20
-Research will be shared with colleagues and
published
Appendix B
Math Map Scores
Student Fall
Scores
Winter
Scores
Growth
1 211 215 +4
2 193 214 +11
3 219 226 +7
4 207 222 +15
5 215 219 +4
6 205 210 +5
7 180 185 +5
8 210 213 +3
9 188 202 +14
10 206 213 +7
Student Fall
Scores
Winter
Scores
Growth
11 214 225 +11
12 214 211 -3
13 200 207 +7
14 192 191 -1
15 195 189 -6
16 220 229 +9
17 202 207 +5
18 219 221 +2
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19 205 207 +2
20 213 221 +8
Class
Average
205.4 211.35 5.45
Appendix C
Reading MAP Scores
Student Fall MAP Winter MAP Growth
1 205 214 + 9
2 202 211 +9
3 221 213 -8
4 211 226 +15
5 209 222 +13
6 192 205 +10
7 179 192 +13
8 218 219 +1
9 191 210 +19
10 202 202 -
11 219 217 -2
12 219 227 +8
13 182 207 +25
14 195 207 +12
15 195 208 +13
16 220 226 +6
17 185 206 +21
18 200 204 +4
19 189 192 +3
20 197 201 +4
Class
Average
201.5 210.3 8.8
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Appendix D
Math Grades for Quarters 1 & 2
Student Quarter 1 Quarter 2 Change
1 92 93 -1
2 85 91 +6
3 97 89 -8
4 98 96 -2
5 85 93 +8
6 78 70 -8
7 70 71 -1
8 90 93 +3
9 78 82 +4
10
11
12
13
14
15
16
17
18
19
20
87
93
94
85
78
81
93
79
95
89
85
82
95
92
77
79
73
88
76
94
82
84
-5
-2
-2
-8
+1
-8
-5
-3
-1
-7
-1
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86.6 85.5 -1.1
Appendix E
Reading Grades for Quarters 1 & 2
Student Quarter 1 Quarter 2 Change
1 89 96 -1
2 93 91 +6
3 96 90 -8
4 98 96 -2
5 87 93 +8
6 81 77 -4
7 77 76 -1
8 99 93 +3
9 78 80 +4
10
11
12
13
14
15
16
17
18
19
20
89
94
96
77
84
83
98
77
85
85
85
82
91
96
74
81
80
94
80
86
90
90
-5
-2
-2
-3
+1
-8
-5
=3
-1
+5
+5
87.5 86.8 -0.7
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Appendix F Name __________________________
Date__________________________
Feelings Towards Mathematics
(Adapted from NAEP 1996)
Agree Not Sure Disagree
1. I like math 3 2 1
2. I am good at math 3 2 1
3. Math is useful in everyday situations 3 2 1
4. Everyone can do math if they try hard 3 2 1
5. Math is boring 3 2 1
6. Math is hard 3 2 1
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7. If I had a choice, I would never do math again 3 2 1
8. Math is mostly memorizing 3 2 1
9. What is the hardest thing for you in math?
10. What do you think would help you to be better at math?
11. Do you learn better alone, with a partner, or with a group when learning new concepts
in math?
12. Explain why you do or do not like math. Be specific.
13.
Appendix G
Name_______________________
Date______________________
Attitudes about Working with a Partner
(adapted from NAEP-1996)
Agree Unsure Disagree
1. Working with a partner is helpful 3 2 1
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2. I learn from a partner 3 2 1
3. I like working with a partner 3 2 1
4. I do not like being assigned an partner 3 2 1
to work with
5. I don’t get a lot done when I work 3 2 1
with a partner
6. It is hard to get along with a partner 3 2 1
7. I would rather work with a partner 3 2 1
than do math alone
8. If I work with a partner, I am not working 3 2 1
as hard
9. Do you like working with a partner in math? Why or why not?
10. Why do you think teachers do not have as much group work in math?
Appendix H
Name________________________
Date________________________
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Math Pre/Post Test for 4th
Grade
_______ 1 35624907
Where should a decimal be placed in the above number
to make the largest amount?
a. between the 6 and the 2
b. between the 4 and the 9
c. between the 3 and the 5
d. between the 5 and the 6
_______ 2 In the number shown above, the digit '4' is holding what
place value?
a. millions
b. ten-millions
c. hundred-thousands
d. billions
_______ 3 If the letter 'X' is replaced by the number '2' in the above
equation, the answer will be what?
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a. greater than 50
b. exactly 50
c. less than 25
d. half of 50
_______ 4 When solving the multiplication problem above, why is it
important to place the zero (beside the question marks) in
the correct place?
a. because the number 2 is in the tens column and it
is being multiplied by 9
b. because the sum of 9 and 2 is greater than 10
c. because the number 4 is in the ones column and
it is being multiplied by 9
d. because the sum of 9 and 4 is more than 10
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_______ 5 Which title is most appropriate for the sample work shown
above?
a. "Solving Simple Equations Using Fractions"
b. "A Simple Way to Find the Product of Two Large
Numbers"
c. "Understanding the Place Values of Decimals"
d. "The Basic Steps of Long Division"
_______ 6 In the number shown above, which number is in the
hundredths spot?
a. 4
b. 5
c. 9
d. 2
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_______ 7 The mathematical sentence shown above becomes true
when which symbol replaces the question mark?
a. =
b. <
c. =
d. >
_______ 8 Shown above is 3/4 of a circle. This is also equal to what?
a. 6/9
b. 9/12
c. 6/12
d. 4/6
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_______ 9 The drawing above represents which of these equations?
a. .67 + .33 = 1
b. .50 + .50 = 1
c. .75 + .25 = 1
d. .50 + .25 = .75
_______ 10 In the picture above, what portion of the blocks are
shaded?
a. 4/100
b. 2/10
c. 4/10
d. 4/5
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_______ 11 Which two of the numbers shown above are equal?
a. 1 1/4 and 1.75
b. 7/4 and 1.75
c. 7/4 and 1 1/4
d. 1.75 and 6/8
_______ 12 In Pattern A (shown above), what will be the next number
following 16?
a. 21
b. 20
c. 18
d. 19
Csiszer Page 32

_______ 13 If the pattern above were to continue, what shape should
replace the question mark?
a. a triangle
b. a quadrilateral
c. a pentagon
d. a hexagon
_______ 14 The equation shown above is only true if the letter 'X' is
equal to what number?
a. 6
b. 4
c. 5
d. 7
Csiszer Page 33

_______ 15 If the letter 'X' is replaced by the number '2' in the above
equation, the answer will be what?
a. 2
b. 50
c. 20
d. 25
_______ 16 In the pattern above, which of the following is true about
the number of blocks needed to complete the bottom row
of each step?
a. the bottom row remains constant each time
b. the bottom row doubles each time
c. the bottom row increases by two each time
d. the bottom row increases by one each time
Csiszer Page 34

_______ 17 What is one thing that all of the shapes shown above
have in common?
a. they all have parallel sides
b. they all have right angles
c. they are all quadrilaterals
d. they are all pentagons
_______ 18 The drawings above are intended to represent which of
the following?
a. parallelograms
b. 3-dimensional objects
c. quadrilaterals
d. objects with no depth
Csiszer Page 35

_______ 19 In the above picture, "Object D" is a sphere. What is true
about this shape?
a. it contains only right angles
b. all of the points on the surface are equal distance
from a straight line
c. all sides are parallel to one another
d. all of the points on the surface are equal distance
from a single point
Csiszer Page 36

_______ 20 In the above picture, which transformation between Step
1 and Step 2 resulted in the shape being reflected across
a line?
a. Transformation C
b. Transformation D
c. Transformation B
d. Transformation A
_______ 21 In the picture above, Letter 'C' shows the triangle slid a
short distance between Step 1 and Step 2. This sliding is
known as what
a. translation
b. reflection
c. rotation
d. congruency
_______ 22 In the above picture, which two shapes are congruent?
a. Shape B and Shape C
b. Shape A and Shape D
c. Shape A and Shape B
d. Shape B and Shape D
Csiszer Page 37

_______ 23 In the above graph, which point has the coordinates (2,
3)?
a. Point C
b. Point A
c. Point B
d. Point D
Csiszer Page 38

_______ 24 In the above picture, which of the tools would be best for
measuring a volume that is equal to 4 quarts?
a. measuring spoons
b. the gallon bucket
c. balance scale
d. spring scale
Csiszer Page 39

_______ 25 Which of the angles above is commonly referred to as a
"right angle"?
a. Angle D
b. Angle B
c. Angle C
d. Angle A
_______ 26 Which of these is the best estimate for the measurement
of Angle A (shown above)?
a. 90º
b. 10º
c. 180º
d. 45º
Csiszer Page 40

_______ 27 In the above picture, the car weighs 1 ton. This is equal to
which of the following?
a. 10,000 ounces
b. 10,000 pounds
c. 2,000 pounds
d. 2,000 ounces
_______ 28 What is the perimeter of Shape B (shown above)?
a. 7 cm
b. 28 cm
c. 70 cm
d. 36 cm
Csiszer Page 41

_______ 29 In the picture above, every square is 1 cm x 1 cm. What is
the area of the square?
a. 16 square centimeters
b. 4 square centimeters
c. 8 square centimeters
d. 32 square centimeters
Csiszer Page 42

_______ 30 In the above picture, Clock A is shown in the morning
(AM), and Clock C is shown in the evening (PM) of the
same day. What is the time difference between the two
clocks?
a. 23 hours and 47 minutes
b. 11 hours and 47 minutes
c. 12 hours and 13 minutes
d. 0 hours and 13 minutes
Csiszer Page 43

_______ 31 In the graph above, the greatest amount of total students
enjoyed which type of TV show?
a. Drama
b. Reality / Game Shows
c. an equal amount of students enjoyed each type
the same
d. Comedy
Csiszer Page 44

_______ 32 Which fraction correctly describes the above circles?
a. 2/3
b. 3/2
c. 5/2
d. 8/3
Csiszer Page 45

Appendix I
List of Manipulatives That Will be Used During Tutoring
Pattern Blocks
Unifix Cubes
Fraction Squares
Base Ten Blocks
Judy Clocks
Protractors
White Boards/markers
Colored tokens
Die
3-demensional shapes
Nets
Csiszer Page 46

Final Using Peer Tutoring Strategies to Increase Mathematic Achievement

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