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 ConductedJanuary 31-February 4 Gain approval from the school’s administration

to conduct studyFebruary 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 MathematicsTrain 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 FallScores

Winter Scores

Growth

1 211 215 +4

2 193 214 +11

3 219 226 +7

4 207 222 +15

5 215 219 +46 205 210 +57 180 185 +58 210 213 +39 188 202 +1410 206 213 +7

Student FallScores

Winter Scores

Growth

11 214 225 +1112 214 211 -3

13 200 207 +7

14 192 191 -1

15 195 189 -616 220 229 +917 202 207 +518 219 221 +2

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19 205 207 +220 213 221 +8

Class Average

205.4 211.35 5.45

Appendix C

Reading MAP Scores

Student Fall MAP Winter MAP Growth1 205 214 + 92 202 211 +93 221 213 -84 211 226 +155 209 222 +136 192 205 +107 179 192 +138 218 219 +19 191 210 +1910 202 202 -11 219 217 -212 219 227 +813 182 207 +2514 195 207 +1215 195 208 +1316 220 226 +617 185 206 +2118 200 204 +419 189 192 +320 197 201 +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 -12 85 91 +63 97 89 -84 98 96 -25 85 93 +86 78 70 -8

7 70 71 -18 90 93 +39 78 82 +41011121314151617181920

87 93 94 85 78 81 93 79 95 89 85

8295927779738876948284

-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 -12 93 91 +63 96 90 -84 98 96 -25 87 93 +86 81 77 -4

7 77 76 -18 99 93 +39 78 80 +41011121314151617181920

8994967784839877858585

8291967481809480869090

-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

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_______ 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

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_______ 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

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_______ 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

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_______ 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

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_______ 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

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_______ 23 In the above graph, which point has the coordinates (2, 3)?

a. Point C

b. Point A

c. Point B

d. Point D

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_______ 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

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_______ 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

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_______ 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

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_______ 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

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_______ 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

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_______ 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

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_______ 32 Which fraction correctly describes the above circles?

a. 2/3

b. 3/2

c. 5/2

d. 8/3

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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

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Documents

Final Using Peer Tutoring Strategies to Increase Mathematic Achievement