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The Effects of Peer and Self-Assessment in a

Middle School Mathematics Classroom

A Master Research Project Presented to

The Faculty of the Patton College of Education

Ohio University

In Partial Fulfillment

Of the Requirements for the Degree

Master of Education

By: Brittany Hammonds, B.S. Mathematics and Life Science

August 2013

This Master's Research Project has been approved

for the Department of Teacher Education

Ralph Martin" Ph.D.Professor Emeritus

Department of Teacher Education

Frans Doppen" Ph.D.Associate Professor and Interim Chair

Department of Teacher Education

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Table of Contents

Abstract . 4

Chapter 1: Introduction .. 5-11

Statement of the Problem .... 6-7

Rationale for the Problem ....... 7-9

Research Question ... 9

Explanation of Significant Terms 9-10

Organization of Paper .. 11

Chapter 2: Literature Review ... 12-17

Layout of Chapter .. 12

Learning Needs .. 12-13

Peer Learning ...... 13-14

Self and Peer-Assessment .. 14-15

Self-Efficacy .. 15-16

Motivation .. 16

Summary . 17

Chapter 3: Methods of Research . 18-23

Setting . 18-19

Participants ...... 19

Data Collection .. 20-22

Data Analysis . 22-23

Summary 23

Chapter 4: Results .. 24-36

Chapter 5: Analysis and Discussion ...... 37-48

References ... 49-52

Appendix Table of Content ..... 53

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Abstract

Learning is acquiring new knowledge or skills and can occur through being taught and studied or

by practicing: through experience. Educators play a large role in teaching and encouraging study

habits in students. However, there are ways that educators can encourage and foster the

independent learning process in students. A possible method of encouraging an increase in

motivation and self-efficacy in a classroom learning environment is the addition of self and peer-

assessment into the daily structure within a classroom. The purpose of this study is to determine

if peer-assessment effected individual self-assessment, including an increase in self-efficacy or

motivation in mathematics. An additional question this research studies is the effect the addition

of the assessment procedures into a mathematics unit has on the overall achievement of students.

This study is designed to determine the effect of introducing self-assessment and peer-

assessment methods into a middle school mathematics classroom. During the unit observed by

this study, students individually completed four self-assessments and worked in partners to

perform two peer-assessments. These assessments were designed to teach students to evaluate

their own abilities and the abilities of their peers. Interviews and portfolios were collected for

six participants: two low achieving, two high achieving, and two mid-achieving students. These

portfolios and interviews showed that the addition of these assessment methods had varying

effects on student achievement. Overall, student achievement improved. However, high, mid,

and low achieving students each showed different responses to the addition of these assessment

methods.

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Chapter 1: Introduction

Mathematics is a difficult content area which many students struggle in. In

mathematics, topics build upon one another. It is essential for students to learn the basic

concepts so that they have a strong foundation for higher level mathematics. Because

mathematics is a subject which builds and depends upon prior knowledge, it is essential for

students to master new concepts so that they are prepared for the next layer of skills that they

will be learning. The deeper students go into mathematics, the more problem solving skills they

learn. Mathematics teaches logic and problem solving, which are critical skills for surviving in

the twenty first century. Middle school mathematics is a pivotal time for students. These grade

levels are when students solidify foundational mathematics skills. It is extremely important that

these skills be shored up so that students have an opportunity to succeed in higher level

mathematics courses which they will encounter at the high school level and also allows them to

build skills which they will require later in life (Achieve, p.2).

There has been some research done which shows that mastery of a concept can be

achieved when someone teaches that concept to another person. It has also been discovered that

the more times a student hears a concept explained, the more likely they are to remember or

understand that concept. For some students, it is difficult to understand a new concept as the

teacher is presenting it. Some students struggle with understanding the teacher, however, many

of these students can gain a better understanding of mathematical concepts and procedures from

their peers. This is particularly true in students who have learning or behavioral disabilities or

delays. Receiving explanations from peers may be more effective for some students because

students share a similar language and can translate difficult academic language into words that

their peers understand (Farivar, p.3).

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Problem Statement

In these foundational years, many students struggle with learning the new mathematics

concepts and procedures. There are many suggested causes for the high proportion of students

who struggle in mathematics. One major problem is that students lack the motivation to work on

their own time. Another large concern is that students do not know how to rank their own

knowledge. They have not developed self-assessment skills and therefore do not know which

concepts they most need to work on. Because students have not developed self-efficacy and do

not know how to assess their own progress, they do not feel motivated to put the additional effort

that it takes to understand difficult concepts (Dupeyrat, p.241).

A large aspect of studying is acknowledging that there is work that needs to be done.

Students often do not know how to evaluate what they know. Because of this deficit, students

are unable to identify what they need to work on and what they have already mastered. In

mathematics, students often get extremely frustrated because they cannot figure out a complex

problem, but they cannot identify where within the problem they are confused. Students most

often assume that they simply cannot do the problem. Most often this is not the case at all.

Sometimes there is simply one spot within a problem that students are struggling with because

they never fully mastered a certain skill. Once they get beyond this portion of the problem, they

are often able to solve the problem successfully (Cupani, p.659).

As a society, we understand that no one is perfect and yet we expect perfection. One of

the greatest downfalls that our students have working against them is their inability to recognize

strengths and weaknesses; not only in others but also in themselves. In mathematics, it is

important for students to be able to recognize areas where they are mathematical weak and also

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for them to be able to identify areas that they are mathematically strong. Recognizing strengths

and weaknesses not only assists students in studying and preparing for major assessments; it

prepares them for the real world, where although they will be great at many things, there will

always be some aspects of any students life that need some work.

Rationale for the Problem

This study was designed to explore an alternative method of learning for middle school

students; a style of learning which would allow students to learn from their peers concepts that

were previously presented by the teacher in class. In this method, students used guidelines set

out by the instructor to assess their peers knowledge on the mathematical concept being studied.

Students also were given the opportunity to evaluate their own knowledge using self-assessment.

The purpose of this study was to study student motivation. This study attempted to

determine if facilitating peer and self-assessment can impact students motivation towards

mathematics. More importantly this study was meant to determine if peer assessment could

assist students in developing their own self-assessment skills. The study was used to determine

the effect of peer assessment on students self-assessment and self-efficacy in mathematics.

Self-assessment is an individuals ability to look at their own work or behavior and make

an evaluation about their progress. Self-assessment is not only about making evaluations after

work or actions have been completed, but self-assessment is also about recognizing important

aspects of an activity and setting expectations or goals for ones self. This process of goal setting

and evaluation is extremely valuable in an educational setting, specifically mathematics. Self-

assessment is an important part of learning because it enables students to identify their learning

needs, set learning-goals, and monitor their progress (Aedyemi, p.4). This process is essential

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to prepare students for higher level mathematics courses where more of the learning

responsibility will belong to the students themselves. Self-assessment is also an important

foundational life skill which will serve students later in life as they begin their professional

careers.

Self-assessment places the responsibility of learning squarely on the shoulders of the

students. It requires them to think about their work and their behavior. Through self-assessment

students begin to think about how they learn and form goals to improve their own learning. Self-

assessment is important because it reminds students that they are responsible for their own

learning. This emphasis on responsibility provides students with a sense of ownership. It

ultimately gives them a choice and forces them to choose between working through a process to

be successful or choosing to continue doing the same things that have not worked. Self-

assessment provides an alternative way of viewing their progress and can give students a path to

success if they believe that they can succeed.

Self-efficacy is closely tied to self-esteem but it is not only about self-esteem and self-

confidence but also about ability and motivation. Self-efficacy is based upon a students

confidence in their ability to complete a task. It is a students internal desire to work towards a

goal of success in a particular area. Self-efficacy is about an individuals personal belief of their

ability to complete a task with success (Aedyemi, p.2). At the root of self-efficacy is a persons

desire to complete a task or belief of importance to themselves. Unless people believe that they

can produce desired outcomes by their actions, they have little incentive to act or to persevere in

the face of difficulties (Bandura, p.1). A persons self-efficacy impacts their decisions,

motivations, and most importantly their actions.

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Self-efficacy is extremely powerful. Students with high self-efficacy are more willing to

work on difficult tasks to better their understanding and push themselves with something

challenging (Cupani, p.660). However, students with low self-efficacy are extremely hard to

motivate because they cannot see the benefit in completing work or struggling through

something difficult. If self-efficacy can be encouraged and fostered in a mathematics

environment it is possible that students motivation will improve and their learning will be

positively impacted.

Research Question

The primary research questions for this study are: In a middle school mathematics

classroom, can peer assessment be used to improve self-assessment and increase students self-

efficacy? Does utilizing peer and self-assessment in a mathematics classroom improve student

motivation? The overall question that this study seeks to determine is do peer and self-

assessment improve student achievement in a mathematics classroom.

Explanation of Terms:

Honors Classroom

This is a classroom for high achieving students in a specific content area.

Typically these students have scored at the accelerated or advanced achievement

levels on their Ohio Achievement Assessments. These classes typically involve

critical and higher level thinking.

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Peer Learning

This is any activity in which students work together to increase their knowledge

or complete an assignment (Johnson, p.1).

Peer Assisted Learning Strategies (PALS)

This is a method implemented in a classroom, which involves students working

cooperatively together. This method utilizes traditionally successful teaching

strategy but puts an extra emphasis on the interaction and mediation between

students. Typically these strategies form pairs to impact each students unique

needs.

Self-Efficacy

This is the freedom that ever person has to choose their own course of learning

and direction of learning. It is the willingness to learn that a student has within

themselves (Aedyemi, p.4). It also refers to the capacity which a student is

willing to take charge of their own learning.

Self-Assessment

This term refers to individuals making evaluations on their own learning,

behavior, and progress in a specific area. Other terms that are commonly used to

describe this are self-reflection and self-evaluation. This is an important learning

strategy. It allows students to identify their learning needs, set learning goals,

and monitor their progress (Aedyemi, p.6)

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Organization of Paper:

This paper is organized into five chapters. Chapter one includes an introduction, a

statement, and an explanation of terms. Chapter two includes an outline of research in the area

of peer learning, various types of peer and self-assessment, motivation, and self-efficacy.

Chapter three describes the design of this research, including all the various methods of research,

descriptive information about the study setting and participants, and information about data

collection. Chapter four provides an explanation of the results of the research study. Finally,

chapter five discusses possible implications of the data which was collected. This chapter also

reasons through the meaning of the data and results collected through this research study.

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Chapter 2 Literature Review

Introduction:

There is a noticeable deficit in research being done at the middle school level in peer

assisted learning and self-assessment. Part of the reason behind this deficit could be attributed to

the complexities involved in coordinating cooperative learning and peer learning activities at the

middle school level. There are two distinct challenges that middle school students face. The

first is the adjustment to the various biological and chemical changes that their bodies are going

through (Johnson, p.2).

The second is the changing of their routine. In primary schools, there are typically no

bell schedule and no passing period. There is a lot less responsibility and students do not switch

classes but the teachers switch. However, when students arrive in middle school there is a lot

more responsibility and changes (Johnson, p.2).

Layout of the Chapter

This chapter discusses the various learning needs of students. It continues by pointing

out various methods of peer learning and assessment. Then the chapter details research on self-

assessment and self-efficacy. Next, the chapter discusses research on motivation, specifically in

a mathematics environment. The final element of this chapter is a summary of the research

discussed in this chapter.

Learning Needs

There are some important aspects associated with teaching students academic content at

school. Students need to feel like what they are doing satisfies their needs or will benefit their

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future. One of students main needs is to be social and to belong. Students want to feel that

they fit into their environment. They need to believe that they are equal to their peers. Albert

Bandura describes students need to have a good reason to imitate (Bandura).

Another of students current needs is success. Students need to experience the feeling of

achievement. Often in school, there are not enough opportunities for students to succeed or all of

these opportunities are restricted to the traditional academic success. Educators desire to have

students work hard and succeed, but often forget students need something to work hard for and

they need to feel like they can achieve this success. Often students do not see success in the

same light as educators. Student opportunities to achieve success and their perception of

achieving success are both integral to their confidence and motivation in mathematics. It is not

always the actual outcome that is the greatest factor but a students perspective of the outcome

that actually determines if a performance was positive or negative (Hoffman, p.276).

Peer Learning

Although cooperative learning techniques have become more and more common, they are

not always automatically effective. In an article studying the relationships involved in

cooperative learning, the authors state that learning from peers is not universally recommended.

Peers can have bad reputations (Johnson, p.1). However, later on in this article, the researchers

argue that there are other researchers who strongly defend peer learning as a positive academic

method of learning for students (Johnson, p.2-3). Another article on producing helping

behaviors from cooperative learning states that, students can learn from each other in many

ways: by giving and receiving help, by recognizing and resolving contradictions between their

own and other students perspectives, and by internalizing problem-solving processes and

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strategies that emerge during group work (Farivar, p.1) One integral portion of peer learning is

teaching students to recruit positive attention and instructional feedback from their peers may

promote appropriate social interactions while increasing the academic productivity (Alder, p.2).

Peer learning is a cooperative learning method that has become popular in various

content area classrooms. Class wide reciprocal peer tutoring is meant to give students the

opportunity to practice their skills at newly learned concepts. This PALS method is meant to

give both students the opportunity to act as a tutor and a tutee. The process of reciprocal peer

tutoring is designed to help both the tutor and the tutee (Farivar, p.2). An important part of

learning in peer tutoring is being able to give explanations. However, it is equally important for

students to learn how to receive explanations from their peers as well. Explanations must be

appropriate for their peers needs at the specific time the explanation is needed (Farivar, p.3).

Peer tutoring has also shown to increase the amount of time students are academically engaged

and furthers understanding (Dufrene, p.1).

Peer and Self-Assessment

One thing that is interdependent with self-efficacy is self-assessment. Students who are

able to use self-evaluation increase their competency in mathematics (Ramdass, p.5). When

students have more mathematical competence, their self-efficacy increases (Ramdass, p.5). Self-

assessment is a skill, which is critical in any path of life, but is extremely important in school. In

a mathematics class, self-reflection and evaluation is essential. Although instructors can use

forms of formative and summative assessment to gage the conceptual level of their class, it is

much more successful for students to gage for themselves whether they truly have mastered new

material. Adeyemi references Boyd in her article and states that self-assessment, involves

students taking responsibility for their own learning (Adeyemi, p.5). This form of self-efficacy

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can build student confidence and help them to grasp important mathematical concepts and build

critical life skills. It has been found that when students self-evaluate a task; they improve their

performance and increase their knowledge (Ramdass, p.4). When students are able to evaluate

their own work accurately, they improve their own competence in mathematics (Ramdass, p.5).

One problem that often occurs with students when they are evaluating themselves is that

they are not always accurate (Ramdass, p.5). This problem is somewhat due to the fact that

students do not always know the best way to assess their own abilities. Students who are

underachieving often give themselves low evaluations. Some students overestimate the

competence of their abilities, some underestimate the competence of their abilities, and some

have an accurate assessment of their competence level (Dupeyrat, p.242). It is possible that

underachieving students give themselves poor evaluations as a self-defense mechanism because

they have low self-confidence (Chang, p.137). Because many students are not able to accurately

identify their strengths and weaknesses, many teachers have utilized peer-assessment (Chang,

p.135). The process of peer-assessment allows for students to become actively involved in the

evaluation of their peers (Chang, p.136). Research shows that because of the emotions and

development involved in adolescence, students are more likely to mold to their friends

perceptions (Chang, p.136). There has been concern that using self and peer assessment in a

classroom setting might be too time consuming across an entire classroom (Chang, p.137). In

their study on self-correction, Ramdass and Zimmerman, propose that through self-regulation,

students can increase their academic abilities (Ramdass, p.3). Self-regulation requires students

to have emotionally and behaviorally acted on previously created goals in order to reach a

positive outcome (Ramdass, p.3).

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Self-efficacy

Stimulating and developing self-efficacy is a major tool that educators can use to

encourage students to work hard in mathematics. Students with higher self-efficacy persevere in

solving more cognitively difficult problems and typically these students do not have issues with

mathematics anxiety (Hoffman, p.277). There is a positive relationship between self-efficacy

and effective problem solving (Hoffman, p.279).

Motivation

One of the biggest barriers to successful student learning is motivation. Because

mathematics is such a difficult subject, many students have little or no motivation to study and

work to understand the material. For many students there is a large correlation between

mathematics anxiety and negative performance or mathematics achievement (Hoffman, p.276).

A difficult task for educators is finding a way to overcome this anxiety and motivate their

students to work for mastery of mathematics skills. In Adeyemis research article on developing

self and peer reflection, there is a clear opinion of student motivation. Learners tend to avoid

taking responsibility for their own learning because of the lack of motivation and it sometimes

gives rise to negative feelings. Students are passively involved in the selection and show no

interest to take the responsibility for their learning (Adeyemi, p.3). There have been various

studies done to try and determine if there is a certain gender which has a higher degree of

mathematics anxiety or lower degree of mathematics motivation, however, these studies cannot

conclusively find either males or females to have more discomfort with mathematics (Hoffman,

p.277). It seems that all students have equal likelihood to be anxious about mathematics. This

anxiety can cause students to have a predetermined attitude towards mathematics and can have a

negative impact on their competency in mathematics (Hoffman, p.278).

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Summary

This chapter discussed important needs that students have. These needs must be met in

order for students to have a successful experience in school and a positive learning experience in

mathematics. There was also mention of the great benefit that can be provided from working

with peers. Students can explain things to their peers in ways that adults cannot; in many ways

students have their own language, which teachers cannot interpret. Peer learning allows a

positive way for students to assess one another and get feedback on their work. A huge point in

this chapter was the importance of self-assessment and self-efficacy. Self-assessment is an

integral skill for an individual to understand how they learn and ways that they can improve.

Self-efficacy is important because it steers an individuals attitude as they begin and proceed

with a task. Finally this chapter concluded with a section on motivation. Motivation is

extremely important in an educational environment.

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Chapter 3 Methods

Introduction

Cooperative learning techniques and peer assisted learning has been a topic studied at

great length. However, there was a noticeable deficit in research being done at the middle school

level in peer assisted learning, specifically in peer assessment methods in middle school

classrooms. This study was done in an eighth grade classroom. It examined the implementation

of self and peer-assessment into two honors eighth grade mathematics classrooms. Specifically

this study examined the effects peer assessment had upon students self-assessment and self-

efficacy.

Setting

The school district that this study was performed in was in a mid-to-low socioeconomic

community. This school district contains kindergarten through twelfth grade in a single building.

The study will take place in the Junior High School, specifically in an eighth grade honors

mathematics classroom. The schools in this region are considered high needs schools. The

schools in this county often struggle to maintain a proficient score on the annual standardized

test scores in mathematics. However, the school district examined for this study produced the

highest test scores in its county in the 2011-2012 school year.

The school district is in southeastern Ohio. The communities surrounding this school

district have firm traditional beliefs and strong religious values. These communities are made

up of families from low to middle socioeconomically backgrounds. Many of the students

attending this school have never been outside the state of Ohio and neither have their parents.

There are many broken families in the southeastern Ohio area. Many students have siblings with

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different parents or live with only one of their parents or with none of their parents at all. There

is a high percentage of students who live with legal guardians or in state facilitated homes.

Many of the students in this school district have families who depend upon them for additional

wages and/or for babysitting other children within the household. The Appalachia communities

surrounding the school district are very close to nature and land is a very important part of their

culture.

This study was held in two honors mathematics classes, specifically eighth grade honors

algebra. The honors algebra classes are the highest mathematics classes offered for junior high

students in this school district. These two classes are designed to fast track students through

mathematics courses at the school. The majority of the students in these classes are high

achieving eighth grade students; however, there are also three accelerated high achieving seventh

grade students in these two honors classes. Students who take the honors algebra classes in

eighth grade are expected to take Calculus as seniors in high school and seventh graders in the

honors algebra classes are expected to complete calculus their junior year in high school and

continue into collegiate mathematics courses at neighboring universities.

Participants

The participants in this research study are members of two eighth grade mathematics

classes consisting of 36 students. Because of the nature of the honors class, these students

typically perform at a higher level mathematically than their peers. There were six students

selected to answer interview questions during this study.

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Data Collection

Instruments

There were several instruments used in this study. There was a pre and post assessment

for the material covered during the study. These assessments were used to measure students

actual knowledge of the material covered in the units before and after they received instruction.

Another instrument used in this study was the self-assessment worksheets. These were used to

evaluate how students perceived their knowledge of the material as the unit proceeded. Another

instrument used was the peer-assessment worksheets. These were used to help students learn

how to evaluate others and themselves. They were also used to determine if students self-

assessments were altered based on the evaluation they received from their peers. Additional

instruments utilized in this study were an initial survey and interviews with students. The

interviews were designed to determine the perceptions and opinions students had about peer-

assessment, self-assessment, and motivation.

Self and Peer Assessment Worksheets

Students completed out self-assessment sheets throughout the unit. There were two peer-

assessment opportunities during the unit. Students individually filled out self-assessment sheets

at the beginning of the period. Students were divided into pairs formed for peer-assessment

purposes. Each dyad received two sheets. These partners worked out a series of problems

associated to what was being taught in class. After completing these problems, the peer

assessment sheets were filled out by a partner about a students progress and competence on that

particular concept. Each student was responsible for filling out their partners peer reflection

sheet. Students completed out self-assessment and peer-assessment sheets on a regular basis. At

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the end of each class period, the teacher collected the peer-worksheets. There was class time set

aside for assessment every week. A sample of the self-assessment sheets and peer assessment

sheets is located in the appendices C, E, F, I, J, and K.

Pre and Post Assessment

This study spanned one unit, wherein students studied factoring monomials and

polynomials. There was a pre-assessment at the beginning of the unit and a post-assessment at

the end of the unit. The pre-assessment contained statements about concepts covered in the

factoring unit and students determined if these statements were true or false. The post-

assessment was a unit test, which was given as the conclusion of the study. This measured actual

student knowledge about the content prior to direct instruction, peer assisted learning, and

increased assessment. Additionally, the previous unit test was used to create a base line of

achievement for the participants. These assessments attempted to demonstrate if there was any

major improvement difference with the addition of peer and self-assessment.

Survey

There will be one survey performed and presented in this study. The survey will be given

to students a week before the study starts. This survey will be given to both of the classes at the

beginning of the class period. The instructor went through each question with the students in an

effort to minimize confusion. The purpose of this survey was to obtain student ideas and

perceptions of their own abilities. It is also meant to gage the students self-efficacy. The survey

was designed to determine if students opinions and perceptions of their abilities changed when

peer and self-reflection were added to the class.

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Interview

Interviews were set up at the end of the study. Six students were interviewed. There

were three students selected from each of the classes. These students were selected based on

their initial achievement level based upon the pre-assessments performed on all the students.

The students who were selected included one high achieving student, one student who performed

at a mid-level achievement, and one student who was from a low achieving group. This process

was used for both classes. There were three male and three female participants selected to be

interviewed.

In the two honors algebra classes, six students were selected to participate in the

interviews. Interviews were held the week after the conclusion of the study. There was a single

interviewer who conducted a one on one interview with each of the students. All students were

interviewed in the same room, using the same protocols.

Data Analysis

Pre and Post Assessments

Pre assessments included sample questions over materials covered during the units the

study included. These questions were analyzed for correctness. An average was taken to

determine the questions that students had the most and least knowledge of prior to the start of the

unit. Post assessments were used to determine if peer and self-assessment increased student

success. These were also analyzed according to percentages.

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Peer and Self-Assessment Worksheets

Peer-assessment sheets were used to provide a peers perspective into the abilities of

students. These were used to determine if there was an effect on the self-assessments done by

the students themselves. The self-assessment and peer assessment sheets for six students were

arranged in order from start to finish and analyzed to determine the amount of change that had

occurred in self-reflection and motivation.

Survey

The survey was measured on Likert-based scale. Half of the surveys measured

mathematical anxiety, self-efficacy, and self-assessment. The other half of the questions on the

surveys measured the effectiveness of peer-assessment and the competence of students in

mathematics.

Interviews

The interviews were used to determine the perceptions of students. The responses to the

interview questions were compared and contrasted to look for similarities. The perceptions of

each of the interviewed students were also noted and compared.

Summary

This chapter discussed the methods which were used to carry out this study. First this

chapter pointed out the unique socioeconomic status and rural ideals which influence the

community where this study took place. Next the study outlined the difference in achievement

aptitudes for different types of classes. The chapter described the different instruments from this

study, how they were used, and the way they would be analyzed.

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Chapter 4 Results

This study researches the effectiveness of self and peer assessment methods. The

timeline which these self-assessments and peer-assessments were given to students is outlined in

diagram 1. As shown below, this study refers to data collected

over the course of two units in a middle school mathematics

classroom.

In the pre-assessment for unit 8: Factoring Polynomials,

students were asked to show prior knowledge before beginning the

unit. Students were given a worksheet with nine statements about

factoring and asked to decide if the statements were true or false.

Because this was a pre-assessment, students were also given the option to choose I do not know

or neither true or false. The student responses for the pre-assessment to the factoring unit are

shown in table 1. As shown in diagram 1, after students completed the pre-assessment there was

one lesson given on factoring. The following day students completed the first self-assessment

worksheet. This self-assessment worksheet contained three different sections. Table 2 shows

the first section and student responses. In this section, students were asked to rank their

knowledge of the concepts listed as No Idea, I have heard of this, or Confident I know what this

means. The second section of the self-assessment sheet asked students to either agree or disagree

with five statements involving the classroom environment and motivation (table 3). The final

component of the first self-assessment required students to rank their own ability at specific

mathematics procedures being learned during the unit on factoring polynomials. The participant

responses are shown in table 4 and diagram 2 displays a graphic visual of the male and females

who listed confidence in each of the concepts identified in the first self-assessment.

Unit 8 ProgressionPre- AssessmentSelf-Assessment 1Peer-Assessment 1Self-Assessment 2Mid Unit QuizPeer-Assessment 2Self-Assessment 3Final Self-AssessmentSummative Unit Test

Diagram 1

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Results for Pre-Assessment for Factoring Unit Table 1

Statement

Cor

rect

A

nsw

er

Agr

ee

Nei

ther

Disa

gree

Perc

ent

Cor

rect

A monomial is in factored form when it is expressed as the product of prime numbers and variables, and no variable has an exponent greater than 1.

A 4 18 12 12%

The greatest common factor (GCF) of two or more monomials is the product of their unique factors when each monomial is written in factored form.

D 7 24 3 21%

Any two numbers that have a greatest common factor of 1 are said to be relatively prime.

A 15 11 8 44%

If the product of any two factors is 0, then at least one of the factors must equal 0.

A 19 14 1 56%

A quadratic trinomial has a degree of 4. D 14 13 7 41% To solve an equation such as x2 = 8 + 2x, take the square root of both sides. D 15 11 8 44% The polynomial 3r2 - r - 2 cannot be factored because the coefficient of r2 is not 1.

D 8 22 4 24%

The polynomial t2 + 16 is not factorable. A 8 18 8 24% The numbers 16, 64, and 121 are perfect squares A 28 2 4 82%

Self-Assessment 1: Part 1 Recognition of Mathematical Terminology

Table 2

L H C

I can recognize a monomial. 3% 0 97% I know how to factor polynomials. 9% 19% 72% I can recognize prime numbers and composite numbers.

0 9% 91%

I can find the Greatest Common Factor. 22% 22% 56% I can use the Distributive Property. 0 3% 97% I can use the Distributive Property to factor. 13% 34% 53% I can identify a quadratic polynomial. 28% 56% 16% I can factor a quadratic into two binomials. 47% 50% 3% I can factor a monomial out of a polynomial. 22% 47% 31% I can identify the zeros of a quadratic polynomial. 56% 31% 13% I can recognize a difference of squares polynomial. 25% 47% 31% I can identify a perfect square. 0 9% 90% I can recognize a perfect square polynomial. 6% 50% 44% I can factor a perfect square polynomial. 25% 28% 47% I can factor a difference of square polynomial. 31% 47% 22% L Lost H Have heard about C Confidant I

know

26

Self-Assessment 1: Part 2 Motivation and Environment

Table 3

Agree Disagree Neither I am respectful to my classmates. 100% 0 0 I am respectful towards my teachers. 97% 0 3% I ask questions when I am confused. 66% 13% 22% I will ask my teacher questions. 69% 6% 25% I will answer questions when asked. 97% 0 3%

Self-Assessment 1: Part 3 Evaluation of Ability Table 4

Not

at a

ll

Hel

p of

a

teac

her

Hel

p of

a

frien

d.

By m

ysel

f

Identify a monomial. 0 0 16% 84% Find the Greatest Common Factor. 0 3% 9% 88% Factor Polynomials. 3% 16% 19% 63% Factor Polynomials using the distributive property. 9% 25% 25% 41% Use the Distributive Property. 0 3% 16% 81% Factor a monomial out of a polynomial. 9% 25% 41% 25% Identify prime and composite numbers. 3% 0 19% 78% Identify the zeros of a quadratic polynomial. 38% 16% 38% 9% Factor a perfect square polynomial. 6% 28% 34% 31% Factor a difference of a squares polynomial. 13% 31% 38% 19%

Graph 1

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10

Female

Male

27

Following the first self-assessment, there were two additional days of lessons, which

students learned more about factoring polynomials. Next the students worked in pairs to

complete a worksheet with ten factoring problems (Appendix D). Each pair had two different

worksheets and one answer key for each worksheet. One of the students acted as the grader or

observer while the other student completed the worksheet. If the student who was working

started to struggle with one of the problems, they could ask their partner for help. If both

students were unable to figure out one of the problems, they were able to ask the teacher to assist

them. After the first student completed their worksheet, the students switched roles and the other

student would complete their own worksheet. Once both students had completed their

worksheets, they would each grade their partners work and fill out the peer-assessment sheets.

After the peer assessments had been completed by both partners, they discussed any

misunderstood problems and the evaluation on the peer assessment. In table 5 below are the

recorded evaluations for the first peer-assessments.

The second part of the peer-assessment required partners to rank their peers ability level

with each of the identified areas of factoring. The partners were ranked using a Likert scale, a

score of 5 for often correct and a score of 1 for often incorrect.

28

Peer-Assessment: Part 1 Motivation, Ability, and Autonomy with Mathematical Concepts

Table 5

Not

at a

ll

Hel

p of

a

teac

her

Hel

p of

a

partn

er.

On

thei

r ow

n w

ith

mist

akes

On

thei

r ow

n co

rrect

ly

Identifying prime factors. 0 0 3% 10% 87%

Factor Monomials completely. 0 0 3% 6% 90% Identify the Greatest Common Factor. 6% 0 10% 10% 74% Find the greatest common factor between two monomials.

0 3% 10% 3% 84%

Use the distributive property to factor polynomials.

3% 0 0 16% 81%

Use factor by grouping to factor polynomials. 3% 3% 10% 16% 68%

Peer-Assessment: Part 2 Ability Ranking Table 6 Class

Average Factoring Monomials completely. 4.8 Identifying the GCF between two monomials. 4.6 Using the distributive property to factor. 4.6 Using factor by grouping to factor. 4.3 Solving for x after factoring and finding the zeros of the polynomial. 3.8

29

Through the entire factoring unit, students completed four self-assessment sheets; each

time the students were responsible for evaluating their own knowledge. The tables below show

the class wide evaluations students gave in the self-assessments throughout the factoring unit.

Each of these self-assessment sheets involved the three subdivisions contained in the first self-

assessment. The first subdivision required students to identify their comfort level in recognizing

the concepts covered in the entire unit. Student responses for the second self-assessment are

shown in tables 7, 8, and 9. The second category gave students the chance to gage their

motivation level within the classroom environment. This is displayed in table 8. In the third

subdivision, students evaluated their own ability level on specific concepts. Students selected

one of four statements to describe their competence at the skills described. These four possible

descriptions and student responses are shown in Table 9.

At the midpoint of the study there was a mid-unit quiz given to the students to determine

their progress with factoring polynomials. This mid unit quiz consisted of sixteen questions on

material covered in the first part of the factoring unit (see Appendix G). The scores of this

assessment are shown in Diagram 3.

30

Self-Assessment 2: Part 1 Recognition of Mathematics Terminology

Table 7

L H C

I can recognize a monomial. 0 9% 91% I know how to factor polynomials. 3% 9% 88% I can recognize prime numbers and composite numbers.

0 15% 85%

I can find the Greatest Common Factor. 3% 9% 88% I can use the Distributive Property. 0 6% 94% I can use the Distributive Property to factor. 3% 15% 82% I can identify a quadratic polynomial. 9% 30% 61% I can factor a quadratic into two binomials. 9% 33% 58% I can factor a monomial out of a polynomial. 3% 30% 67% L Lost H Have heard about C Confidant I know

Self-Assessment 2: Part 2 Motivation and Environment

Table 8

Agree Disagree NeitherI am respectful to my classmates. 100% 0 0 I am respectful towards my teachers. 97% 3% 0 I ask questions when I am confused. 70% 6% 24% I will ask my teacher questions. 73% 9% 18% I will answer questions when asked. 94% 0 6%

Self-Assessment 2: Part 3 Evaluation of Skills

Table 9

Not

at a

ll

With

the

help

of

a te

ache

r

With

the

help

of

a fr

iend

.

By m

ysel

f w

ith c

ompl

ete

conf

iden

ce.

Identify a monomial. 0 0 12% 88% Find the Greatest Common Factor. 0 6% 6% 88% Factor Polynomials. 0 6% 15% 79% Factor Polynomials using the distributive property.

0 6% 21% 73%

Use the Distributive Property. 0 3% 6% 91% Factor a monomial out of a polynomial. 0 6% 36% 58% Identify prime and composite numbers. 3% 3% 15% 79%

31

Peer-Assessment 2: Part 1 Ability Independence Table 11

Not

at a

ll

With

the

help

of a

W

ith th

e he

lp o

f a

On

thei

r ow

n w

ith fe

w

mist

akes

On

thei

r ow

n co

rrect

ly

Find the greatest common factor between two monomials.

0 3% 0 9% 88%

Use the distributive property to factor polynomials.

6% 9% 3% 26% 56%

Use factor by grouping to factor polynomials. 3% 3% 6% 9% 79% Factoring a trinomial into two binomials. 6% 0 0 18% 76%

Peer-Assessment 2: Part 2 Evaluation of Skills

Table 12

Class Average

Using the distributive property to factor. 4.4 Finding the factors of a monomial. 4.7 Factoring a trinomial into a binomial. 4.7

Participants Grade Average: Mid-Unit Quiz

A

B

C

D

F

A

F

D

C

B

Diagram 3

32

The second peer-assessment was completed following the mid-unit quiz. Students

worked in pairs to complete a worksheet with seven factoring problems (see Appendix H). This

peer-assessment was done using the same procedure as the first peer-assessment. In table 11 are

the recorded evaluations for the second peer-assessments. In the first part of the peer-

assessment, the partners evaluated the level of independence students were able to complete the

assignment with. In the second part of peer-assessment 2, partners ranked one another on a

Likert based scale. In table 12, the paired responses are displayed. A score of 1 was given to

partners who were unsuccessful in completing problems on their peer worksheet. A score of 5

was given to partners who completed the peer worksheet with complete accuracy.

In the third self-assessment, students ranked their ability using a Likert based system,

shown in table 13. In this self-assessment, students once again evaluated their own ability level

on specific concepts. Students selected one of four statements to describe their competence at

the skills described. These four possible descriptions and student responses are shown in Table

14. The students responses to questions asked about motivation and classroom environment are

displayed in table 15.

33

Self-Assessment 3: Part 1 Confidence in Skills Table 13

Class Average

I can recognize a monomial. 4.5 I know how to factor polynomials. 4.5 I can find the Greatest Common Factor. 4.6 I can use the Distributive Property to factor. 4.5 I can identify a quadratic polynomial. 4.2 I can factor a quadratic into two binomials. 4.1 I can factor a polynomial in the form . 4.0 I can factor a monomial out of a polynomial. 3.9

Self-Assessment 3: Part 3 Evaluation of Skills Table 14

N

ot a

t all

With

the

help

of a

te

ache

r

With

the

help

of a

fri

end.

By m

ysel

f w

ith

com

plet

e co

nfid

ence

.

Identify a monomial. 0 3% 9% 88% Find the Greatest Common Factor. 0 3% 3% 94% Factor Polynomials. 0 3% 9% 88% Factor Polynomials using the distributive property.

0 3% 18% 79%

Factor a polynomial in the form .

0 45% 30% 55%

Factor a monomial out of a polynomial. 0 12% 24% 64%

Self-Assessment 3: Part 2 Motivation and Environment

Table 15

Agree Disagree NeitherI am respectful to my classmates. 100% 0 0 I am respectful towards my teachers. 100% 0 0 I ask questions when I am confused. 79% 3% 18% I will ask my teacher questions. 76% 3% 21% I will answer questions when asked. 97% 0 3%

34

The final self-assessment was divided into three categories. However, in this self-

assessment students were not asked any questions about their motivation or environment. In the

first category, students used a Likert scale to rank their ability with a particular skill. In this

assessment, a score of 5 describes complete confidence and a score of 1 describes being

completely lost (table 16). The second part of the final self-assessment was the same evaluation

students used in all the other self-assessments for this unit. Students described their ability level

through one of four statements: not at all, with the help of a teacher, with the help of a friend, or

by myself (table 17). The final portion of the final self-assessment asked students to write two

special polynomials described during the unit on polynomials. Students were asked to give

examples of a perfect square polynomial and a difference of squares polynomial. In table 18, PS

refers to a perfect square and DS refers to a difference of squares.

The research questions in this study deal with the effect that peer-assessment has upon student

self-assessment. In order to study any effect that peer assessment had upon the students

individual self-assessment and to analyze student progression through this unit, each piece of

work was documented into a portfolio to observe any progression or changes made to the

assessment processes. Six selected students have their entire progression through the study

displayed in Appendices T through Y.

Students one and two are students who were both absent several times during the unit.

Both of these students struggled throughout learning about factoring. Student one (participant 7

S) is a female student in the larger of the two honors algebra classes. She was absent during

the pre-assessment, self-assessment 1, and peer-assessment 1 portions of the factoring unit.

During an interview student one claimed that she felt like when we worked with the partners it

helped me know better what I needed to fix. She then stated that, during some of the self-

35

assessments it was hard for me to rate how well I knew stuff (see Appendix N). Student two

(participant 8 M) is a male student in the smaller of the two honors algebra classes. He was

also absent during the pre-assessment, self-assessment 1, and peer-assessment 1 portions of the

unit. During an interview student two stated that this was a waste of time. I dont think that it

helped me at all. It only reminded me that I didnt really know any of the stuff that was going to

be on the test (see Appendix O).

Students three and four were mid-level students in the honor algebra classes. The third

student (participant 8 D) is a female student in the smaller of the two honors algebra classes.

She was present every day of the factoring unit. Student four (participant 7 B) is a male

student in the larger of the two honors algebra classes. He was also present during all portions of

the factoring unit.

Students five and six were high achieving students in the honors algebra classes. The

fifth student (participant 8 H) is a high achieving student in the smaller of the two honors

algebra classes. She was present every day of the factoring unit and has maintained a high A in

the course during the second semester. During a discussion following the study she said, The

sheets that you gave us helped with the tests. It had everything on it that we needed to study. I

started studying early on and thats how I did good on the test, even though I think that this was

one of the hardest things weve done this year (Appendix R). The final selected student

(participant 7 T) is a male student in the larger of the two honors algebra classes. He was

present every day of the factoring unit. During the interview following unit 8 he said, I dont

know if it helped or not. It might have made me think about what to study more and thats good

(Appendix S).

36

Final Self-Assessment: Part 1 Ranking of Confidence Table 16

Class Average

I can recognize a monomial. 4.8 I know how to factor polynomials. 4.6 I can recognize prime numbers and composite numbers. 4.9 I can find the Greatest Common Factor. 4.9 I can use the Distributive Property. 4.6 I can use the Distributive Property to factor. 4.4 I can identify a quadratic polynomial. 4.4 I can factor a quadratic into two binomials. 4.4 I can factor a monomial out of a polynomial. 4.4 I can identify the zeros of a quadratic polynomial. 4.0 I can recognize a difference of squares polynomial. 3.9 I can identify a perfect square. 4.6 I can recognize a perfect square polynomial. 4.4 I can factor a perfect square polynomial. 4.3 I can factor a difference of square polynomial. 4.1

Final Self-Assessment: Part 2 Evaluation of Skills Table 17

Not

at a

ll

Hel

p of

a

teac

her

Hel

p of

a

frien

d.

By m

ysel

f Identify a monomial. 0 0 9% 91% Find the Greatest Common Factor. 0 0 9% 91% Factor Polynomials. 0 3% 18% 79% Factor Polynomials using the distributive property. 0 0 33% 67% Use the Distributive Property. 0 0 12% 88% Factor a monomial out of a polynomial. 0 3% 27% 70% Identify prime and composite numbers. 0 9% 18% 73% Identify the zeros of a quadratic polynomial. 3% 3% 45% 48% Factor a perfect square polynomial. 0 6% 36% 58% Factor a difference of a squares polynomial. 0 9% 34% 56% Recognize a difference of squares polynomial. 0 6% 52% 42% Recognize a perfect square polynomial 3% 0 36% 61%

Table 18 Example Incorrect PS 42% 58% DS 26% 74%

Table 18: Final Self-Assessment: Part 3 Recognition of Special Cases

37

At the conclusion of the study there was a summative unit test given to the students to

determine their comprehension and skill with factoring polynomials. This unit test consisted of

twenty questions on material covered throughout the factoring unit (see Appendix M). The

scores of this assessment are shown in Diagram 4.

Participants Grade Average: Unit Test

A

B

C

D

F

AF

D

C

B

Diagram 4

38

Chapter 5 Analysis and Discussion

There are three primary questions that this study researched; these questions sought to

determine the effectiveness of peer and self-assessment in middle school mathematics

classroom. The first research question was: In a middle school mathematics classroom, can peer

assessment be used to improve self-assessment and increase students self-efficacy?

The first research question deals with the effect that peer-assessment has upon student

self-assessment. In order to study any effect that peer assessment had upon the students

individual self-assessment, each piece of work was documented into a portfolio to observe any

progression or changes made to the assessment processes. These portfolios were documented for

six students in Appendices T Y.

Students 8-H and 7-T are both high achieving students in the algebra class. Their

previous test scores were in the high B and A range. During the post study interview, student 7-

T stated, When Im not good at something, I ask questions and practice until I get better. Those

sheets helped me know what was important and made me think about it. In student 7-Ts

portfolio (Appendix S), it does not appear that the peer assessment has any effect upon student 7-

Ts self-assessment abilities. In the interview following the study, 7-T stated, It helps me to

work on my own. I am okay working with other people but I usually work better alone. I am

pretty good about figuring it out on my own better than with other people. I think that the peer-

assessment stuff worked really well for some people but it did not really help me (Appendix S).

Student 8-H agreed when she responded that, I like to work alone. I usually get put with

partners who need my help, which is why Id rather work alone (Appendix R). Later on when

student 8-H was asked if she thought peer-assessment helped her. She replied, The peer-

assessment didnt help me at all. My partner needs lots of help and I felt like I didnt get

39

anything out of it. But I really think that the self-assessments were helpful. We should do them

more often (Appendix R).

Student 8-D, a mid-achieving student, claimed that, the peer-assessment made it easier

for me to see my own and 8 E s mistakes. She was able to help me better and I think I helped

her too (Appendix P). In 8-Ds portfolio (Appendix V), her progress from the self and peer

assessments is notable. At the beginning of the unit, student 8-D reported that she had complete

confidence on all of the important concepts within the factoring unit. However, later in the unit

following two self-assessments, a peer-assessment, and the mid-unit quiz, student 8-D was more

precise about her knowledge and placement on her third and final self-assessments. This shows

that the work through the peer-assessment did impact her self-assessment process. Student 7-B,

another mid-achieving student agreed with student 8-D, stating that, It did help me to do the

peer-assessment with 7 I. I dont know how much it helped him. I think that it helped a lot to

have him see some of my mistakes and it helped me fix them. We didnt always fill out the sheet

right but we talked about how to fix stuff and what we were doing right and wrong (Appendix

Q).

When asked what he thought about the peer-assessment process, student 8-M, a low

achieving algebra student, stated that, I think that it was embarrassing. All it did was make my

partner tell me all sorts of stuff I did wrong and she helped me figure out some of it, but I didnt

like it (Appendix O). When he was asked if he thought that the peer-assessment was helpful, he

responded, I think that working with partners is a good idea but not the peer-assessment sheet. I

dont think that it helped me at all. It only reminded me that I didnt really know any of the stuff

that was going to be on the test (Appendix O). Another low achieving algebra student, 7-S,

disagreed, saying; when we did the peer-assessment sheets in class, I could tell what I didnt

40

know and then I asked questions and tried to do more problems like that. I think that working

with the partners was really helpful. 7 A and I have some of the same problems but there was

stuff that we could help each other on and we asked the teacher when we didnt know something.

I think that the peer-assessment sheets were good. I felt like when we worked with the partners

it helped me know better what I needed to fix. I think that it is easier working with other people

than when I work by myself (Appendix N).

Looking at the responses in the self and peer-assessment sheets, there is a slight change in

the responses in the self-assessments after the students begin the peer-assessments. In the first

self-assessment, the vast majority of the students recorded that they not only knew the concepts,

but could complete these concepts by themselves with complete confidence. However, this was

not necessarily reflected in their homework scores. The peer-assessment created more variety in

responses and the next self-assessment that students completed showed responses that were

appeared to be more honest. Following the peer-assessment, the class self-assessments seemed

to have been effected. Students seemed to look at their own abilities in a different light.

Through the analysis of the assessment sheets and the interviews with the high achieving

students, it would appear that they have a higher motivation to work individually. They seem to

have a high self-efficacy for the ability to work on their own, however, some seem to struggle

working with their peers. The evidence presented in this study seems to indicate that for high

achieving students, while additional self-assessment procedures is helpful; peer-assessment does

not seem to positively impact their learning or motivation. However, for mid and low achieving

students there seems to be a mixed effect when peer-assessment is introduced. Overall, peer-

assessment seems to have a positive impact on low and mid-level learners. It seems to motivate

them to do better and it also increases their success in a mathematics unit.

41

The second research question presented in this paper is: Does utilizing peer and self-

assessment in a mathematics classroom improve student motivation? This question poses a

quandary as to whether self and peer assessment effect student motivation and self-efficacy in

mathematics. In order to better analyze this specific questions were presented to students on

their self and peer assessment worksheets dealing specifically with motivation and attitude.

When considering motivation, attitude, and self-efficacy, high achieving students are not

often students targeted to improve motivation or attitudes. Because of their success in

mathematics, high achieving students are often assumed to have high amounts of self-efficacy

and motivation. In the post study interview with student 7-T, he explained that he does not study

because, I dont really need to. Once I understand something in math, I can do it pretty well. I

have always been good at math (Appendix S). However, when he was asked about the

influence of self-assessment and peer-assessment, he indicated that he had utilized these

processes to study when asked if the self or peer-assessment processes were helpful. The sheets

might have given me an idea of what was going to be on the test so I worked on more of those

kinds of problems (Appendix S). Student 8-H also noted the helpful nature of the self-

assessments. The sheets were like an outline of the important stuff in the book that we were

talking about. So they helped me know which problems were really important. When I could

mark off all of the things on the sheet, I knew I would do well on the test (Appendix R).

In this study, the effects of the peer and self-assessment procedures were most noticeable

in the mid-level and low achieving students on motivation. In the portfolio for student 8-M,

there does not seem to be any notable difference in motivation or achievement. His responses

during the interview session indicate a lack of motivation to succeed mathematical. Throughout

the self and peer-assessment process, student 8-M seems to have the maintained the same

42

achievement level. The additions of these assessment procedures do not seem to have had a

positive influence upon his self-efficacy, achievement, or motivation.

However, student 7-S had some success with the peer and self-assessment processes

during unit 8. Student 7-S was absent for the first two days of unit 8, and therefore started out at

a disadvantage. She claims, however, that, after I got back we did the partner work and the

peer-assessment. It helped that my partner knew what she was doing and when I didnt know

some things like the greatest common factor, I asked her (the partner) and the teacher for help

(Appendix N). Student 7-S was noticeably more forthcoming about her misunderstandings and

by the end of unit 8, she was able to frankly ask questions to the teacher and to classmates when

she did not understand the material. This shows an increase in 7-Ss motivation to improve her

own mathematics skills and it also indicates an increase in her self-efficacy.

Student 7-B and student 8-D were mid-level achieving students. They consistently

present average scores and understanding of the material presented. During the previous unit,

student 7-B maintained an average score of B or C for his assignments. During the post study

interview when he was asked about his study habits, student 7-B stated, I try to (study). I do the

homework problems and I do the practice problems in the book. And when we get a review for

the test, I try to do those problems too (Appendix Q). In his first self-assessment, he did not

agree with the statements about asking questions from a teacher and a classmate when needed.

This shows a lack of motivation to improve mathematically. Student 8-D showed a similar lack

of motivation in the first self-assessment and in the behavior observed during the class sessions

during the study. When asked about her study habits, 8-D stated, I look at my homework and

re-work some of the problems that I had trouble with. If I still have problems, I ask about them.

43

Later in the interview when 7-B was asked how he decided which problems to study, he

brought up the self-assessment process and its helpfulness with his studying. I used to just do

the practice problems. But the sheets (self/peer-assessment sheets) gave all the important

problem topics so I found problems that matched and made sure I knew how to do those ones

(Appendix Q). When talking about changes in his study habits, student 7-B noted, They (self-

assessment sheets) gave me an idea of which problems to work on. I used them to study the

problems I didnt get real well and didnt spend as much time on some of the other problems

(Appendix Q). This shows a change in student 7-Bs self-efficacy. Instead of simply completing

the review problems, he found problems related to a factoring procedure which he needed to

improve upon and he worked those problems. This change in his motivation and study strategy

might be directly linked to student 7-Bs increased scores on assignments throughout unit 8 and

his post test score of a 100%. Student 8-D was also asked about any changes in her study habits.

She explained that, the assessment sheets that we did in class made me see what stuff was

important for me to work on (Appendix P).

On a class wide level, there did not appear to be a significant change in student

motivation during this study. On the self-assessment sheets when students were asked if they

would ask questions or seek assistance when they struggled to understand something, the

responses to these questions remained constant throughout the study. Through the individual

portfolios and interviews, it was possible to closer examine a change in motivation in four of the

six students; however, there was not a significant change in motivation on a class wide scale.

Both of the mid-level students discussed changes in their study habits and an increased focus on

mathematics when working with the peer and self-assessments. One of the low achieving

students also claimed that the peer-assessment impacted her learning process and altered her

44

study habits. The other low achieving student was not impacted positively by the addition of

these assessment procedures. This student seemed to have a negative experience with these

assessment processes. Both of the high achieving students claim to appreciate the self-

assessment process. However, only one of these students had a change in motivation between

the previous unit and the unit this study addressed. There does not seem to be a particular

pattern of students who are positively or negatively affected by the addition of these assessment

methods.

The final general purpose of this vein of research was meant to explore the effectiveness

of the methods of self and peer-assessment in a mathematics classroom. Students were asked

questions about the progression of the factoring unit. The students were specifically asked about

their opinions of self-assessment and peer-assessment.

The low achieving students had very different opinions about the helpfulness of these

assessment processes. Student 8-M was convinced that neither self-assessment nor peer-

assessment helped him in any manner. I think that this (self and peer-assessment) was a waste

of time. I dont think that it helped me at all. It only reminded me that I didnt really know any

of the stuff that was going to be on the test (Appendix O). Student 7-S had a different opinion;

believing that the peer-assessment was extremely beneficial. She believed that working with her

partner helped improve her mathematics skills greatly. When asked whether the self-

assessments or the peer-assessments were more helpful, she replied, The peer assessments it is

just easier for me to work with other people and it makes more sense when I do (Appendix N).

As a mid-level achieving student, student 7-B continuously presents average scores and

understanding of the material presented. During the previous unit, student 7-B maintained an

45

average score of B or C for his assignments. He completed the previous unit with a cumulative

test score of a low A. During unit 8, student 7-B showed improvement with the addition of self

and peer-assessment. Throughout the majority of unit 8, student 7-B showed higher achievement

with scores averaging in the high A range. Following the unit when this study was completed,

student 7-B once again struggled. He started off the following unit with high scores, but his

scores decreased and fell below his typical average by the units summative assessment. During

the post study interview, student 7-B stated, I think that the self-assessment stuff helped me to

do better on the test and understand. I thought that I did pretty good this chapter (Appendix Q).

The second mid-level student also showed high achievement during this unit. Student 8-D

maintained a high B or A average throughout the unit, which was different from her traditional

average in other units. Student 8-D expressed her improvement in assessing her own abilities

when she said, I think that I have gotten better at it (self-assessment). I still have a hard time

figuring out what I need to work on to get better but I think that the self-assessment sheets

helped (Appendix P). She also emphasized her belief that the peer-assessments helped her to

improve: I like working with others and I think that it gave me a better sense of where I needed

to improve (Appendix P). Student 8-D ended the factoring unit with a high A, which was also

the highest score that she had received on a mathematics assessment.

The two high achieving students both had serious complaints against the peer-

assessments. These two students did not feel that there was a benefit for them in the peer-

assessment. However, they both agreed that they could see a positive impact on some of their

peers, including their own partners resulting from the peer-assessment work. Student 8-H

believed that the self-assessment was extremely helpful in preparing for the unit test. She stated,

I think that this (self-assessment) was the best part of what we did. I am not that good at

46

figuring out what I need to work on. I usually just work on all of it. The self-assessment sheets

helped me see what I needed to spend the most time on. I think that it (self-assessment) is really

helpful before the quiz and the test (Appendix R). While Student 7-T agreed with student 8-H,

he was much less adamant about the helpfulness of the self-assessments; saying that, I dont

know if it (self-assessment) helped or not. It (self-assessment) might have made me think about

what to study more and thats good. Working with partners was okay, but I dont think that I got

a lot out of it (Appendix S).

Through the interviews at the end of this study, the six selected students had varied

opinions about the success of self and peer-assessment. Overall, however, all six of them agreed

that these methods seemed to work, but needed to be spread out. One of these students greatest

concerns was the fact that so many assessments were done in such a short time. All of the

students agreed that it was too much. While the students agreed that there was too much

assessment in a short period of time, they had different opinions about the most helpful

assessment processes and the best way to implement these procedures.

The two mid-level students each suggested that both the peer and self-assessments were

helpful but that they needed to be more spread out. The mid-level students also indicated that if

they had to choose they believed that the peer-assessments were more helpful because of the

work with a partner. The low achieving students agreed with the mid-level students, they both

had a more positive experience with the peer-assessment. However, one of the low achieving

students made it clear through the interview that the addition of these assessment procedures was

not helpful and rather was almost demeaning rather than positive for him. The two high

achieving students agreed that there was too much happening but they were not as adamant about

the overload as the four other students. These two students each felt strongly that they most

47

benefited from the self-assessment process. Each of them felt that they spent more time helping

their partners without receiving any help in return. Neither of them felt that there was any value

gained in working with the peer-assessments. The two high achieving students felt that the self-

assessments were extremely helpful and requested that they continue.

Limitations

There were some limitations to this study. The time period for this study was originally

designed to occur over a period of five to seven weeks and observe students through the addition

of self and peer-assessment over the course of three academic units. However, because of school

cancelations and other interruptions, the time frame was reduced to one unit observed over a

three week time span. During this time, students were taught the processes of self-assessment

and peer-assessment, however, they were not able to be observed after they had developed these

skills. In many ways, these students were still learning how to assess themselves and their peers.

In a follow-up study, it would be interesting to observe the effects of self and peer-assessment

over a more extended period of time.

An additional drawback to this study was that during the time period that this study was

being completed there was one unanticipated event which occurred and affected the results of the

study. During the second week of the unit, the eighth grade students began the process of

scheduling their courses for their freshman year of high school. Many of these students were

distracted during this four day period and some of them had a serious attitude shift. The addition

of a new problem and unanticipated added responsibility created the distractions and some

additional stress in the students daily activities.

48

There was also a serious attitude shift in many of the students. The participants in this

study were students in two honors algebra classes at the eighth grade level. These students were

used to being the best in their peer group and had significant expectations to take the highest

course levels and get high recommendations from all of their teachers. For some of these

students, they were not recommended to make the fast tracked advancement that they had

anticipated. In some cases these disappointments occurred in the scheduling of their

mathematics courses and some occurred in their other classes. The students who exhibited the

most negative alteration in attitude were those who did not receive a recommendation to proceed

to the next mathematics honors course. This negative attitude greatly affected student motivation

and therefore made it difficult to make conclusive findings about the effect of self and peer-

assessment have on student motivation in mathematics.

Conclusion

This research study addressed the motivation and self-efficacy of middle school students

in an honors mathematics classroom. The purpose of this study was to determine the

effectiveness of self-assessment and peer-assessment in a middle school mathematics

environment. Additional purposes of this study were to determine the effect of peer-assessment

on individuals self-assessment and to determine if the addition of these assessment procedures

influenced student motivation and self-efficacy.

This study used a survey, multiple self and peer-assessment worksheets, pre and post-

assessments, and an end of study interview to compile information on the effectiveness of self

and peer-assessment. Through the analysis of this information, it has been determined that both

self-assessment and peer-assessment do have an effect in a mathematics classroom. The effect

49

that each of these processes has are different and additional research must be completed to

further determine the most effective method to gain the best outcome in a mathematics

classroom.

50

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Appendix Table of C