Fostering Autonomy, Purpose, and Competence in Math

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Fostering Autonomy, Purpose, and Competence to Build Motivation in Math:

A Case Study in an Elementary Classroom

Jordan A. Yoshihara, Undergraduate

University of California, San Diego

June 12th, 2015

Dr. Jim Levin

EDS199: Independent Study

FOSTERING AUTONOMY, PURPOSE, AND COMPETENCE IN MATH 2

Fostering Autonomy, Purpose, and Competence to Build Motivation in Math:

A Case Study in an Elementary Classroom

Abstract

One of the key determinants of students’ success in school is the amount of effort they

invest in their learning. This effort is usually directly related to how motivated the students are to

learn. Although students are motivated by a wide variety of factors, many of their sources of

motivation share underlying principles of autonomy, purpose, and competence. In this case

study, I examine the experiences of six third-grade students and what motivated them to learn

math. By participating in the classroom, I was able to try various motivational strategies with

them. In the end, I argue that their responses to competition, leadership, goals, role models, fun,

and community all relate to these three principles of motivation.

The purpose of this paper is to examine how a learning environment can foster students’

motivation in elementary math. I will begin by presenting background information to set up the

problem. I will then review recent research and classic studies about how to foster motivation.

Next, I will explain the research methods used in this qualitative study. I will analyze findings

for my case study of six third-grade students who each responded differently to the various

motivational techniques we introduced to the classroom. Specifically, I will look at how different

techniques influenced their motivation to learn math. I will then discuss the results of my study,

limitations of this study, and future steps for study.

Background

As an undergraduate student, I see many of my peers struggle with math-oriented classes

because they fail to grasp the fundamental concepts in the material and develop math anxiety


because of this. Some end up dropping their classes and changing out of science and engineering

majors. Unfortunately, this is not an uncommon occurrence in America, as it is ranked the 25th

country out of 27 countries in terms of students who understand math. The National Center for

Education Statistics reported that two-thirds of students in eighth-grade score below proficient in

math (NAEP, 2011). Math is an accumulative subject where learning new topics builds on

previous topics, so if the majority of students are not understanding math by the end of eighth

grade, this means that they will be behind going into higher education. This creates a gap in

students’ math proficiencies, which prevents them from being able to learn more. If our

economy, technology, national security, and medical practices rely on people’s ability to solve

problems, the lack of this ability could present a serious problem.

One of the causes of this problem might be that when students fall behind, they cannot

move forward in their understanding in math. This can potentially discourage students from

trying to continue their learning, leading them to believe they “can’t do it.” As time goes on,

these feelings become more potent and in some cases may debilitate students’ learning. In such

cases, it is important to motivate these students to learn new concepts even if they struggle at

first. This, however, can be difficult to accomplish as these students might be particularly

unmotivated to learn these concepts because they doubt that they will be able to understand the

new material. In the following sections, I will be discussing methods of motivating students

despite whether they feel they are incapable of understanding new ideas.

Literature Review

The question I seek to answer is, how can a learning environment foster student

motivation in math? I reviewed many articles, both foundational classic studies and recent

research discussing students learning math, teaching methods, and what motivates people in


general. Here, I will provide an analysis of the literature to first understand motivation, then I

will discuss some techniques for motivating students. This analysis will provide a framework for

my case study.

Understanding Motivation

To understand how to improve student motivation, I wanted to understand what

motivates students in the first place. During their study on self-determination across many

different school settings and grade levels, C. Niemiec and R. Ryan (2009) analyze three basic

principles that foster motivation: autonomy, purpose, and competence. All three of these

elements can be applied to a classroom to motivate students to learn. (pp. 133-141). Despite the

effectiveness of these components, many classrooms seem to be missing these three principles

today. T. Urdan and E. Schoenfelder (2006), in their evaluation of theories about motivation,

observed that when teachers see that students are unmotivated to learn, they often attribute the

students’ lack of motivation to factors that are beyond the scope of what they can control in the

classroom (p. 332). Whether or not this is true, it is still possible to develop feelings of

autonomy, purpose, and competence in the classroom despite external factors that student

motivation in powerful ways (see Turner, 2011)

Principle 1: Autonomy

Autonomy refers to the idea that students are free to explore whatever they are learning in

their own ways. According to studies performed by E. Deci and R. Ryan, teachers who support

autonomy tend to foster student motivation whereas teachers who do not support autonomy

discourage student initiative (2000, p. 59). With this sense of freedom comes the sense that

students are in control of their learning, empowering them to determine whatever outcomes they

wish to reach. Furthermore, according to findings by B. Zimmerman (2000), a student’s level of


perceived control can help students become more engaged in the classroom, work more

diligently in learning new concepts, and endure struggling through problems more persistently.

In sum, self-efficacy leads to more effort from students (pp. 85-86).

One of the challenges to creating autonomy is that students must ultimately meet certain

standards by the end of the year. Without enough external control from the teacher, it is uncertain

whether they will reach those standards. According to research done by J. Bransford, A. Brown,

and R. Cocking (2000), young learners especially have a natural curiosity about the world around

them, which leads them to want to learn more about their surroundings. When presented with a

challenge and little guidance, students are more inclined to creatively seek out a novel way to

overcome the challenge (p. 102). If teachers gradually decrease how much they are guiding

students, students can tap into their natural inclination to discover the world around them

(Bransford, 2000, p. 214). By creating autonomy, a teacher is using students’ natural inclinations

to discover the world around them and converting those inclinations into motivation to learn new

concepts.

Principle 2: Purpose

Purpose describes how students feel the material they are learning applies to them. In

other words, it answers the question, why do I want to learn this? When students feel that the

material is meaningful to their lives in some way, they tend to organize their thinking around it

so that they will understand it on a more personal level (Bransford, 2000, p. 9). When students

feel that they are personally invested in the material, they are more prone to set their goals,

schedules, and priorities around the material. In a classic review done by A. Chickering and S.

Ehrmann (1996), the effectiveness of this is best summed up when the authors write, “Learning

is not a spectator sport… [Students] must talk about what they are learning, write about it, relate


it to past experiences, and apply it to their daily lives. They must make what they learn part of

themselves” (p. 3).

One challenge to creating purpose is that every learner is different, so what might be

meaningful to some students might not be meaningful to other students. Despite their

differences, Bransford et. al. identify one aspect most students deem as meaningful: social

opportunities, or the idea that they can help others (2000, p. 61). Niemic and Ryan expand on

this when they explain, “People tend to internalize and accept as their own the values and

practices of those to whom they feel, or want to feel, connected, and from contexts in which they

experience a sense of belonging” (2009, p. 139). Essentially, when students feel that they are

contributing to others, they feel they have a personal purpose in learning, which can motivate

them to learn more.

Principle 3: Competence

Competence refers to the idea that students feel they are capable of learning what they

need to learn. In their study on over 600 elementary and middle school-aged children, A.

Wigfield and J. Eccles argue, “Children’s and adults’ competence and efficacy beliefs relate to

their achievement performance, choice of achievement tasks, amount of effort exerted, cognitive

strategy use, achievement goals, and overall self-worth” (1994, p. 108). As such, when students

do not believe they can do something, they are more likely to resort to what Urdan et. al. call

“self-defeating practices.” These practices include avoiding learning activities, inserting

impediments into the activities, or giving up on the activities altogether (2006, p. 334).

Conversely, students who believe they are capable of accomplishing a task tend to develop what

Bransford et. al. call “competence motivation.” This means that students are more likely to


devote more time and effort to their learning because they know they can handle any topics in

the material (2000, p. 60).

One of the challenges to creating competence is that students must build competence

internally. It is not enough for teachers to tell students they are competent; students must believe

it for themselves. Fortunately, autonomy and purpose, the two aspects of motivation teachers can

influence directly, can help students to build a sense of competence. According to Zimmerman’s

review of self-efficacy theories, when teachers grant students autonomy to set their own goals

and expectations, students will perceive their accomplishments as a reflection of their own

abilities, not something the teacher forced them to do. In turn, they tend to be more committed to

achieving their learning goals and meeting their own expectations. (Zimmerman, 2000, p. 88).

As discussed earlier, when students recognize purpose in their learning, they are more likely to

identify with what they are learning on a more personal level. When students are personally

invested in their learning, they usually feel the need to explore the material more fully. As such,

they might adopt what Bransford et. al. describe as a more adaptive view of learning in that they

are constantly seeking ways to improve their understanding. In other words, they are always

asking themselves what they can do to ensure that they are fulfilling their purposes to their

utmost potential (Bransford, 2000, p. 48). In order to speculate on what they can do, they must

reflect on what they can do already. This establishes a sense of competence, which only grows

stronger each time students affirm for themselves where they are in their learning.

Combining the Principles of Motivation

These three motivations are not mutually exclusive with each other. Each of these three

principles can work towards developing the other two (see Figure 1). Autonomy can build

competence as students know they are fully responsible for all of their accomplishments because


they are given control over their own learning. Autonomy also can build purpose as it allows

students to discover personal purpose in what they are learning for themselves. Competence can

build autonomy as students feel more empowered to explore new ideas because they know they

are capable of understanding these new concepts. Additionally, competence can enhance

students’ sense of purpose as they will feel more confident in their ability to handle real-world

problems or issues that are important to them. Finally, purpose can influence autonomy as

students are more invested in their learning, giving them more drive to explore different aspects

of the material. Purpose also can build competence as students feel they can handle something

that is valuable and significant, leading them to believe they can learn other topics.

Figure 1: Relationship between autonomy, purpose, and competence.

Research Design and Methods

In this section, I will describe my case study, discuss different approaches to learning in

the classroom, and examine how these approaches helped foster autonomy, purpose, and


competence, which in turn developed motivation. To get a deeper understanding of my study and

its results, I will use a qualitative approach with observations and data-gathering directed toward

developing a better understanding of the lived experience of six students learning math.

Personal Background as the Investigator

As with any qualitative, social science study, it is important to note that any data

analyzed will be gathered and interpreted from the researchers’ perspectives. That being said, I

will now provide a little background information on myself to establish the perspective from

which I am analyzing the data from my case study. I am currently an undergraduate computer

science student with minors in cognitive science and education studies. In my computer science

major, I have found that many of my peers have math anxiety and some end up switching majors

to avoid math. This led me to want to investigate why many students might not develop the

problem-solving skills they need to succeed in their classes. Like many, I began with the

assumption that this lack of development stemmed from the students’ poor study habits or lack

of effort. As I conducted this research, I found that many of my assumptions were false and

developed a better understanding of what motivates people to learn math.

As a researcher in this study, I had the opportunity to participate in a third-grade

classroom with the students and their teacher. I was able to interact directly with the students as

they math problems in ALEKS, listen to the teacher’s lessons, and observe how the students

responded to those lessons. Additionally, I had access to the ALEKS account for the class as

both an administrator and a student. Essentially, I was able to go through the students’

curriculum as if I also was a participant, and I was able to access each student’s data and

progress reports from ALEKS.

Meaning


Context

My data were collected using interviews with the students and their teacher, various

assessments, progress reports generated by ALEKS, and general observations I made in the

classroom. The classroom in which I participated was a third-grade math class participating in a

pilot study developed by S. Heise, a research scientist at the University of California, San Diego,

as part of her PhD research work as a PhD candidate at Walden University. The third-grade class

was taught by Ms. Betty Fletcher, a Master Teacher, at McGill’s School of Success, a charter

school located in the Golden Hill neighborhood, close to downtown San Diego. For my research

study, I had the opportunity to conduct a case study with this class over a period of two months

(January–March, 2015). During this time, Ms. Fletcher incorporated ALEKS as an intelligent

tutor for her students. Every class I observed would start with a number talk session, when Ms.

Fletcher would give the entire class a lesson in math. After these sessions, students would work

on ALEKS using their individual Google Chromebooks. ALEKS was first used in this classroom

starting in November 2014 in a small pilot study with five students (n=5). After success with

these students over several months, the rest of the students in the class (n=20) started using

ALEKS early in January 2015.

Case Study

For my case study, I will focus primarily on the experiences of six students, whose names

I have changed to protect their identities. I have grouped these students together as high-

performing students, average-performing students, and low-performing students based on their

progress through the third-grade curriculum. Here, I will introduce them and provide my reasons

for choosing them to be a part of my case study.


High Performing Students. The first group, the high-performing students, is comprised

of students who had completed the third-grade curriculum well before the end of April. In the

classroom I observed, there were nine students who had completed third-grade math by April.

From this group, I will be focusing primarily on the experiences of Luke and Isaiah. I chose to

study Luke because he spent the most time in ALEKS and was studying fifth-grade math at the

time of this study. Luke’s total time in ALEKS amounted to 65 hours and 47 minutes over a span

of five months. Compared to the average time the class spent in ALEKS (32 hours and 34

minutes), Luke had invested a considerable amount of time into learning math, which may be

indicative of motivation. I also chose to study Isaiah because he seemed to express the most

interest in the rewards we gave the class as he would frequently ask us about any prizes he could

win. When we did introduce a prize, his time spent in ALEKS peaked, reflecting a correlation

between prizes and his effort in learning math.

Average Performing Students. The second group, the average-performing students, is

comprised of seven students who had completed at least half of the third-grade curriculum before

the end of April. In this group, I will be focusing on Chelsea and Manny. I selected Chelsea to be

a part of my case study because she started out disliking math. Before we introduced any

possible motivational factors, she did not seem confident in her ability to solve math problems

and actively avoided answering questions when the teacher called on her. After a few months,

she became more assertive and even admitted to liking math. Additionally, she was the first

student to start working on ALEKS outside of the classroom. I also chose to study Manny

because he spent the second-most amount of time in ALEKS at 49 hours and 2 minutes. In the

classroom, he was sitting next to Luke, a high-performing student. Since the classroom was set


up to support peer-learning, I wanted to see if peer-interaction contributed to the fact that Manny

and Luke spent the most and second-most amount of time in ALEKS.

Low Performing Students. The third group, the low-performing students, is comprised

of three students who had not mastered half of the third-grade curriculum before the end of

April. In this group, I will be focusing on the experiences of Andy and Rose. I decided to study

Andy because he started the year as a student who seemed particularly unmotivated to learn. He

seemed resistant to learning math in that the teacher would have to tell him multiple times to get

started on his worksheets. Additionally, he would not participate in peer learning activities or

classroom discussions voluntarily. After we played Chinese checkers with him and introduced a

prize for finishing third-grade, his time in ALEKS tripled. Rose also stood out to me as a student

who seemed extremely unsure of herself and her ability to solve math problems. She progressed

through ALEKS at a much slower pace than the rest of her classmates. However, after we made

her a deal that she would receive a board game for the entire class to play, she began to take

more initiative in her learning and began spending more time in ALEKS. In fact, she began to

study multiple topics at each session and doubled her mastery level in only a few weeks.

Each of the students I have named seemed to exhibit a different response to the various

motivational techniques we introduced to the classroom. In the end, I hope to show that although

these students were at different points in their learning, there were some similarities in what

ultimately motivated each of them to learn.

Findings

I began my study with the goal of seeing if there was any particular method of motivation

that worked for the majority of students. In the end, I found that each student was unique, so no

motivational technique is always better than the other. Thus, a differentiated approach was


needed for each student. However, different approaches to motivation may share common

underlying principles that drive students to work towards learning more. In the following

sections, I will take a closer look at what seems to motivate students the most. Each of the

students I selected to study had expressed a strong interest in at least one of the various

motivational factors in the classroom. I will be describing the experiences of each of these

students and what seemed to motivate them the most.

High Performing Students

As stated earlier, the high performing group of students consisted of nine students who

had finished the third-grade curriculum by the end of April. While there were many students who

fell into this category, Luke and Isaiah stood out to me in particular.

Luke. When I first started observing the classroom, Luke struck me as a more reserved

student who did not stand out to me compared to the rest of his classmates. In fact, according to

his initial assessment in ALEKS, Luke began as an average student in the class, knowing as

many topics as most of the other students in the class (See Figure 2). However, by the end of the

year, he ended up as the top performing student in the class with the most topics mastered and

the most time spent in ALEKS. Moreover, Luke finished going through the third-grade, fourth-

grade, and fifth-grade curriculum on ALEKS over a span of five months. He was able to

accomplish this by spending numerous hours working on math in ALEKS after school, during

the weekends, and even during spring break. Although he had finished the third-grade

curriculum by the beginning of April, he continued to spend a considerable amount of time in

ALEKS to finish going through fourth-grade and fifth-grade math. Going through fourth-grade

and fifth-grade curricula and working outside of class were completely optional, so it seemed


Luke was motivated to learn by something other than classroom deadlines or pressure from the

teacher. This led me to investigate what was driving him to work so diligently in learning math.

Figure 2: Percentage of Luke’s initial and final mastered topics compared to rest of class.

When I interviewed Luke, I asked him what made him want to learn math. He replied,

“Because the first time I learned math, I thought it was fun. It’s the competition. I like the

competition. People are trying to catch up with me, and I keep trying for them not to catch up to

me.” According to Ms. Fletcher, Luke, like most of the boys in the classroom, “is highly

competitive with other students. When students see one student doing something, they want to do

it better.” Ms. Fletcher taught her students that everyone learns in his or her own way, so

students did not gloat or put each other down despite the competition. This helped to create a

friendly competition that motivated students such as Luke to learn more.

We were able to further foster this competition by using ALEKS. ALEKS is set up so

that students have a differentiated, individualized learning experience. Every student has a pie

chart reflecting his or her own progress through ALEKS (see Figure 3). Each slice of the pie

represented a topic in math that the student must learn. Students had the ability to pick what

topics they wanted to study each time they went on ALEKS. This allowed them to go through the

material at their own paces according to their own learning preferences. For the more

competitive students, this gave them the opportunity to try to learn as many topics as they could

21%

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January April

Initial and Current Assessments LukeAverage


each time they went on ALEKS. Each student has a percentage reflecting his or her mastery in

ALEKS. When we visited the school, we would tell the students these percentages and made a

display for them to visually see their progress, including what topics they had mastered and what

topics they had yet to learn.

Figure 3: Example pie chart in ALEKS. Each slice represents a topic, in this case place value and money.

For Luke, this gave him the opportunity to see where his other classmates were and

pushed him to stay ahead of them. When we started encouraging competition in the classroom by

telling students their percentages and offering rewards for those who had mastered the third-

grade curriculum, Luke’s time spent in ALEKS more than tripled as shown in Figure 4. Like

many of the students, Luke started working on ALEKS in the mornings at school and at home.

By the end of the year, he had amassed about three times the amount of time on ALEKS than any

of his other classmates. Luke’s time in ALEKS was not distributed equally, however. Luke

tended to spend more time in ALEKS when other students were catching up to his percentage.

For instance, when Luke started working on fifth-grade curriculum, his time in ALEKS started to

decrease (see Figure 5). However, when another student started working on fifth-grade

curriculum too, Luke’s time in ALEKS increased. This is most likely because he felt his position

as the top student in the competition was at stake when another student joined him in studying

fifth-grade math.


Figure 4: Luke’s time in ALEKS compared to other high performers in the class.

Figure 5: Luke’s time increased when he had another competitor in the fifth-grade.

This led me to ask, why did being the top of the competition matter so much to Luke? At

the surface, it would seem that being the top of the competition gave Luke a sense of

accomplishment, which inspired him to work more. However, after talking with Ms. Fletcher, it

seemed being the top of the competition meant much more than that to Luke. According to Ms.

Fletcher, the students who were at the top of the competition were seen as the ones “with all the

knowledge.” Other students followed these top students by striving to learn more, spending more

time learning in ALEKS, and adopting similar attitudes towards math. Being at the top of the

competition motivated Luke to work to be the one with the most knowledge in the class. This

was further reflected in the way he started to actively look for new things to learn. Ms. Fletcher

noted that every time she introduced a new concept, Luke received it as something he needed to

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know and explore. This included concepts that were not related to what the students were

learning in the classroom. For example, Ms. Fletcher recounted a time when they made ice cream

in the class. When she mentioned the periodic table, a topic that usually is not covered until

middle school, Luke went home and learned about fifteen elements from the periodic table.

Considering that Luke was not nearly as adamant about learning before the competition, it is

likely that his efforts to learn about topics that were far beyond the scope of a third-grade

classroom were motivated by his desire to be the student “with all of the knowledge.” To him,

learning math in a competitive setting gave him the means to become that student.

Isaiah. Isaiah stood out to me not for being a high-achieving student, but for being a

student who was most enthusiastic about earning the prizes we gave to the class. Aside from

frequently asking how he could earn a prize, Isaiah’s time in ALEKS increased whenever we

offered him a prize (see Figure 6). When the class’ subscription to ALEKS was scheduled to end

during the last week of March, we offered a marble and click-clack to the first student to finish

the third-grade curriculum hoping that students would finish before their subscriptions expired.

All of the students, including Isaiah, started spending more time in ALEKS. When the

subscription was extended to April 12th, we offered more marbles to any student who finished

the third-grade. Even after we extended the subscription to ALEKS until the end of the school

year, we kept offering prizes to any student who finished third-grade. Again, Isaiah’s time in

ALEKS increased dramatically. When students started to move onto the fourth-grade curriculum

in April, we started offering special marbles for students who finished the fourth-grade. We also

noticed that another student, Rose, was falling behind in terms of progress, so we offered her a

board game for finishing third-grade. At this point, Isaiah approached us and asked if there was

anything he could do to get a prize. We told him that if he helped Rose, he would also get a


prize. Isaiah eagerly replied that he could help Rose in class and at home, and then asked what he

would get for helping Rose. To this, we told him that he would receive a “special surprise.” Even

though he did not know what the prize would be, his time in ALEKS still peaked. After we

found that the students were becoming more competitive, we started offering car kits to students

who finished fifth-grade math. As seen in Figure 6, every time we offered the students a prize,

Isaiah spent more time trying to go through ALEKS whether the prize was a marble, car kit, or a

“special surprise.”

Figure 6: Timeline showing when we introduced new prizes to the classroom. Isaiah spent more time in

ALEKS whenever we introduced a new prize.

Originally, I thought that simply earning a tangible prize such as a marble or car kit was

the reason for Isaiah’s increased efforts in learning. Essentially, I assumed that Isaiah was

excited to receive prizes because it meant that he would get to play with new toys. During my

interviews with Isaiah and Ms. Fletcher, however, I found that my presuppositions were incorrect

for the most part. When I asked Isaiah about the prizes we had been offering, he replied,

“There’s a certain time when you get prizes, but not all the time. That’s why even if I don’t get a

prize today, tomorrow, or whenever, it still makes me want to learn math.” This surprised me

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because it seemed contradictory to his eagerness to receive prizes. For this reason, I asked him

what earning prizes meant to him. Isaiah said that he liked to put the prizes near where he slept.

That way, every time he woke up or went to sleep he would be reminded of what he had

accomplished and how he needed to keep working to learn more. This went against what I had

initially thought when I assumed that Isaiah enjoyed getting marbles and car kits because he

could play with them. Since he kept them by his bed without actually playing with them, it

seemed that Isaiah treated these prizes as being trophies of his accomplishments. In this way, the

prizes physically symbolized Isaiah’s past achievements, reassured him that he was capable of

overcoming new challenges, and inspired him to work towards mastering more concepts in

ALEKS. Essentially, these prizes held more symbolic value than material worth to Isaiah.

These prizes’ symbolic value originated from the way the prizes gave Isaiah recognition

for his achievements in the classroom. Whenever we gave students a prize, we announced their

achievements to the rest of the class and gave them their prize for the other students to see. Isaiah

admitted to being competitive, so being recognized for his achievements in front of the entire

class gave him a lot of satisfaction in his ability to stand out from the rest of his classmates.

Furthermore, when other students saw Isaiah getting a prize, they wanted to be like him and

worked towards achieving the same accomplishments as Isaiah and getting the same prizes. Ms.

Fletcher stated that this dynamic put Isaiah into a leadership role. Given this leadership role,

Isaiah became a more influential student in the classroom in that other students would want to

follow him in doing whatever he was doing. This sort of attention pushed Isaiah to learn more as

he wanted to maintain his role as a leader. In fact, according to Ms. Fletcher, this leadership role

meant so much to him that whenever he got into trouble at recess or at lunch, he would be too

ashamed to come up to the classroom and face the other students. Although he learned that he


needed to face his mistakes, this same level of devotion to being a leader was reflected his desire

to accomplish more in ALEKS. It is likely that his time spent in ALEKS peaked when we

offered him prizes because they presented him with opportunities to accomplish something that

would help him to maintain his role as a leader. The prizes further solidified his role as leader

because they caused other students to recognize him as being someone whom they could follow.

In the end, the prizes motivated Isaiah because they gave him something to work towards and

assisted him in becoming what he wanted to become, a leader in the classroom.

Average Performing Students

The average performing students refers to the seven students in the classroom who had

finished over half of the third-grade curriculum in ALEKS by the end of April. Here I will be

discussing the experiences of Chelsea and Manny and what motivated them to learn.

Chelsea. Before Chelsea started using ALEKS, she thought she could never understand

math. She had very little confidence in her ability to solve problems and was one of the lower

performing students in the class. As such, many of Chelsea’s peers probably would not have

guessed that she would have improved as much as she did. According to her progress report in

ALEKS, Chelsea mastered roughly the same number of topics as even the higher performers in

the class (see Figure 7). The main difference was that Chelsea started the year knowing fewer

topics than the higher performers. These results indicate she was putting effort into her learning,

but needed something more than rote instruction. She needed to believe in her abilities and take

control of her learning.


Figure 7: Chelsea learned 123 topics; other students learned 176 topics on average.

According to Ms. Fletcher, Chelsea needed an environment where she would not feel like

a failure for not performing as well as the high performers in the class. To accomplish this, we

tried implementing peer learning in the class where we paired high performing students with low

performing students. Students participated in a variety of cooperative activities, such as sharing

stories about math problems with each other, helping partners with ALEKS, and offering

solutions to problems Ms. Fletcher provided. These activities seemed to spark interest and

excitement in Chelsea. According to Ms. Fletcher, Chelsea was more motivated to learn when

she could verbalize her thinking. It was not enough that she could go through the problems in

ALEKS - Chelsea needed reciprocal learning activities to build her confidence in being able to

articulate problems and help other students solve problems. In fact, Chelsea stated that she

absolutely loved “teaching the class” by telling her stories and having the other students solve

them. It is through these interactions that Chelsea went from a student who avoided answering

the teacher’s questions to a student who came to believe she could be good at math.

Once she started to believe in herself, Chelsea became much more motivated to learn

math. Although she was still struggling, she realized that struggling was natural for students of

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all performance levels- it was merely a part of the learning process. Ms. Fletcher made a point of

making this clear to the students whenever students made mistakes. Instead of telling them that

they were wrong outright, she would tell that in making those mistakes, they were helping

everyone else to learn. This seemed to encourage Chelsea to become more confident in solving

math as her struggling could be beneficial to all of her peers. This confidence was further

inspired when Chelsea was told that ALEKS would be her “secret weapon” to wield against

math problems. Rather than being told what to learn, Chelsea had to take charge of her own

learning and determine for herself what needed to be done. Chelsea rose to the challenge and

ended up exceeding everyone’s expectations in terms of how much she learned. For her, being

able to visually see her progress on the pie chart made her want to learn math more because it

reminded her that she was capable of learning. In response to this newfound confidence, she

started to work on ALEKS at home, something that is completely optional for students to do.

Moreover, she discovered that she could work on ALEKS at home without anyone telling her

about it. This demonstrated dedication and commitment to learning math, which stemmed from

Chelsea’s inner drive to overcome her struggles in learning math.

This dedication was further exemplified in the way Chelsea started to set her own goals.

From the end of April to the beginning of May, Chelsea’s time in ALEKS decreased

considerably. Ms. Fletcher noted that the reason for this was partially due to the fact that she had

encountered problems that she was struggling to understand. This seemed to discourage Chelsea

from learning as she would only spend about a minute in ALEKS before quitting. Then,

seemingly out of nowhere, her time in ALEKS skyrocketed (see Figure 8). After asking her

about this, I found out that this increase in time was a result of Chelsea realizing that she was

extremely close to mastering the third-grade curriculum. During our conversation, Chelsea said,


“I just realized that I really want to get to fourth-grade, so I started working really hard on

ALEKS.” In response to this realization, Chelsea started creating checklists of what topics she

needed to learn and spent more time in ALEKS to complete the items on her checklist (see

Figure 9).In essence, she began to set goals, which then motivated her to work more on ALEKS.

These goals helped her to overcome the topics that were causing her to struggle as they kept her

focused on her goal of finishing the third-grade. Ms. Fletcher explained Chelsea’s progress as a

common occurrence for students when she said, “They know what they want to do, they may see

something as a challenge and challenge themselves, they may go back and do something easier.

When they finish the easier thing, they’ll feel good about going into the next challenge.” With

these feelings of confidence, Chelsea began to attempt more topics every time she went on

ALEKS, which led to her mastering an additional ten percent of the third-grade curriculum over

the span of two weeks.

Figure 8: Chelsea’s time in ALEKS increased once she realized she could finish the third-grade

curriculum.

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Figure 9: Chelsea’s checklist (M=Multiplication & Division, G=Geometry, Measurement, & Graphs,

F=Fractions, P=Place Value & Money, A=Addition & Subtraction, C=Completed).

Chelsea’s goal-setting was a reflection of how she had taken control over her own

learning. With Ms. Fletcher, her peers, and ALEKS giving her support, Chelsea wielded her

efforts to learn math to the point where she could overcome obstacles she faced without any

handholding from others. In setting goals, she made a personal commitment to learning, which

also indicated her confidence in her ability to achieve these goals. Furthermore, when I started

observing the class, I asked Chelsea what she wanted to be when she grew up. In January, she

said she wanted to work at a deli or a bar as these occupations did not involve many complex

math problems. When I asked her the same question again in May, she answered that she wanted

to be an engineer. Her going from wanting a career to avoid math to wanting a career that deals

with a lot of math was remarkable as it proved she was no longer afraid of approaching more

difficult problems. Over the course of my study, she had learned that she could solve math

problems, even if she did not understand the concepts at first. This led her to pursue a better

understanding of math by setting goals for herself. These goals motivated her to face the

challenges in learning math with confidence and determination.

Manny. If one were to observe Manny in the classroom, he or she probably would not

expect that he worked as diligently in ALEKS as he did. Manny was one of the more reserved

students in the classroom who did not appear to react to many of the different motivational


tactics we tried to implement. He did not seem to participate in the competition as ardently as

many of his peers did. In fact, during my interview with him, he mentioned that he found the

competition to be somewhat frustrating as he saw his peers surpassing him in math. While he

wanted to be like his peers, it seemed they only kept getting further away in their progress.

Additionally, he said he did not need to earn the prizes we gave to the class. As such, one would

not expect that he was one of the students who spent the most time working on ALEKS (49

hours and 2 minutes), second only to Luke. According to his reports in ALEKS, he consistently

either met or surpassed the class’ average time spent working in ALEKS on a daily basis (see

Figure 10). One of the most noteworthy examples of this happened over the classroom’s spring

break, which is highlighted in Figure 10. While most of the students’ times tapered down,

Manny’s remained as high as it had been and even increased on some days. This meant that he

was spending time learning during a period that was specifically given to students as a break

from learning. Instead of enjoying his break like his classmates, he voluntarily chose to work in

ALEKS. Needless to say, this reflected a deep commitment to learning math. Since he did not

respond as much to the competition or prizes, it seemed there was something much deeper that

was driving him to want to learn math.

Figure 10: Manny spent a considerable amount of time in ALEKS compared to the rest of his classmates.

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This intuition was proven to be correct when I interviewed Manny. When I asked him

what motivated him to learn math, he answered, “Well, actually my mom inspires me to do math

in ALEKS. She says if I work hard, I can be very smart, and I would achieve more things.” He

went on to describe how his mom was the “brains of the house,” and how he wanted to become

more like her. It was also interesting to observe how Manny sat next to Luke when the students

worked together in ALEKS (see Figure 11). The classroom was set up specifically to encourage

peer learning so that students could help each other when going through ALEKS. Unlike many

traditional classrooms, students sat around a table facing each other and discussed the problems

they were trying to solve. According to Figure 11, Manny was surrounded by high performing

students, one of whom was Luke. Ms. Fletcher observed that when students were surrounded by

a group of high performing students like that, they were bound to “catch on” and try to do what

the others were doing. This included putting more effort into their work, expressing more

excitement to learn, and exhibiting more initiative in trying to approach new concepts. Manny

was no exception. When I asked Manny about how he felt sitting next to Luke, he said that Luke

helped him with his work and made him want to try to learn more. By being with his mom at

home and the high performers at school, Manny was surrounded by people who exemplified how

learning math could lead to accomplishments. Seeing them work diligently in math inspired him

to put more effort into learning math as he could see how learning math made them “better

people.” Essentially, they became role models for Manny to follow in his journey through math.


Figure 11: Seating chart for classroom. Manny was surrounded by high performing students.

After getting to know Manny better, I realized that Manny’s desire to become like his

role models was a key driving force behind him putting a large amount of effort into his learning.

Manny identified his role models as being intelligent, successful people who were proficient in

math. In this regard, learning math was his way of working towards becoming an intelligent,

successful person like his role models. In the scope of the classroom, being an intelligent and

successful person meant finishing the third-grade curriculum in ALEKS. For this reason, Manny

poured hours upon hours into finishing the third-grade curriculum working both during

weekdays and weekends whether he was at school or at home. Moreover, whenever he learned a

new strategy to solve problems, he felt more inspired to keep working because he felt that he was

becoming more proficient in math. By spending numerous hours in ALEKS, Manny was able to

acquire new strategies in solving math problems on his own. This helped him to become more

like his role models in terms of their levels of expertise. This desire to gain expertise also kept

Manny going in the face of difficult challenges. He commented, “I’ve really enjoyed the ALEKS

program and math. It’s kind of hard, but that makes you smarter. If you don’t get it, ALEKS


gives you more chances to help you learn.” This attitude towards ALEKS evidenced how

Manny’s drive to become a smarter person outweighed his feelings of frustration in not being

able to solve problems. Instead of viewing his struggles as being indicative of his shortcomings,

he accepted them as opportunities to learn and to improve himself. This was similar to how his

role models handled their struggling. He noted that being able to overcome these difficult

problems encouraged him to keep learning more because it proved to him that he was “learning

new things and doing good at [his] work in ALEKS.” In other words, mastering strategies and

overcoming difficult challenges brought him closer to becoming an expert in math and thus

brought him closer to becoming like his role models.

Low Performing Students

I will begin this section by clarifying what I mean when I use the term “low performing.”

This seems necessary to me because when one reads the words “low performing student,” he or

she might be prone to believe that the low performer is unintelligent or feeble-minded. This was

not the case for the students I am describing in my case study. Low performing students are those

students who had not finished at least half of the third-grade curriculum by the end of April. Of

these three students, I will be focusing on the experiences of Andy and Rose.

Andy. When I first observed Andy in the classroom, I thought that he was particularly

unmotivated to learn. Almost every time Ms. Fletcher prompted students to engage in an activity

such as working on ALEKS or offering solutions to problems, Andy would be reluctant to join

the other students in doing these activities. In fact, Ms. Fletcher often had to tell him to do these

activities multiple times before he actually started doing them. Even when Andy started

participating in these activities, he seemed to be putting the minimal amount of effort into


completing the activities. This continued for about two months from the beginning of January to

the end of February (see Figure 12). As seen in Figure 12, Andy spent relatively the same

amount of time in ALEKS as his peers, which primarily consists of the time Ms. Fletcher had

allotted for her students to use ALEKS. In other words, Andy was only spending time in ALEKS

when he had to work on ALEKS. Figure 12 also shows that Andy’s time doubled during the

month of March. Additionally, Andy attempted more topics during each session and continued to

do so throughout April. The reason he attempted fewer topics in May was that he had started

working on his Quick Tables, a module in ALEKS to help students master their times tables.

When he started to work on Quick Tables in April, he had already mastered about half of his

addition tables. By the end of May, he had mastered all of his addition tables, making him the

first student to master addition tables completely. Although he attempted fewer topics in ALEKS

during this time, he was still putting in the same amount of effort into his learning. It seemed

something led Andy to increase his effort he in a lasting way.

Figure 12: Andy’s time and topics attempted in ALEKS from January to May.

In order to understand what sparked this change in Andy, I took a closer look at his

progress during March since his efforts increased most dramatically then (see Figure 13). His

sudden change in effort seemed to happen the week we introduced prizes and games. During my

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interview with Andy, I quickly discovered that the prizes did not have a substantial impact on

Andy as he commented, “Toys aren’t learning, they’re just stuff. I like to do math just as it is.”

We also let the entire class play Chinese checkers. I participated in the same game as Andy did,

so I was able to see his response to being able to play a game firsthand. In all of my observations,

I had not seen him as enthusiastic as he was when he played Chinese checkers. Ms. Fletcher

noted that Andy was shy, so he tended to downplay his excitement over things in the classroom.

In Andy’s case, overcoming some of his initial shyness gave him the ability to get more out of

his interactions with his peers. When I asked Ms. Fletcher how she helped Andy to overcome his

shyness, she answered that she was able to help Andy by leaving him alone with a few

instructions on what he needed to do for the day. This does not mean that she ignored him.

Rather, she allowed Andy to discover things for himself, which made him feel encouraged

instead of forced to learn. Indeed, this allowed him to feel more comfortable with others, which

helped him to open up to them. Watching him play Chinese checkers, this sense of security was

evident in the way he was making comments throughout the game and moving his pieces in

animated ways, complete with sound effects and dramatic movements. According to him,

“Chinese Checkers has made things more competitive, but it’s fun though.” This was when I

realized what was behind Andy’s increased efforts: Andy wanted to have fun in learning. Despite

his shyness, he expressed more enthusiasm in doing something when he was having fun. Just as

in Chinese checkers, Andy became more excited and driven to learn when we created a fun and

competitive atmosphere in the classroom.


Figure 13: Andy’s time and attempted topics increased when we introduced prizes and games. The drop

in his time and attempted topics was more of a reflection of the school’s break.

In order to gain a better understanding of what made learning fun for Andy, I asked Ms.

Fletcher about methods she had found to be effective. Ms. Fletcher said that one of the biggest

challenges to making learning fun was trying to make lessons interesting. One of the ways she

overcame this challenge was to ask, “Am I delivering something that is interesting enough that

they’ll care about it in that they can relate to it?” By planning her lessons with this question in

mind, she was able to gear her lessons towards creating interest in learning math. This interest

provided a foundation for motivating students to learn math. After describing how she created

interest and motivation in the classroom, Ms. Fletcher added:

“You have to tell them that’s why we’re here. We’re here, let’s have some fun and make

sure at the end of the day they do take something home. You have to show some

excitement. If you show it’s exciting, then they’ll jump on.”

When Andy saw that learning math could be fun, he wanted to work on ALEKS more. It did not

matter whether he would get a prize, he simply wanted to participate in ALEKS because he

found that competing with his classmates was fun. When Ms. Fletcher made the lessons more

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interesting, performance in the competition became more valuable to the students as it meant

something to them on a more personal level. This added to fun atmosphere of the classroom as

students, including Andy, became more enthusiastic about what they were learning. Ultimately,

learning math became fun and motivational for Andy when he was able to compete with his

classmates who were just as enthusiastic about learning as he was.

Rose. Occasionally, teachers will have students in the classroom who are dependent on

others to the point where they want others to solve math problems for them. Rose was one of

these students. With only 4% mastery when she started using ALEKS in January and only 9% by

the end of February (see Figure 14), it seemed Rose needed an extra push to jumpstart her

learning. Between the months of March and May, we tried several motivational tactics to help

her to reach a higher mastery level overall, which seemed to be effective based on the results in

Figure 14. At the end of May, I asked Rose to describe math in three words. She replied,

“Confidence, and I can be strong, and I can be undistracted.” This perception of math was

drastically different from that of the dependent student she was from January to early March.

Since much of Rose’s change in attitude seemed to occur between March and May, I combined

the motivational tactics we implemented and Rose’s progress through ALEKS to see if there

were any correlations (see Figure 15). Looking at Figure 15, it seemed there was indeed a

correlation between our motivational tactics and Rose’s efforts.


Figure 14: Rose’s mastery percentages at the end of each month.

Figure 15: Rose’s time spent in ALEKS and the number of questions she attempted combined with the

different motivational tactics we implemented.

We started by introducing prizes and games to the classroom. In addition to giving

students incentives to learn, this also fostered competition among the students. When all of the

students joined the competition, their enthusiasm for learning math increased overall. This

enthusiasm- combined with the peer learning that had already been added to the classroom-

encouraged students to become more adamant about helping each other. For Rose, this sense of

camaraderie gave her exactly what she wanted: for other people to help her to learn. Although

her peers were not solving the problems for her, they did act as a support system that pushed

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Rose to overcome challenges and reminded her that she could excel in math if she tried. When I

asked Ms. Fletcher about this, Ms. Fletcher commented:

“It’s a bit of a camaraderie type of thing as well as a competitive thing. They just feel

good because they can help someone else out, and that’s what you want. You want them

to feel good about helping someone else, and then they can learn too at the same time.

They have a buddy with them, and sometimes having a buddy to stand with them when

they are in front of the class or at a desk helps them to feel safe and not judged.”

This camaraderie continued to help Rose in April when we made a deal with her that she would

get a marble for every topic she mastered. When we made this deal, Rose tried out a topic in

every subject area in ALEKS. Ms. Fletcher noted that even though she did not master all of these

topics, this did give her a “boost of confidence” so that when she came back to work on them,

she was already familiar with all of them. Later that month, we made another deal with Rose

when we told her she would earn a Mouse Trap board game and play it with the rest of the class

for completing the third-grade curriculum. Rose said she wanted this game very badly, and it

made her want to learn more. On top of this, the entire class began to support Rose even more as

they also wanted to play the game. Again, Rose started to attempt to solve more questions in

ALEKS. In addition to this, we created a display to show students their progress in ALEKS.

After Rose realized she was at the bottom of the class, she began to concentrate more on

mastering topics, which she continued to do for the next week. A few weeks later, we gave her

an account in ST Math, an educational software site. In this software, students must help a

penguin named Jiji by using their math skills. Rose said she enjoyed helping Jiji, and that Jiji “is

very, very kind because she wants me to learn, and she lets me try the same problem again if I


get it wrong. So, I keep trying.” Initially, Rose struggled with helping Jiji. However, with Jiji and

other peers telling her she could solve math problems, she was able to overcome that struggle.

In all of these cases, it seemed Rose put more effort into her learning because they gave

her a chance to be a part of her community of peers. This community of peers gave her the

support and encouragement she needed to become more independent in her learning. When she

started to show more initiative by trying out more topics in ALEKS and by helping Jiji in ST

Math, she experienced what it was like to be an independent learner. This, combined with her

peers encouraging her, helped her to believe that she was capable of understanding math on her

own. This independence also gave Rose the tools she needed to contribute to her community of

peers, which to her meant earning a board game for them to play. For this reason, when we

brought more of the same board games for the entire class to play, she was visibly disappointed

that she was not the one who earned a chance for her classmates to play the game. If she had just

wanted the game, it would not have mattered whether other students were playing it or not. What

made earning the game special to her was that others would reap the benefits of her work in

learning math. This was similar to the way she responded to being at the bottom of her class. In

both of these situations, it seemed Rose wanted to feel like she could contribute to her

community of peers by having a better understanding of math. In sum, Rose’s responses to our

motivational techniques reflected her desire to be a part of a community where she could help

others and be helped by others. This need for reciprocal relationships with her peers became the

source of her motivation in learning math.

Discussion

As found in my review of literature, motivation can be boiled down to three main

components: autonomy, purpose, and competence. Every student manifested these three


components in different ways. For Luke, being able to compete with his classmates motivated

him to learn because it gave him the chance to be the top student of his class, thus giving his

learning purpose. Within this competition, he had autonomy in being able to choose what topics

he wanted to study, how much time he spent learning each day, and what new knowledge he

could try to acquire. As the school year progressed, it seemed Luke began to build competence in

being able to approach problems, the competition, and new ideas in general. This was reflected

in his attitude towards learning in the way he said he knew he was going to finish fourth-grade

and fifth-grade before he had even started. Essentially, by combining purpose through

competition and autonomy through ALEKS, Luke developed the feelings of competence he

needed to excel in learning math.

For Isaiah, receiving prizes motivated him to learn more because they represented

something meaningful to him: they reflected his accomplishments and gave him opportunities to

become a leader in the classroom. His purpose in learning math was to earn these prizes so that

other students would follow him as a leader. With Ms. Fletcher encouraging autonomy without

imposing any strict boundaries on what he could do, Isaiah had more freedom in going after

prizes, which helped him to distinguish himself as a leader. With his prizes reminding him of his

past achievements, Isaiah felt competent in being able to learn math and maintain his role as a

class leader. For him, prizes motivated him to learn not for their material worth, but for their

symbolic purpose.

For Chelsea, being able to accomplish her goals seemed to motivate her to learn more.

With support from Ms. Fletcher, her peers, and ALEKS, she gradually became more confident in

her ability to fulfill these goals as she began to believe that she was capable of understanding

math. Given a learning environment with a high level of autonomy, Chelsea could set and


complete these goals in whatever way she chose, forcing her to take active control of her

learning. These goals gave her purpose in learning as completing them confirmed that her ability

to solve math and took her one step closer to finishing her much larger life goals. Ultimately,

these goals gave her something to strive towards accomplishing, and with the belief that she

could fulfill them, Chelsea was motivated to learn math.

For Manny, seeing other people exceeding in math pushed him to want to learn math. His

purpose was to become more like them- intelligent and successful. Because Ms. Fletcher gave

the students autonomy, Manny was able to pursue his learning to his fullest potential, spending

countless hours working on ALEKS inside and outside of the classroom. When Manny was able

to solve problems using new strategies he acquired, this gave him the confidence that he was

competent in understanding math. This competence helped him to feel as if he was one step

closer to becoming like his role models. Being able to see his role models and knowing that he

was capable of becoming like them in his own way gave Manny a strong drive to learn math.

For Andy, having fun gave him a purpose in learning math and motivated him to work

more diligently in ALEKS. His ability to have fun was made possible by the autonomy Ms.

Fletcher granted him by leaving him alone to explore math for himself. Through this autonomy,

Andy got more out of interacting with his peers, which gave him a chance to see how exciting

math could be. Because he felt comfortable and secure with his peers, he exuded confidence and

competence in being able to compete with them in a friendly way. Through this competition,

Andy discovered how much fun math could be, which drove him to learn more. In this way, the

fun Andy was having in the classroom motivated him to invest more time and effort into

understanding math.


For Rose, being a part of the classroom community was her main motivation to learn.

Being able to contribute to this community gave her purpose in pursuing a better understanding

of math. Moreover, she was able to learn more when she was given the autonomy to pursue math

on her own terms. In order to make this autonomy more effective, she needed encouragement

from her community of peers that did not involve them solving math problems for her. With the

support of the entire classroom, Rose felt more competent in that she could handle math

problems. This attitude was further reinforced when Rose was able to successfully utilize her

math skills to help others. In the long run, Rose was motivated to learn math because she desired

to help and be helped by her community of peers.

From these results, it seems there are many different aspects of learning that can motivate

students of all performance levels to learn. In dividing the students from my case study in terms

of high performers, average performers, and low performers, I hoped not to show how students

of different performance levels differ in what motivates them, but how students of different

performance levels can be motivated by similar principles of purpose, autonomy, and

competence. With purpose, students have something to work towards whether it is acquiring

knowledge, maintaining leadership, accomplishing goals, becoming like role models, having fun,

being part of a community, or some other end that was not discussed in my case study. With

autonomy, students are given the freedom to develop those purposes and to determine how they

will fulfill those purposes, which allows them to pursue learning in a way that suits their needs

more effectively. In the end, students can build feelings of competence when they accomplish

what they are working towards using an approach they built for themselves. This feeling of “I

can do it” can give students the confidence they need to handle difficult problems and the

motivation they need to follow through with their learning.


Limitations

With limited time and access to the classroom, I was not able to collect all of the data that

would have further defined my arguments. For instance, in this study I only studied six out of

twenty students in Ms. Fletcher’s classroom. If I had the time to study all of the students, I would

have most likely discovered many different ways autonomy, purpose, and competence contribute

to student motivation. Also, it would have helped to study more students from other classrooms

as that could have made my findings more generalizable. As my study stands, every student is

different, so it is impossible to guarantee the same success with these students for other students.

Additionally, it would have helped to have studied other classes to compare and contrast learning

methods. Ideally, I would have been able to look at a class that incorporated ALEKS with a

different teacher to be able to see differences in teaching strategies and another class that did not

use ALEKS to be able to definitively attribute changes in students’ learning to ALEKS.

However, this was not possible in the scope of this project. Finally, I would have liked to collect

more information from teachers to see what they have noticed to be effective in students’

learning.

Next Steps

There are many other ways to build motivation, which were not discussed in this paper. It

is my hope that my findings from McGill School of Success will contribute to understanding

what motivates students and how that motivation can influence their learning. Not every student

will be exactly like the students in my case study as every student learns differently and is

motivated by different means. In future studies, I would like to see what motivates students in

higher grades. Obviously, the same motivators that were present in my study might not be nearly

as effective in higher grades, but some of the underlying principles of autonomy, purpose, and


competence might still be present. There are many students from all grade levels with math

anxiety who feel they “can’t do it.” Perhaps these feelings of incompetency can subside if, like

the students in my case study, they are given the tools for autonomous learning and are given

opportunities to find purpose in their learning. Given these as a foundation for learning, perhaps

more students will be more motivated to learn math whether they believe they are capable of

understanding it or not.

Conclusion

The purpose of this paper was to examine how to foster students’ motivation in learning

elementary math. I began by presenting background information to set up the problem. I then

reviewed recent research and classic studies about how to foster motivation using autonomy,

purpose, and competence. Next, I explained the research methods used in this qualitative case

study. I analyzed data for my case study of six third-grade students who were learning math.

Specifically, I looked at how different approaches to learning helped to motivate students. I then

discussed the results of my study, the limitations of this study, and future steps for research.


References

Bransford, J. D., Brown, A. L., & Cocking, R. R. (2000). How people learn: Brain, mind,

experience, and school. Washington D.C.: National Academy Press.

Chickering, A., & Ehrmann, S. C. (1996). Implementing the seven principles: Technology as

lever. AAHE Bulletin, 39, 3-7.

Niemic, C. P., & Ryan, R. M. (2009). Autonomy, competence, and relatedness in the classroom:

applying self-determination theory to educational practice. Theory and Research in

Education, 7(2), 133-144.

Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic motivations: classic definitions and

new directions. Contemporary Educational Psychology, 25, 54-67.

Turner, J. C., Warzon, K. B., & Christensen, A. (2011). Motivating mathematics learning:

changes in teachers’ practices and beliefs during a nine-month collaboration. American

Educational Research Journal, 48(3), 718-762.

Urdan, T., & Schoenfelder, E. (2006). Classroom effects on student motivation: Goal structures,

social relationships, and competence beliefs. Journal of School Psychology, 44, 331-349.

Wigfield, A., & Eccles, J. (1994). Children’s competence beliefs, achievement values, and

general self-esteem: Change across elementary and middle school. Journal of Early

Adolescence, 14(2), 107-138.

Zimmerman, B. J. (2000). Self-efficacy: An essential motive to learn. Contemporary

Educational Psychology, 25, 82-91.

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Fostering Autonomy, Purpose, and Competence in Math