Fostering Improved Learning in Math

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Fostering Improved Learning in Math:
A Case Study in an Elementary Math Classroom
Jordan A. Yoshihara, Undergraduate
University of California, San Diego
March 20th
, 2015
Dr. Mia Minnes
CSE199: Independent Study

FOSTERING IMPROVED LEARNING IN MATH 2
Fostering Improved Learning in Math:
A Case Study in an Elementary Math Classroom
The purpose of this paper is to examine how a technology-rich environment can foster
students’ learning 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
learning. Next, I will explain the research methods used in this qualitative study. I will analyze
findings for my case study of a third-grade student who was struggling with math. Specifically, I
will look at how technologically-mediated teaching practices helped improve her learning
outcomes in 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. As time continues, this continues to worsen as
students struggle to establish the fundamental knowledge needed to build the skills they need to
understand more complex math concepts. According to the teacher from my case study, many
teachers are often limited in their ability to help struggling students, as they must follow a set
curriculum. The teacher in my study mentioned she tried to take some students aside to help
them or to allow the whole class to redo assignments and retake assessments, if the majority of
the students are struggling. However, with all of these methods, she still found it was “very hard
to do it,” as students ultimately do not learn in the same ways or at the same pace as the
curriculum plan that the teacher is required to follow.
Literature Review
The question I seek to answer is, how can a technology-rich environment foster student
learning to improve student learning outcomes in math? I reviewed many articles, both
foundational classic studies and recent research discussing students learning math, teaching
methods, and how people learn in general. Here, I will provide an analysis of the literature to
first understand the problem, then I will discuss two possible approaches: by using technology
and with student collaboration. This analysis will provide a framework for my case study.
Understanding the Problem
To understand how to improve student learning outcomes, I want to first understand how
to foster learning. A common misperception is that students fall behind because they may be less
intelligent than others. However, there are multiple factors that contribute to this gap- none
having anything to do with intelligence. One of these factors, found by D. Fuchs, L. Fuchs,
Mathes, and Simmons in their classic case study on peer assisted learning, was that teachers have

a tendency to spend less time helping low-performing students understand the material and give
them less time to practice using the concepts (1997, p.177). If some students are getting adequate
help to succeed and other students are not, this could lead to students falling behind.
Solution 1: Technology
A way of mitigating this problem is to create what Bransford, Brown, and Cocking
described as learner-centered environments, or “environments that pay careful attention to the
knowledge, skills, attitudes, and beliefs that learners bring to the educational setting” (2000, p.
133). In most classrooms, this is difficult to create as teachers must teach classrooms consisting
of twenty to thirty students who need to reach a certain standard by a set timeframe. Here, a
technological response might be appropriate as technology allows for one-to-one interaction
between students and the material. In Bolley’s dissertation, Bolley examined an instruction
design called Computer Assisted Instruction. According to Bolley’s research, Computer Assisted
Instruction is useful for individualizing research and allowing students to interact with the
material directly (2013, p. 41). After studying how technology was incorporated into a high
school classroom, Bolley concluded that technology piqued students’ interests in math and
helped them understand concepts better (2013, pp. 20-21). Based on this, incorporating
technology in the classroom could be potentially effective in creating learner-centered
environments.
ALEKS (Assessment and LEarning in Knowledge Spaces) has achieved much success in
facilitating student learning in many different schools (Craig, 2013; Sullins, 2013; and Nwaogu,
2012). According to research done by Sullins, Meister, Craig, Wilson, Bargagliotti, and Hu,
ALEKS increased students’ math proficiencies by providing more continuous assessments of
students’ progress, which promoted better alignment with the material. Additionally, it addressed

students’ weaknesses by determining the concepts they were ready to learn or needed to practice
more (2013, pp. 74-78). This feedback was useful for what Roll, Aleven, and McLaren called
metacognitive learning, in which students reflect on their learning to make appropriate
adjustments in their ideas (2007, pp. 125-129). This individualized progress and feedback could
contribute to learner-centered environments, as these elements focus on the students rather than
the teacher and foster learning.
Solution 2: Collaboration
Another way to create learner-centered environments is to promote collaboration among
students. In a classic study by D. Fuchs and L. Fuchs et. al., peer-assisted learning was studied
across 22 elementary and middle schools. Peer-assisted learning involves students working
together to collectively come to a better alignment with the material. Instead of the teacher
working with the students all at once, peer-assisted learning allows students to work in smaller
groups, giving them more time to respond to ideas, receive feedback on their ideas, engage in the
material for a longer period of time, and receive more individualized support on their learning
(1997, p. 198). This sort of peer interaction can lead to what Bransford et. al. defined as
“intellectual camaraderie,” which can encourage students to help each other, ask for
clarifications, and suggest new approaches (2000, p. 25).
Another way to promote collaboration is through storytelling. Bransford et. al. argued
that “Storytelling is a powerful way to organized lived and listened-to experiences” (2000, p.
108). When applied to a classroom setting, creating stories can help students organize their
mathematical thinking in a contextualized manner. When students tell these stories, they can help
their peers imagine scenarios in which these concepts apply, essentially making abstract ideas
more concrete and hence more understandable.

Research Design and Methods
In this section, I will describe my case study, describe the technological and collaborative
approaches used, and examine how these approaches helped foster learning. To get a deeper
understanding, I will use a qualitative approach with observations and data-gathering directed
toward developing a better understanding of the lived experience of a student 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 give a little background 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 how people 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 by
helping them with math problems in ALEKS including listening to the stores they created as a
strategy to illustrate their ALEKS math problems. I also was able to 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. So, 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.
Data Collection
My data were collected using interviews with a student and her teacher, various
assessments, progress reports generated by ALEKS, and general observations I made in the
classroom. The assessments I used included the California Standards Test (CST), which
evaluates if students are up to academic standards set by the state, and the Number Knowledge
Test (NKT), which is used in the Number Worlds program to assess students’ abilities to perform
mental math.
Context
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 was beginning to incorporate ALEKS as
an intelligent tutor. 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 one student, Chelsea (I
have changed her name to protect her identity). Chelsea stood out to me in particular because
like many students, she thought she could never understand math. As a part of my case study, I
conducted an interview with Chelsea. During our interview, Chelsea mentioned, “I was kind of
not really able to do math before ALEKS.” Ms. Fletcher noted that Chelsea was a student who
was afraid to learn math and had little confidence in her ability to understand it. Whenever she
was selected to answer a math question during class, she would reply, “I don’t know.” After
using ALEKS for a few months, Chelsea’s scores in math improved dramatically, rising above
the average score on the CST (See Figure 1).
Figure 1: (CST) Chelsea’s California Standards Test scores before and after using ALEKS
This figure shows Chelsea’s starting point – where she started and what happened over
time and where she ended up. What is most striking about this figure is that she was able to not
only reach the state standards but surpass them in the span of three months. Chelsea also became
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more confident in her ability to solve math problems and participated in more classroom
activities dealing with math. Since her struggle with math reflects the way many other students
struggle with math, I hope that my findings will hold implications for how learning environments
may be designed to foster improvement for a more general student population even though I
focused on one student in this study.
Findings
As stated earlier, when Chelsea started at the beginning of the year, her scores were
below-standard for a third-grade student. When a student scores below the standard, many
instructors are prone to believe that it is because the student is not trying hard enough. This was
not the case for Chelsea. In fact, according to her progress report in ALEKS, she learned almost
as many topics as the other students did on average (See Figure 2). This means she was putting
effort into her learning, but needed something more than traditional teaching techniques. In
Figure 3, I have summarized the features of a technology-rich environment that was particularly
effective in Chelsea’s improving learning experience. These features will be used as a framework
for my analysis.
Figure 2: (ALEKS progress report) Chelsea learned 123 topics; other students learned 176 topics on average
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Property Description
Comprehensive Ensures students are actually understanding the material
Immersive Provides contexts for concepts in the material
Active Encourages students to explore the material for themselves
Structured Directs student learning according to curriculum
Differentiated Adapts to students’ unique learning styles
Corrective Aligns student thinking to information in the material
Collaborative Allows students to come to a collective understanding together
Figure 3: A summary of the properties of an effective learning environment
Comprehension in the Classroom
Based on Chelsea’s improvement in her ability to approach math, she was able to
comprehend mathematical concepts better. According to Ms. Fletcher, mental math, or problems
that students solve in their heads, are the most difficult thing to teach. This is because it relies
solely on students’ levels of comprehension and there is no room for wild guessing. In order to
solve problems correctly, students must comprehend the concepts and how the concepts are used.
The NKT tests for this as it is administered orally, and students cannot use a pencil or paper to
compute the answers. Chelsea scored a 27 out of 30 on this test, the average score for a 3-4
grader. Although she mostly used counting rather than algorithmic approaches, she was still able
to demonstrate she understood what adding and subtracting entailed. This means she did not
need to make any wild guesses about how to solve problems as was the case with some of the
students in another class I tested. This means her ability to comprehend math had improved. This
was also true of the rest of her classmates. This was not true, however, of another third grade
class as each student scored a year behind where they should have been (See Figure 4). Clearly,
this other class was missing something that the class in my case study had.

Figure 4: (NKT Scores) Chelsea and her classmates’ scores were much higher than the other class’ scores
One of the main differences between the two classes was the incorporation of a program
of activities, many of which involved ALEKS. It would be incorrect to assume that ALEKS was
the sole contributor to the difference between the classes as there were many different
approaches to teaching that were used in one class and not the other. However, ALEKS did play
a major role in Chelsea’s success as she remarked, “ALEKS makes math easier. I can’t explain
why, it just does.” According to Ms. Fletcher, ALEKS helps students learn as its explanations are
excellent in showing them how to solve problems. ALEKS is also effective in getting students to
practice the material by giving them pie charts, which are divided by topics (See Figure 5). In
order to fill out a section of these pie charts, students must answer two problems correctly in a
row to master a topic. Every time they get a problem wrong, they must answer another similar
problem correctly. This gives them the practice to be able to form mental chunks of information
they need to master the material. Based on the NKT results, students who were given this sort of
practice were able to comprehend the material to the point where they could use concepts
automatically.
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Figure 5: (ALEKS Report) Chelsea’s pie chart displaying her mastery of concepts
Immersion in the Classroom
When I asked Chelsea what topics she preferred, she said she loved counting money and
geometry but hated multiplication and division. This interest towards money and geometry is
reflected in Chelsea’s progress through ALEKS (see Figure 6). Students go through ALEKS by
choosing the topics they would like to focus on during each session. Chelsea had a tendency to
favor money and geometry over multiplication and division. Surprisingly, this tendency to
choose those topics was also seen in the progress report for the rest of the students.
Figure 6: (ALEKS Report) Chelsea and other students focused on counting money and geometry mostly
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My interview with Chelsea might help explain why students chose money and geometry
over other topics. When I asked Chelsea if math is important, she responded, “Math is important
because it is everywhere because everything is shapes.” This response reveals that Chelsea’s
understanding of geometry extends beyond ALEKS as she is immersed in an environment that is
comprised of shapes. As a result, she sees how these concepts apply to real-life situations and
how they can be used to solve problems in those situations. Multiplication and division, on the
other hand, are usually presented as numbers and operations only. Since these are presented out
of context, students tend to only see the algorithms, and not why to use them. As a result,
students were more motivated to study money and geometry because they could understand their
applicability. It is still possible to contextualize abstract concepts. In the classroom I observed, I
had students create stories (or word problems) about these topics to contextualize them. Many of
them generated stories that drew from their family lives and then they shared their stories with
others. According to Chelsea, creating stories was effective for her learning because it made
concepts fun and helped her imagine how to apply the material. Using strategies like this,
students could use their own contexts as starting points for understanding the content. This
ensures the contexts are familiar to students, making it easier for them to connect their ideas
together.
Active Learning in the Classroom
One way to make students feel confident in their understanding is to give them control of
their learning. For Chelsea, ALEKS helped her gain this control as it became a “weapon” for her
to wield against math problems. This idea of a weapon is often associated with a quest or journey
where a person must overcome obstacles along the way. Likewise, Chelsea’s experience with
math became a journey where her struggles were merely part of the learning process and her

anxiety was reduced. She noted that this perspective made learning fun and helped her
understand math better. However, this perspective seemed to do more than just that. After using
ALEKS, Chelsea started offering answers for the first time during Ms. Fletcher’s Number Talks
and sharing stories about problems with her peers. At one point, she even presented her stories to
the entire class and had other students solve them. Not only did this reflect a boost in Chelsea’s
confidence in math, but also demonstrated that she had taken active control over her learning.
This is consistent with the rest of the class, as Ms. Fletcher found other students enjoyed
using ALEKS because they had the freedom to choose the topics they wanted to study. This
sense of freedom gave students an active role in making their learning personal. It seemed that
when students identified with the concepts, they had a more personal stake in their learning. This
seemed to be the case with Chelsea as she started working on ALEKS outside of the classroom-
something that is completely optional for students to do. In fact, the students were not told they
could access it at home- Chelsea figured that out on her own. Many students tend to take
classwork home after school when they do not complete it in class. Chelsea, however, was not
behind in terms of topics mastered, so this indicates that she wanted to fill out more of her pie
chart. Because the pie chart was her own, Chelsea’s learning became a personal matter that could
only be developed through her active involvement in the learning process. Moreover, she
enjoyed filling out her pie chart by going through the lessons on her own.
Structure in the Classroom
One of the challenges for Ms. Fletcher was incorporating ALEKS and simultaneously
keeping up with the standards of core curriculum. While she did have Number Talks at the
beginning of each period to keep students on track, she still gave students time to go through
ALEKS. This allocation of time followed a cognitive apprenticeship model where she modelled

the content for students during Number Talks then had them practice the concepts on their own
in ALEKS. She was also able to coach the students through lessons by prompting their thinking
with questions then bringing them together to figure out a correct solution. Intuitively, creating
shorter lessons with emphasis on the students presents the risk that they might fall behind
academic standards. This, however, was not the case for Chelsea’s class.
As seen earlier in both the CST and NKT, Chelsea and her classmates all scored right
where they should have been in terms of standards despite the shorter lessons. Moreover, some
of them were ahead of the curve as they already had been exposed to some concepts before Ms.
Fletcher even taught them. For instance, one day she gave a lesson on fractions, a topic that is
often difficult for students to understand, as the idea of partial numbers can be complicated.
However, when she taught this lesson, she found that some of her students, including Chelsea,
said they already knew about fractions from ALEKS. ALEKS is set up so students can work at
their own paces, but also guides them to learn topics they are ready to learn, which means all of
them would learn fractions at some point. Its problem sets follow the same academic standards
that the teacher is following in the classroom. According to the standards report on ALEKS,
Chelsea and her peers were all on their way to reaching standards even though Ms. Fletcher was
mostly coaching them through the concepts during short Number Talks sessions (see Figure 7).
Essentially, ALEKS and Ms. Fletcher set the structure, Ms. Fletcher guided students using this
structure, and then students were allowed to explore the material within the parameters of that
structure. For Chelsea, this pushed her to meet standards and, as seen with her CST scores, even
surpass them.

Figure 7: (ALEKS Report) 3.OA (Operations & Algebra), 3.NBT (Number & Operations), 3.NF
(Fractions), 3.MD (Measurement & Data), 3.G (Geometry), MP (Mathematical Practices)
Differentiation in the Classroom
In many classrooms, teachers do not have time to help every student catch up to the
curriculum. For Chelsea, this means that her CST score would most likely have stayed below
average as she would not be given the feedback to improve. Fortunately, ALEKS gave her this
attention as every student’s experience with ALEKS is their own. ALEKS starts off by giving
students an initial assessment that determines the topics they already know and what they have
yet to learn. This ensures that each student has a firm grasp of the material before moving onto
more complex concepts. When Chelsea started using ALEKS, she did not know as many topics
as some of her peers. For this reason, it appeared that she was learning at a slower pace.
However, because ALEKS was able to differentiate between her and her peers, her progress
reports showed that she was learning approximately as many topics as her peers (see Figure 8).
She simply needed to spend more time on topics her peers had already mastered in order to
master them before moving onto other topics. This sort of individualized progression is difficult
in classrooms as teachers often move along according to curriculum rather than student
understanding.
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Figure 8: (ALEKS Report) Chelsea learned at approximately the same pace as her peers
Because ALEKS is geared towards individual learning, students can go through this
process of aligning ideas and building on them according to their levels of expertise. Ms.
Fletcher noted that for her students, the idea that they had their own accounts and pie charts
motivated them to go through this process at their own pace, using their own approaches. In fact,
during my interview, Chelsea excitedly told me that she had almost finished the counting money
slice of her pie. This confirms the pie charts were motivating for students, which helped
differentiate their learning experiences. What Chelsea may not have noticed is that her
excitement over filling in a slice indicated that she was getting the individualized feedback she
needed to foster her learning. Although Chelsea was behind, the fact that she could learn at her
own pace motivated her to keep working towards understanding problems to fill in slices. This
individualized learning definitely helped to build her confidence and her ability to approach math
as she was given the time she needed to actually understand the material for herself according to
her personal learning needs.
Correction in the Classroom
In the classroom, Ms. Fletcher would ask students for answers and write them down
whether they were correct or incorrect. Students would then explain their answers, a practice that
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often led them to discover flaws in their reasoning. When this happened, she would reassure the
student that making mistakes is okay as it helps other students to learn as well. As stated earlier,
Chelsea started the class by simply answering “I don’t know” to questions the teacher asked her.
After a few months, Ms. Fletcher’s positive perspective on making mistakes seemed to
encourage Chelsea to participate as she started offering her own answers during Number Talks
without being called on by the teacher. Even though she occasionally got the answer wrong, this
did not discourage her from presenting her answers to the class anyway.
ALEKS also uses this type of feedback in the way it functions. When ALEKS gives
students problems, it also gives them the option to answer the problem or ask for an explanation
about the problem. If students answer incorrectly, ALEKS shows an explanation on how to reach
the correct answer. Ms. Fletcher mentioned these explanations have been “very helpful in getting
students to correct their thinking.” In fact, when I interviewed Chelsea, she said that the
explanations have really helped her to understand math. This is reflected in Chelsea’s progress
through the “Geometry, Measurement, and Graphs” topics. According to Figure 9, as time
continued, Chelsea relied on the explanations less and was able to give the correct answer more
frequently. By the end of the five weeks, she no longer needed explanations and was able to give
the correct answer the majority of the time. This demonstrates how Chelsea used the feedback
from ALEKS to understand the material more to the point where she could correctly solve the
problems on her own. In other words, her strategies for solving these problems became better
aligned with the content due to the feedback she was given.

Figure 9: (ALEKS Report) % of answers correct, incorrect, and explained over five weeks
Collaboration in the Classroom
Aside from ALEKS, one of the defining features of the classroom I studied was how the
students collaborated with each other. Students participated in a variety of cooperative activities,
such as sharing stories about problems with each other, helping partners with ALEKS, discussing
concepts with their peers during Number Talks, and offering solutions to problems Ms. Fletcher
provided. These activities seemed to spark interest and excitement in Chelsea. According to Ms.
Fletcher, Chelsea learned better when she could verbalize her thinking. It was not enough that
she would solve problems using a paper and pencil- Chelsea needed reciprocal learning activities
with her peers to jumpstart her learning.
This need for reciprocal learning activities was especially evident when students were
sharing stories with each other. Chelsea was paired with a high-performing student, and they
ended up creating new math problems for each other that were more difficult than the questions
originally posed by ALEKS. This exemplifies how peer interaction can lead to students
discovering new ideas together by building off of each other’s knowledge. This also led to
Chelsea gaining confidence in sharing stories with the entire class. In her interview, Chelsea
stated that she absolutely loved “teaching the class” by telling her stories and having the other
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Chelsea's Progress in Geometry,
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students solve them. She further remarked that this was one of the more effective activities that
helped her learn math. In essence, these collaborative activities served a dual purpose by helping
Chelsea refine her ideas through peer interaction and by motivating her to pursue a better
understanding of math as this understanding provided her with the basis for these interactions. 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.
Recently, when Chelsea was asked if she liked math, she replied, “Yes.” This change in
her perspective towards math was accompanied by her remarkable improvement in her math
proficiency. Furthermore, Ms. Fletcher and those around her can tell she has confidence in
solving problems by the way she is excited to participate in classroom activities and ALEKS. As
Ms. Fletcher comments, “I guess you could say we have brainwashed her into loving math.”
With ALEKS and the way the classroom was run, it is clear that Chelsea’s journey through math
has been completely transformed with the help of these teaching methods. Through these
methods, she now feels she “can do it” and has displayed a noteworthy improvement in her
mathematical achievement.
Discussion
Many of the practices, such as directly incorporating ALEKS in the classroom and telling
stories about problems, had not been previously used at McGill. Like the studies from other
research, Chelsea improved her math proficiency better when she was able to interact with
technology that created a learner-centered environment by giving her immediate feedback to
improve her understanding (see Bransford, 2000; Bolley, 2013; Craig, 2013; Sullins, 2013;
Nwaogu, 2012; and Roll, 2007). Technology-rich environments can foster learning in math by
providing foundations for activities which increase students’ math comprehension. As shown in

my case study, learning can be further encouraged by immersing students in contexts about the
concepts and allowing them to actively explore the content for themselves. It is important to
maintain structure by guiding students along the concepts, but equally important to remember
that every student learns differently and should not be ignored because of those differences. This
was seen in the study by D. Fuchs and L. Fuchs, et. al. and in Chelsea’s progress through
ALEKS. These technology-rich environments can help students keep up with the material by
correcting them when their thinking is incorrect. Additionally, collaborative methods such as
peer-assisted learning and storytelling, which have been researched by others (Bransford, 2000;
D. Fuchs and L. Fuchs, 1997), seemed to help Chelsea and her peers to collectively reach a better
understanding of the material.
This combination of technology and collaboration seemed to have a profound impact on
Chelsea’s learning in math. While it is impossible to pinpoint what feature influenced her
success, it is possible to see that her understanding of math improved when these features came
together in a powerful way. In doing so, these features transformed a student who thought she
could never understand math and gave her the confidence she needed to approach math. This
confidence allowed her to explore math more fully and talk about it with others. This was
evidenced by her improvement on the CST assessment and ability to perform well on the NKT.
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, it would have helped to study multiple
students with math anxiety 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
Chelsea 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 span 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 learning environments can be designed according to these
features that were not discussed in this paper. It is my hope that my findings from McGill will
contribute to understanding how these learning environments might be designed. Not every
student will be exactly like Chelsea, as every student learns differently. However, there are many
students with math anxiety like Chelsea and feel they “can’t do it.” Perhaps these feelings can
subside if, like Chelsea, they are given a learning environment that better matches how they
learn. It is through this process of reexamination and implementation that we can begin to foster
improved learning in math.
Conclusion
The purpose of this paper was to examine how a technology-rich environment can foster
students’ learning in 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 learning.
Next, I explained the research methods used in this qualitative case study. I analyzed data for my
case study of a third-grade student with math anxiety who was learning math. Specifically, I
looked at how technologically-mediated teaching practices along with other approaches helped

to improve her learning outcomes in math. I then discussed the results of my study, the
limitations of this study, and future steps for research.

References
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Craig, S. D., Hu, X., Graesser, A. C., Bargagliotti, A. E., Sterbinsky, A., Cheney, K. R., &
Okwumabua, T. (2013). The impact of a technology-based mathematics after-school
program using ALEKS on student's knowledge and behaviors. Computers &
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Sullins, J., Meister, R., Craig, S. D., Wilson, W. M., Bargagliotti, A., & Hu, X. (2013). The
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Roll, I., Aleven, V., McLaren, B. M., & Koedinger, K. R. (2007). Designing for metacognition-
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