students’ experiences in a math analysis flipped classroom...
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Students’ Experiences in a Math Analysis Flipped Classroom
A Thesis by
Hugo Sierra
Chapman University
Orange, California
College of Educational Studies
Submitted in partial fulfillment of the requirements for the degree of
Master of Arts in Teaching
May 2015
Committee in charge:
Amy Ardell, Ph.D., Chair
Dr. Keith Howard, Ph.D.
Dr. Luis Ortiz-Franco, Ph.D.
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Students’ Experiences in a Math Analysis Flipped Classroom
Copyright © 2015
by Hugo Sierra
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ACKNOWLEDGEMENTS
There are many amazing people I want to thank. First, I would like to thank my
parents, Rodolfo and Emelia Sierra, for all their support throughout my education. They
have encouraged me throughout my life to never give up. Secondly, I would like to thank
my older siblings, Rodolfo Jr., Luis, Angela, and Alvaro for their support on a daily basis.
Next, Adriana Montes de Oca, you are a true friend who never lets me down. You were
the one that: 1) helped me enrolled into Chapman, 2) pushed me all through my
undergraduate and graduate program, 3) motivated me into getting my first substitute
teaching job, 4) organized the study sessions with Pedro, Nancy, Carina and Lizbeth, and
5) was there throughout my ups and downs. I don’t know what I would have done
without you. I will miss those Red Robin, Jamba Juice and Cold Stone runs. Adriana
you will get the A.T., I promise. My Jurupa Hills colleagues: Carrera, Corrales, Flores,
Garcia, Moreno-Cuevas and Ramos, thank you for the advice. Mrs. Crystal Kirch,
congratulations on your new job! Lastly, I would like to thank my thesis advisor and
chair, Dr. Amy Ardell, who has consistently encouraged me since day one either on the
phone or in person. I will miss all the Wednesday calls.
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ABSTRACT
Students’ Experiences in a Math Analysis Flipped Classroom
by Hugo Sierra
A flipped classroom is a new way of learning, which has been established in the
last few years. The flipped classroom has been used at high school and college levels,
including the high school in this study where it was observed in a math analysis
classroom. In a flipped classroom, students watch a video lesson at home and come to
class for hands-on activities and real life applications (Bergmann & Sams, 2012). This
qualitative case study of the flipped model seeks to understand the students’ experiences
in the math analysis classroom. I will answer the following research questions: 1) What
is the students’ experience in a math analysis classroom with a flipped approach? and 2)
What do students perceive to be strengths and areas of growth in the flipped classroom
model in terms of their engagement and content learning?
Vygotsky’s (1978) theoretical framework, in particular his notion of problem
solving moments, was used to code the data. Vygotsky’s (1978) notion of the social
environment and cultural environment were also used to interpret the findings. The
findings show that students reacted positively to the integration of the flipped model.
Although there was hesitation at the beginning, students grew to accept and adopt the
model and became more accepting of the flipped model over time.
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TABLE OF CONTENTS
Chapter 1: Introduction……………………………………………………………………1 Traditional Model.…………………….…………………………………………..1 Purpose……....……………………………………………………….……………2 Technology…….……………………………………………………………….…2 Flipped Model…………...…………………………………………………...........4 Rationale…………...…………………...…………………………………………5 Site Description…………...………………………………………………………6 Theoretical Framework……..…………………………………….……………….7 Conclusion…………………………………………….………………………..…8
Chapter 2: Literature Review…………………………………….………………………10 Theoretical Rationale for Constructivism.…….…………………………………10 Social Constructivist Framework…………………….....…...…………………...11 Problem Solving.………………………………………………………………...12 Social Environment………………………………………………………………14 Cultural Environment…………………………………………………………….16 Teacher Role……………………………………………………………..………18 Empirical Research on Flipped Classrooms…………………....………..……....20 Higher Education Flipped Classroom……………………………………..……..20 High School Flipped Classroom…………………………………………………24 Conclusion………………………………………………………………….……26
Chapter 3: Methods…………………………………………………………...………… 28 Qualitative Design……………………………………………………….………28
Background of Study…………………………………………………….………29 Setting……………………………………………………………………………29 Background of Teacher……………………………………………………..…....31 Limitations………………………………………………………......……...……32 Participants………………………………………………….……………………32 Data Collection…………………………………….….…………………………35 Observations……………………………………..………………………………35 Field Notes…………………………………….....………………………………35 Student Work……………………………….......………………………………..36 Focus Group Interview………………………..…………………………………36 Data Analysis…………………………………………………………………….38 Time…………………………………………….………………………………..38 Problem Solving Moments………………………..……………………………..38 Social Environment………………………………………………………………39 Cultural Environment…………………………………………………………….40 Strengths and Areas of Growth……………………….………………………….41 Conclusion…………………………………………………….......……………..42 Chapter 4: Results………………………......……………………………………………43 Background of This Flipped Model Classroom.…………………....……………43
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Time…………………………………...…………………………………………45 Blog……………………………………..………………………………………..48 Problem Solving Moments…....….………………………………………………51 Cultural Environment………....……………………………..……...……………51 iPhone/iPod………………………………………………………...…………….52 Computers……………………………………………………………….……….54 Calculators………………………………………………………….......………..55 Social Environment……………………………………………......…………….56 Peer Assistance……………………………………………….........…………….56 Teacher Assistance…………………………………………........………………59 Strengths……………………………………………………....…………………61 Areas of Improvement…………………………………….......…………………63 Conclusion……………………………………………….....……………………63 Chapter 5: Summary Conclusion, and Recommendations………………………………65 Interpretation of Findings…………………………………..……………………65 Implications for Instructional Change……………………...........………………67 Recommendations for Further Research……………….......……………………70 Conclusion……………………………………………..........……………...……71
References………………………………………………………………………………73
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LIST OF TABLES
Table 1.1: Levels of participation…………………………………………………..........34
Table 2.1: Use of Time……………………………………………………………..........46
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Chapter 1: Introduction
Gloria (all names are pseudonyms) is a twelfth grader in Mrs. X’s math analysis
flipped classroom. Her perceptions of a flipped model of teaching changed throughout
the school year:
In the beginning, I hated it [math analysis flipped classroom] with a passion. I
don’t like using technology for homework, so I was frustrated all the
time. Especially when I got home from school, I had to watch a lesson and I got
angry because I never got a break from math. But in second semester, I got used
to it. What I noticed was that I knew the math material so well that I could teach
someone. My hard work paid off in every test and quiz, and I am so happy with a
flip class. I have an A as my semester grade!
Despite her early struggles, the math flipped model had a strong impact on Gloria’s
performance.
This study on the flipped model seeks to answer the following questions: What is
the nature of students’ experience in a math analysis classroom with a flipped approach?
What do students perceive to be strengths and areas of growth in the flipped classroom
model in terms of their engagement and content learning? With these questions, I hope to
learn more about this particular instructional practice from the students’ point of view.
Traditional Model
Lecturing is the main teaching method used in many higher education classrooms
(McGarr, 2009). Classrooms have historically been set up with a focus on the teacher.
Teachers lecture from the front of the classroom, usually from their podiums, to a large
number of students (McGarr, 2009). If a student has a question, they are usually allowed
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to raise their hand. However, the teacher is the one that controls the delivery of the
instruction. The students often come to class needing clarifications from the previous
night’s homework. The first twenty-five minutes is spent doing a warm-up activity
(focusing on the previous day’s lesson content) and going over the homework problems.
After clarifications, the teacher would present new content, usually ranging from thirty to
forty-five minutes. The remainder of the class time is often spent on independent
practice and/or a lab activity (Bergmann & Sams, 2012).
Purpose
With the increased availability of technology, teachers are looking for new ways
to deliver instruction, and increase student engagement to produce stronger academic
competencies. Today’s youth is experiencing classroom instruction differently than
previous generations due to the accessibility of technology. Classroom teachers find
themselves incorporating technology into their classrooms in order to engage their
students in everyday lessons and potentially change education (Koehler & Mishra,
2005). Teachers use the technology to present instruction using a projector or computer-
assisted learning applications (Ian & Lowther, 2009). Modern technologies include: the
Internet, digital video, and computers (Koehler & Mishra, 2005). The advancement of
technology has also made it easier to use other mediums beyond the teacher’s voice when
presenting material.
Technology
There have been changes in the technological world ranging from smart phones to
new devices including tablets, MP3 players, SMART Boards, calculators and computers
(Parker, Bianchi, & Tsui, 2008). Schools that have attempted to integrate technology
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have faced challenges because they have limited resources. In recent years, whiteboards
have replaced chalkboards, PowerPoints have replaced overhead transparencies, and
electronic communications have replaced traditional teaching and learning in some cases.
In addition to the replacement mediums, software such as Blackboard and WebCT have
served in facilitating communication to distribute information electronically to many
higher education institutions (Parker et. al., 2008).
One technological innovation is podcasting. Podcasting has been growing in
popularity in education, in both K-12 and college settings in the past few years (McGarr,
2009). The term “podcasting” emerged from Apple’s audio player, iPod. Podcasting has
been used to deliver information across wide groups of learners using the traditional
model. Podcasting is used to distribute audio and/or video files into a digital format and
can be downloaded using the Internet. Podcasting has had a significant growth in
education by supporting mobile learning and by building upon the traditional education
model (McGarr, 2009). The major consequence of podcasting is a decline in retention of
information (McGarr, 2009). At the time that the students are transferring the
information from the podcast to their notes on paper, they are neither putting into practice
any critical thinking skills nor applying their knowledge to the task at hand. All that is
potentially being done is a transfer of information.
Similar to podcasting, handheld devices have been evolving in their use in schools
including higher education, but this has resulted in some unintended consequences (Song,
2007). Classrooms that have been integrating the handheld devices in the classrooms
seemed to be leading to less interactivity and collaboration (Song, 2007). Technical
problems with the handheld devices arise because of the complexity of the applications.
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Utilizing handheld devices can also have repercussions because it limits the capacity for
accessing larger resources, causes short battery life, results in low resolution and ends
with limited wireless connectivity. Wireless connectivity is a critical component of the
podcast system of instruction delivery, but, as we are all aware, technology is neither
perfect nor foolproof and has its limits and glitches. When technology fails to work in
the way expected, connectivity falls at times, leading to a loss of instructional time.
Instruction is not only lost by connection failure, but also the time spent trying to regain
connection (Song, 2007). Due to their size and software capacity, handheld devices have
a limit to the amount of available applications (Song, 2007).
Schools have attempted various approaches for integrating technology into the
modern classroom. However, since many schools lack the resources to undertake this
implementation, they look for alternative ideas to incorporate technology and develop
new ways of teaching. One of these approaches is the flipped model (Bergmann & Sams,
2012).
Flipped Model
This study seeks to explore the flipped model utilized in a high school math
analysis classroom. The flipped model of instruction has only been implemented in some
secondary school settings in the last few years. In 2007, two high school science teachers,
Bergmann and Sams, experimented with new ways of teaching during a block schedule,
consisting of ninety-five minutes every other day. Bergmann and Sams felt they had to
refine a new teaching approach in order to incorporate additional science labs in the
classroom (Morgan, 2014). Instead of lecturing to their science classes, Bergmann and
Sams made videos allowing students to view lectures at home. This new method of
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teaching has spread to many K-12 settings, especially in math and science classrooms,
enhancing learning in many ways. I will elaborate more on this point in Chapter Two.
The flipped model is one of the more popular technological innovations that
delivers content and implements practices in unique ways (Earle, 2002). The flipped
classroom model is completely recreated from the traditional model because it starts with
teachers putting lectures on video. Students are expected to watch a recorded lesson
video prior to attending class as a homework assignment (Bergmann & Sams, 2012).
Students come to class with any questions that may have arisen during the video lesson,
which helps them to clear up any misunderstandings before applying their understanding
incorrectly. After clarification from the video lesson, the students spend the remainder of
the class time working on guided practice, independent practice, hands-on activities or
direct problem-solving tasks (Bergmann & Sams, 2012). The flipped model approach
often has a great impact on students’ learning, as Gloria mentioned.
Rationale
Since the flipped model is a relatively new approach to pedagogy, it needs to be
studied from multiple angles. Educators often try their best to find out new strategies that
might work for their students, but they are rarely able to learn about the experience of a
new curriculum from the students’ point of view in a systematic way. A qualitative
approach was utilized in this research study to allow the thoughts and views of the
students to be recorded. The students in this particular math classroom experience the
flipped model on a daily basis. By allowing students to express their opinions and views,
it permits educators to understand the impact of the flipped model on their learning
process and possibly make adjustments accordingly. Educators can use these strategies
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to implement new ways of teaching and adjusting the model. The limitations to the
current study include the fact that this is an investigation of only one math analysis
flipped classroom, which is not representative of a larger group beyond students in this
data set. Thus, the findings of this study are not generalizable to a larger population.
Site Description
In order to answer the research questions, I have chosen to observe one classroom
at High School Y where the flipped model has been in use and is considered to be
effective. I was first introduced to High School Y through my observations hours in my
credential program. High School Y is a public school that opened in 2005 in Orange
County, California, and has managed to maintain high Academic Performance Index
(API) scores through highly professional teachers, strong parental involvement and
engaged students. It has approximately twenty-five hundred students, predominately
Hispanic/Latino and is located in an urban community. The majority of the student
population is socioeconomically disadvantaged and qualifies for free and reduced lunch.
High School Y has one of the highest average California High School Exit Examination
(CAHSEE) scores in the school district.
According to the administration, for the past three years the flipped model has
contributed positively to those scores. The students benefit from the acquired skills even
when they are enrolled in a course that does not utilize the flipped model because they
have access to all the math flipped classroom videos. This was the most appropriate
school to explore students’ experiences in the flipped classroom in part because all
students have been formerly taught in a traditional model. Many of the students continue
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to struggle in classrooms that follow a traditional approach and have managed to better
understand the content in the flipped classroom.
With the assistance of the administration, I was able to identify an experienced
teacher, Mrs. X, who has successfully utilized the flipped model in all her math analysis
classes and algebra classes since the 2010-2011 school year. After speaking with Mrs. X,
she recommended her fourth period math analysis class because of the high degree of
engagement, making it an extreme case sample. A math analysis course is taken after
Algebra Two, usually during eleventh or twelfth grade; it is simply a condensed version
of algebra and trigonometry (Sullivan, 2005). This new approach intrigued me, and
influenced my decision to pursue the model more in-depth for this thesis project.
Theoretical Framework
Teaching using the flipped model has shifted from students receiving information
from teachers to students building new knowledge through collaboration with peers. This
learning theory of constructivism seems more relevant, not just for this approach, but for
a technologically based society in general. Social constructivist perspectives focus on the
interdependence of social and individual processes in the co-construction of knowledge
(Palincsar, 1998). Constructivism results in a creation of knowledge by learners as they
interact with their physical and social environments (Roth, 1993). Students build new
understandings during the process of social interaction, helping learners to participate in
the give and take of collaborative activities (Sakulbumrungsil, 2009). Students are able
to discover their own solutions and try out new ideas, as educators become the facilitators
of learning in a constructivist classroom.
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Lev Vygotsky refers to the tools that facilitate constructivism as problem-solving
moments (Vygotsky, 1978; Palincsar, 1998). The problem-solving process include: 1) a
series of steps, 2) analysis of a problem, 3) creating possible solutions, and 4) checking
solutions and using other strategies when a solution is not successful. With the increase
in technology, technological tools are necessary to solve everyday problems (Mills,
Chandra, & Park, 2013). Using a collaborative approach, problem-solving skills are
essential for individuals to achieve a social environment goal (Mills et al., 2013).
According to Vygotsky, socialization plays a large part in learning (Wink & Putney,
2002). Through interactions with others, students learn to apply information gathered.
Individuals decide what information is important to understand and retain. In addition,
the cultural environment serves as a tool in knowledge, which Vygotsky considers
another significant factor for learning (Vygotsky, 1978; Wink & Putney, 2002).
It is best to study a flipped model through the lens of constructivism because it
has the potential to facilitate learning through students’ experiences with technological
materials and student interactions. Teachers assist in a classroom environment in which
students can learn through interaction from peers and teachers. Through various
activities, students are able to 1) interact and teach one another in the classroom or at
home, 2) manipulate the video recorded lessons by rewinding or fast forwarding without
the support of a teacher and 3) use technology in a math class.
Conclusion
Educators look for ways to adjust their teaching techniques and improve academic
outcomes continuously. The flipped model has been successfully implemented in some
settings as a new way to blend technology into the classroom. It is important to study the
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flipped model to see what its potential might be both in math and in all content areas. As
a result, there is much research to be done in order for educators to fully understand its
impact in learning and education. Through this examination of a flipped model
classroom, I plan to show how it is experienced from the students’ point of view.
While Chapter One provided an overview, Chapter Two will describe the
theoretical framework as well as the available research in both higher education and K-12
classrooms using the flipped model. After the literature review, I explain the
methodology and analysis in Chapter Three. In Chapter Four I present the results of my
particular investigation and in Chapter Five I discuss those results.
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Chapter 2: Literature Review
The increased availability of technology in the classroom manifests itself through
different mediums and devices, changing the way we teach. In this study, the learning
theory of constructivism is utilized to explore a flipped model approach that is designed
to be a student-centered classroom. In this chapter I will explore: 1) the theoretical
framework of constructivism, which offers an overview of the learning theory; 2) the
related empirical work on high school math classrooms that are constructivist in nature;
and 3) the empirical studies of the flipped model of instruction on K-12 and higher
education courses in the past 15 years.
Theoretical Rationale for Constructivism
Constructivism is a learning theory based on the science of how people acquire
knowledge (Brooks & Brooks, 1999). The theory of constructivism provided the
framework for this study because students have the potential to further their talents in a
flipped model by creating new understandings and by gaining knowledge during the
process of social interaction, helping learners to participate in the give and take of
collaborative activities (Sakulbumrungsil, 2009). In a traditional approach, students
come to class and prepare to take teacher-lecture notes for the class period. In a
constructivist classroom, learning involves applying their newly acquired expertise to
hands on activities and cooperative projects that often connect to real life situations
(Sakulbumrungsil, 2009).
Constructivism is a learner-centered educational theory that asserts that to learn
anything, each learner must create his or her own understanding by making connections
between new information and prior experiences (Henson, 2003). Constructivism has two
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focus points: strong interaction among students and students’ perceptions on the material
presented to them. The strong interaction among students focuses on the students’
collaboration as they work with one another. Students’ perceptions are shaped by the
amount of their involvement in the learning process of the student-centered classroom
(Henson, 2003). The construction process is based on personal interactions and
experiences with the environment. Every student experiences the learning process
differently because they construct different interactions with the environment, in part due
to their background.
Social Constructivist Framework
The social constructivist framework for student learning comes from theorist Lev
Semionovich Vygotsky (Moll, 2014). This framework assumes that children build
knowledge through social interaction that empowers the construction of learning
(Vygotksy, 1978). To Vygotsky, language is the most important medium to build upon
in the learning process. The social constructivist lens acknowledges culture and language
in student learning. Knowledge is built collectively through this process. The lens of
social constructivist theory can be used to describe individual student learning through
problem-solving situations (Wink, 2002). Students are able to go beyond the limits of
their own capabilities in a class by collaborating with classmates on a daily basis.
Interaction with the environment plays a crucial role in learning, according to
Vygotsky (1978). Today, students of all ages are growing up in a culture that heavily
relies on technology. Students are constantly engaging with technology for recreational
purposes. Attending a classroom where technology is not utilized may create a
disconnect between the environment at school and the environment outside of school. A
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classroom that successfully integrates technology as a medium for facilitating learning
may encourage students to be more contented. Students who are comfortable in their
environment may be more likely to be positive when they are constantly interacting with
technology.
The flipped classroom provides the opportunity for students to be practical by
facilitating access to materials. Students with access to the Internet may watch videos
from anywhere on their own time, something many of them are accustomed to doing,
since many of them engage in social media and other internet-based practices. The
technology component allows for the flipped model to potentially fall in line with
constructivist approaches to learning (Parker, Bianchi & Cheah, 2008). Technology
provides embellishment in student interactions both in content and peer communications,
thus enhancing knowledge construction (Parker, et al., 2008).
Problem Solving
Constant social interactions, combined with opportunities to engage in hands on
work in a flipped classroom model, promote an environment that allows for problem
solving. Through the use of investigation, learners acquire and construct their own
knowledge within their social and cultural environments (Vygotsky, 1978). Students are
able to gather ideas in the classroom with the assistance of others and are capable of
enhancing their potential knowledge, which helps develop their skills. In this section, I
will be reviewing empirical studies that focus on problem solving moments in high
school math classrooms.
Allsopp (2014) used Solving Division Equations, an algebraic program, for
problem-solving instruction. The math curriculum was developed to assist students with
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the process of thinking by solving division equations and algebraic word problems using
twelve direct instruction lessons. The first lesson was created with the incorporation of
manipulatives, increasing to more abstract constructions throughout the twelve lessons.
Participants included 262 students from general math classes in a Florida public school.
Ninety-nine of those students were identified as at risk of math failure. The research
instruments used in this study included a pretest, a posttest, and a maintenance test, which
measured the basic algebraic equations and word problem solving abilities. Results
indicated a benefit from the problem skills instruction. Students retained problem skills
from the first week of instruction and were able to apply them throughout the duration of
the twelve weeks of instruction. Participants also showed positive effects on student
performance from pretest to posttest.
Similarly, Maccini & Hughes (2000) investigated the effects of a problem-solving
strategy in an introductory algebra class from a secondary public school located in central
Pennsylvania. The lessons consisted of computing and problem solving involving integer
numbers. Students were able to advance through three levels of instruction: 1) concrete
application/manipulating objects to represent mathematics problems, 2) semi-concrete
application/drawing pictures representations of math problems and 3) abstract
applications/writing mathematical symbols to represent and solve problems. The results
included students improving their strategy-use on all integer operations. In addition,
students responded positively using a Likert scale by strongly agreeing that they became
better problem solvers.
Abidin & Hartley (1998) incorporated FunctionLab, a computer-based program,
to assist with problem solving and the development of problem solving skills in algebraic
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and word problems. The study included a pre-test, a FunctionLab training session, using
FunctionLab in problem solving and a post-test. The ten participants were part of two
training sessions: 1) introduction to the FunctionLab and 2) demonstration of the program
including various tasks. Upon completing a two-phase session, the ten participants
partook in three sessions of the FunctionLab. After each session, students completed a
post-test individually. The results demonstrated student improvement in problem
comprehension, performance, as well as the development of a capacity to self-reflect.
Solving problems that encourage critical thinking had a strong positive impact on
student learning (Allsopp, 2014; Maccini & Hughes, 2000; Abidin & Hartley, 1998). By
utilizing different curricula and various math programs in the classroom, students were
able to build on their problem-solving skills. Based on the results, students showed a
growth in critical thinking skills through problem solving moments in some high school
math classrooms. Vygotsky’s (1978) learning theory of constructivism categorizes
problem-solving moments into two subcategories: social and cultural environment, as
discussed in the upcoming sections.
Social Environment
In a social environment, learning occurs as students exchange background
information and contribute in collaborative activities (Vygotksy, 1978; Sakulbumrungsil
et al., 2009). In a cooperative setting, students discuss their ideas with their peers, which
enhances learning in the classroom. The studies discussed next highlight the importance
of peer interaction during the learning process.
Francisco (2013) discusses the group work of five tenth-graders at a school
district located in a working class community. Students were encouraged to collaborate
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on twelve open-ended mathematical World Series problems in several content elements
of probability. The goal of the study was to identify the student’s development of
mathematical ideas and different forms of reasoning as they worked collaboratively. By
doing so, the students were encouraged to justify their solutions to each other, and given
extended time to work on tasks when needed. The collaborative exercise demonstrated
students had the capacity to develop several approaches to the problems, both correct and
incorrect. Francisco’s findings suggest that teachers need to find ways to facilitate the
student’s mathematical dialogue without taking away the student’s initiative and
ownership of the mathematical activity (Francisco, 2013). The study highlights the
importance of collaboration in learning. Students interacting with one another were able
to build on each other’s knowledge and apply them on real life applications.
Webel (2013) examined the view of eight high school students who worked
collectively to solve open-ended math problems. The study included: 1) observations for
twenty-three classes during the semester; 2) two interviews for each student and 3) video
clip examples shown to each student about their participation. Students worked together
on different tasks that involved applying mathematics to real-life situations. One task
was connected to summer jobs. In self-selected groups, students worked through real-life
problems. The results depicted a more equal distribution of work. Students shared
similar thoughts on collaboration, group responsibilities, idea contributions, dispute
resolution, and persuasion among group members. In regards to collaboration, students
felt that working together was mostly about helping or getting help.
Bosse & Kwaku (2011) developed a geometry course a school located in
Greenville, California, in which students taught lessons to other students through the use
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of the Geometer’s Sketchpad, a geometry software program. For each geometrical unit,
students were required to collaborate by completing a group assignment in which they
focused on a geometry theorem. In the demonstration of each theorem, students needed
to include real-world examples. They also showed positive attitudes in many ways.
Students engaged in these activities were more likely to take pride in the resources they
created while teaching their classmates. Students took ownership of both their individual
and group learning.
In terms of the social environment of the classrooms in these studies, teamwork
was key in having students develop their own understanding of geometric ideas. Student
cooperation had a great impact in math classrooms (Francisco, 2013; Webel, 2013; Bosse
& Kwaku, 2011). Through collaboration, students were able to build upon knowledge
and ultimately have a positive outcome by coming up with a correct solution.
Cultural Environment
Vygotsky’s learning theory of constructivism also recognizes the importance of
the cultural environment. The cultural environment serves as a tool in knowledge, which
is consistently present (Vygotsky, 1978; Wink & Putney, 2002). While many “tools” are
present in student’s lives, for the purposes of this review I will focus specifically on
technology. Currently, we must include technology as part of the cultural environment
since it has become such an integral part of students' lives and it encompasses much of
the interaction that the pupils have with peers, teachers, and parents.
Casey (2013) conducted a largely qualitative case study of student data that came
from online interactions on Ning, a social networking site. The student sample consisted
of twenty-five students with a middle class socioeconomic profile by creating a Ning
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social network and encouraging them to participate in online chats, blogs, groups, and
discussion forums. Results showed that, through the use of social and participatory
media, students connected to a variety of real-world mathematics examples online. The
platform also provided the opportunity for students to share ideas of how math could
relate to real world applications in their lives. Findings of the study showed how the
Ning social networking site provided a more engaging social environment than face-to-
face interactions. According to interviews, participants were very comfortable with
social software tools. The comfort level helped students acquire a better understanding of
the activities designed by the teacher.
Similarly, Goos (2010) contrasted combinations of the factors known to influence
technology integration using four secondary mathematics teachers in his study. Two out
of the four teachers were chosen from The University of Queensland in Australia early
career teachers program who had experienced a technology-rich pre-service program.
The other two teachers were picked from experienced teachers who developed their
technology-related expertise solely through professional development experiences or self-
directed learning. During this study, there were three main sources of data: 1) a scoping
interview inviting the teachers to talk about their knowledge; 2) using a Likert-type scale;
and 3) lessons of cycles consisting of observations, video recordings and interviews.
Results showed that the majority of the low-performing schools can be very inventive in
exploiting available technology to improve students’ understanding of mathematical
concepts. Due to limited resources, teachers seek out professional learning opportunities
consistent with innovative practices on their own time.
As technology develops, it plays a significant role in people’s lives and in the
18
classroom. In most cases, technology plays a positive role in the classrooms (Casey,
2013; Goos, 2010). Beyond subject content, students build skills to utilize technology
and must continue to build their skills to continue to utilize different gadgets and software.
The skills students learn in the classroom may be utilized in the real world. The use of
technology in a classroom contributes to student learning because it is part of their
cultural environment. Teachers play a critical role in classrooms that include technology
in teaching and learning activities.
Teacher Role
Constructivism is a theory of learning and not a theory of teaching (Richardson,
1997). Teachers help guide the students by being facilitators to help with their learning
strategies. If a question arises or a topic is misunderstood, the teacher assesses the
understanding with questions and comments. The role for a constructivist teacher is to
shift from a lecture format to moving around the classroom teaching (Richardson, 1997).
The Montana Public Schools adopted a Computer-Assisted Instruction (CAI)
intervention program for the purpose of helping students recover credits (Snow, 2011).
Teachers were able to access student records including; quizzes, test scores, online
activity durations and dates from seven semesters of the algebra credit recovery classes.
Results were used to better understand the role of an effective teacher in a credit-recovery
program that relied heavily on CAI. It became obvious that having adults wandering
around, looking over students’ shoulders, offering encouragement, or providing
instruction had a positive impact on student achievement. When the students have
trouble understanding the material, teachers were able to provide support and tutor
students because they were knowledgeable in the content area. Additionally, the
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classroom layout and seating arrangement are in place to alleviate chronic distractions
and provide the teacher the opportunity to better accommodate all students. Teachers can
direct students who are steeped in different topics, work at different speeds, and need
additional assistance.
Similarly, Clarke (1997) studied two math classrooms from a school in a
Midwestern town in the United States. The teachers met weekly for collaboration in
mathematics and other curriculum areas. The curriculum was written for the
Mathematics in Context (MIC) project, a curriculum development project funded by the
National Science Foundation and based at the University of Wisconsin. Classroom
observations and interviews with teachers were used to build a picture of the role of the
teacher in the classroom. In addition to the teacher interviews, other mediums of data
included; team meetings, in-service sessions, and semi-structured interviews. Results
showed three different categories of components of the teacher’s role: 1) the use of non
routine problems; 2) adaptations of materials and instruction; 3) the use of variety of
classroom styles; and 4) the use of information assessment methods to inform
instructional decisions. The results address the critical role of the teacher when using the
newly adapted curriculum.
The responsibility of the instructor is to monitor the students’ processing around a
content topic, allowing instructors to design and structure learning activities for students
(Rungpetch, et. al., 2009). By doing so, students are able to construct more knowledge in
a collective activity with the supervision of adults (Vygotsky, 1978). As a result, flipped
teaching can be a representative example of the learning theory of constructivism.
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Empirical Research on Flipped Classrooms
The flipped classroom model began to be explored in higher education in 2000.
Due to the positive feedback in college courses, the flipped model continues to be utilized
and has evolved. Since then, it has also influenced classrooms in K-12 education.
Recently conducted empirical studies in higher education and K-12 education have
resulted in positive feedback from students and teachers. Next, I will analyze the two
types of empirical research: 1) higher education and 2) K-12 education.
Higher Education Flipped Classrooms
Lage, Platt & Treglia (2000) inverted all sections of principles of microeconomics
in a college classroom for a semester at Miami University twice a week for a total of
seventy-five minutes per session. The students were expected to come to class prepared
in order to discuss the current material, which led to a mini-lecture of about ten minutes
per session. Using a quantitative approach, the two instructors administered an end of the
semester survey. Students reported that they felt the inverted model proved to be useful
when studying microeconomics. Students experienced the economics classroom in a
positive manner, when compared to a “traditional” lecture format, citing pleasant
experiences when working in groups. Overall, most students enjoyed this approach to
learning and preferred to take principles of macroeconomics through this format;
claiming learning the content was easier.
In 2008, faculty at California State University, Los Angeles, flipped the freshman
and sophomore Introduction to Digital Engineering courses in order to increase
collaborative project-based learning during a ten-week quarter, each class period lasting
one-hundred minutes (Warter-Perez & Dong, 2012). About 25 to 30 freshmen and
21
sophomores partook in this study. Over 40% of the class time was dedicated to lecturing,
25% dedicated to in-class collaborative projects and 15% to interactive problem solving.
Through the pre and post surveys collected, students self-ranked their knowledge and
skills. Overall, using both a quantitative and qualitative approach, the flipped classroom
generated a positive impact on student learning through the implementation of a variety
of instructional strategies. Specifically, these included: inquiry-based activities,
interactive problem solving, interactive lectures and periodic assessments.
In 2012, the flipped classroom model of instruction was applied to two classes in
the Cinema and Television Arts (CTVA) department at the California State University
Northridge (Enfield, 2013). This flipped model was implemented to study the
effectiveness of the instructional approach. Two sections of the CTVA 361 were inverted
to the flipped model during the Spring 2013 semester. During the semester, forty lessons
were created to provide all students with instructions outside the classroom that included
thirty-eight lessons of instructional videos and two focused on assigned readings. A
sequence for each class session included: 1) watching two to three video lessons for
approximately 1 hour; 2) a short quiz was given during class; and 3) students led small
groups for class activities. Surveys were administered throughout the semester using a
quantitative approach. Results indicated increased engagement with the learning
experience, which was reported to be effective for students in terms of both: 1) learning
the content and 2) increased self-efficacy to learn independently.
Similarly, Zappe, Leicht, Messner, Litzinger, & Lee (2009) flipped an
undergraduate architectural engineering course in the spring of 2008. Students in this
course were expected to watch the lecture outside the classroom, which allowed
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professors to utilize active learning during the classroom time. Using a quantitative
approach, student’s responses from two methods were gathered to evaluate the impact of
the flipped model. The first method consisted of open-responses on two surveys. The
outcome revealed that the flipped classroom had a positive impact on active learning.
The active learning in class included: group work, think-pair-share, clicker questions,
student response systems, and minute papers. Students particularly benefited from
watching lecture videos outside the classroom.
Kay & Kletskin (2012) developed a series of fifty-nine problem-based video
podcasts covering five key areas in mathematics (operations with functions, solving
equations, linear functions, exponential and logarithmic functions, and trigonometric
functions) for a first year undergraduate calculus course. The video podcasts were posted
to the course website over a three week period. A custom-designed tracking tool by the
professors was used to track the total number of video podcast visits using a custom
website. The data showed that about two-thirds of students used the video podcasts
regularly over the 21-day period. Student feedback was collected using a survey and
open-ended response question and it revealed that students found the podcasts useful,
easy to follow, and effective in helping them understand new material over the three
weeks.
Talley & Scherer (2013) used the flipped classroom method at a mid-Atlantic
university for an undergraduate psychology course. To help with the flipped model,
online lectures were introduced the previous semester in order to create the flipped
classroom format. Using an online site that uses whiteboard effects on a computer,
fifteen-minute lectures were recorded by the instructor and were posted on the course
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blog site. Students were able to access the videos using their laptops or mobile devices.
Throughout the course, students were asked to record a lesson video that would be used
in a classroom. The student-made videos were viewed by the instructor and were
reviewed in class. Students reported that the delivery of the lecture material helped with
their understanding of the course content and relevant information.
In spring 2012, a Basic Pharmaceutics II course was inverted for 22 students in
two different campuses for all students enrolled in the University of North Carolina
(UNC) Eshelmean School of Pharmacy (McLauglin, LaToya, Esserman, Davidson, Glatt
& Roth, 2013). The class met two times a week for approximately thirteen weeks, each
class session lasting seventy-five minutes. During this course, twenty-five course
lectures were recorded and transmitted throughout the course website in order for
students to watch before class. Class time was dedicated to active-learning exercises, two
course projects, three midterm examinations, eight graded quizzes and one
comprehensive final examination. Results revealed that the content viewed prior to class
helped them better understand the material presented in class. Students were able to
more easily acquire higher thinking skills required for engagement, empowerment, and
development. Students who engaged with one another were more interested in the
material and were more likely to think critically when applying the concepts they learned.
In essence, the flipped model approach, created an environment that increased learning
and student confidence. Lastly, through development, students guided themselves to
additional content and accessed their own learning.
The outcomes for college students in all courses of architecture, psychology,
mathematics and economics were positive. Students enrolled in semester courses that
24
utilized the flipped model of instruction reported their success was attributed to the way
the materials were presented as well as built-in collaboration (Lage et al., 2000; Warter-
Perez & Dong, 2012; Zappe et al., 2009; Kay & Kletskin, 2012; Talley & Scherer, 2013;
McLaughlin et al., 2013). Next, I will review the use of this flipped model of teaching as
it has been implemented in some secondary school settings.
High School Flipped Classrooms
The flipped model was not put into practice in K-12 classrooms until ten years
ago. Most of the research that has been conducted so far has involved high school
science and math classrooms. The following studies discuss the impact the flipped model
has on student learning at the high school level.
Fulton (2012) describes a high school mathematics class that was inverted at
Byron High School in Minnesota. In 2009, the math department at Byron High School
decided to eliminate textbooks and flipped their classrooms as a result of their poor
performance on the state exam. By doing so, teachers wrote curriculum and used free
materials from online sources to use in the flipped model. As a result, the percentage of
students passing the mathematics state exam increased forty-three percent.
Bergmann & Sams (2012), Colorado high school teachers, flipped their high
school chemistry classrooms in 2012, allowing for slide presentations and annotations to
be recorded into online files. The flipped model was implemented because of students
frequently missing classes for competitions, games or events. In addition, both science
teachers wanted to incorporate more laboratory projects into their block schedule.
Bergmann and Sams created lessons alternately for all chemistry units and applying them
in both their classes. As a result of the flipped model, student and teacher interactions
25
increased during class. Bergmann & Sams (2012) were able to work with students who
were struggling while the advanced students remained challenged by the content.
In the 2011-2012 school year, Clintondale High School in Michigan implemented
the flipped learning model in all freshmen core classes. Teachers videotaped all their
lectures and had students watched the videos as their homework assignments.
Approximately 82 percent of the students owned an electronic device at home to watch
the videos and for those that did not, computers were available to them before and after
school. In the classroom, students worked on assignments that facilitated collaborative
learning. Students in classrooms where the teacher used the flipped model were more
likely to have higher test scores, graduate, and attend college. There was an increase of
nine to nineteen percent passing rate on the state exam across all subjects. This helped
teachers share classroom materials and ensured consistent curriculum with all teachers
and substitute teachers. It also helped students when they were absent.
Throughout the academic year 2012-2013, Davies High School in Fargo, North
Dakota, used the flipped classroom approach for an Advance Placement (AP) chemistry
course (Schultz, 2014). Twenty-nine tenth to twelfth graders were part of the flipped
model program for duration of four months. Students were assigned a lecture video,
ranging from ten to fifteen minutes. Following each video, students completed a video
reflection using Google Forms. The first five minutes of class focused on reviewing
contents of the video and questions. The rest of the class time, about forty to forty-five
minutes, were spent on book problems or other activities. At the end of the study, an
assessment and questionnaire were administered to measure academic performance and
student perceptions. The majority of the students preferred or strongly preferred the
26
flipped classroom model to the traditional one. The most frequent response was in favor
of the pause, rewind, and repeat the lesson feature. Once again, students felt they were
more successful because the technology integrated into the course allowed them to
control the pace of the lesson.
The flipped model in K-12 education has been recently employed (primarily at the
high school level) and empirical research is still limited in scope. Existing studies have
mostly described flipped models that have been implemented in the content area of
science. Still, students in these high schools have achieved higher test scores (Fulton,
2012; Morgan, 2014; Bergmann & Sams 2012; Schultz et al., 2014), similar to the results
from studies of students who have experienced the flipped model in college (Lage et al.,
2000; Warter-Perez & Dong, 2012; Zappe et al., 2009; Kay & Kletskin, 2012; Talley &
Scherer, 2013; McLaughlin et al., 2013). Students attribute their success to the
collaborative environments and the ease of pacing themselves during lessons
(McLaughlin et al., 2013). The integration of technology strongly impacted academic
achievement and student satisfaction level (Fulton, 2012; Morgan, 2014; Bergmann &
Sams 2012; Schultz et al., 2014).
Conclusion
Quantitative research conducted so far is favorable towards the flipped model, but
the model continues to evolve as it is experienced in different classrooms. Little research
has been conducted using a qualitative approach. Qualitative data would compliment
these studies so that we can better understand why students seem to be satisfied with this
approach. In this study, I want to analyze the impact of a math analysis flipped
classroom on students' experiences in learning math. Some research has been performed
27
in science classes, but research has not yet documented the impact of a flipped model in a
high school math analysis classroom. It is important to gain insight about the students'
experience in a flipped classroom because educators need to know more about how to
improve learning for the students. As a result, there is much research to be done in order
for educators to fully understand its impact.
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Chapter 3: Methods
This chapter describes the methods used to analyze students’ experiences in a
high school math analysis flipped classroom. Research questions were identified to
pinpoint specific and measurable constructs in this case study (Heppner, 2004). The
research questions are the following: What is the students’ experience in a math analysis
classroom with a flipped approach? What do students perceive to be strengths and areas
of growth in the flipped classroom model in terms of their engagement and content
learning? The two research questions allow for an open-ended stance and a deep
understanding from the participants (Creswell, 2011).
To address the two research questions, this exceptional case study (Creswell,
2011) was conducted in one high school classroom where the flipped model was utilized
throughout the 2013-2014 school year. A case study design of Mrs. X’s fourth period is
most suitable for my research questions because it focuses on one exceptional class and
explores in-depth perspectives from a group of individuals (Creswell, 2011). In order to
answer my research questions, I collected multiple forms of data including classroom
observations, focus interviews and student work.
Qualitative Design
The qualitative research methodology is the best approach for the study because it
allows me to focus on students’ perceptions of the flipped model. Specifically, the
research questions emphasize identifying what students perceive to be strengths and
needs in Mrs. X’s flipped model classroom. This methodology utilizes general
interviews, observations, field notes and student work that do not restrict the views of the
participants (Creswell, 2011). These data sources are the most suitable for this case study
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because they allow for in depth student responses. The focus group interviews permit
students to respond to questions about their views. Observations help the researcher to
gather information witnessed in the classroom. Qualitative data include different data
sources that triangulate each other to ensure validity and reliability (Creswell, 2011). The
triangulation process corroborates information from different individuals; types of data,
and methods of data collection, insuring the study will be accurate because the
information is derived from multiple sources (Creswell, 2011).
In this qualitative study, the focus group is a better approach for interviewing
since the research questions focus on the views of the group population (Creswell, 2011).
This research focuses on the students’ views and by using this approach the participants
are able to give their opinions of the flipped model in groups. Moreover, students can
build their responses by listening to ideas offered by their classmates in a focus group.
Background for the Study
The flipped model was introduced to me when I was performing observation
hours at High School Y during my credential program in 2010-2011. This new approach
intrigued me and for that reason I decided to study the model more in-depth.
Setting
High School Y, a public school, was founded in 2005 in an urban community in
Orange County, California. High School Y has managed to maintain high Academic
Performance Index (API) scores through the strong commitment from highly professional
teachers, engaged students, and strong parental involvement. The most recent API score
is 817, a 7-point increase from the previous year 2012-2013, meeting the state’s standard
achievement by seventeen points.
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Due to the high demand for enrollment, prospective parents must submit their
child’s name into a lottery-style drawing. Selected students are notified and the rest are
placed on a waitlist. If any openings occur during the school year, the waitlisted students
are enrolled. High School Y prides itself in having strong discipline rules and procedures,
including policies that involve dress code, homework and tardies. Parents and students
must sign an agreement and abide by that agreement in completing their assignments,
maintaining good attendance habits, and complying with the school’s various other
policies in order to maintain enrollment from year to year.
High School Y is home to approximately 2,525 students. During the calendar
year 2013-2014, the student body was 86.1% Hispanic/Latino, 8.5% Asian, 2.4% White,
1.1% Black/African American, 0.8% Filipino, 0.6% two or more races, 0.2% Native
Hawaiian, and 0.2% American Indian. Student enrollment included 6.6% receiving
special education services, 15.9% receiving English language services, and 78.9% are
classified as socioeconomically disadvantaged. According to the district’s website, in the
school year 2013-2014, 77% of the students achieved the proficient or advanced level in
both the mathematics section and English language arts section of the California High
School Exit Exam (CAHSEE). Ten students achieved a perfect score on both English
and math.
High School Y places a high value on academics, athletics, and extracurricular
activities. Approximately two-thirds of the student population is involved in athletics.
All students are required to complete at least sixty community service hours or volunteer
work prior to graduation. The majority of the student population is involved in clubs and
organizations on campus.
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Background of Teacher
Mrs. X started teaching mathematics at High School Y upon receiving her single
subject mathematics teaching credential from Vanguard University, California, in 2007.
Upon completion of her master’s degree in technology, she started employing a flipped
approach for all her algebra and math analysis classes starting in 2010.
Mrs. X, a middle age White/Caucasian female, has been an integral part of the
mathematics department at High School Y for the past seven years. She enjoys a good
rapport with her students and colleagues as evident by her School Site Educator of the
Year Award in 2012. Mrs. X has held leadership positions for the past three years
including two years as a member of the school’s Instructional Leadership Team (ILT). In
addition, Mrs. X was the Math Department Chair from 2010-2012.
While she has taught a variety of math courses, she has mainly focused on Math
Analysis Honors and Algebra 1 during her time at High School Y. Mrs. X developed
curriculum (including video and online resources) and has been utilizing the flipped
model for both Math Analysis and Algebra 1 courses over the past three years. In
addition, she volunteers for before and after school tutoring and support programs
including California High School Examination Exam (CAHSEE) prep course and
California State Testing preparation course for students in order to promote their success.
Mrs. X is a contributing author of a 2014 mathematics flipped model book
published by the International Society for Technology in Education. Mrs. X’s trainings
and staff development include the following:
● Creating and leading professional development opportunities for teachers on-
site, but also at the district and county level. Topics include: Strategies for
32
Teaching English Learners, Implementing the Daily Assessment Intervention
Model, Thinking Maps, SIOP (Sheltered Instruction Observational Protocol)
Strategies, Introducing the Flipped Classroom, Integrating Technology in the
Classroom with the Flipped Classroom, Engaging Parents in Flipped Learning,
and Structuring Flipped Learning for Student Success.
● Creating and leading online Professional Development on Flipped Learning for
teachers across the globe. She leads multiple webinars hosted by a variety of
organizations such as: Sophia.org, SchoolWires, and the Flipped Learning
Network.
● Presenting and sharing Mrs. X’s experiences at local and national conferences
and trainings, including: the CUE Flip Tour, NSBA (National School Boards
Association) conference, and Cerritos College CTX program.
Given Mrs. X’s qualifications, studying her classroom as an exceptional case makes
sense. In the 2013-2014 school year, Mrs. X taught three sections of math analysis; one
of which was the focus of this analysis.
Limitations
There are a few limitations to this study. The study includes one math analysis
flipped classroom, which is not representative of the other two flipped classrooms taught
by Mrs. X. The findings of this investigation may not be representative of Mrs. X’s
flipped courses beyond the group of students in this case study. Furthermore, the
findings of this study are not generalizable to a larger population.
Participants
At the suggestions of Mrs. X, I conducted this case study in her fourth period
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math analysis class, a course traditionally taken during students’ third or fourth year of
high school. Mrs. X enjoys a high degree of engagement and participation from her
students, making this an exceptional case. All thirty-six students from the fourth period
math analysis class were invited to participate in the study.
The fourth period class consists of thirty-six high school juniors and seniors.
Sixty percent of the students were Hispanic/Latino, thirty percent were Filipino/Asian
and the remaining ten percent were Caucasian/White. The class has equal gender
representation, and students range from 16 to 18 years of age. Most of the students were
in eleventh and twelfth grade. The majority of the students had never been exposed to a
flipped model mathematics classroom prior to this school year. All students are in
Advanced Placement and/or Honor classes.
A cafeteria-style checklist consent form for participation in the research was used
to allow for greater student and parent choice on the assent/consent forms. Students
participated in observations, collection of work, and focus group interviews after they and
their parents granted assent/consent. Out of the thirty-six students enrolled in the class,
fourteen students signed up for partial or full participation in the research study.
The participants included three boys and eleven girls. The research study
consisted of eight Hispanic/Latino, five Filipino/Asian, and one Caucasian/White student.
Three students assented and their parents gave consent to one or more of the following
parts of the study: focus group interview, audio-recorded group interview, student work
and observations. The rest of the participants assented and their parents gave consent to
all parts of the study as shown on Table 1.1. The participants were allowed to self-select
their pseudonyms, which were used to keep their identity safe.
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Table 1.1
List of Participants
Student Name
Focus Group Interview
Audio-Recorded Focus Group Interview
Observations Student Work
Eden X X X
Bluey X X X X
Bom X X X X
Nessa X X X X
Gloria X X X X
Neocat X X X X
Superman X X X X
Spiderman X X X X
The Doctor X X X X
Wally X X X X
Charlie X X X X
Stripes X X X
T-Rex X X X
Telephone X X X X
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Data Collection
The data collection tools use in this qualitative case study included: observations,
field notes, focus group interviews, and collection of student work.
Observations
The first part of the data collected was in the form of six classroom observations,
each lasting approximately 55 minutes. Open-ended, firsthand information was gathered,
focusing on the utilization of technology, student engagement, teacher student interaction,
and student interaction (Creswell, 2011). At the beginning of each week, Mrs. X
communicated with me the days when no summative assessments were given, allowing
me to observe lessons, activities and group collaboration.
As Creswell (2011) points out, “multiple observations is the best approach to
understand the site and individuals (pg. 237).” The classroom observations for this study
were completed during fourth period twice a week for a total of three weeks. The
classroom was divided into eight teams with five to six students in each team. Since the
classroom was divided into six groups, on the first observation, I focused on one group of
students and rotated around all groups during the remaining five visits. I had the
opportunity to converse with all student participants. Questions were asked to students
and the teacher for clarification when necessary, though minimal to no disruption of the
regular school activities took place as a result of the research project.
Field Notes
Data were collected through observations and field notes during each visit. Field
notes were taken utilizing a time interval frame from the beginning of class until the end,
approximately fifty-five minutes. The field notes also focused on the instructional
36
activities, student-to-student conversations, and interactions between students and teacher
and instruction (Creswell, 2011). At the end of the class period, I wrote down a
reflection of the class period that included personal thoughts, broad ideas and themes that
emerged during the observations. This helped me to identify a daily routine that was
established in Mrs. X’s classroom.
Student Work
As part of each regular unit assignment, students were required to write
summaries and ask questions in their notebook. In addition, students were required to
post blogs and comment on other students’ blogs from the units, allowing students to
write their thoughts about the math content. Because my research is based on students’
perceptions of a flipped classroom, it was important to include student work to learn
more about their experience with the lessons and to see what they were learning. Over
six observations, I collected students’ work from each group I observed.
Focus Group Interview
Students from Mrs. X’s fourth period math analysis class were invited for a one
twenty minute focus group interview. Those students who were interested were able to
write down their name on a list located on a bulletin board next to the teacher’s desk.
Once three or more students were on the list, a focus group was created. Two student
focus groups were used to provide insight on the flipped classroom model during
lunchtime. There were a total of five students who participated in the first focus group
and the second focus group consisted of nine students. The interviews took place in the
school’s library media room and were audio-recorded. The students were asked to reflect
on their experience in the flipped classroom. In each focus group interview, the
37
researcher asks a small number of general questions and obtained responses from the
individuals in the group (Creswell, 2011).
The focus group interviews contained three open-ended questions that encouraged
the participants to express their perceptions and relay their experiences in a math analysis
flipped classroom. The following questions were addressed in each of the two focus
group interviews:
1. Tell me what is it like to be in a flipped classroom. How does it compare to
other learning experiences you have had in school?
2. How does the flipped classroom impact your learning? As a result of the
flipped classroom, do you feel you are a stronger mathematician? Why or
why not?
3. What do you wish was different in the flipped classroom in order to
improve your learning experience? What would you keep the same?
Each student was given the opportunity to formulate his or her response to the three open
ended questions by providing them a copy of the questions a week ahead of time. They
were able to respond at their own pace and contribute to each other’s responses during
the interview itself. During the focus group interviews, questions were asked one at a
time before moving on to the next one.
There were times the students themselves clarified the questions. For example, in
the first focus group interview, eleventh grader, Bluey, used the term “WSQ.” After
clarification, I learned that the “WSQ” was a daily assignment that stood for Watch,
Summary and Question from each video lesson that students had to complete. Students
were given the opportunity to add any information at the end of the focus group
38
interviews. After each focus group interview, the researcher used the pseudonyms
created by the students to transcribe the audio recordings.
Data Analysis
In order to learn about the students’ experience in a mathematics analysis flipped
classroom, I analyzed the data in three ways: 1) the use of time; 2) the problem solving
moments through lenses of the social environment and cultural environments; and 3) the
strengths and areas of growth for the model in this classroom.
Time
I first needed to analyze how time was used in the flipped model approach. I
looked across the six classroom observations and recorded my field notes using time
increments as a way to establish a baseline for what was happening in the classroom.
This allowed me to get a sense of how time was utilized in this flipped model approach.
Problem Solving Moments
By analyzing students’ learning experience in the flipped model, I was able to
code for problem-solving moments in mathematics. In the theoretical framework of
Vygotsky (1978), problem-solving moments are defined as “the level of potential
developmental level under guidance or in collaboration with more capable peers.
Through the use of problem solving moments, learners acquire and construct their own
knowledge within their social and cultural environments (pg. 44).” Students are able to
gather ideas when a problem-solving moment occurs in the classroom with the assistance
of others. As a result, students are capable of further enhancing their potential knowledge
that helps develop their skills.
Using Vygotsky’s (1978) framework, I recorded a total of sixty problem solving
39
moment codes. An example of a problem solving moment was when a student was
working with his teammate on a math problem. A non-example was a student picking up
a unit practice problems packet for his group. I realized that, given the large amounts of
codes in this category, the problem solving moments could be categorized further into
two additional categories: social and cultural environment. I will describe these
subcategories next.
Social Environment
The flipped model provides an opportunity for a different participation structure
in the classroom. I analyzed the problem solving moment data set using a subcode of the
social environment. This code was applied when students were in collaboration with
other students about math related content. I defined social environment as moments
when students were able to work closely with their peers and teacher in the classroom.
As result, coding for the social environment was used to understand the capability of the
flipped model approach. Due to the large amounts of codes in the social environment, I
created two further sub categories to help me narrow the problem solving moments in
social environment: peer assistance and teacher assistance.
The two sub categories were looked at through the lenses of a peer and a teacher.
In the peer assistance category, the students were observed assisting other students during
problem solving moments. For example, if I observed a student asking questions to peers
about how to solve a certain problem then the observation was coded within the social
environment of peer assistance. On the other hand, a non-example for the social
environment moments with peer assistance was when a student was asking another
student about the game time for the CIF Water Polo game. There were a total of twenty
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codes for social environment moments of peer assistance.
The second category, teacher assistance, of the social environment for the
problem solving moments, students had the opportunity to ask the teacher for assistance
as they completed their assignments. In this teacher assistance category, I looked for
moments where students interacted with their teacher during class in order to solve a
problem related to their math work. For example, if a participant asked the teacher about
which formula to use in order to complete the problem, then it was coded within social
environment of teacher assistance. A non-example of a social environment moment with
teacher assistance would be a student discussing with the teacher something other than
math work, such as what is on the lunch menu. There were a total of ten codes for social
environment moments of teacher assistance. When I thought of the problem solving
moments I analyzed those codes through social and cultural environment in order to look
for trends.
Cultural Environment
The cultural environment refers to the instruments that were the most
predominant in the flipped model classroom. Since the flipped model focuses mostly on
technology use rather than a standard textbook, I decided to code for moments when
students were using electronic devices to solve their math problems and mentioned
during interviews. The tools that were consistently present and used in the majority of
the class included: iPhones, iPods, computers and calculators. Based on these mediums I
divided the codes into three subcategories: iPods/iPhones, computers, and calculators.
Although iPhones and iPods are different electronic gadgets I classified them in the same
sub category because they had the same use in the classroom.
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The electronics were used during problem solving moments when completing a
math task and/or watching math videos. This category also applied to interviews and
observations. For example, if a student mentioned during an interview the use of an iPod
to log into the Kahoot.it website then the interview was coded under the cultural
environment category of iPods/iPhones. On the other hand, an observation involving a
student using their iPod/iPhone to look up their math test scores during class would not
fit into this category. Five codes were used for computers, ten for calculators and fifteen
codes for iPhones/iPods across the six observations.
Strengths and Areas of Growth
Finally, I categorized the data for strengths and areas of growth in the flipped
classroom. The code for strengths was used in observations and interviews for students
who benefited from an activity or assignment in the flipped classroom based on their
words. Keywords used in identifying strengths included: “useful”, “helpful”, “I liked it”,
“let’s do more”, “fun” and “informative.” For example, if the participants mentioned that
a website was useful for a lesson or activity then that was coded under strengths. A non-
example would be if a student mentioned that an activity or assignment was useless.
The second code, areas of growth, was used for areas of improvement in the
flipped classroom. This code includes students’ opinions regarding things that can be
strengthened further in the flipped classroom. Key words used to identify areas of
improvement included: “frustrated”, “boring”, “wasted”, “long”, “tired” and “pointless.”
For example, if the students mentioned that a website was pointless then that was coded
under areas of growth. However, an example of student failing an exam was not coded as
an area of growth.
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Conclusion
This qualitative research case study was conducted in one math analysis flipped
classroom at High School Y. I was able to study students’ experiences in a flipped
classroom through observations, student focus group interviews, student work, and field
notes. A qualitative approach was deemed suitable for this study because it helped gather
open-ended responses from the participants during the six visitations. The theoretical
framework from Vygotsky (1978) was used to code problem-solving moments in
mathematics. Codes for the cultural and social environment were used to further
categorize problem-solving moments. I was able to narrow down my data by creating
sub groups of the problem solving moments in the social environment into peer and
teacher assistance. In the next chapter, I analyze the results.
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Chapter 4: Findings
In this chapter, I present the findings of my data analysis. The purpose of this
study was to document students’ experiences in a math analysis classroom using a flipped
model. The findings mentioned in this chapter are derived from classroom observations,
student work, field notes and student focus interview groups that were first broken down
into Vygotsky’s (1978) framework of problem solving moments. In order to identify
problem solving moments in the mathematics flipped classroom, the data were analyzed
in three ways: 1) a class time analysis, 2) a categorization of social environment and
cultural environment, and 3) a focus on the strengths and areas of growth from the
students’ perspective, based on their experiences with the model.
Background of This Flipped Model Classroom
In Mrs. X’s flipped classroom, students were expected to watch a recorded lesson
video prior to attending class as a homework assignment. Students came to class with
any questions that may have arisen during the lesson using their WSQ (Watch,
Summarize, Questions) packets. The WSQ is something that Mrs. X came up with when
she started flipping her classes in 2012 as a way to hold her students accountable for 1)
watching the video lessons and 2) coming to class ready with questions in order to 3)
apply their knowledge to real world scenarios. Mrs. X created a WSQ for each unit,
which has a total of five to eight sections, each ranging from fifty to eighty problems.
Working at their own pace, students were expected to complete each packet
before completing the unit. Typically, this process would take three to four weeks. In the
watch section (W), students were expected to watch the video from the lesson. Videos
created by Mrs. X for all math analysis lessons were available online on her website. The
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(W) section needed to be signed on the WSQ packet by a classmate or parent agreeing
that the student had watched the video lesson. In the section of the Summary (S),
students were required to complete a summary report (about one paragraph) about the
lesson content in their math notebooks. Lastly, in the question (Q) section, students were
allowed to write down clarifying questions about a particular component of the lesson.
The (Q) section was completed on the student’s math notebook and helped students study
for unit assessments.
In addition to the WSQ packets, students had a total of twenty problems to
complete from their Unit Review Packet. In this unit review packet, students had a
combination of algorithms and “justifying your reasoning” problems. Upon completing
two to three lessons from the unit, students were then required to complete quizzes
independently during class. Quizzes were completed throughout the class period after
students finished all assignments. The classroom was set up so that all the quizzes that
needed to be taken were only allowed on the right side of the classroom, close to the
teacher’s desk. Once students turned in their quizzes, they were given back with
feedback within one school day. The students were allowed to retake any quiz before the
unit exam.
At the beginning of each class, Mrs. X made sure the class was more structured so
everything that needed to be done was successfully completed within the fifty-five
minute class period. In one of the observations, Mrs. X assured the class that:
There is something that needs to be done, we don’t miss a second of the class time,
today’s agenda will be a review for tomorrow’s test but this review will be for the
entire class period. We have a lot going on today, make sure you have an iPod on
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your desk ready to go.
Attaching a structure to the flipped model helped increase learning time in Mrs. X’s
classroom. One of the daily routines for students was to have their electronic devices on
their desks at the beginning of class. For students who did not own an electronic device,
Mrs. X gave them the opportunity to check out an iPod (ten iPods were provided by the
school district to use in the classroom) in exchange for their identification cards. There
were a handful of students who utilized their personal iPhones in class on a daily basis
since they had internet access.
In order to provide insight of the flipped approach, a time pattern was created to
help better understand the model. The time allowed me to get a sense of how daily
activities were accomplished. In the next section I explain a breakdown of a typical day
in the flipped classroom.
Time
In order to categorize the data, a class time analysis was used to establish a
baseline for what was happening on an average day using time increments. In all six-
classroom observations, less class time was dedicated to lectures and more to hands-on
activities and project-based learning structures. The use of time was important to look at
in order to partially answer the research questions regarding the flipped model. To help
record the time on the daily activities observed, Table 2.1 was developed.
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Table 2.1
Use of Time
Activity Time
Announcements 2 minutes
Warm-up activity/Review from Video Lesson 5 minutes
Lesson Content
Teacher Lecturing
Group Collaboration
Independent Support
Guided Practice
Hands-on Project
5-7 minutes
35-40 minutes
Closure/Review/Final Announcements 5 minutes
Based on the Table 2.1, lesson content was a major component in the flipped classroom.
After reviewing the previous night’s lesson, Mrs. X usually lectured for about five to
seven minutes based on the content of the assigned lesson. After lecturing for about five
minutes, Mrs. X said that she “will give the rest of the class period to complete the
review packet.” During the review time, students were allowed to work on their unit
packets individually and/or with their table classmates.
There was a recurring trend in the classroom observations where no class time
was wasted on non-mathematical information. Lectures from Mrs. X were only for
clarifications from the previous night’s lesson. There were a couple of times that Mrs. X
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took a little more time on teacher lecturing, especially when reviewing for a unit exam.
Students like eleventh grader, Charlie, compared the teacher lecture to his other classes.
He explained how, “it [classroom lecture] makes it different because I can review a
lesson on my own time. There are other classes where I often have to be listening to
every single detail and sometimes missed something while trying to figure something else
I could be confused on.” Having a little portion of the class time focused on teacher
collaboration helped students like Charlie review the material at their own pace rather
than having to hear the teacher lecture for a major part of the class.
Since most of the students watched the same lesson video, Mrs. X was able to
elaborate or clarify any misunderstandings, depending on the students’ questions from
their WSQs. For example, on my first observation, eleventh grader, Superman, was
confused about the lesson on permutations and combinations. Mrs. X was able to clarify
the difference between a permutation and combination by giving an extra example that
was not part of the video. Mrs. X made sure to mention the difference in combinations
and permutations was that “in combinations, [the] order does not matter.” This helped
the students clarify the difference between a permutation and a combination, then apply it
to their practice problems.
The majority of the class time was focused on the group collaboration that
included: independent support, guided practice and hands-on projects. In the independent
support, students were able to receive help from peers on math problems from each unit
packet. The independent support was mostly completed at the beginning of the unit in
order for students to understand the new concepts. The problems students completed
from each unit packet during the independent work prepared them for the unit exam.
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Guided practice was defined as either students working with the teacher or
students working with their table partners. An example of guided practice included the
teacher going over practice problems with individuals, small groups, or the whole class
before a unit test. Most of the practice problems included review problems where
students had trouble and/or needed additional clarification. For example, in the unit on
trigonometry, students like twelfth grader, Neocat, were having trouble with the concept
of co-terminal. Neocat understood the content but had trouble memorizing the key
concepts. Mrs. X made sure to clarify the concept of co-terminal using a kinesthetic
activity to help students like Neocat. Mrs. X had students stand up and perform an angle
using their arms. Mrs. X said: “with your arms do a standard position. Co-terminal of
angle 150 degrees. Give me the positive terminal. I will give you a minute to think about.
Go back to standard position with the arms again.” Students like Neocat, used both arms
to create an angle that was a co-terminal to the angle of 150 degrees. Once this
kinesthetic activity was completed, students were able to use their arms as an aid to check
answers when completing problems from their unit review packets.
Hands-on projects included times when students were working with their table
partners on watching videos or reviewing activities with the purpose of gathering
information with real world scenarios to further enhance the students’ understanding and
comprehension of the content. When assignments of blogs were given, all students
contributed to the blogs individually or with a partner, depending on the assignment.
Blog
All students created a free blog at the beginning of the school year using the free
website www.blogger.com. Students were given step-by-step instructions on how to
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create their own blog page by using their free Google account. Upon creating a blog
page, students were asked to choose a title, web address, template and title for their blog
that they would use throughout the school year. For example, in Nessa’s blue blog page
she created a section titled “About me.” In this section, she shared some pastime
activities including volleyball and folkloric dancing. She mentioned how her main focus
for college was to have a career in the math field. She enjoyed helping other people and
if she was not doing something she felt unproductive.
On the other section of Nessa’s blog was the “Home” section. In the “Home”
section, Nessa included all the blog posts she had created in the course since the first unit
in the month of September. The blogs were saved according to the month. When clicked
on the March unit, Nessa had a total of six blogs. The blogs were from Unit O, Unit P
and Unit Q with the titles of Solving Clues Using Identities, Pythagorean Identities,
Solving Law of Sines/Cosines, How to Derive the Law of Sines, How to Solve
Depression/Elevation Problems and How to Derive Special Right Triangles. In each blog
post, a video was created using a Word Problem Play List and uploaded to the post. For
example, in the blog post of How to Solve Depression/Elevation Problems, Nessa created
a picture of her assigned problem to help her visualize the concept and she uploaded on
her post. This helped Nessa described step-by-step instructions on how she derived the
solution. Each month she had from two to six blogs depending on the unit of study.
All students were responsible for completing at least two blog entries per unit on a
given question provided by Mrs. X. Throughout each unit Mrs. X clarified if the blog
would be accepted individually or with a partner. Mrs. X tried to have one written
individually and one written with a partner for each unit. For example, if students
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completed an individual post at the beginning of the unit, then the second blog post
became a partner blog.
Partners for blogging were made up of only two students. Students were able to
choose a partner from their table. For example, eleventh grader Nessa and twelfth grader
Bom worked in collaboration for the blog posts of the Trigonometry Unit (Unit P). In the
partner blog post, both students worked on two problems together and each of them had
an active role in the creation. The first problem consisted of writing one Law of Sines
word problem. This problem needed to include the information about two angles and one
side. The second problem consisted of the Law of Cosines using one angle. In order for
students to upload the picture of the problems, Nessa and Bom embedded the video using
the Word Problem Playlist. The Word Problem Playlist (WPP) was a hyperlink that was
accessible to all students on their blog sites in order to include pictures. When
completing the WPP, Nessa needed to include on her blog the following: “This WPP 13-
14 was made in collaboration with Bom. Please visit the other awesome posts on her
blog by going here [the word here was hyperlinked with the URL of Bom’s blog site].”
After completing the blogs for the unit, each student was responsible for commenting on
two blog posts of other students. Students were able to reference the blogs when trying
to practice additional problems or prep for a unit test.
The time analysis was a baseline to determine average classroom activities in a
flipped classroom. By the use of a time analysis, the activities in the classroom were
broken down into sections including: announcements, warm up, lesson content, and
closure. In the next section I will discuss how I analyzed the problem solving moments.
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Problem Solving Moments
I was able to code problem-solving moments using Vygotsky’s social
constructivist framework (1978). For Vygotsky (1978), problem-solving moments are
defined as “the level of potential developmental level under guidance or in collaboration
with more capable peers.” (pg. 44). While the time analysis gave a picture of the
classroom as a whole, the problem solving moments provided a micro view of the model.
In the problem-solving moments, students received help with the assistance of
others. The learning theory focused on the interdependence of social and individual
processes in the co-construction of knowledge (Sullivan, 1996). Teachers facilitate a
classroom environment in which students can learn through interaction. In Vygotsky’s
(1978) learning theory of constructivism, he explains how “learners acquire and construct
their own knowledge within their social and cultural environments (pg. 46).” An
example of a problem-solving moment in this study was a student working on a project
with their team partners. Students were capable of further enhancing their knowledge,
which helped developed their skills, as a result of problem solving moments.
Through observations, field notes and focus group interviews, I coded a total of
sixty problem solving moments. Because this data was so large, I further utilized
Vygotsky’s framework to focus on two key aspects of the classroom; the social and
cultural environments, which are discussed next.
Cultural Environment
The cultural environment referred to the tools that were most predominantly used
in the flipped model classroom. I was able to code cultural environment using
Vygotsky’s framework (1978). From the theoretical framework of Vygotsky (1978),
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cultural environment is defined as “the tool that is consistently present.” All activities
and lessons observed in the flipped classroom dealt with electronic devices that helped
students learn the math concepts. Eleventh grader, Superman, agreed that the students
had to, “rely on a computer/smart phone and internet/data” for the flipped classroom.
Using an electronic device was a key component for the success in the flipped model
classroom. This cultural environment was categorized into three categories: iPhone/iPod,
Calculators and Computers, as discussed in this section.
iPhone/iPod
The first category derived through observations, interviews and student work was
the usage of iPods/iPhones in the classroom. Students like eleventh grader, Bluey, used
her iPhone at the beginning of class to review the lesson from the previous night. Bluey
said, “the more I watched the video lesson, the more information I can use before my
quiz.” Not only did electronic devices helped students like Bluey excel in the class but
gave them the confidence to repeat the lesson at home or school.
iPods were used in the classroom on a daily basis to look up lessons or receive
extra assistance. Mrs. X had a total of 10 iPods in her classroom (two per table).
Students were able to use their own iPod/iPhone for activities done in class or to watch
videos. One of the activities completed during the last observation was a test review
using the Kahoot.it website.
Mrs. X made sure all students logged into Kahoot.com and added their partner’s
name. Students like Nessa were able to partner with her table classmate, Gloria, during
the test review in the Unit of Trigonometry. Nessa was the phone monitor, which meant
that she needed to lock in the answer on her iPhone once they both agreed on the solution.
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At the start of the activity, Mrs. X showed the students how to change the setting on their
phones in order for the screens to not shut off after a minute. Adjusting the time allowed
the students to not automatically log off from the review session because the activity,
Kahoot.it, allowed 120 seconds per problem (maximum limit) to solve. Mrs. X gave all
the students a list of questions without multiple-choice answers the day before allowing
them to prepare during the actual review. Before the review activity, students had ten
minutes to work on the unit review packet with their table partners.
When the review activity started, the students had the answers from their review
packet, but after a couple of problems, the students started to take more time to work on
them (especially those students who did not complete at home). There were a few
instances where some answers did not show up on the screen, so students like Charlie and
Wally had to go back to find their mistakes. After students had submitted their answers
from their phones, Mrs. X had the students raise their phones and Mrs. X was able to
check the partners that had the incorrect answer (if the screen turned an orange or red
color then the question was answered incorrectly). Mrs. X allowed students who had
their answers marked correct (green color screen) to help out the struggling students.
This team challenge help students complete review problems as the teacher walked
around and provided extra help.
The tool (phone) use allowed for independent learning inside and outside the
classroom for all types of students and situations. In an interview, Mrs. X talked about a
student being out for surgery for about two to three weeks. Because of the flipped model,
the student was able to catch up with the rest of the class before coming back from
surgery with the assistance of her peers and the videos from the phone.
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In another example, eleventh grader, T-Rex, made it clear that her school load and
job were hard to balance. T-Rex stated how, “during [her] lunch and break time [she] can
watch videos using my iPhone.” Students had a total of thirty-five minutes for lunch and
were able to watch the lesson video while having their lunch. The majority of the video
lessons ranged from ten to twenty minutes, T-Rex was able to review one video during
each lunch, giving her the extra opportunity to re-watch the videos especially before a
unit exam.
Computers
There were times when students couldn’t get access to the internet at home. At
the start of each class, students who were unable to watch the previous night video
lessons had the opportunity to go on the computer at the beginning of class. Mrs. X gave
the students a few minutes at the start of the classroom to watch the lesson. Students like,
twelfth grader Stripes, gathered her materials, including earplugs, and moved back to the
classroom by a computer to see the missed video lesson. During my first observation,
Stripes was watching the lesson on permutations and combination. Stripes had not
completed the video at home since she arrived home late from her game the night before.
As Stripes was watching the video lesson, she made sure to complete the WSQ packet.
In doing so, she was able to pause the lesson and continue her notes.
Mrs. X also modified videos when needed to help improve instruction. One
example observed was the use of “pause” component on many of Mrs. X’ video lessons.
Pausing the video was a key component that helped all students whether it was using a
computer, iPhone or iPod. This school year, Mrs. X had students pause the video during
the actual lesson on many videos. This gave the students the opportunity to pause the
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video and look through their notes and apply their knowledge on the problems from the
WSQ and/or Unit Review Problems packet. For example, when I observed Stripes
watching the permutations videos, Mrs. X said on the video a couple of times, “now I
want you to pause the video and try it on your own.” Giving the students the opportunity
to pause the video was successfully implemented in many videos. Students like Stripes,
used Mrs. X’s cue to pause the video in order for her to complete the practice problems.
On a similar note, students like Neocat had the opportunity to intuitively pause the
video at any time without waiting for Mrs. X to mention it. When observing Neocat
using the class computer to watch the lesson on trigonometry, she paused the video every
minute to practice her word problems on the law of sines and law of cosines.
Calculators
Calculators were a must in the math analysis flipped classroom. Students were
able to check out a graphing calculator with the teacher by leaving their identification
cards before class started. When reviewing a trigonometry lesson, twelfth grader, Gloria,
asked her teammate, “What trigonometry ratio can I use in my calculator?” when she got
confused. With the assistance of her partner she was able to use the graphing calculator
to help her guide towards finding the solution of the math problems. Gloria made sure to
ask for the assistance of her table buddy when using the calculator functions.
The calculator played an important role in the instruction of the flipped model.
Mrs. X’s students understood the basic skills, but she wanted to push all her students to
understand the actual content of the classroom. The time in class was not spent on basic
calculations, but on learning the concept of the day.
The cultural environment was a key component to look at when discussing the
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tools of iPhones/iPods, computers and calculators. After narrowing my findings, I was
also able to code for aspects of the social environment, as discussed next.
Social Environment
A code of social environment focused on the moments when students had the
opportunity to work with their peers and teacher in the classroom. An example of a
social environment was when a student was observed asking questions to another student
about a specific math topic. In the social environment, the problem solving moments
were further categorized as peer assistance and teacher assistance to help narrow them
down.
Peer Assistance
As students worked closely to help other classmates, the data was coded as peer
assistance. Students worked at different paces with other students but had to complete
the quizzes individually anytime over the course of three to four weeks. Eleventh grader
Bluey, mentioned:
The whole idea of the flipped classroom is for everyone to understand and going
at their own pace and being able to take quizzes when you are ready like I think
it’s going because we are not forced to cram it all on our heads and we don’t
completely understand it and wait until everyone is caught up.
Working at one’s own pace is key for peer assistance because students can receive
additional help from their classmates at any time regardless of whether or not they are on
track with the teacher’s recommended pacing. Students like Bluey were able to, “pause
the videos when needed and assist classmates when someone needed further clarification.”
Since Bluey had finished his work early, he was able to put his math skills to work by
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helping other students.
As already mentioned, students taught using the flipped model were assisted by
their classmates at any time throughout each unit. This especially helped students who
participated in extracurricular activities and needed to miss class time because of field
trips, events or academic related activities. For example, there were a total of four
participants that needed to be excused before spring break because of a field trip to
Washington D.C. As Mrs. X mentioned, “since spring break is around the corner, I have
those cheesybuckets [students] that will be missing two or three days before spring break
starts. You need to make sure you choose a partner in order to complete the unit test
before the break.” Since spring break was around the corner, Mrs. X gave the
opportunity to those students who had been caught up to speed to work on the test if they
were going to miss class because of other school activities. The students who had
planned to miss a couple of days were responsible to come in before or after school with
their chosen partner to complete the unit test. Partners for team tests were made up
based on a five percent differential range of their current grade. Students were able to
choose a partner who had a grade five percent higher or lower from their own score.
Other students like Nessa had the flexibility to watch the videos with a classmate
until the class began. As Nessa mentioned “some nights I wouldn’t do the homework,
but I had all the way up until class to do it and my partner helped me. There wasn’t a set
that was due at midnight so it helped me when I had busy afternoons.” Not having an
assignment due at midnight helped Nessa balance her class workload schedule and
receive the additional help from her peers at any time of the day. Nessa, along with the
majority of her classmates, were taking one or more Advance Placement classes. This
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helped make the flexibility of the learning a key point in the flipped model.
Peer assistance is a different experience in the flipped classroom. More
responsibility was put on students in the flipped model as opposed to a traditional model.
Wally said:
In this class, I definitely feel a lot more responsibility and my ethics are more
grounded. Yes, I learn at home but this way class time is spent learning the
technique and the information with the help of my peers. I fully comprehend it all
rather than sitting there bored taking notes and listening to the teacher drone on.
Students like Wally comprehended that independent learning was done at home and
practicing the material was completed in the classroom with assistance of peers, which
made the class more interactive and social. The flipped model helped students practice
the material in class after learning it the night before.
Stripes explained how, “the learning method overall is just different. Through
this class I learned to teach myself independently but also received great help from my
peers.” Students like twelfth grader, Stripes, were able to adapt to the peer assistance
learning method throughout the year. Stripes love the idea of blogging with a partner.
Similar to Nessa and Bom, Stripes made sure to work with her partner to complete all
blog posts for each unit. This allowed Stripes to collaborate with her partner and upload
the same video while still getting credit for the work.
Mrs. X made sure all students were logging into Kahoot.it.com and added their
partner’s name. As previously mentioned, students logged into the Kahoot.it website and
logged in with a name made up from their partner. For example, Nessa and Bom
collaborated together to come up with the name “Team Nessa&Bom.” Their name
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appeared on the Kahoot.it.com screen that was shown on the classroom screen. As Mrs.
X closed the “Adding Your Name” link, students then proceed to wait for the first
question to be shown by Mrs X. As the first question appeared on the screen, Nessa
collaborated with Bom on finding the correct solution in less than two minutes. Both
used their notes and decided on a solution from the multiple-choice option and submitted
their correct answer on their electronic device. Bom and Nessa alternate the device and
both had an equal opportunity to submit their answers once they both agreed.
Teacher Assistance
The sub-category of teacher assistance in the social environment focuses on
student-teacher interactions on problem solving moments in the classroom. Students had
the opportunity to ask the teacher for any questions they might have.
Eleventh grader, Telephone, made it clear that the flipped model class was
different in Mrs. X’s room because “the lessons are not recorded by other people from
other states, instead our teacher [Mrs. X] records them and we can ask questions to her
about them.” Telephone was enrolled in a science class that many of his classmates had.
His science teacher had a similar video component as Mrs. X, but these were created by a
teacher from the East Coast. Asking questions to Telephone’s science teacher was
difficult because at times the teacher did not have an immediate response. Mrs. X is the
teacher who recorded all the lessons from the units. This helped Mrs. X clarify any
misunderstanding students had from the lesson they watched. When many questions
were asked about a concept, Mrs. X would go back and revise her videos to help for
further re-teaching and future classes. For example, as previously mentioned, adding the
“pause” component was seen throughout more video lessons that were modified by Mrs.
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X in the current school year. Mrs. X wanted to make sure students had some extra time
to attempt the problems on their own.
In addition to incorporating the flipped model, Mrs. X made the learning
environment unique. In the six observations visits, Mrs. X was an active participant with
all students. Twelfth grader, The Doctor, stated “the environment is just so friendly and
understandable. There are no judgments on you if you ask a stupid question or if you ask
for help on a problem or a lesson to the teacher. It really made me feel welcomed and
more secure. We sang and danced.” Going out of the way from the ordinary teacher
lecturing was seen throughout the observations of the flipped classroom. Mrs. X was also
building a relationship with all her students, which it seemed they really responded to.
Learning in the flipped model required a tremendous amount of intense work for
Mrs. X. Mrs. X treated all students equally and at times let the students off the hook.
There were times that Mrs. X had to take a break with the students that allowed them to
receive math content but with a different approach. In one instance, I walked in at the
beginning of the class and Mrs. X gave an alternative assignment for the students who did
not complete the homework the previous night. Her alternative assignment was to sing
and dance to the alphabet with a kinesthetic approach using math vocabulary terms. Mrs.
X called out the alphabet and the students had to come up with the letter using their hands
and body. This alternative activity allowed the students to be relaxed and receive math
content in a lighter way.
Mrs. X holds high expectations for all students. One example of a high
expectation in the flipped model was “Club 95.” Next to Mrs. X’s desk, there was a
bulletin board with the heading “Club 95.” If students received a ninety five percent on a
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test they are given a small ticket that they had successfully accomplished a unit. Each
unit had a different color Club 95 ticket, representing the unit. On the third observation,
Mrs. X placed all graded tests on the center table of the classroom and allowed students
to pick them up the last 7 minutes of class. Mrs. X allowed the students to who received
a 95 percent or higher on their test to pick up a Club 95 ticket from Mrs. X’s desk. The
tickets were different colors, representing a different unit. For example, eleventh grader,
Telephone, picked up a dark blue Club 95 ticket and wrote down the first and last name
with the current unit. Telephone then stapled the Club 95 ticket on the Club 95 wall.
Twelfth grader, Wally, made it clear that she, “really enjoyed the flipped
classroom style simply because Mrs. X was always available.” Students were able to
work at their own pace during class and the teacher always made sure to check in with
students for any questions for clarifications they may have on the assignments or lesson
videos. This made students like Wally really confident about reaching out to the teacher
anytime building a teacher-student relationship. In order to answer the final research sub
question, students were asked directly for their feedback on the flipped model as
discussed in the following section.
Strengths
Students perceived a variety of strengths with the flipped approach. Keywords
used in identifying strengths included: “useful”, “helpful”, “I liked it”, “let’s do more”,
“good”, “enjoy”, “clear”, “fun” and “informative.”
Individual and partner blogging in the math analysis classroom was a recurring
strength. This was the first semester doing some partner blogging. For example, when
eleventh grader T-Rex was interviewed, “[she] really enjoy the blogging for the class
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because it’s not doing math problems but instead we are writing, which I really enjoy.”
T-Rex made sure to work closely with her partner when completing partner blogging.
Twelfth grader, Bom, referred the flipped model as “more work than my AP
classes.” Students like Bom, made it clear that the workload of the flipped model was a
lot. Throughout the semester the workload became easier once a routine was put in place.
Students needed to complete watching lessons, quizzes, blogs and assignments for each
unit, every three to four weeks. These helped students to keep up the pace and not fall
behind.
Twelfth grader, Eden, made it clear that the flipped model, “doesn’t allow me to
procrastinate, so that’s a plus. Also I feel like I am more able to ask for help during
actual class time when I don’t understand to my teacher.” Keeping up the pace and not
falling behind is a key component in the flipped model. This allows students to keep on
track with the lessons at home. Similarly, video lessons were clear and concise. Eden
pointed out how “it was relatively easy to understand the concept and focus on the most
important details. Learning is done at home so if I needed any extra help, I could've
consulted with classmates or Mrs. X in class.” Eden, like most students, liked how the
video lesson focused on the important information from the content.
Twelfth grader, Neocat, pointed out how “whole group of letting us choose where
we sit and its good vibes all around and were able to help each other and have fun.” The
friendly environment, helped students like Neocat work in collaboration with other peers
without being afraid of asking questions. Not only did the collaboration help but the
small groups were a big focus. Neocat, agreed how she received more “one on one with
the teacher in small groups,” which helped her learn a lot from the course.
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Areas of Improvement
Students perceived a variety of areas of improvement with the flipped model
approach. Key words used to identify areas of improvement included: “frustrated”,
“boring”, “wasted”, “long”, tired” and “pointless.”
In the beginning of the school year, students like twelfth grader, Bom, were
confused about all the acronyms like "WSQ", "WPP" and “PT.” The acronyms were
used on a daily basis for all assignments from the unit. It was difficult for students to
understand all the flipped model acronyms at the beginning of the school year.
In addition, the words “peer grading of blog posts” was noted as reoccurring
words from students in interviews and observations that indicated frustration. Twelfth
grader, The Doctor, agreed that “grading other people’s blog post doesn’t help me learn.
I just see what their thought process is, if it makes sense I agree.” The Doctor discussed
how the peer grading of the posts made it difficult to focus on the lesson content since
students are only grading their classmates’ posts as opposed to giving them additional
feedback.
Conclusion
In summary, this qualitative case study examined the students’ experiences in the
flipped model within one math analysis class. The results show that students reacted
positively to the integration of the flipped model. Although there was hesitation at the
beginning, students grew to accept and adopt the model and became more accepting of
the flipped model. Students feel confident in taking a rigorous math course next year.
Eleventh grader, Spiderman, made it clear that, “this is a class where I can communicate
and ask question whenever I need help. Working and solving problems has made me
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more confident about taking AP Calculus next year. Honestly, I am worried about going
back to the traditional math class.”
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Chapter 5: Summary, Conclusion, and Recommendations
The purpose of the research study was to examine the impact of a flipped model
in a high school classroom. The following research questions were explored: What is the
students’ experience in a math analysis classroom with a flipped approach? and What do
students perceive to be strengths and areas of growth in the flipped classroom model in
terms of their engagement and content learning? In this chapter, I discuss the findings,
connect them to the literature review, provide suggestions for instructional change, make
recommendations for future research studies, and conclude my research.
Interpretation of Findings
My findings began by using a time frame approach to the flipped model. The
flipped model minimizes teacher lecturing and maximizes hands-on activities and student
collaboration (Bergmann & Sams, 2012). Upon completing the table of the activities
done in the classroom as discussed in Chapter Four, I noticed that there was a increased
use of class time on lesson content, in particular hands-on group problem-solving, with
Mrs. X’s flipped model instruction. Time management is a key point in this flipped
model; once the distribution of class minutes is established, students were able to focus
more on collaborating with others.
In Mrs. X’s class, students were given time to try out, dialogue, and rehearse
newly acquired strategies through language, allowing them to reinforce their math
learning. Collaboration is essential in a flipped classroom because it enhances the
students’ critical thinking skills and it reinforces their social skills by being able to learn
from each other and support their peers (Vygotsky, 1978; Francisco, 2013). This study
further expressed how student collaboration has a great impact in a math classroom
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because students learn from each other and have the opportunity to interact, making it a
positive experience. Students were able to build upon knowledge and ultimately have a
positive outcome by coming up with a correct solution. Through constant interaction,
students had fewer distractions that impeded them from completing their assignments. In
turn, they were able to master concepts in depth since they learned things in small groups
or with partners, thus increasing retainment of the information or mathematical concept
(Webel, 2013; Bosse & Kwaku, 2011).
A positive safe social environment played a critical role in Mrs. X’s classroom by
increasing participation among students. Mrs. X had a strong positive environment in the
classroom by implementing mathematical lessons with a different style and forming
secure student relationships. By freeing up lecture time, Mrs. X focused on personal
engagement with students, increasing her opportunity to develop personal relationships
with them. One example of a mathematical lesson in Mrs. X’s classroom was the
incorporation of a kinesthetic activity. Through this approach students were able to get
out of their seats and attempt math in different ways by engaging in the lessons. Students
like twelfth grader, The Doctor, emphasized the idea of how the learning environment
was so friendly and understandable. Mrs. X. made sure to build a positive relationship
with all her students in which they responded well by having them choose their own
classmates for blogs, tests and groups.
I found that the use of technology in the classroom played a positive role in the
math analysis classroom by allowing for flexibility in learning. Students liked that the
classroom was technology-based so they had access to content materials at all times
(Casey, 2013; Goos, 2010). The tools were present and allowed students to be active in
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extracurricular activities, balancing the workload of Advance Placement classes and/or
having a part-time job. By doing so, students did not fall behind with the math content.
Since the majority of the video lessons ranged from ten to twenty minutes, students like
twelve grader, Stripes, was able to view the video lessons during lunch-time because she
had arrived home late from a game the previous night. Other students had to miss some
days before spring break for a school trip to Europe. These technology tools allowed
students to not feel left out and increased their potential for student participation even
when they are absent. These helped improved learning inside and outside of the
classroom because students were able to use the technology tools any time (Casey, 2013;
Goos, 2010).
This study shows the importance of integrating the flipped model into one high
school math class. By creating a student-centered classroom, the teacher is able to focus
on those who are struggling (Warter-Perez & Dong, 2012). As a result of the different
needs of each student according to their respective level, students were motivated to
understand mathematical concepts. In the flipped model, students were accountable for
lessons. Students like twelfth grader Eden, felt the flipped model approach did not allow
them to procrastinate. They needed to learn the concepts to not fall behind. Viewing it
on their own time is usually more productive because it allowed them to repeat, rewind,
or fast-forward the lesson.
Implications for Instructional Change
The results from this study are important. Mrs. X created a safe and rigorous
environment for all students involved. My study utilized a combination of Vygotsky’s
framework on the learning theory of constructivism and the flipped model (Vygotsky,
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1978). The findings in this study may help teachers evaluate if this instructional model is
appropriate for them.
The teacher’s role is a crucial factor in classrooms (Clarke, 1997; Snow 2011). In
this flipped model approach, Mrs. X created all the unit video lessons. Eleventh grader,
Telephone, made it clear how this flipped approach was different than his science flipped
classroom. In the math class, he was able to get an immediate response as opposed to his
science class in which the videos were recorded from teachers on the East Coast. This
indicates that even with the heavy reliance on technology, it is really still the teacher-
student relationship that forms the basis for success in this model. Mrs. X was more
available in class to interact with students. In addition, Mrs. X also could modify her
videos when she needed to help improve her instruction based on what she was seeing
happening with her students during class time. One example was the incorporation of the
“pause” component in the throughout the lessons videos. As students watched videos, a
“pause” signal was repetitive, giving the students an opportunity to pause their video,
look over their notes and apply their knowledge on math problems.
Additionally, it is important to analyze if teachers are fulfilling student
expectations, since the student-teacher interaction is different in a flipped classroom
(Bergmann & Sams, 2012). In many cases, Mrs. X was able to have a more direct
relationship with students. She served as a facilitator who help students navigate through
content, instead of always providing it, giving students the opportunity to analyze and
problem solve. This flipped model can have greater success with the feedback from
students to more accurately highlight the components that work in the model.
My study showed how students had a positive relationship with their teacher in
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part because of this approach. All students in Mrs. X’s classroom were treated equally.
The majority of the time was focused on group collaboration that included: independent
support, guided practice and hands-on projects (Bergmann & Sams, 2012). There was
one instance in which a majority of the students didn’t complete a homework assignment
so Mrs. X had an alternate assignment that included singing and dancing with math
content. Students regularly talked with their peers in small groups either by watching
videos, working on blogs or reviewing activities with teacher support. Because of this,
students were exposed to a strong and positive teacher collaboration (Bergmann & Sams,
2012; Zappe et. al., 2009).
Educators sometimes think that is it difficult for students to demonstrate a positive
outcome when a new learning model is put in place. A flipped model doesn’t change the
curriculum because students still need to master the essential skills. Having the
flexibility in flipped classrooms is a crucial component because it provides for shared
accountability. The accountability for the teacher would entail utilizing preparatory time
to create the lesson in various modes and allow accessibility to the students. In turn, the
student will be held accountable by being prepared prior to class in order to be an active
participant in the activity provided by the teacher.
Insight into students’ experience in a flipped classroom is important because it
provides evidence necessary to improve learning for students. Even though teachers may
perceive this model to be the best for student learning since it allows the student to dictate
their own schedule and work at their own pace, it is important to recognize the transition
may be difficult for some students. Also, it requires students to be more self-directed as
learners and more self-disciplined, which could pose a challenge to some students. While
70
these kinds of habits may be what we want to cultivate, students who are not “self-starters”
or who are more in need of explicit direction may struggle in this environment.
Additional difficulties may range from accessibility of technology in terms of
internet and/or electronic devices to the lack of face-to-face interaction with the teacher.
Although technology has become a major part of students’ lives, it is wrong to assume
that all the students have access to a phone or any type of electronic device. Meticulous
consideration of the resources that the students have on and off campus is essential if a
teacher is preparing to implement this type of teaching model. Also, they must consider
that since it is abstract to students at the beginning, their motivation to complete the
assignment on their own may be low. Some students may need that extra encouragement
to fully buy in to the newly adopted model since they may feel it is too impersonal. This
can also cause the students to skip the lecture and activity since they may feel they can
make it up simply by going to the website given by the teacher.
The results of this study indicate that the flipped model redirects attention from
the teacher to the students. Students can manipulate the lesson according to their various
learning needs. The model actively involves students in the learning process, in part
through facilitating an environment where they may develop their understanding through
classmate interaction.
Recommendations for Further Research
Based on the findings of this study, I have a few recommendations for future
studies. My study was three weeks during the spring semester. More data could have
been collected if the study had a longer time frame. A yearlong study could show the
evolution of the students’ progress from the beginning to the end of the school year. This
71
would allow the researcher to follow up with the students across a longer period of time.
It may also document the transition for students from a traditional model to a flipped one
to see how teachers set up the classroom, how students experience this transition and the
process of recording video lessons.
It is also important to understand the teacher’s experience of the flipped model.
Since teachers implement the lessons and observe the students’ development, they are a
key to the outcomes of the model. A teacher must be able to put in place the critical
components of the flipped model. The flipped model has been utilized in different
content areas in college level courses (Lage et. al., 2000; Enfield, 2013; Warter-Perez &
Dong, 2012; Zappe et. al., 2009; Kay & Kletskin, 2012; Talley & Scherre, 2013;
McLaughlin et. al., 2013). It would be interesting to analyze the results of utilizing the
flipped model of instruction in different content areas. Studies across different content
areas would reveal nuances about the flipped model. This would help educators
determine in what areas the model would better serve students. These suggestions will
help contribute to the understanding of the flipped model. Each study can help educators
gain insights of how to strengthen the flipped model from the students’ point of view.
Finally, an exploration of various research methodologies, including qualitative,
quantitative and mixed methods design could further our understanding of a flipped
approach.
Conclusion
This qualitative case study examined the students’ experience in a math analysis
classroom using the flipped model by answering two research questions. The first
focused on students’ experiences in a math analysis classroom using the flipped model of
72
instruction. The second focused on what students perceive to be strengths and areas of
growth in the flipped classroom model in terms of their engagement and content learning.
The results show that through strong student/teacher collaboration and rich-technology,
students reacted positively to the integration of the flipped model in the math analysis
classroom. Although there was hesitation at the beginning, students grew to accept and
adopt the model and became more accommodating of the flipped model over time. This
study shows that students can be successful in a student-centered classroom that caters to
their specific needs. Successful instruction models, like the flipped model, allow for
individualized attention, leading to a better student experience in high school math
classrooms.
73
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