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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iii

Students’ Experiences in a Math Analysis Flipped Classroom

Copyright © 2015

by Hugo Sierra

 

iv

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.

 

vi

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

 

2

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

 

3

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.

 

4

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

 

16

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

 

17

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

 

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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

 

19

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

 

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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

 

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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

 

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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

 

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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.  

 

30

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

 

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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

 

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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

 

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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

 

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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.  

 

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