THE IMPACT OF KHAN ACADEMY MATH REMEDIATION ON

NINTH GRADE STUDENT ACHIEVEMENT

by

Sandra Lee Kelly

Liberty University

2

THE IMPACT OF KHAN ACADEMY MATH REMEDIATION ON

NINTH GRADE STUDENT ACHIEVEMENT

by

Sandra Lee Kelly

A Dissertation Presented in Partial Fulfillment

Of the Requirements for the Degree

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ABSTRACT

The purpose of this quasi-experimental study was to determine if using Khan Academy as math

remediation for fifteen minutes per day during a ninth grade Math I class would significantly

affect student math achievement as measured by the North Carolina READY Math I End-of-

Course Assessment. This quantitative study conducted at two rural high schools in West

Virginia used remediation theory to make a comparison against a control population with the

independent variable being grade level instruction only or grade level instruction plus math

remediation using Khan Academy. The participants in the study included 131 ninth grade high

school students taking a Math I class in a traditional classroom setting between October 2016

and those receiving regular instruction along with Khan Academy for math remediation.

Suggestions for further research are included.

Keywords: mathematics, remediation, achievement, college-ready, career-ready,

prerequisite, foundational

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Dedication

After graduating with my master’s degree in May of 2008, I asked my mother if she

thought I should one day pursue a doctoral degree. After all, I said I would most likely be 50

years old or even older before completing it. Her response was typical of such a wise person.

She said, “Sandy, you’ll be 50 whether you get your doctorate or not, you might as well be 50

with a doctorate.” This work is dedicated to my precious mother, Betty Arbaugh, who went to

be with the Lord November 5

th

, 2008. I love you Mom, and I’ll see you again one day.

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Acknowledgments

First, I thank my God for being with me and guiding me throughout this endeavor. I was

blessed with wonderful parents who valued education and always supported me. I thank my

father, Earl Arbaugh, a teacher, who passed down the desire to educate another generation. I

thank my mother, Betty Arbaugh, who always was and still is my greatest cheerleader. I thank

my husband, David Simmons, for his patience and support through it all. I am so grateful for the

two children that the Lord blessed me with. My son, Jacob, and my daughter, Jessie, are my

inspiration and a driving force in this achievement. I am forever grateful for all of my family

and friends who have supported me with their prayers and words of encouragement. Many

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Table of Contents

ABSTRACT.....................................................................................................................................3

Dedication........................................................................................................................................4

Acknowledgments............................................................................................................................5

List of Tables...................................................................................................................................9

List of Figures................................................................................................................................10

List of Abbreviations.....................................................................................................................11

CHAPTER ONE: INTRODUCTION...........................................................................................12

Background........................................................................................................................12

Overview............................................................................................................................23

Remediation Theory...........................................................................................................24

Foundational Math Skills...................................................................................................27

Cognitive Science..............................................................................................................30

Prior Knowledge................................................................................................................34

Online Resources...............................................................................................................37

Khan Academy...................................................................................................................41

Discussions and Conclusions.............................................................................................52

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CHAPTER THREE: METHODS.................................................................................................55

Design................................................................................................................................55

Research Question.............................................................................................................55

Hypothesis..........................................................................................................................55

Participants and Setting......................................................................................................56

Instrumentation..................................................................................................................57

Procedures..........................................................................................................................61

Data Analysis.....................................................................................................................64

CHAPTER FOUR: FINDINGS....................................................................................................67

Discussion..........................................................................................................................74

Additional Analysis...........................................................................................................74

Implications........................................................................................................................77

Limitations.........................................................................................................................78

Recommendations for Future Research ............................................................................80

REFERENCES..............................................................................................................................82

APPENDIX A: REQUEST TO CONDUCT RESEARCH...........................................................92

APPENDIX B: TEACHER INTRODUCTION TO STUDY........................................................95

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APPENDIX C: KHAN ACADEMY TEACHER PRESENTATION...........................................97

APPENDIX D: PERMISSION FROM NC PUBLIC SCHOOLS...............................................102

APPENDIX E: COMMON CORE STANDARDS MAPPING BY STATE..............................103

APPENDIX F: NC MATH I RELEASED FORM 2012-2013 ANSWER KEY........................104

APPENDIX G: UNMAPPED MATH I COMMON CORE STANDARDS..............................108

APPENDIX H: MATH I PACING GUIDE................................................................................109

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Table 3.1: EOC Math I Reliabilities..............................................................................................57

Table 3.2: NCDPI Validity Evidence for Math I Assessments.....................................................58

Table 3.3: Unmapped Test Items...................................................................................................60

Table 3.4: Distribution of Sample..................................................................................................65

Table 4.1: Descriptive Statistics....................................................................................................69

Table 4.2: Khan Academy Mission One Completion Levels........................................................70

Table 4.3: Experiment Group Khan Academy Mission Treatment Levels...................................72

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reinforcement, and the resulting changes in behavior (Boylan & Saxon, 2015). A study by James

and Folorunso (2012) that investigated the instructional strategies of feedback and remediation

effects on secondary school students’ mathematic achievement was driven by the behaviorist

theory. Their results showed that students receiving remediation with feedback outperformed

students who only received feedback. The lowest performances came from the control group

who received neither instructional strategy (James & Folorunso, 2012).

In a postsecondary remediation study by Barh (2008) similar findings were produced.

College students who remediated successfully reached the goal of college-level mathematics

achievement and had comparable outcomes to students who didn’t require remediation. The

regardless of the level of deficiency or the number of deficiencies, students who remediated

successfully achieved mathematics and English competency and had similar levels of

achievement overall. Thus, remediation was proven to be effective for students regardless of the

severity or number of their learning deficits (Barh, 2010).

In a pilot study by Wenner, Burn, and Baer (2011), geoscience course students received

mathematics remediation via supplemental online asynchronous learning modules. It was

determined that student success was dependent upon their participation and completion of the

modules and the successful remediation of the necessary quantitative skills. The study resulted

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in at least modest gains in overall achievement with more significant gains achieved by students

who completed all of the modules (Wenner, Burn, & Baer, 2011).

Research has shown remediation to be a valuable tool for leveling the field for students

with deficiencies at both the secondary and postsecondary levels. To produce college-and-

career-ready high school graduates and reduce the number of students enrolling in postsecondary

remedial courses, remediation must begin earlier in a student’s education. Since the fourth and

eighth grade scores reported by NCES were promising, but deficits appeared by twelfth grade,

ninth grade is a logical starting point for the identification and remediation of deficits in

mathematics (U.S. Department of Education, 2012). If a stand-alone remedial course for

mathematical foundation (Barh, 2008; Barh, 2010; James & Folorunso, 2012). This would make

reaching the goal of high school Algebra II a possibility for more students and in turn help them

attend and graduate from college, thereby increasing their earning potential (U.S. Department of

Education, 2008). A solution must be developed that allows for some remediation during regular,

grade-level, high school mathematics courses (Harvey, 2013).

Problem Statement

In 2008, the NMAP’s Final Report recommended that curricular content should not

revisit topics from prior years or previous mathematics courses. Instead, the curriculum should

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progress through math topics emphasizing student proficiency at each level. Proficiency is

described as an understanding of key concepts and competently executing standard algorithms

with automaticity (U.S. Department of Education, 2008). The Obama Administration’s

Blueprint for Reform (2011) called on all states to adopt state-developed standards in

mathematics that produce college-and career-ready high school graduates. States were given the

option of upgrading their own standards or adopting CCSS (U.S. Department of Education,

2011). In response to these recommendations, curricular changes have occurred across the

nation resulting in a more rigorous curriculum that doesn’t allow for the review of prerequisite

skills or the remediation of students who have gaps in their mathematical foundation. Research

eliminated the review of previously-learned mathematical concepts. There is a need for cost-

effective, alternative methods of math remediation for high school students that enable them to

take college level mathematics courses (Harvey, 2013). Currently, interventions or remediation

designed to improve college readiness in mathematics are promising, but limited (Hodara &

Barton, 2014). While there are many studies of the effects of remediation at the postsecondary

level there are not many at the high school level and none that included the use of online

supplemental programs for math remediation used within a grade-level course. Most research at

the middle and high school level involves after school and summer programs, stand-alone

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remedial classes, or double dosing algebra courses for students needing remediation (Bushweller,

1998; James & Folorunso, 2012). There are some studies on the use of the online program, Khan

Academy, as part of a regular grade-level curriculum that were successful in increasing student

engagement and math achievement (Kronholz, 2012; Light & Pierson, 2014). While these

studies were not specifically using Khan Academy as a remediation tool, the program itself was

remediating some students in the studies due to its individualized instructional aspect.

More research is needed in the area of math remediation in high school grade level

courses using online supplemental resources. A study using Khan Academy during regular ninth

grade class meetings to remediate basic arithmetic and pre-algebra skills would fill a gap that

short assessments (Khan Academy, 2015).

Purpose Statement

The purpose of this quasi-experimental study is to determine whether receiving fifteen

minutes a day of mathematics remediation using Khan Academy during each regularly scheduled

Math I class will significantly improve ninth grade students’ mathematics achievement as

measured by the North Carolina READY Math I End-of-Course Assessment. It will make a

comparison against a control population with the independent variable being grade level

instruction only or grade level instruction plus math remediation using Khan Academy. The

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dependent variable will be the North Carolina READY Math I End-of-Course Assessment scores

at the conclusion of the study, and the pretest scores from that assessment will serve as the

covariate for analysis.

Significance of the Study

This study will strengthen current research in several different areas in the field of

educational research. While studies exist on the effects of math remediation at the secondary

level (Bushweller, 1998; James & Folorunso, 2012) most involve standalone classes or summer

programs. There are also several studies at the postsecondary level regarding math remediation

(Attawell, Lavin, Domina, & Levey, 2006; Bahr, 2008; Bahr, 2010) and some that used online

2014; Murphy, Gallagher, Krumm, Mislevy, & Hafter, 2014; Kronholz, 2012). This study is one

of the first to use Khan Academy as a supplemental online resource for mathematics remediation

during a ninth grade CCSS Math I class. This is important because it could provide high school

teachers and school leaders with an option when looking for ways to remediate foundational

mathematics skills during grade-level mathematics courses. This study does not seek to

determine the best tool for mathematics remediation available but rather to review the

effectiveness of one. This study seeks to determine the effectiveness of using Khan Academy as

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a free, online math remediation tool in ninth grade classrooms to increase student mathematics

achievement.

Research Question

RQ1: What is the effect of using Khan Academy as a supplemental online remediation

tool on ninth grade students’ math achievement?

The null hypothesis for this study is:

H

0

1: There is no significant difference in the math achievement of ninth grade students

who use Khan Academy as a supplemental remediation tool in addition to grade level instruction

as opposed to ninth grade students who do not use Khan Academy as a remediation tool to

Definitions

Department of Education, n.d.).

George W. Bush to advise him and the Secretary of Education on the advancement of

teaching and learning of mathematics (U.S. Department of Education, 2011a).

organization run by the Commissioner of Education Statistics (U.S. Department of

Education, 2012a).

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entity in charge of collecting and analyzing educational data (U.S. Department of

Education, 1996).

that outline what students should know and be able to do at the end of each grade (CCSS,

2015).

different content areas (Khan Academy, 2015).

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CHAPTER TWO: LITERATURE REVIEW

The purpose of this quantitative study is to determine whether receiving fifteen minutes a

day of math remediation during a regularly scheduled grade-level Math I course will

significantly improve ninth grade students’ mathematics achievement. Math I is a CCSS course

that replaced the previously named Algebra I course in high schools residing in states that

adopted Common Core. The remediation process involves the reviewing and relearning of the

foundational skills that are prerequisite to learning algebra. The researcher reviewed literature

related to remediation theory, algebra prerequisite skills, cognitive science, and the use of

within a larger context. The second section examines the basic foundational mathematics skills

that are prerequisite to learning algebra. The third section highlights the cognitive science of

mathematical learning including several current brain-based studies made possible by recent

technological advances. The fourth section discusses the importance of prior knowledge in the

acquisition of new information and academic achievement. The fifth section explores the use of

supplemental online resources to increase student achievement, and the sixth section introduces

Khan Academy as a math remediation tool. Finally, the last section summarizes the literature

reviewed and how this study addresses the gaps in the current literature within the topic of math

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remediation at the high school level.

Educational remediation involves reteaching and reinforcing previously taught material

that was not mastered or retained. The purpose is to fill in the gaps of missed content usually

because it is prerequisite to current grade level content. Remediation is grounded in the

behaviorist theory developed by B. F. Skinner in 1938 in his first book, The Behavior of

Organisms (Boylan & Saxon, 2015). The theory is based on learning strategies, feedback or

reinforcement, and resulting changes in behavior. Skinner’s theory presents the idea that

behavior is learned and reinforced by the environment using a schedule of reinforcement much

reinforced by the testing out of the remediation program once their performance meets the

standard expectations (Boylan & Saxon, 2015).

Educational remediation, for many years, was viewed as a solution to a problem and was

not researched or considered a topic worthy of study. It became a recognized field of study in

the late 1960s when John Roueche, a researcher from the University of Texas in Austin, along

with his colleagues, began studying existing remedial educational programs to discover what

techniques were producing the best results. Much of their early research in the decade between

1968 and 1978 involved studying college level developmental mathematics courses that were

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mostly watered-down versions of the regular college-level courses delivered by lecture (Roueche

& Kirk, 1974). Their findings offered several recommendations for developing a successful

remediation program at the college level. They supported the behaviorist techniques used at that

time and reported them to be successful in remediating underprepared students. Roueche (1973)

highlighted the importance of establishing clear goals and objectives for remediation, which was

shown to help students be successful.

Figure 1. Behaviorism Remediation Flow Chart.

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remediate students in their areas of weakness in a particular subject matter.

Menon (2014a) in Arithmetic in the Child and Adult Brain created a comprehensive

handbook examining the brain and the cognitive processes that are involved in learning and

doing arithmetic operations. He completed numerous studies that shed light on what parts of the

brain are involved with the learning of new arithmetic facts and what parts are involved with

working and long-term memory. The hippocampus and its circuitry make up the area of the

brain that is directly involved with the development into adult like ways of processing. When

children learn new math facts they gradually progress from problem solving like finger counting

to memory retrieval. According to a recent study by Stanford University (Menon, 2014b) the

of the brain.

Studies have shown that an extensive network in the frontal and parietal cortices along

with the basal ganglia are involved during procedural strategies (Grabner, Ansari, Koschutnig,

Reishofer, Ebner, & Neuper, 2009). This phenomenon is negatively correlated with age, with

younger children having more activations than adults. This is due to the fact that children are

using strategies that require more effort as opposed to the fact retrieval processes of adults

(Rivera, Reiss, Eckert, & Menon, 2005). At some point after basic arithmetic facts are initially

learned and stored in the hippocampus, they are written to the well-developed information stores

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of the neocortex or long-term memory (Menon, 214b). So, the hippocampus is the scaffold to

the neocortex, and this schema is built in a child’s brain for future retrieval of information. If

something happens to short circuit the transfer or transition from the hippocampus to the

neocortex as in the case of a brain lesion, the information will not be written to long-term

memory and will only reside in working memory for a short time before it is replaced with other

information (Menon, 2014b). A study by Qin, et al., (2014) showed the hippocampal system as

pivotal to this transfer. Their study revealed that retrieval strategy use improved from childhood

through adolescence and into adulthood. They were able to detect this by decreased activation in

the hippocampus (Qin, et. al., 2014). Working memory has limited resources that must be shared

they get to algebra and beyond.

Menon’s study (2014a) found that addition and multiplication predominantly utilize

memory retrieval, while subtraction and division rely on strategies. This is because addition

algorithms and the multiplication tables are generally memorized while subtraction and division

require strategies for solving. He states that elementary school is the most important period for

the mastery of basic arithmetic facts, and over time a progression occurs from counting and other

effortful procedures to direct retrieval from memory (Menon, 2014a). Without this progression,

a student will forever have to rely on strategies or a calculator for basic arithmetic. This will

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ultimately be too slow for higher-level mathematics and taxes working memory capacity that is

needed for more complex problem solving. A plan of remediation supplementary to grade level

mathematics courses over time could help students regain foundational arithmetic skills and

thereby reduce in-class cognitive load and help them succeed in high school mathematics and

beyond.

Prior Knowledge

Students who require remediation have a lack of prior knowledge in the given subject

area or have a lack of knowledge in the prerequisite skills required for the given subject. Prior

knowledge is what a learner already knows about a topic and according to Ausubel (1968) is the

likely to use the voluntary online resources provided than those with prior knowledge. In a study

by Yüksel (2014) that examined the impact of activity-based mathematics instruction on

mathematics performance, and investigated the factors that contributed to mathematics

performance, the researcher found that students with high prior knowledge and high self-

regulation skills made greater gains in mathematics performance. The study discovered that

students with high prior knowledge also had a more positive attitude toward mathematics, which

leads to further success in the subject.

Seery and Donnelly (2012) found that the incorporation of new information by a novice

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is more strongly influenced by their prior knowledge of a topic. This has to do with how well

new information can be linked to some pre-existing knowledge in long-term memory. Thus,

learners without prior knowledge use a significant amount of their limited working memory

capacity accommodating new information, while learners with prior knowledge link the new

information to existing knowledge. For learners with prior knowledge this decreases cognitive

load on working or short-term memory. In the Seery and Donnelly (2012) study, ten pre-lecture

online resources were developed addressing introductory chemistry topics. College students in

their first year of chemistry were given access to the materials every week prior to lecture. The

resources included a main objective, vocabulary, and a four-question quiz on the lecture material.

experience with various configurations of the problems that can influence student learning. A

student has to read and understand both text and diagrams while making the connection with

previously learned configurations. In a study of geometry problem solving by Lin and Lin

(2014, p. 616), five problems involving similar triangles were presented to students with and

without prior knowledge of the topic. Results of the study showed that prior knowledge of

similar triangles was a significant predicator of the pass rate for a given problem. This was true

for the first four problems that had simple configurations. However, the pass rate for the fifth

problem was significantly lower for students with and without prior knowledge. This particular

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problem required mentally rotating the triangles and identifying hidden elements. This showed

that even students with prior knowledge of similar triangles still struggled with configuration

comprehension (Lin & Lin, 2014). Pass rate on a problem with a complex configuration was

dependent upon the prior knowledge of both the topic and the configuration of the triangles.

This is another way that prior knowledge affects the learning of new information in mathematics

and is strongly influenced by and affects the ability to link new information with existing

knowledge in long-term memory. Thus, a lack of prior knowledge in a concept and in the

configuration of the problem increases cognitive load on the learner and can overload the limited

capacity of the working memory (Seery & Donnelly, 2012).

instructional materials that require too much working memory increase the extraneous load and

decrease the learning capacity (Seery & Donnelly, 2012, p. 668). Lastly, germane load is the

mental effort or load on the human cognitive system required for learning. Since working

memory is limited, germane load is dependent on the prior knowledge of the learner that results

in a lower intrinsic load on the cognitive system (Seery & Donnelly, 2012). Therefore, the

intrinsic and extraneous loads can hinder learning while the germane load enables it (Lin & Lin,

2014). The goal of remediation in this study is to reduce intrinsic load caused by a lack of prior

knowledge and limit extraneous load by choosing an online tool like Khan Academy that has a

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relevant instructional design that is easy to use.

The use of supplemental online resources to reduce cognitive load and close the gap

between students with and without prior knowledge has been well researched. Online

supplemental resources have been used in a variety of ways with various educational strategies,

interventions, and remediation to increase learning and deepen conceptual understanding in

mathematics as well as other subjects. In math and science in particular there is a plethora of

terminology and concepts that must be mastered in order to proceed to the next level of the

curriculum. When these terms and concepts are missed or are not fully understood, it creates a

learning. Their study found that supplemental online resources providing problems for repeated

practice, spacing, and timely feedback, and by requiring students to view the feedback and

correct mistakes increased the learning and retention associated with weekly homework

assignments. This simple and inexpensive intervention provided students with repeated practice

spaced over time, allowing them to practice the retrieval of new information and correct any

misconceptions early (Butler, Marsh, Salvinsky, & Baraniuk, 2014). Since the intervention was

online it gave students access to the materials any time, allowing them to be in control of their

own learning. Although the principles of cognitive science used in the study could have been

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applied without the use of online resources, it is their belief that using technology to deliver the

resources exponentially increased the effectiveness and impact of the principles. Technology

provided a personalized learning experience that allowed each student to go at his or her own

pace (Butler, Marsh, Salvinsky, & Baraniuk, 2014, p. 339).

Another study conducted by Vandewaetere and Clarebout (2013), showed that a learner-

controlled online environment was associated with higher motivation and was determined not to

increase extraneous cognitive load on the learner. When learners have full or partial control over

the sequencing, pacing, or presentation of the learning environment, it is considered a learner-

controlled (LC) environment. Learners are given the ability to define at least part of their own

A case study conducted by Seery and Donnelly (2012) analyzed the impact of using

supplemental online resources on those with and without prior knowledge in chemistry. Their

study, mentioned earlier, created ten online prelecture resources introducing key concepts and

included a quiz to be completed prior to the corresponding lecture. The resources allowed

students to test their understanding and identify misconceptions caused by new terminology and

concepts. This helped students without prior knowledge in chemistry by reducing cognitive load

during lectures. The results of the case study revealed that the final exam scores for students

with no prior knowledge in chemistry had improved significantly and that there was no longer a

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stark difference in grades between students with and without prior knowledge of chemistry. The

results of the study concluded that the use of online resources is an effective remediation method

for increasing student-learning capacity in students lacking prior knowledge of the content

(Seery & Donnelly, 2012).

In a blended learning environment, the Internet compliments traditional learning by

providing access to tutorials, practice, review, and assessments with immediate feedback outside

of the classroom. According to López-Pérez, Pérez-López, Rodríguez-Ariza, and Argente-

Linares (2013) from a study at the University of Granada, the use of supplementary online

activities can improve the learning process and contribute to an overall improvement in student

improvement in students’ final grades especially for students lacking prior knowledge. Those

students made greater use of the online resources and achieved positive effects from the online

supplemental materials (López-Pérez, et al., 2013). The study showed that online supplemental

resources could improve the learning process and contribute to an overall improvement in

student achievement if they were designed appropriately. Online activities that provide some

feedback with an explanation of why a response is wrong are particularly effective at building

understanding of course content. Although this study involved accounting classes, this type of

blended learning that provides immediate feedback and gives students the ability to correct

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misconceptions is beneficial with any content. The study results encouraged teachers to try this

approach to help students lacking prior knowledge and to improve learning outcomes and student

achievement (López-Pérez, et al., 2013).

Pilot studies conducted by Wenner, Burn, and Baer (2011) revealed that online

asynchronous learning modules effectively remediated students’ quantitative skills in

introductory geoscience courses in community college and university settings. According to the

authors, an increasing number of students are entering college underprepared in mathematics,

creating a high demand for remedial mathematics courses. This is particularly disturbing since

interest in STEM (science, technology, engineering, and mathematics) disciplines is influenced

course that will meet all of their needs. Wenner, Burn, and Baer (2011), infused introductory

geoscience courses with quantitative concepts via online tutorials. The online modules were

assigned prior to each new quantitative concept being covered in the geoscience course. Pretests

and posttests showed that the online modules increased students’ quantitative skills and survey

responses indicated that students perceived that the modules helped them in the mathematics

portion of the geoscience courses (Wenner, Burn, & Baer, 2011). When instructors introduced

the modules, provided clear instructions for using the tutorials, and reinforced the use of them it

resulted in higher levels of student completion. So, these instructional methods positively

41

influenced student motivation to use the modules and the post-module quizzes as tools for

success in their geoscience course (Wenner, Burn, & Baer, 2011).

As early as 1986, studies by Kulik and Kulik (1991) using computer-based instruction to

supplement regular instruction were found to be successful in employing the computer as a tutor.

They reported more student learning in less time and higher post-test grades. In a later study of

students with low prior knowledge, the researchers concluded that computer-based instruction

raised student achievement. The study included computer-based instruction in several subjects

including mathematics, science, reading and language, social studies, and vocational training,

and the computers were used for tutoring, drill and practice, and programming (Kulik & Kulik,

and quizzes in many different content areas. Its mission is to provide “a free world-class

education for anyone, everywhere” (Khan Academy, 2015). The nonprofit education website

was founded in 2006 and has about 3,500 math instructional videos available for viewing along

with over 100,000 practice problems that offer instant feedback for students who can work at

their own pace in or out of the classroom environment (Murphy, Gallagher, Krumm, Mislevy, &

Hafter, 2014). It has become extremely popular, with users working over 700 million problems

in 2013 alone. It started with math, science, and economics and now has expanded its offerings

to include arts and humanities, computing, and test prep. Khan Academy is part of a new

48

students separately and in no particular order, allowing students to focus on areas of weakness or

skip ahead when they were ready to move on. This aspect of Khan Academy also allowed

teachers to differentiate instruction within the classroom (Murphy, et. al., 2014). Teachers

reported that the most valuable benefit of using Khan Academy was the rapid feedback without

having to grade worksheets or homework to determine weak areas. Teachers also liked that

Khan Academy gave students the ability to take charge of their own learning, which helped build

their confidence in their ability to learn and work independently.

In response to this study, Khan Academy redesigned its website in July of 2013 releasing

grade-level “missions” and a “learning dashboard” (Murphy, et. al., 2014). These changes were

reports via email to the teacher/coach in the form of simplified, customizable summaries at both

the class and individual student levels.

Overall, this study reported positive outcomes for teachers, educational leaders, and

students, showing that schools with diverse student populations could adopt and implement Khan

Academy in their math curriculum. Teachers in the pilot study reported that Khan Academy was

a valuable tool to support instruction, that it helped students, and that they planned to continue

using it in the future while experimenting with different methods of implementation (Murphy, et.

al., 2014). Students also indicated that they liked Khan Academy, and student learning was

49

shown to be positively impacted based on scores from achievement tests taken prior to and

subsequent to the study.

Kronholz (2012) wrote about two more of the schools in the previous pilot study that

used Khan Academy to supplement classroom math lecture. In Los Altos, California, 115

students in fifth and seventh grade classes piloted Khan Academy and provided Khan feedback

for refining the website and tools. The results were that 41% of the seventh grade remedial

students who used Khan Academy scored proficient or advanced on their standardized tests

compared to 23% the previous year. Ninety-six percent of the fifth graders in the pilot study

were proficient or advanced compared to the rest of the district, 91%.

mathematics skills while the traditional class spent all of its time on algebra (Kronholz, 2012).

Another Khan Academy pilot study supported by the J. A. and Kathryn Albertson Family

Foundation took place in Idaho during the 2013-2014 school year. The study included 47

schools in 33 districts with 173 teachers and over 10,500 students. The pilot was designed to

support innovation, learning, and flexibility for both teachers and students (Phillips & Cohen,

2015). The main focus of the study was to offer individualized learning for the students.

Personalized learning is defined as tailoring learning to match each student’s weaknesses,

strengths, and interests. This includes allowing students some control over their own learning

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and supports the flexibility needed to help ensure mastery of the highest standards (Phillips &

Cohen, 2015). Khan Academy offers a personalized learning platform with virtually a free tutor

available to each student 24 hours a day, 7 days a week. Using Khan Academy in the classroom

supports differentiated instruction by allowing students to work at their own pace and enabling

teachers to offer more one-on-one help. Although it wasn’t the main purpose, the pilot study in

Idaho did provide an analysis of the relationships between academic outcomes and Khan

Academy usage (Phillips & Cohen, 2015).

Teachers were allowed to choose how they would use Khan Academy in their

classrooms: as a tool to remediate, accelerate, supplement, teach, reteach, or as a primary

The analysis showed a positive correlation between academic progress and Khan Academy usage

(Phillips & Cohen, 2015). A “target growth” was calculated for each student based on

nationwide norms using their grade level and their fall percentile. Students completing 60% or

more of their Khan Academy mission achieved 1.8 times their expected growth. Students

completing 40% or more of their Khan Academy mission achieved 1.5 times their expected

growth (Phillips & Cohen, 2015). Students who hardly used Khan Academy, completing 10% or

less of their mission, grew as expected. The results of the analysis showed that students who

completed more of their mission scored higher and showed more improvement than their peers.

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The study cautioned the reader not to draw definitive conclusions due to the confounding factors

including the various ways that Khan Academy was implemented across all the classrooms

(Phillips & Cohen, 2015).

It is Khan Academy’s simple, straightforward approach that makes it a highly adaptable

tool that is easy to integrate into any curriculum (Murphy, Gallagher, Krumm, Mislevy, &

Hafter, 2014). Teachers can create classes in Khan Academy and have their students sign up,

choosing them as their coach. They can also assign missions for their students to complete or

allow the program to assign missions based on short assessments of individual student needs. At

the beginning of every mission, the student is given a quiz with a short set of problems used to

enough.

Math fluency development was the focus of a study by Poncy, Skinner, and Axtell (2010)

that targeted struggling students for mathematics remediation. With the use of Khan Academy,

students can receive the individualized instruction that allows for math fluency at the student’s

pace without slowing down the pace of the classroom. According to a study by Light and

Pierson (2014), the Khan Academy digital learning environment increased student engagement

and changed the way that students engaged with the math content. Recently, the New England

Board of Higher Education (NEBH) received a grant from the Lumina Foundation for Education

52

to support community colleges implementing Khan Academy materials in developmental

mathematics courses.

Educational leaders are drawn to Khan Academy because it is free to everyone, engages

students, gives instantaneous feedback, has modular resources, and facilitates student-directed

learning. The educational community can benefit from further research of detailed use cases that

describe how Khan Academy can be used in different environments under different instructional

goals and the possible impact on student math achievement (Murphy, et. al., 2014). For the

purpose of this study, Khan Academy will be used as a mathematics remediation tool to reteach

foundational math concepts to students to support their success in their current grade-level Math

reteaching and reinforcing the prerequisite skills necessary for algebra and subsequent

mathematics courses. A review of the literature discussed Skinner’s behaviorist theory as the

foundation of remediation theory. As with remediation, behaviorism assumes that the

environment is at fault for foundational knowledge gaps and uses a schedule of reinforcement to

increase student achievement (Boylan & Saxon, 2015). The researcher also introduced the basic

arithmetic skills necessary for learning algebra. These include addition, subtraction,

multiplication, and division of all real numbers including integers and especially fractions

(NMAP, 2008). The review also included a discussion of the cognitive science of mathematical

53

learning and the significant role of prior knowledge in academic achievement and its association

with cognitive load on working memory. The use of eye-tracking technologies discovered that

students with prior knowledge transitioned more between graphics, texts, and diagrams than

students without prior knowledge, signifying a greater ability to integrate text and graphics. In a

study conducted by Anderson, Love, and Tsai (2014), the students with prior knowledge of the

subject directed their attention more appropriately than students lacking prior knowledge. A

study that measured the cortical electrical activity of the brain during operations on functions

also showed that struggling students had the greatest brain activity indicating a higher cognitive

load than students who reported the task as easy (Anderson, Love, & Tsai, 2014). The researcher

needs of the various students affects multiple departments (Wenner, Burn, & Baer, 2011). The

use of online resources like Khan Academy can provide remediation tailored for the individual

student available outside of the classroom.

The need for remediating basic arithmetic skills at the high school level must be met with

research-driven programs that will prepare students to be college or career ready at graduation.

Many of the existing programs are expensive and hard to implement. Much of the research in

this area focuses on afterschool programs, tutoring, and stand-alone remedial courses. This study

will investigate a supplemental program of remediation that can occur during regular class time

54

and specific to mathematics. Using a free online resource like Khan Academy for short periods

of time during regular class meetings to supplement grade-level mathematics courses may be a

solution. If successful, this type of remediation could become self-regulating and continue

throughout a student’s high school and college career.

55

CHAPTER THREE: METHODS

A quasi-experimental nonequivalent control group research design was intended for this

study because the random assignment of research participants was not feasible (Gall, Gall, &

Borg, 2003). A static-group comparison was used, however, because the data failed to pass the

assumptions necessary for ANCOVA. Intact ninth grade student groups in established

classrooms were used as treatment or control groups. A pretest and posttest were given to all of

the ninth-grade students. The dependent variable, mathematics achievement, was measured by

the posttest and the pretest was to be used as a covariate. The control, grade level instruction,

Research Question

RQ1: What is the effect of using Khan Academy as a supplemental online remediation

tool on ninth grade students’ mathematics achievement?

The null hypothesis for this study is:

H

0

1: There is no significant difference in the math achievement of ninth grade students

who use Khan Academy as a supplemental remediation tool in addition to grade level instruction

as opposed to ninth grade students who do not use Khan Academy as a remediation tool to

supplement grade level instruction as measured by the North Carolina READY Math I End-of-

Course Assessment.

56

Participants and Setting

The participants for the study include a convenience sample of ninth grade students from

two rural southern West Virginia high schools (A and B) during the fall and spring semesters of

the 2016-2017 school year. According to Public School Review (2016), for the 2013-2014

school year, high school A had approximately 660 students in grades 9-12. The student to

teacher ratio is 14:1, which is lower than the state average of 15:1. Minority enrollment is 2% of

students are eligible for free or reduced lunch. While the results of this study are not transferable

to all ninth-grade students in the United States, it is a representative sample of the population of

ninth graders attending rural high schools in the state of West Virginia.

The study consisted of 131 students enrolled in twelve ninth grade Math I classes taught

by five different teachers from two different high schools. The treatment group consisted of six

different Math I classes with a total of 74 students. There were also 57 students from six

different Math I classes in the control group. The sample exceeded the 15 participants for each

group being compared in an experimental research study as recommended by Gall, Gall, and

Borg (2003). The average age of the participants was 14. All of the Math I classes used the same

pacing guides developed by the county board of education and the same curriculum as outlined

57

classes.

The pretest and posttest scores from the North Carolina READY Math I End-of-Course

Assessment were used to determine the achievement levels in mathematics.

The North Carolina READY Math I End-of-Course Assessment was administered

operationally for the first time in North Carolina during the 2012-2013 school year. This test

was chosen for this study because it is aligned to Common Core, and it meets or exceeds the

industry norm for reliability. At the time of this study, the State of West Virginia’s end of course

EOC Math I Reliabilities (Edition 2)

EOC A B M N

Math I 0.91 0.91 0.9 0.9

Validity

Table 3.2 presents the validity evidence for the Math I end-of-grade and end-of-course

assessments provided by the North Carolina Department of Public Instruction (NCDPI) (The

64

the first mission, the teacher gave them the new class code and notified the researcher. Both the

Arithmetic and the Pre-Algebra missions cover 3-8 grade math content and are specifically

designed for older students needing remediation due to gaps in their math knowledge. If students

finished both of these missions before the end of the study, they were given a class code for the

Algebra Basics mission. This was done so that the students would still be participating in the

class warm up activity without having to provide them with something different for this portion

of the class or for their grade. This mission reviews the foundational ideas of algebra, pre-

algebra, and geometry (Khan Academy, 2015). So, it provided drill and practice of concepts

currently being covered in their class within the Math I content.

their students on a specified date.

This study hypothesized that statistically significant differences in mathematics

achievement would be found for ninth grade math students based on level of instruction, i.e.

grade level only and grade level plus remediation. Khan Academy, a supplemental online

resource, was used to provide the remediation.

The pretest and the posttest used in this study was the North Carolina READY Math I

65

instruction, served as the independent variable. In the fall of 2016, all students in Math I were

given the North Carolina READY Math I End-of-Course Assessment. The researcher collected

the data and used the Statistical Package for the Social Sciences (SPSS) software version 22.0 to

run the descriptive statistics on the data including the mean and standard deviation by level of

instruction i.e., grade level only and grade level plus remediation. Table 3.4 shows a distribution

of the students participating in the study.

Table 3.4

Distribution of Sample

Total

Grade level 57

Grade level + Khan Academy remediation 74

Total 131

66

variance, and for each independent variable, the relationship between the dependent variable (y)

and the covariate (x) is linear with a homogeneity of regression slopes. According to Gall, Gall,

and Borg (2007) histograms can be used to determine assumptions of normality since

achievement results are continuous. For the homogeneity of variance, a Levine’s test can be

used to verify that assumptions are equal among different samples. To ensure the homogeneity

of regression slopes, scatter plots for linearity and univariate tests can be performed.

The data in this study failed to pass the assumptions necessary for ANCOVA. The

histograms were non-normal and positively skewed, and the data failed the Levine’s test for

homogeneity of variances. So, a nonparametric test, Mann-Whitney U, was used in the analysis

67

In response to recommendations made by the federal government calling on all states to

adopt standards in mathematics that produce college-and-career-ready high school graduates,

curricular changes have occurred across the nation resulting in a more rigorous curriculum that

does not include the review of prerequisite skills or the remediation of students who have gaps in

their mathematical knowledge (U.S. Department of Education, 2011). Unfortunately, students

enter ninth grade with mathematical skill deficits that tend to expand during high school.

According to the National Center for Education Statistics (NCES), only 35% of eighth graders

research design. A Mann-Whitney U test was used to detect any differences in mathematics

performance between the two different levels of instruction i.e., grade level only and grade level

with remediation. A pretest was used to measure mathematical performance before treatment,

and the same test was used as the posttest to measure the dependent variable—mathematical

performance after the treatment. The pretest was administered in the fall of 2016 close to the

beginning of the school year, and the posttest was given in May of 2017 at the end of the year.

The tests were given to twelve ninth grade, Math I, classes from two different high schools.

68

Math I is the common core replacement for Algebra I. Six of the classes were assigned to the

control group, and six were in the experimental group.

Research Question

RQ1: What is the effect of using Khan Academy as a supplemental online remediation

tool on ninth grade students’ math achievement?

H

0

1: There is no significant difference in the math achievement of ninth grade students

who use Khan Academy as a supplemental remediation tool in addition to grade level instruction

as opposed to ninth grade students who do not use Khan Academy as a remediation tool to

measured by the posttest.

First, the researcher screened the data for missing data and outliers. Any participants that

failed to take both the pretest and the posttest were removed. Then, tests were performed in

SPSS including descriptive statistics to test the assumptions for parametric statistics. Histograms

revealed that while the control group posttest data was close to a normal distribution, the

experiment group posttest data was not normally distributed. The posttest data for the

69

experiment group was positively skewed and contained several outliers. The posttest scores for

the experiment group also failed the Levene’s test for homogeneity of variances.

The researcher screened the data again to determine if the outliers were the result of data

entry errors, measurement errors, or were genuinely unusual data values. All of the pre and

posttests were reviewed to rule out any grading errors. The instrument used for both the pre and

posttest had a short answer section that was hand-graded and a multiple-choice section that was

machine-graded. All of the hand-graded test sections for both the control and the experiment

group were regraded for accuracy. When reviewing the machine-graded sections of the tests,

two tests were found that had not been finished by the students. The researcher removed these

them significantly affected the results, the researcher took a closer look at the records within the

experiment group to determine an appropriate course of action.

Table 4.1

Descriptive Statistics

70

The study originally planned for all of the experiment group participants to finish both

the Arithmetic and the Pre-Algebra missions in Khan Academy at 100% before the posttest was

given. When the data was sorted by the percent complete of the first Khan Academy mission,

Arithmetic, only 8 students had completed 100% of the first mission. Although 92% of the

experiment group completed more than half of the first mission, only 17 students, 23% of the

group, completed 91-100% of the Arithmetic mission. Therefore, limited participation caused

the treatment, Khan Academy, to be applied in varying degrees across the experiment group.

Table 4.2 and Figure 2 show the different levels of completion of this first mission by the

students in the study.

71

Figure 2. Khan Academy Mission 1 Participation Bar Chart.

72

Given this change, a Khan Academy variable was created to hold the sum of the

Arithmetic and Pre-Algebra mission’s percent’s complete. This Khan Academy variable was

used to evaluate the total Khan Academy participation of the students in the experiment group.

The researcher sorted the data by the Khan Academy variable to organize the records by the

degree that the treatment was applied within the experiment group. The researcher used the

Khan Academy variable to help determine whether the posttest score outliers were genuinely

unusual values based on level of treatment.

The researcher divided the data sorted by the Khan Academy variable into four

subgroups based on the total Khan Academy participation (Table 4.3). Nine of the ten outliers in

change the results of the study.

Table 4.3

Experiment Group Khan Academy Treatment Levels

73

Figure 3. Control Group (1) and Experiment Group Subgroups (2-5) Posttest Means.

80

allowed students to continue working in Khan Academy during class while waiting for the next

Mastery Challenge to become available.

Recommendations for Future Research

Future studies are needed to determine whether Khan Academy improves student

learning when used for remediation. A shorter study requiring students to complete the Pre-

Algebra module only could possibly produce better results, especially if more control was

exerted over student participation. Competition between classrooms and a reward system for

completing sections of the module could help promote participation. The study should begin in

the fall and end sometime between January and March before spring fever and student burn out

remediation of past skills. Ideally, students would be placed in the Pre-Algebra module at the

beginning of the year and then be advanced to the Algebra module at a set time to finish out the

study with the posttest at the first of March, before spring break. This would be an interesting

study combining some review and remediation of prerequisite skills followed by drill and

practice of current algebra content.

Another interesting study would be to follow up with the experimental group of this

study to see how many of these students are still using Khan Academy as an online math tutor

when they are in the eleventh and twelfth grade. A questionnaire asking them if they are still

81

using Khan Academy and if they are using it for any subjects other than math would be an

excellent tool for research. The researcher has noticed that some students from classes in 2015

are still accessing the program in 2018, three years after being introduced to it in the ninth grade.

Once students learn to use the search feature in Khan Academy, many do continue to use it

throughout high school and possibly in college as well. Further studies of high school students

in urban and suburban areas with more diversity is also recommended.

82

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for remediation and review of basic pre-algebra skills will help our ninth grade students master

Math I content.

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Khan Academy Teacher Presentation

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Permission from North Carolina Public Schools

Request submitted 3/19/16 to http://www.ncpublicschools.org/newsroom/lets-talk/

Hello,

Your website, http://www.ncpublicschools.org/accountability/testing/releasedforms, grants

various educational purposes.

As a doctoral student at Liberty University I am interested in studying the effect of using Khan

Academy as a remediation tool in Math I classes to increase student math achievement. This

study will provide educators with a tool for remediating students who have gaps in their

mathematical foundation. I have been searching for a reliable and valid Math I assessment to use

as a pretest/posttest in my study.

as a pretest/posttest for my dissertation study?

Please feel free to contact me for more information. Also, if you are interested, I can provide you

Sandra Kelly

Sandra,

Thank you for your patience. I confirmed that you can use the released forms with the

understanding the released forms and the information contained within must not be used for

I wish you the best of luck!

XXXX XXXXX

Accountability Services Division

999-999-9999 (phone)

103