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Continuing to Assess 1 Running head: CONTINUNING TO ASSESS TECHNOLOGY Continuing to Assess Technology in Math Classroom for State Assessments Jeremy Hendrix Brett Tracy Copyright Jeremy Hendrix, Brett Tracy 2009

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Continuing to Assess 1

Running head: CONTINUNING TO ASSESS TECHNOLOGY

Continuing to Assess Technology in Math Classroom for State Assessments

Jeremy Hendrix

Brett Tracy

Copyright Jeremy Hendrix, Brett Tracy 2009

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Abstract

Every Arizona student has to pass the state mandated Arizona Instrument to Measure

Standards (AIMS) test before they can graduate from high school. Ensuring some weaker

students pass this test is seemingly impossible due to their lack of involvement in their own

learning, their teachers’ lack of caring, or the failure to conducting a proper review before the

test. A central problem in preparing for the AIMS test is providing immediate feedback on

practice tests in the classroom setting. This feedback is vital to all teachers and students because

it makes them aware of deficiencies as students prepare to take the AIMS test. A dull and

uninviting environment causes student participation and engagement in lessons to be less than

desirable. Students need to be engaged in material in a way that they find stimulating and

entertaining if they are too succeed. In order to assist in preparation for AIMS, interactive

technology was implemented into a math classroom in an Arizona high school for a two year

period to determine if a specific combination of technology would affect student success on the

AIMS assessment. Results over the investigated period of time showed, that when students

received immediate feedback and remediation during preparation for the AIMS students had

increased engagement which led to higher assessment scores and ratings.

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Introduction

While teachers prepare students to take state mandated tests, both teachers and students

are usually unaware of how well the students are acquiring the necessary skills and knowledge in

order to pass these tests. The passage of time during which no feedback occurs can be

detrimental to students’ development and progress while preparing for state mandated testing.

Once it is discovered students have fallen behind, the time needed to go back and review during

so mastery can occur can delay teachers and students assessment of students’ knowledge of the

material. The teacher can become frustrated in having to review material again and feel

pressured to get back on a timeline that has been set previously to cover all important and

required concepts for state mandated testing. The students, in addition to their development and

progress being stifled, can become frustrated with the material and stop learning.

With the development of a new interactive technology, student engagement,

participation, and performance can be monitored and assessed quickly. These technology tools,

such as interactive whiteboards (SmartTech’s Smartboard) and Student Response Systems

(eInstruction’s Classroom Performance System), allow teachers to create dynamic lessons and

assess student learning immediately. These new tools encourage students to become engaged as

active participants in their own learning, and allow them to maintain a comfort level with the

material that is being presented.

There has been several research studies conducted on student engagement and

participation in education over the past several years. Such research has demonstrated a direct

correlation between student success and the amount of time they are actively engaged (Wu &

Huang, 2007). However, research studies focused on outcomes when technology is infused into

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the course have occurred primarily at the post-secondary level. At the conclusion of a previous

study, (Tracy & Hendrix, 2008) on the topic, the researchers recommend a study in which

…one teacher collects all of the data … [in order to] will take the element of different teachers and their styles out of the equation. By incorporating this modification, the data should solidify the idea that technology tools which focus on engagement and participation will have an impact on student assessment. (Tracy & Hendrix, 2008)

he purpose of this study is to incorporate this recommendation in a high school math class to

T

determine if interactive technology affects student learning at the secondary level and

successfully prepares students for state mandated testing.

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Context

The community where the study took place is located in central Arizona in the

southwestern United States. In 2002, the State of Arizona mandated the Arizona Instrument to

Measure Standards (AIMS) as a requirement to ensure that its student population met a

satisfactory performance level in order to graduate with a high school (Arizona Revised Statutes

in Section 15 Article 701).

The study was conducted in a school district comprised of nine traditional and one

alternative high school. The student population of this district is approximately 15,000 students

with 900 teachers and administrators. The school district’s mission statement is to “Empower

All Students for the Choices and Challenges of the Twenty-first Century.” In the 2008 Arizona

LEARNS School profiles, seven of the high schools in this district were designated “Excelling,”

the highest possible ranking. The remaining two traditional schools received “Highly

Performing” labels, the second-highest ranking.

The school where the study took place has approximately 1700 students locally on its

campus as was classified as “Excelling.” The high school where the study was conducted was

recently re-classified as a “Title I school”, in which 60% of the students qualify for free and

reduced lunch. The school’s mission statement is “Every student can learn”.

There were approximately 450 sophomore students --the focal group of the study --in the

school each of the last two years. The mathematics area – the academic area focused on in the

study -- consists of twelve highly-qualified teachers in the area of mathematics of whom five

teach sophomore level mathematics. The AIMS review materials used during the study were

used by all five teachers.

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During the first year of research there were 54 students who participated in the study vs. 515

students that took the AIMS math test. In the second year of research 56 students participated in

the study vs. 460 students that took the AIMS math test. In the study, the two “experimental”

groups were compared to each other as well as the rest of the student population – the “control

group” -- during the appropriate academic years.

Most of the technologies utilized by the sophomore teachers are the same in that classrooms

have a computer at the teacher’s station, a projector, and an interactive whiteboard. The only

exception is one technology, a Student Response Systems, which was used by the students in

these experimental groups only.

The Student Response Systems manufactured by eInstruction is a classroom set of

handheld devices that allow students to communicate acquired concepts to their teachers in real

time. Teachers can assess these acquired skills in test format or during a classroom lecture. This

interactive technology promotes student engagement, participation and knowledge acquisition.

Currently, eInstruction’s classroom performance system is being used by over 4 million students

in more than 100,000 K-12 and higher education settings (einstruction.com, 2009)

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Theoretical Framework

Change is consistently occurring in all areas of life. Schools districts and individual

schools are not an exemption to this fact and there have been many changes in school districts,

schools, and classrooms. One of the more prominent changes in these entities has focused on

technology availability and integration. In many areas, money for technology integration has not

been distributed equally amongst states, schools districts, schools, or classrooms (Snyder &

Prinsloo, 2007). Due to this disparity of technology within schools and classrooms the pressing

issues of what technology to purchase, how it is implemented, and how can it change instruction

for students and teachers have begun come to the fore. In 2002, the United States federal

government passed the No Child Left Behind Act (Synder & Prinsloo, 2007) which includes

(Title II Section D) a stated goal of assisting all students to cross the “digital divide” to ensure

that they become technologically literate (Synder & Prinsloo, 2007). How can school districts

and schools help students become technology literate if they cannot purchase and implement

technology into their classrooms?

These events place the successful use and implementation of technology in schools and

classrooms squarely on the shoulders of administrators, teachers, and instructors. Teachers and

instructors will benefit from using technology in their classrooms if their students are motivated

and use technology in the class Great care must be taken when adopting new technologies into

classrooms because they can interfere with the learning process (Hashemzadeh & Wilson, 2007).

In order to avoid this interference, some classroom materials and philosophies would have to be

abandoned in favor of a total redesign of the course (Hedberg, 2006). These new courses would

have to extend beyond the current implementation -- and move beyond just passing information

to students -- into making the students more interactive with the information (Hedberg, 2006).

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Los Angeles-based educator and 1-to-1 computing advocate Gary Stager believes that when

educators become aware of new ways for students to learn, they also realize that many of the

traditional ways we expect students to learn are ineffective (Wambach, 2006). Christensen’s

(Hedberg, 2006) idea of disruptive innovations describes how these changes with technology can

occur and states:

Disruptive innovations or technology is one that eventually takes over the existing dominant technology in the market, despite the fact that the disruptive technology is both radically different from the leading technology and that it often initially performs less successfully that the leading technology according to existing measures of performance, but over time the functionality or the attributes of the new way of doing things replace the other technologies.

This idea of disruptive innovation can then be implemented into the concept that in order to

achieve specific desired effects many tools, instead of one, may need to be employed to create a

range of interactive activities using technical resources by the teacher to create motivation in the

student so he/she will commit more time and energy to learning (Hedberg, 2006).

There have been many research studies conducted on student engagement, participation,

and performance in education over the past several years. Research that has focused specifically

on student participation and engagement has shown that there is a direct correlation in student

success to the time they are actively engaged (Wu & Huang, 2007). However, research studies

that investigated student participation, engagement, and performance with technology infused

into the course have occurred primarily at the post-secondary level. These studies have focused

only on the implementation of a specific form of technology, instead of integrating multiple

technologies into the course. In order to determine if technology can help improve student

engagement, participation, and ultimately performance, all of the technologies need to be

investigated as a single form.

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One of the systems researched to investigate student engagement, participation, and

performance are remote devices that students used to answer questions and provided personal

thoughts to the teacher regarding information being presented during class activities and

presentations. These systems commonly referred to as Student Responses Systems, have begun

to be implemented into educational settings with varying results. Pemberton, Borrego, and

Cohen (2006) noted that with the use of student response systems final grades were not

significantly different between similar groups, but the value of the learning and teaching in

psychology classes that used the Student Response System was much higher than the psychology

classes that did not use this technology at Texas Tech University. In addition, a study conducted

by Texas Instruments and the University of Texas demonstrated that the ability to respond to

questions anonymously created a non-threatening environment in which students felt they were

equals, causing greater participation and engagement in class activities and discussions (Davis,

2003).

Interactive whiteboards are a second form of technology that has been researched to

determine their effects on student engagement, participation, and performance. Interactive

whiteboards bring on a different form of student interaction with the teacher and students.

Haldane (2007) noted in her research that although teachers at the beginning of her study did not

feel interactive whiteboards would affect their planning and teaching of lessons, they did note

that the interactive whiteboard had significantly changed their preparation and teaching practices

by the end of the study. She continued, “It is the user of the board who chooses whether or not

to take full advantage of the digital whiteboard’s interactive potential. The digital board simply

provides an opportunity for interactivity to occur” (p. 259). It is this interactivity that allows the

questions and suggestions to be posed by students, to help ensure that everyone in the classroom

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has grasped the concept to further their own knowledge base. In addition, interactive

whiteboards help in keeping the momentum of the class consistent. Teachers can simply tap an

icon to bring up previous or new material to review at any time during class activities. This is in

contrast to having to make sure the information is consistently available on the static whiteboard,

which may get erased at any time.

Lastly, many forms of technology are still relatively new to education (Moallem,

Kermani, & Chen, 2005), which is especially the case when incorporating online testing systems.

Paper and pencil tests traditionally do not show if students are acquiring the needed knowledge

and skills through the instructional methods that their teachers are currently practicing

(Woodfield & Lewis, 2003). Due to the time it takes to assess results from paper and pencil

tests, many important missing pieces of information are lost in order to move on in the class. If

the information was immediately available teachers could look at tests scores quickly, decide if

the students met expectations in order to explore new topics in the class, or if concepts needed to

be re-taught using different methods before moving on so the information makes sense at that

present moment (Woodfield & Lewis, 2003). The ability to facilitate instantaneous feedback

through online testing allows the teachers and students to quickly assess their own strengths and

weaknesses in their teaching and learning (Moallem, Kermani, & Chen, 2005). This form of

testing has proven to be more motivating than traditional test forms (Woodfield & Lewis, 2003).

Teachers who have implemented this form of testing have additionally reported that student

interest and attention have increased when using the computer to take class tests (Woodfield &

Lewis, 2003). In most cases, teachers have reported that purchased online tests are appropriately

challenging to all students, measure individual student performance, provide data that can be

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compared and analyzed for specific purposes, and closely engage students and teachers in the

educational process (Woodfield & Lewis, 2003).

Instead of looking at each of the technical systems listed above individually, if a teacher

were to look at them as a whole, Christensen’s idea of disruptive innovation would allow for an

investigation into the impact on student motivation, participation, and performance. In order for

successful tasks to occur with multiple forms of technology the following properties need to be

in place within the classroom and supported by the teacher: 1) the tasks to be completed by the

student are complex enough to engage students in upper level thinking and performance skills; 2)

they exemplify authentic work and learning; 3) they are open enough to encourage different

learning approaches, but constrained enough so they do not become out of hand; and 4) records

and information can be collected and calculated quickly for assessment (Collins, Hawkins, &

Frederiksen, 1993). By integrating interactive whiteboards, anonymous response systems, and

immediate feedback systems together, students can accomplish these tasks in addition to

interacting with the information as an individual or as a group, practicing self-assessments,

taking assessments, and receiving feedback immediately (Collins, Hawkins, & Frederiksen,

1993). All of these pieces together can help facilitate non-dominating conversations, debates,

and arguments so that ideas and knowledge can be shaped or reshaped allowing students to own

the information and ensuring success in the future (Masters & Oberprieler, 2004). To confirm

that learning, participation, and motivation are occurring it is suggested that work discussed

should be tied to a classroom assignment. This would serve as encouragement for students to

participate more in class (Masters & Oberprieler, 2004).

With the teachers integrating multiple tools to increase participation, motivation, and

performance in their classrooms, they now have vast amounts of data about their students at a

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moment’s notice. Teachers who use all of these tools can track how students are interacting and

performing in class (Morris, Finnegan, & Wu, 2005). With this information in hand, teachers

can then direct students towards areas that refinement and review needs to occur (Morris,

Finnegan, & Wu, 2005). This immediate directional change by the teacher demonstrates to the

student the teacher is invested in their success in class. By the students knowing the teacher is

invested in them, the students then begins to grow an excitement for learning and their

confidence continues to grow so they are prepared for success on the next homework

assignment, quiz, test, and the future. Teachers can have an enormous impact on their students

by holding them accountable to the material that is being presented.

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Method

The district has implemented various forms of technology into classrooms to better prepare

students for the AIMS test, including interactive whiteboards and LCD projectors. However,

with these technologies student success on the AIMS math assessment has not improved and, in

fact, has remained relatively unchanged throughout the last five years with a few moderate

increases and decreases in the rate at which students pass. There have been no formal

comparison studies to see if these technologies have made an impact on the students’ AIMS test

scores and the technologies have been implemented sparingly and not used as a whole.

The high school district, in which the school-site where the study took place, has

implemented a three-week AIMS preparation module into the curriculum of all sophomore math

classes in conjunction with the technology they have previously implemented. This preparation

came into effect due to low scores by too many students’ on prior AIMS tests. The experimental

investigation coincided with the delivery of the AIMS preparation module lasting three weeks

and including a pre-test, a post-test, and four review packets. The pre-test and post-test, although

proctored by the teachers in their classrooms, are graded and analyzed by the high school district.

Upon analysis completion pre-test and post-test scores are reported back to the teachers in a time

delayed state. The four review packets consist of multiple choice questions designed to simulate

the AIMS math assessment. Their intended purpose is for the student to review questions that

have similar format, scope and sequence, and level of difficulty to the actual AIMS math

assessment.

Based of a previous study (Tracy and Hendrix, 2008), the best technology build out was

to incorporate all the technologies previously implemented by the district with the addition of the

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Student Response System. With the addition of this interactive technology teachers and students

were able to communicate directly about what concepts were mastered in preparation for the

AIMS math assessment. During the study the Student Response System was used in the testing

mode to instantaneously show the students and teacher what concepts were mastered from the

district created review module. From this information the teacher was able to immediately

review only the concepts that were not at a mastery level, so that students could continue to

progress through the material in a timely fashion. When compared to other teachers who had to

manually grade the review packets and return them the next day, the student response system

accomplished this time intensive task immediately. In addition, the Student Response System

provided immediate analysis of student progress helping the teacher better prepare the students

to focus only on weaker concepts. Whereas the teachers who had to grade by hand were at a

disadvantage because they had to calculate this information on their own.

In the two study groups the students would spend approximately 20 to 30 minutes of the

allotted class time to work on small portions of the review packets and input their answers using

the Student Response System. The remaining 20 to 30 minutes was spent covering the questions

that were missed by the students. With the use of the Student Response System the teacher knew

exactly which students missed which questions. This allowed the teacher to direct the attention

towards the students that needed remediation and away from the students that had already

mastered these concepts.

During this remediation time the teacher would call on students that missed particular

questions to work the problem on the interactive whiteboard and then would poll the class using

the Student Response System so the student could get peer feedback to determine if they did the

problem correctly. If the problem was done correctly the teacher would move on to the next

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problem. If the problem was done incorrectly another student was randomly selected to rework

the same problem on the interactive whiteboard to fix any mistakes that were made. The class

was then polled again to make sure of mastery on this particular problem. The original student

called to the interactive whiteboard, was then questioned to make sure that they understood the

mistake they had made and why the correction was needed.

Once an entire review packet was completed, the teacher would post the grades of all

students for the class to see. When the teacher posted these scores students names were

displayed next to their scores for the whole class to see. The teacher made sure to tell the class

that every student is here to learn and nobody is to be made fun of for their score. After the

posting of the overall score for the review packet, the teacher then posted the individual question

report that also had students names displayed with what they had previously answered on the

question. The teacher then went over this again question by question, filling in any gaps that the

students may still have had on these problems. This process was repeated for the four review

packets as well as the pre and post-tests.

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Findings

It is hypothesized that the implementation of technology on reviews for state mandated

testing reveal that the students are engaged, that the students will participate, and that their scores

will have an increase of at least 10% in a three-week period. The goal of this study is to prove

that you can get students to improve in preparation for state mandated testing at a faster rate

using technology to foster your review session than without such technology.

The use of several technology tools acting as one will not only increase student engagement

and participation, but will also increase performance on the state mandated AIMS math

assessment. The students will receive immediate feedback on their learning so they can ask

questions for clarification and refinement. All students will at least achieve the “meets” rating

on their AIMS assessment. Thirty percent of all the students will receive an “exceeding” rating

on their AIMS assessment.

The study is centered on a group of 54 students (Year 1 grouping), and a group of 56 students

(Year 2 grouping) who took a district pre- and post- assessment. The study measured growth for

the three-week periods in which the district review module was implemented. The ultimate

success will be measured by the AIMS ratings for each student. Minimal growth would be

defined as zero to ten percent, whereas substantial growth would be any growth over 10%. The

number of students who will achieve a “meets” or “exceeds” rating on the AIMS assessment will

determine the ultimate success of the project. After the state reports back the AIMS results to the

district the researchers will be able to determine if the intervention was a success or not.

The study participants not only met the desired outcomes that were set forth, they

completely exceeded them. With the substantial growth goal being set at 10%, only one student

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out of the 54 students in study group #1 (Appendix A & B) , and 3 students out of the 56 students

in study group #2 (Appendix C & D), had less than substantial growth. The highest level of

growth experienced in study group #1 was 50% while the highest in study group #2 was a 61%

increase in scores during the three week study window. The average growth for all the students

in study group #1 was 23% and in study group #2 was 29.97% (see Appendix E- J for

comparison data). This result was rather unexpected, but proves that the use of technology that

the students are familiar with had a profound impact on the district reported scores.

The last part of this study was to see if this interactive technology would ultimately have

a profound impact on the AIMS math assessment. While there would be no pretest to show

growth on the AIMS math assessment, one can compare the study group with the entire school

population. Quantitative data analysis demonstrated that the reviews associated with the

implemented technologies helped students receive a high score on their AIMS math assessment

when compared to students who received reviews without the implemented technology. Of the

54 students who participated in the study during year 1, zero failed or approached on the AIMS

assessment. All 54 students (100%) met the minimum passing score on the AIMS assessment.

The average scored of this group was 747 with 900 being a perfect score. Of the 54 students, 25

of them received an “exceeding” rating, the highest rating on the assessment. The remaining 29

students received the “meet” rating, the second highest rating on the assessment. Of these 29

students, 11 of them missed the “exceeding” rating by one correct response on the assessment.

46% of the students “exceeded” on the AIMS math assessment. When compared to the rest of

the student population only 87 students received an “exceeding” rating on their AIMS test, which

means that 29% of the total exceeding population of the school came directly from the study

group (see appendices K, L, M for AIMS data).

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Of the 56 students who participated in the study during year 2, zero failed or approached

on the AIMS assessment. All 56 students (100%) met the minimum passing score on the AIMS

assessment. The average scored of this group was 756 with 900 being a perfect score. Of the 56

students, 27 of them received an “exceeding” rating, the highest rating on the assessment. The

remaining 29 students received the “meet” rating, the second highest rating on the assessment.

Of these 29 students, 7 of them missed the “exceeding” rating by one correct response on the

assessment. 48% of the students “exceeded” on the AIMS math assessment. Included in these

scores was one student who scored a perfect 900 on their AIMS math assessment. Due to a state

embargo on the school and district data, we do not at this time have access to any other students’

scores (see appendices K, L, M for AIMS data).

When comparing study group #1 to study group #2 there was an average increase of nine

points. In study group #2 the average score was six points above the required score of 750 to get

an “exceeding” rating. Whereas in study group #1 the average score was three points below the

required score of 750 to get an “exceeding” rating. Qualitative data analysis demonstrates that

this increase in average raw score is due to higher expectations from the teacher at the beginning

of the review module, more familiarity with the technology and method, a change from a teacher

centered model to a student centered model, and class buy in due to knowledge from study group

#1.

The initial growth data was staggering enough to justify that this research has been a

success, and after the actual AIMS numbers to the study are added there was an amazing

differentiation of how this technology impacted the way students can prepare for state mandated

testing. The research shows that the study groups learned and retained the information being

presented to them for a longer period of time. The study groups were able to take the

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information and apply it to a high stakes test regardless of any predisposed fear of testing. They

used the knowledge gained through the technology to achieve something that the researcher

never thought was possible.

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Implications

The researchers learned many things from this study. First the researchers learned that

regardless of what students you have, if you give them the necessary tools to be successful they

can and they will be successful. Educators need to look at what tools students can benefit the

most from and try to create a learning environment in which students can achieve greater

success. Secondly, the researchers learned that technology is already all around us, and we must

embrace it to help our technology savvy students learn in the same way they play. Students use

technology all the time, as teachers we are doing our students a disservice by taking away the

one thing that keeps them going, technology.

Although the use of technology, the desired outcomes, and way the data was obtained

never change, the class structure and instruction did modify over time to met student needs. In

the first year of research, the researcher followed a teacher centered model where he would

constantly try to help out students using a simple explanation of how to do the problems. In

second year of the research, the researchers let the students explain more of how they did the

problems and why they did the problems that way. Instead of this being a teacher driven review

session as in year one, the researchers would let it be a student centered review session where

they put in all the input to other students in the second year. The change of instruction can be the

indicator why students performed better earlier in the study window in the second year over the

first year.

Due to the benefits of the student centered model being implemented student

accountability was enhanced. The students in the first year of the study were only accountable to

themselves, which takes a special student to remain on task and keep focus for the whole entire

time of the study. As the researcher, posting of student scores without names for all to see

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created a level of accountability without the humility of other students seeing your name. Doing

this increased the anxiety level of the student just one step more and allows them to have a sense

of accountability placed on them by the other students in the room. It goes back to the old

saying; it takes a community to raise a child. In this aspect you are allowing the students to help

each other out. The researchers foresaw weaker students seeking out stronger students for

assistance and clarification in order to improve their own scores. This idea of transparency for

all students is generally not well received by the educational community and is looked down

upon. The main thing about this is you have to maintain an open learning environment for all

students to be successful.

In conducting further research using this same type of technology and method, the

researcher recommends that a learning environment be created where students feel comfortable

sharing ideas with the instructor. A positive learning climate must be maintained in order to

achieve the same amount of success. Classroom management is a huge key to the successful

results obtained from this study. Keeping students on task and free from misbehaving is

absolutely vital to maintain an engagement level you need for this study. Lastly being a good

teacher and adapting to the variety of students is necessary. The teacher cannot be rigid in their

presentation, must be willing to stop and take the time to answer any necessary questions that the

students have.

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References

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Students: The Role of Technology in Assessing Student Performance. Journal of the

Learning Sciences, 3(2), 205. Retrieved October 30, 2007, from Academic Search

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Davis, S. (2003). Observations in classrooms using a network of handheld devices. Journal of

Computer Assisted Learning, 19(3), 298.

EInstruction-Simple Solutions. Real Results. 23 June 2009 <http://www.einstruction.com/>.

Haldane, M. (2007, September 1). Interactivity and the Digital Whiteboard: Weaving the Fabric

of Learning. Learning, Media and Technology, 32(3), 257. (ERIC Document

Reproduction Service No. EJ772462) Retrieved September 30, 2007, from ERIC

database.

Hashemzadeh, N., & Wilson, L. (2007, September). Teaching With The Lights: Out What Do

We Really Know About The Impact Of Technology Intensive Instruction?. College

Student Journal, 41(3), 601-612. Retrieved October 30, 2007, from Academic Search

Premier database.

Hedberg, J. (2006, July). E-learning futures? Speculations for a time yet to come. Studies in

Continuing Education, 28(2), 171-183. Retrieved October 30, 2007, from Academic

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Appendix A

Class #1 (Year 1) from pre-test to post test

Pre-test

In Class #1

Growth #1

In Class #2

Growth #2

Post-Test

Growth Post

Overall Growth

78 84 6 88 4 88 0 10 60 72 12 82 10 90 8 30 72 80 8 82 2 82 0 10 52 66 14 78 12 88 10 36 62 76 14 86 10 88 2 26 68 74 6 90 16 92 2 24 36 66 30 82 16 86 4 50 48 51 3 54 3 72 18 34 72 78 6 92 14 96 4 24 46 82 36 90 8 96 6 50 86 90 4 92 2 98 6 12 76 76 0 86 10 96 10 20 76 86 10 86 0 96 10 20 52 65 13 66 1 80 14 28 54 58 4 62 4 67 5 13 74 76 2 86 10 88 2 14 34 56 22 80 24 82 2 48 64 70 6 86 16 90 4 26 36 50 14 65 15 78 13 42 82 88 6 94 6 98 4 16 80 82 2 90 8 94 4 14 82 80 -2 86 6 94 8 12 64 84 20 84 0 90 6 26 46 76 30 82 6 84 2 38 38 48 10 65 17 76 11 38

61.52% 72.56% 11.04% 81.36% 8.80% 87.56% 6.20% 26.44%

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Appendix B

Class #2 (Year 1) from pretest to post test

Pre-test

In Class #1

Growth #1

In Class #2

Growth #2

Post Test

Growth Post

Overall Growth

64 74 10 86 12 92 6 28 60 68 8 73 5 84 11 24 52 59 7 66 7 68 2 16 70 75 5 80 5 84 4 14 76 88 12 88 0 92 4 16 62 63 1 72 9 80 8 18 54 62 8 92 30 96 4 42 40 53 13 54 1 58 4 18 54 67 13 78 11 80 2 26 60 68 8 71 3 86 15 26 74 76 2 82 6 88 6 14 80 84 4 90 6 92 2 12 46 60 14 73 13 80 7 34 82 82 0 94 12 100 6 18 46 62 16 69 7 84 15 38 52 66 14 73 7 82 9 30 86 86 0 94 8 98 4 12 64 69 5 76 7 80 4 16 74 86 12 86 0 92 6 18 78 78 0 80 2 86 6 8 74 82 8 86 4 90 4 16

64.19% 71.81% 7.62% 79.19% 7.38% 85.33% 6.14% 21.14%

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Appendix C

This is class #1 (Year 2) from pre-test to post-test

Pre-test

In Class Test #1

Growth #1

In Class Test #2

Growth #2

Post-Test

Growth post

Overall Growth

52 70 18 74 4 82 8 3058 90 32 86 -4 98 12 4064 88 96 8 3253 76 23 80 4 90 10 3778 82 4 92 10 98 6 2075 78 3 90 12 84 -6 958 86 28 84 -2 96 12 3878 86 8 86 0 92 6 1472 74 2 78 4 88 10 1644 68 24 78 10 76 -2 3267 74 7 82 8 84 2 1753 78 90 12 3747 78 31 80 2 94 14 4781 88 7 96 8 88 -8 767 82 15 92 10 92 0 2572 84 12 86 2 92 6 2067 80 13 82 2 92 10 2564 68 4 72 4 88 16 2481 92 11 84 -8 98 14 1769 90 21 90 0 100 10 3172 88 16 82 -6 92 10 2058 68 10 64 -4 86 22 2861 78 17 82 4 88 6 2758 86 28 84 -2 96 12 3856 74 18 76 2 80 4 2453 80 27 80 0 90 10 3775 82 7 88 6 100 12 25

64.19 80.08 15.89 82.74 2.66 90.74 8 26.56

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Appendix D

This is class #1 (Year 2) from pre-test to post-test

Pre-test

In Class Test #1

Growth #1

In Class Test #2

Growth #2

Post-test

Growth post

Overall Growth

58 86 28 70 -16 86 16 28 53 80 27 78 -2 90 12 37 50 84 34 78 -6 96 18 46 75 86 11 94 8 98 4 23 78 82 4 88 6 94 6 16 50 64 14 72 8 82 10 32 44 74 30 74 0 84 10 40 64 86 22 88 2 88 0 24 33 70 37 82 12 94 12 61 58 78 20 88 10 92 4 34 56 72 16 82 10 92 10 36 72 80 8 84 4 94 10 22 47 68 21 84 16 80 -4 33 42 78 90 12 48 64 64 0 74 10 96 22 32 39 74 35 72 -2 94 22 55 75 82 7 88 6 92 4 17 50 82 32 82 0 88 6 38 75 78 3 82 4 90 8 15 53 70 17 70 0 90 20 37 42 78 36 66 -12 86 20 44 75 90 15 92 2 98 6 23 58 74 16 78 4 92 14 34 50 68 18 74 6 86 12 36 42 66 24 78 12 90 12 48 56 84 28 82 -2 88 6 32 47 82 35 86 4 94 8 47 86 94 8 88 -6 92 4 6 58 64 6 82 18 82 0 24

56.90 77.14 20.25 80.48 3.34 90.28 9.79 33.38

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Appendix E

Growth of Math Classes when studying for Arizona State Math

Assessment (percent scores)- 1st Year

64 67.1281.48 86.88

69.14 68.8678.33 84.19

Pretest In-Class Test #1 In-Class Test #2 Post Test

Group 1 - Year 1 Group 2 - Year 1

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Appendix F

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Appendix G

Growth Comparison in Math Classes when studying for

Arizona State Math Assessment (raw score) - 1st Year

3.12

14.365.4

19.28

-0.289.48 5.86

15.05

Growth Betweenpre-test and in

class #1

Growth between Inclass Test #1 and

in class #2

Growth between inclass test #2 and

Post Test

Growth betweenPre-test to Post-

Test

Group 1 - Year 1 Group 2 - Year 1

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Appendix H

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Appendix I

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Appendix J

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Appendix K

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Appendix L

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Appendix M

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Appendix N

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Appendix O