Evaluation of a Math Ramp-Up Program

8/3/2019 Evaluation of a Math Ramp-Up Program

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Running head: EVALUATION OF A MATHEMATICS RAMP-UP PROGRAM 1

Evaluation of a Mathematics Ramp-Up Program

for Economically Disadvantaged Students

Adam Williams

Jennifer Worrilow

Ryan Rickard

Georgia Southern University

FRIT 8435


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EVALUATION OF A MATHEMATICS RAMP-UP PROGRAM 2

Table of Contents

Executive Summary...................................................................................................3

Brief Overview of


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Executive Summary

Evaluation of a Mathematics Ramp-Up Program for Economically Disadvantaged Students

The nature of high stakes testing and consequences of failing to meet federal academic

progress requirements collectively have kindergarten through twelfth grade (K-12) institutions

continuously seeking remediation procedures that can improve student achievement. Ten years

after the implementation of the No Child Left Behind Act of 2001 (NCLB), the legislation

remains a controversial piece of educational legislation. Through this legislation, adequate

yearly progress (AYP) was constructed as a method of evaluating schools based on the

percentage of students who attained a proficient level on state-mandated tests. In response to

the legislation, school personnel strive to meet AYP requirements. However, the educational

means, access, and proficiencies that institutions implement to meet these standards vary. Many

inner city and rural institutions already lack the resources, qualified teachers, and technological

elements to accomplish accountability requirements appropriately. The result is a cycle of

institutions punished for failing to meet AYP year after year.

Cass High School, a rural institution in northwest Georgia, consists of a population in

which over half of the students come from low-socioeconomic subgroup (SES). In 2010, Cass

met AYP requirements for the eleventh grade students who completed the Georgia High School

Graduation Test (GHSGT) but failed to have the needed success rates for the economically

disadvantaged (ED) population (Georgia Department of Education, 2010b). With sanctions

inevitable if the school fails to meet AYP for a second year in the same ED subgroup, school

personnel implemented an intervention created for this critical population. Upon completion, the

researcher conducted an evaluation of the Math Ramp-Up program in order to review the success

and efficiency of the intervention.


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Testing and Adequate Yearly Progress

High-stakes testing has become more prevalent as state departments of education, state

school boards, and local schools systems implement these assessments to measure student

progress under NCLB (National Center for Education Statistics, 2008). In order to adequately

assess secondary schools performance annually, Georgia institutions administer a graduation

test to eleventh grade students. The Georgia High School Graduation Test consists of five

elements: Mathematics, Science, Social Studies, English and Language Arts (ELA), and

Writing, yet only the Mathematics and ELA tests are used to assess AYP (Georgia Department

of Education, 2010a). Georgia educators have placed emphasis on student achievement through

standardized assessments, and the consequences of failing to meet these standards have caused

an increase in teacher accountability. Thisheightened accountability on teachers with respect to

student achievement, the weighted emphasis schools have place on meeting standards, and the

dire consequences the federal government has placed on institutions that fail have made

educators desperate to meet AYP.

Many schools have begun to use detailed data analysis and academic-strand achievement

identifiers to create specialized intervention programs that target weak areas of student

performance and enhance learning. These approaches discover the areas where an institution

may fall short within AYP content domains, and seek to improve these areas to adequate levels.

Focus of the evaluation

Members of Cass High Schools staff created the Math Ramp-Up Program through the

collaboration of the Principal, an Assistant Principal, three math teachers who teach eleventh

graders, an external consultant, and officials within the school system (for anonymity, their


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names have been removed from Appendix A). The programs foundation started in reaction to

the school institutions failure to meet AYP in the economically disadvantaged subgroup for

mathematics in the 2009-2010 school year. Consequences exist for schools that do not meet

AYP in a particular subgroup for two consecutive years. In order to avoid sanctions, the school

required an appropriate intervention to ensure proficient test scores from eleventh graders

enrolled for the 2010-2011 school year who are economically disadvantaged. The first step in

creating the Ramp-Up Program involved a brainstorming session with the intervention

committee. These individuals discussed the criteria needed to identify individuals as

participants. The committee identified a list of Cass High School students who qualified forfree

and reduced lunch as economically disadvantaged. The committee then condensed the list to

only eleventh graders because only these individuals are subject to the administration of the

graduation test. Upon completing this list, the members reviewed the Math 2 End of Course Test

(EOCT) results. The curriculum standards of Math 1 and Math 2 contain the majority of the

information included on the Math GHSGT. Those students who did not receive aproficient

score on either of the EOCTs were labeled as at-riskand placed in the program.

After identifying the students that were to participate in the program the committee then

searched for the best methods to remediate the students. A review of state-produced test

resource materials included specifically written GHSGTCoach Books for review lessons and

practice items and anonline Math test preparation program (ExPreSS)online program created

for GHSGT review by the Georgia Department of Education. The committee decided that the

curriculum for the intervention would consist of ExPreSS as the primary source and the coach

books as secondary elements.


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The ExPreSS program consists of approximately 12 modules that involve a standardized

pretest per module, interactive lessons, and a posttest. Each student in the program must start

with the pretest in each module. The committee agreed that if a student attained a perfect score

on a particular module pretest, then the student could skip the lesson and posttest and move to

the next module. Any result lower than a perfect score resulted in the student completing the

interactive module and taking the posttest. A score of 8o or higher on the posttest would allow a

student to progress to the next module. A score of less than 80 on the posttest would require the

student to complete the lesson again from start to finish and retake the posttest. This process

would continue until the student earned the required score. In addition to the modules, ExPreSS

also contained a full-length practice GHSGT for students to complete at the end of the twelfth

module.

The committee decided that the Coach books would complement ExPreSS throughout the

intervention. The books are used when a student encountered particular difficulty completing a

module. A different format in instrumentation, pen and paper instead of computer-based, may

help the student where ExPreSS could not. The Coach books are used by students who may

have difficulty logging in to the computer program for various reasons, for student who complete

all 12 modules before the timeframe of the intervention is completed, or if the student is placed

in In-school Suspension for discipline reasons and the student is not allowed to come to the

computer lab where the intervention takes place.

The committee set the time length for the intervention at 45 school days starting on

January 3rd, the first day back from Winter Break for students. Administration decided that the

at-risk students would be transferred from an elective course to the Math Ramp-Up Program for

a set class period lasting 50 minutes for the duration of the intervention. For this reason, students


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would not miss any core academic courses and would easily assimilate back into the elective at

the conclusion of the program. The program was specifically placed within school hours due to

the transportation issues many students of ED may have if required to come early or stay after

school. However, due to the timing of the intervention classes, teachers would not be able to

adequately serve as administrators of the program. The school system allotted money for a

mathematically certified teacher that would be hired for the 45 days. However, the intervention

required math teachers to work with the at-risk students occasionally during their planning

periods to ensure student content understanding. For a detailed description of the process,

review Appendix A.

The sole purpose of the Math Ramp-Up Program is to assist the at-risk students in

reviewing the mathematic standards that are reviewed on the GHSGT in order to improve upon

their Math 2 EOCT scores and achieve a proficient score on the assessment. In addition, the

school staffs desire is to have these students perform in a manner that will allow the institution

to meet AYP. The stakeholders have a vested interest in seeing Cass High School avoid

sanctions for failing to meet AYP for the ED subgroup in mathematics for two consecutive years.

The Ramp-Up Program serves the purpose of fostering the necessary improvement from the

Math 1 and Math 2 EOCT scores that will help the institution avoid the consequences of not

meeting federal standards.

Evaluative Questions

The evaluation of the Math Ramp-Up Program attempted to answer the question: Did the

intervention have an effect on the at-risk students achievement resulting in a difference between

benchmark test scores? However, beyond simply relying on the numerical scores, a deeper

qualitative element of inquiry seeks to answer these questions: How do the teachers and school


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staff members describe the aspects of the program that were successful and the elements that

could be improved for efficiency of future interventions?

Evaluation Plan and Procedures

The participants of this evaluation consisted of the eleventh-grade students of economic

disadvantage that were labeled as at-risk and placed in the intervention program (n = 101).

However, only existing data was used in assessing the performance of these individuals. To

complement this population, the researcher also interviewed teachers and administrators that

developed the program and others that assisted in the programs implementation (n = 10). The

group consisted of administrators from the initial intervention committee, mathematics teachers

who tutored during the intervention sessions, non-mathematics teachers who assisted in student

tutoring, and the external teacher who acted as the overseer of the entire implementation. These

individuals are valuable due to their close proximity to the elements of the program and the rich

data they can provide through their experiences. The researcher excluded all members of the

program that did not have the depth of involvement as the previously mentioned sample.

To measure the quantitative element of the study, a comparison of means will be conducted

on existing data. The evaluator reviewed the results of the at-risk students three benchmark

tests, aspects of the intervention, so that he could determine if any evidence that supported an

improvement in scores existed. A significant difference is defined as an improvement of ten

points or more, cumulatively among all three tests. In addition to the statistical analysis, the

administrators and teachers completed a questionnaire. The survey consisted of items with a

five-point Likert scale through statements concerning the perceived success of the program and

the adequacy of the elements implemented.


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Findings

The purpose of the evaluation of Cass High Schools Math Ramp-Up Programinvolvedthe process of reviewing the elements and resources that the data showed as effective, those

found as ineffective, and other unused sources that may improve the intervention so that

stakeholders may take appropriate action based on the information. The data collected served

the purpose of answering the question: Did the intervention have an effect on the at-risk

students achievement resulting in a difference between benchmark test scores? In addition, the

evaluator was interested in the responses to the question: How do the teachers and school staff

members describe the aspects of the program that were successful and the elements that could be

improved for efficiency of future interventions? .

Statistical Analysis of Benchmark Tests

Reviewing the existing data from the 101 students of the ramp-up program, means were

calculated for each benchmark assessment. The average scores for the first, second, and third

benchmarks were 25.3, 35.8, and 33.8, respectively (see Appendix C). The difference between

the first and second assessment demonstrated a significant, holistic improvement of +10.5.

However, the mean of the third assessment reveals a change of only +8.8 from the beginning to

end of the program, thus forcing the conclusion that the intervention showed no significant

improvement in students test scores on the benchmark assessments. For this reason a closer

look at the data was necessary. Each benchmark, as well as the GHSGT, is divided into three

strands: Algebra, Geometry, and Data Analysis. The Algebra strands of the assessments

increased from a mean score of 22.6 to a 36.9, for a significant +14.3 differential. A review of

the Geometry strands reflected a +8.4 difference throughout the intervention, a non-significant

score, although not too far from a +10 point variance. The Data Analysis aspect of the


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benchmarks consisted of means of 27.8, 25.0, and 27.6; the result shows a meager -0.2

differential. Upon closer evaluation, it appears that the Math Ramp-Up Program had a

significant effect on students Algebra understanding, a small effect on Geometry competency,

and absolutely no effect with the Data Analysis curriculum intervention.

Quantitative Questionnaire Items

The results from the questionnaires reflected the opinions and observations of the

individuals who assisted in the implementation of the intervention. Based upon a 4 point Likert-

scale, a score of one means that the individual strongly agreed with the statement, a response of

two is equivalent to agreement with the statement, three means that the individual disagreed with

the statement, and four demonstrates that the individual strongly disagreed with the statement. A

not observed response was available as well, if applicable. When asked to respond to the

effectiveness of the Math Ramp-Up Program in terms of the goals outlined by the development

committee, the sample responded at a mean of 1.78 which represents a score between agree and

strongly agree. A statement concerning the reliability and efficiency of the ExPreSS computer

program resulted in a mean response of 2.78, which borders the disagreement scale. The sample

generally agreed (

X = 1.89) that the GHSGT Coach Books were a helpful and necessary part of

the intervention. A mean of 1.88 shows that the individuals involved in the intervention agree

that the benchmark tests were good examples of rigor and relevance to the actual GHSGT.

Finally, the sample agreed, though more moderately than the other items, that the ExPreSS

programs content was congruent to the standards covered by the Georgia Performance

Standards for Math 1, Math 2, and Math 3 with respect to the GHSGT.

Qualitative Questionnaire Items

In addition to the quantitative data, the evaluator desired to give the members of the sample


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an opportunity to voice concerns or positive comments for the elements of the Math Ramp-Up

Program. Of the qualitative responses concerning aspects of the intervention that the sample

believed contributed to student achievement, a common theme that emerged attributed program

success to the self-guided, small class sizes. One member of the sample commented, I believe

that having the students working at their own pace on the computer with a math teacher by their

side was the biggest help of all. Another individual stated that smaller class sizes with direct

GHSGT item instruction was the most helpful aspect of the intervention. The sample also

believed that consistent and direct teacher support contributed to a positive impact as well.

Additional adult/teacher support in the small group and having a former math teacher as the

instructor helped in that Mr. Slider was able to explain concepts in several different ways to

ensure that the students understood the concepts demonstrated the positive regard the sample

has towards the teacher/student interaction the Math Ramp-Up Program fostered. However, not

every aspect of the intervention met the standards of the sample.

Nearly all members of the sample had negative comments concerning the ExPreSS

program. One member assessed the computer-based program by simply stating the Express

Program not as useful as we would have liked. Members of the sample called the program

flawed, full of grammatical errors, and possessing missing pieces in the questions or

answer choices. However, the most glaring issue with the program concerns a glitch that allows

students to answer each question incorrectly multiple times, until they reach the correct answer,

with little or no penalty to their final score on the module test. One member of the sample wrote

the students learned quickly that there are a few different ways to cheat the program and get a

good score on a lesson without having really learned anything from the lesson. The express

program did not work as students would just click on the answers until they guessed the correct


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answer.they did this without reading the question or understanding the content was offered

by another individual. The overwhelming majority of comments demonstrated that the ExPreSS

program did not contribute to the overall goals of the intervention.

When asked to describe materials or techniques that could improve the Math Ramp-Up

Program, the first theme that emerged was earlier implementation. The programs duration

consisted of 45 total days. Members of the sample believed that an earlier start along with more

time spent in the program could help in future interventions; the statement identify at risk

students earlier and implement many of the same strategies sooner demonstrates this need.

Another individual adds that implementation of similar interventions could start earlier if

students who do not pass math in middle school were ramped up before they get to high school.

Yet other members of the intervention believed that better reading comprehension and

vocabulary training could increase the effectiveness of the program. One person stated that

emphasis math on vocabulary would help while another individual delved a little deeper into

their response:

The benchmarks indicated progress for many of the students, but achievement was still

low. Reading comprehension was a big obstacle. Future interventions should be earlier.

We have Math Support, Language Arts needs a READING intervention (this

recommendation comes from a LA teacher). Most of the students in the intervention can

do the algebra, but do not understand what is being asked.

A higher emphasis on reading comprehension and vocabulary can assist students when trying to

decipher the mathematical content and requirements in lengthy, word-laden test items. A longer

implementation period could allow for more time spent not only on mathematics curriculum, but

reading strategies and word recognition as well.


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Conclusions and Recommendations

The purpose of the study consisted of discovering the overall success of the Math Ramp-

Up Program, the elements that contributed and did not contribute to student achievement, and

valuable aspects missing from the intervention. The overarching themes of the data are that of

the programs content and structure.

The elements of the programs curriculum included the ExPreSS self-guided computer

program, the GHSGT Coach Books, and instruction from the outsourced teacher. The data

suggests that the intervention may have not been as successful as hoped, but that the content of

the program was generally acceptable. However, a slight contradiction existed between the

questionnaires quantitative and qualitative elements concerning ExPreSS. The computer

program received a mean score of 2.78 on the quantitative section of survey demonstrating that

at considerable percentage of the sample agreed that the program was reliable. Yet, in the

qualitative responses, nearly all of the individuals of the sample spoke of the flaws of ExPreSS

and the ease in which student could cheat the program, but wrote little or no positive remarks.

Without serious editing to the format of the questions and answers and corrections made to the

computer programming that will correct the score glitches, the ExPreSS program cannot be

relied upon as a valid intervention tool. Conversely, the GHSGT Coach Books received rave

reviews in the quantitative and qualitative sections, and through the samples observation,

contributed to student understanding. The instruction of the outsourced teacher assisted where

the ExPreSS program and coach books could not. The presence of this individual allowed for

students to have consistency in curriculum delivery, which is quite important under the 45-day

duration. In addition, by having an outsourced teacher, employed mathematics teachers could

come at their leisure to assist students and were not forced to sacrifice planning periods for the


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intervention period, thus affecting their preparation for other math courses.

Due to the nature of disadvantages that students with economic disadvantage (ED)

encounter, the format of the program enabled the at-risk students to get relevant learning

experiences that their socioeconomic situation would normally not allow. To implement the

program during school hours at no cost to the individual gave the ED population access to

resources that the students would otherwise not receive. Monetary and transportation issues

often thwart any opportunities that institutions offer to students of ED. Yet, the structure of the

Math Ramp-Up Program accounted for these obstacles and gave access to this marginalized

group. However, improves to the intervention could be made. The Math Ramp-Up Programs

time constraints did not give students the opportunity to get the most out of the intervention

content. Program construction began in December and implementation in January. With the

GHSGT administered in the second week of March, this process only allowed for 45 days of

intervention content. Other than the cost of the outsourced instructor, there is no reason why

identification of at-risk students could not begin after the End of Course Test (EOCT) results

arrive in May of their sophomore year and students be placed in the intervention when they begin

their junior year the following August. This process would increase the interventions timeframe

from 45 days to 135 days. With such an increase in instruction time, the mathematics curriculum

could be covered more in-depth, more emphasis could be placed on standardized testing

strategies, and reading comprehension lessons could be taught. The main argument from the

sample concerning the structure of the intervention simply called for more time.

Elements of the quantitative and qualitative data contribute to practice in the field of

education. Results from Likert-scale items on the questionnaire demonstrate that official, state-

licensed GHSGT review materials were more reliable for curriculum review. The Coach books


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were release by the state of Georgia to serve the purpose of preparing students for the graduation

test. The ExPreSS program, also created by Georgia Department of Education officials, was

intended for at-home use and not for large group intervention methods. Used at the students

home, through individual parent supervision, the ExPreSS program, while still full of many

errors, could contribute to student achievement. However, as seen in the qualitative responses of

the sample, in the setting of this particular intervention, the integrity of the computer-based

program was easily violated and without individual supervision, ExPreSS caused more problems

than it was worth. Finding adequate resources and using them for the purpose they were

intended for will save time, effort, and money when implementing interventions.

Conclusion

The Math Ramp-Up Program intended to serve the purpose of assisting eleventh-grade

students of low socioeconomic backgrounds in improving their mathematics standardized test

scores. Due to the high-stakes nature of the GHSGT and the consequences of AYP, this

intervention can either act as a life-ring for the institution by increasing academic performance,

or lack efficiency and waste resources. The Math Ramp-Up Program did not have a significant

impact on the benchmark test results. However, the existence of this intervention, in light of

issues of access for students of ED, is better than no intervention at all. The GHSGT Coach

Books, the instruction of the outsourced teacher, and the assistance of volunteer teachers

contributed as valuable assets to the program. Unfortunately, the ExPreSS program did not serve

the purpose that the development committee intended and the evaluator questions its efficiency,

reliability, and adequacy for future implementation. Future interventions should have longer

durations and include reading comprehension strategies. The Math Ramp-Up Program serves


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the purpose of providing students of ED the opportunity to review curriculum and access to

resources that their social capital often excludes.


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References

Georgia Department of Education. (2010a). Georgia High School Graduation Tests (GHSGT).

Retrieved from http://www.doe.k12.ga.us/ci_testing.aspx?PageReq=CI_TESTING_

GHSGT

Georgia Department of Education. (2010b). 2009 AYP. Retrieved from http://public.doe.

k12.ga.us/ayp2009/overview.asp?SchoolID=608-0577-g-8-0-0-0-0-0-0-0-0-0


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Appendix A


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Appendix B

Questionnaire

1. I feel that the Math Ramp-Up Program met the goals as outlined by the development

committee.

1 Strongly Agree 2 Agree 3 Disagree 4 Strongly Agree

2. I feel the ExPreSS computer intervention was a reliable aspect of the program.


3. I feel the ExPreSS programs content was congruent to the standards covered by the

GHSGT.


4. The Coachbooks offered were a adequate resource for GHSGT review.


5. The benchmark tests were good indicators of rigor and relevance to the GHSGT.


6. Please explain any aspects of the intervention that you believe were appropriate and ledto student achievement.

7. Please list the elements of the program that you feel did not work. What are the issuesthat you noticed in any of the materials?

8. Please list any materials that you feel would make to intervention better.


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Appendix C

Table 1: Overview of Benchmark Assessment Means (

X) by Strand

AssessmentTitle

Algebra Geometry Data Analysis Overall

Benchmark 1

X=22.

X=25.

X=27.

X=25.

Benchmark 2

X=39.

X=42.

X=25.

X=35.

Benchmark 3

X=36.

X=33.

X=27.

X=33.


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Appendix D

Table 2: Existing Data of Students Scores on all Three Assessments by Strand

4-Feb

15-Feb

8-Mar

Test

#1Test

#1

Test

#1

Test#1

Test

#2Test

#2

Test

#2

Test#2

Test

#3Test

#3

Test

#3

Test#3

StudentNumber Period

Algebra

Geometry

DataAnalysis Total

Algebra

Geometry

DataAnalysis Total

Algebra

Geometry

DataAnalysis Total

5 26 21 28 25 40 40 0 27 43 25 11 28

2 13 29 22 21 30 40 30 33

1 22 17 44 26 20 20 0 13 26 25 22 25

5 17 29 33 25 60 40 30 43 17 58 11 31

4 13 28 14

6 13 29 22 23 30 60 20 37 31 50 44 461 13 38 44 31 20 40 40 33

5 22 33 11 25 60 40 40 47 30 33 33 32

2 4 21 44 22 20 30 20 23 48 38 22 37

4 22 21 28 23 20 30 40 30 26 25 28 26

1 17 33 33 28 40 70 30 47 30 17 39 28

3 26 25 11 21 30 40 10 27 26 29 22 26

4 17 29 28 25 50 20 20 23 61 29 33 42

3 39 29 39 35 20 50 30 33 26 25 33 28

5 35 21 22 28 20 60 10 40 26 38 33 32

2 22 33 22 26 30 30 20 27 57 50 39 49

2 17 33 33 31 60 40 20 40 43 38 39 405 39 38 44 40 30 30 10 23 30 21 17 23

7 13 21 17 17 20 40 30 30 48 46 28 42

2 13 25 17 18 40 50 20 37 30 17 28 25

5 17 13 28 20 50 50 40 47 43 25 22 31

6 22 33 33 29 70 60 20 50 30 58 22 38

3 26 33 44 35 50 50 30 43

5 30 33 39 34 50 70 40 53 56 33 39 43

6 30 10 0 13

4 30 29 17 26 40 70 60 57 48 63 22 46

2 26 21 50 31 40 80 30 50 57 42 22 43

2 4 33 17 23 30 60 30 40 52 38 17 377 30 21 6 20 40 30 10 27 26 13 17 18

7 35 46 39 40 80 30 50 53 57 46 50 51

6 35 46 28 37 70 80 0 50 48 42 33 42

3 30 21 28 26 30 40 20 30 35 33 17 29

2 22 8 22 18 30 80 20 43 26 25 22 25

6 13 13 17 14 20 10 30 20 17 29 11 18

4 9 25 28 22 30 0 20 17


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4 26 17 22 21 10 30 10 17

5 9 8 17 11 20 30 20 23 35 42 50 42

4 35 33 50 38 50 50 40 47 65 46 33 49

5 26 17 33 25 10 30 40 27 48 50 17 38

3 30 33 17 28 30 30 30 30 17 42 39 32

4 22 17 33 23 50 40 30 40 52 46 50 491 30 25 33 23 30 20 20 23

5 35 17 39 29 30 60 50 47 43 42 39 40

6 26 42 17 29 30 20 20 23 35 21 28 28

4 26 21 28 25 60 40 10 37 61 42 22 43

1 23 25 28 25 50 40 30 40 37 17 39 37

5 17 29 17 23 50 50 20 40 52 38 22 37

1 26 13 33 23 20 10 10 13 30 17 22 23

1 17 50 39 35 90 40 30 53 61 38 61 51

2 26 21 17 23 50 50 30 43 26 29 17 25

6 35 29 33 32 70 70 10 50 31 38 17 35

7 17 38 17 28 20 50 40 37 52 50 34 467 17 17 28 20 40 40 50 43 52 29 33 42

1 17 21 22 20 40 30 10 27 9 29 28 22

3 17 21 33 23 40 20 40 33 17 33 28 29

6 22 33 33 28

2 30 29 39 32 20 50 40 37 35 33 28 31

7 22 23 17 25 39 38 39 38

5 50 70 30 50 43 33 22 34

2 22 33 33 31 60 50 50 53 57 46 33 46

6 4 13 17 11 70 20 0 30 61 42 22 43

1 30 13 39 23 30 20 10 20

2 17 25 28 25 60 50 20 43 39 38 17 322 35 29 28 31 70 50 40 53 74 33 50 52

7 26 38 17 28 30 20 20 23 35 38 17 31

5 50 40 20 37 22 13 22 18

1 26 13 6 15 30 40 20 30 39 25 22 31

7 13 21 28 22 10 60 40 37

2 22 29 39 29 40 40 20 33 35 42 50 42

3 17 25 17 22 40 80 30 50 65 46 39 65

4 17 33 33 28 20 40 30 30 26 38 28 31

4 22 33 17 25 50 50 30 43 39 46 28 38

4 22 30 44 29 20 30 30 27 39 42 11 32

3 13 25 33 20 50 40 20 37 30 29 22 287 26 25 0 18 20 30 20 23 30 29 28 29

4 35 38 44 38 60 60 30 50 61 42 28 45

4 22 25 39 28 60 60 20 47

3 13 21 22 18 30 80 30 47 32 35 25 33

4 26 25 39 29 40 30 40 37 17 21 28 20

4 22 13 33 23 40 10 0 17 30 25 22 26

6 22 25 17 22 30 30 20 27 35 17 28 26


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7 26 25 50 32 60 50 30 47

1 13 17 22 17 20 30 10 20 39 33 17 32

3 48 13 33 31 0 40 30 23 12 4 13 22

2 35 21 28 28 30 90 20 47 30 29 22 28

1 13 38 11 23 40 40 40 40 30 38 39 35

2 26 21 17 23 50 50 30 43 48 33 33 385 21 25 17 22 70 50 30 50 26 33 28 29

7 30 8 28 22 30 40 30 33

2 17 21 33 23 40 40 20 33 30 42 17 31

6 17 21 39 25 40 30 10 27 9 25 22 20

6 26 38 33 32 20 40 0 20 35 33 6 28

1 30 25 33 29 30 10 0 13 22 29 17 23

5 17 25 56 29 40 60 40 60 39 17 33 29

4 80 80 60 73 57 38 33 51

5 17 17 11 15 10 60 20 30 17 21 22 22

7 17 38 11 23 40 40 40 40 52 54 22 45

5 13 21 22 18 60 20 10 30 26 29 11 234 26 25 11 23 50 30 20 35 26 46 28 34

4 22 13 33 21 40 40 30 37 9 8 33 15

6 30 29 33 31 40 40 10 30 48 29 33 38


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Appendix E

Table 3: Representation of scores on the Likert-scale items of the Questionnaire

StronglyAgree

(1)

Agree(2)

Disagree(3)

StronglyDisagree

(4)

NotObserved

Mean

Question1

2 7 0 0 1 1.78

Question2

0 5 1 3 1 2.78

Question3

2 6 1 0 1 1.89

Question4

1 7 0 0 2 1.88

Question5

1 5 2 0 2 2.13

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Evaluation of a Math Ramp-Up Program