Editorial Note:

Polygon is MDC Hialeah's Academic Journal. It is a multi-disciplinary online publication whose purpose is to display the

academic work produced by faculty and staff. In this issue, we find seven articles that celebrate the scholarship of teaching

and learning from different academic disciplines. As we cannot understand a polygon merely by contemplating its sides, our goal

is to present work that represents the campus as a whole. We encourage our colleagues to send in submissions for the next issue of

Polygon. The editorial committee and reviewers would like to thank Dr. Goonen, Dr. Bradley-Hess, Dr. Castro, and Prof. Jofre for

their unwavering support. Also, we would like to thank Mr. Samuel Hidalgo and Mr. John Munoz of Media Services for their

work on the design of the journal. In addition, the committee would like to thank the contributors for making this edition possible.

It is our hope that you, our colleagues, continue to contribute and support the mission of the journal.

Sincerely,

The Polygon Editorial Committee

The Editorial Committee:

Dr. Mohammad Shakil - Editor-in-Chief

Dr. Jaime Bestard

Prof. Victor Calderin

Reviewers:

Prof. Steve Strizver-Munoz

Prof. Joseph Wirtel

Patrons:

Dr. Norma M. Goonen, Campus President

Dr. Ana Maria Bradley-Hess, Academic Dean

Dr. Caridad Castro, Chair of Arts and Sciences

Prof. Maria Jofre, Chair of EAP and Foreign Languages

Mission of Miami Dade College

The mission of the College is to provide accessible, affordable, high-quality education

that keeps the learner’s needs at the center of the decision-making process.

Miami Dade College District Board of Trustees

Helen Aguirre Ferré, Chair

Peter W. Roulhac, Vice Chair

Armando J. Bucelo Jr.

Marielena A. Villamil

Mirta "Mikki" Canton

Benjamin León III

Robert H. Fernandez

Eduardo J. Padrón, College President

Editorial Notes i

Guidelines for Submission ii-iii

Waiting for a Pattern in Coin Tossing 1-5 M. Andreoli Common Mistakes Made by Native Spanish Speakers 6-10 M. Orro The Importance of the Study of Evolution in the Course PSC1515 "Energy in the Natural Environment"

11-14 A. Rodriguez

On an Iterative Algorithm in Multiobjective Optimization

15-26 J.A. Serpa

African-Americans in Mathematical Sciences - A Chronological Introduction

27-42 M. Shakil

Survey of Students' Familiarity with Grammar and Mechanics of English Language - An Exploratory Analysis

43-55 M. Shakil, V. Calderin, and L.

Pierre-Phillip Effects of Developmental Courses on Students' Use of Writing Strategies on the Florida College Basic Skills Exit Test

56-80 M. L. Varela

Comments about Polygon 81-82

Disclaimer: The views and perspectives presented in these articles do not represent those of Miami Dade College.  

ii

POLYGON: Many Corners, Many Faces

(POMM)

A premier professional refereed multi-disciplinary electronic journal of scholarly works, feature articles

and papers on descriptions of Innovations at Work, higher education, and discipline related knowledge for

the campus, college and service community to improve and increase information dissemination. It is

published by MDC Hialeah Campus Arts and Sciences Department.

Editorial Committee:

Dr. Mohammad Shakil (Mathematics), Editor-in-Chief

Dr. Jaime Bestard (Mathematics), Editor

Prof. Victor Calderin (English), Editor

Manuscript Submission Guidelines:

Welcome from the POLYGON Editorial Team: The Department of Arts and Sciences at the

Miami Dade College–Hialeah Campus and the new members of editorial committee — Dr. Mohammad

Shakil, Dr. Jaime Bestard, and Professor Victor Calderin — would like to welcome you and encourage

your rigorous, engaging, and thoughtful submissions of scholarly works, feature articles and papers on

descriptions of Innovations at Work, higher education, and discipline related knowledge for the campus,

college and service community to improve and increase information dissemination. We are pleased to

have the opportunity to continue the publication of the POLYGON, which will be anually during the

Spring term of each academic year. We look forward to hearing from you.

General articles and research manuscripts: Potential authors are invited to submit papers for the

next issues of the POLYGON. All manuscripts must be submitted electronically (via e-mail) to one of the

editors at mshakil@mdc.edu, or jbestard@mdc.edu, or vcalderi@mdc.edu. This system will permit the

new editors to keep the submission and review process as efficient as possible.

Typing: Acceptable formats for electronic submission are MSWord, and PDF. All text, including title,

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Style: For writing and editorial style, authors must follow guidelines in the Publication Manual of the

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will be used by readers to search for your article after it is published. Book reviews: POLYGON accepts

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education, Innovations at Work, and discipline related knowledge for the campus, college and service

community to improve and increase information dissemination. Book reviews may be submitted to either

iii

themed or open-topic issues of the journal. Book review essays should not exceed 1,900 words. Please

include, at the beginning of the text, city, state, publisher, and the year of the book’s publication. An

abstract of 150 words or less and keywords are required for book review essays.

Notice to Authors of Joint Works (articles with more than one author). This journal uses a

transfer of copyright agreement that requires just one author (the Corresponding Author) to sign on behalf

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Although such instances are very rare, you should be aware that in the event a co-author has included

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if you prefer to use a copyright agreement for all coauthors to sign.

PolygonSpring 2010 Vol. 4, 1-5

WAITING FOR A PATTERN IN COIN TOSSING

M. Andreoli" "Department of Mathematics Miami-Dade College, North Campus Miami,ß ß

FL 33167 USA, Email: mandreol@mdc.eduß

ABSTRACT

Two commonly held misconceptions regarding a sequence of tosses of a fair coin are addressed. Thereasons for the misconceptions are discussed, and the correct analysis is provided. The results aresomewhat surprising to most people. The mathematical derivation of the correct results is followed by adiscussion of why our intuition may have initially misled us. Suggestions for various generalizations of theproblem follow.

KEYWORDS: Probability, conditional expectation, waiting times.

Mathematics Subject Classification: 60C05, 65C50.

1. INTRODUCTION

The Problem:

Consider a sequence of independent tosses of a fair coin. Suppose we are waiting for a certain pattern tooccur for the first time, say HHTT. We invite the reader to consider the following two questions, andguess the answers before reading on.

Q1: Which pattern requires a longer expected time to occur: or ?HH THQ2: Which pattern has a higher probability of occurring first: or ?HHH THH

Many, if not most people answer the questions as follows:

A1: "The expected times are the same for each pattern." A2: "Each pattern has an equal chance of occurring first."

How many readers answered this way? This certainly seems reasonable, since we have assumed the coin isfair. Unfortunately, as we propose to show in this note, . We will prove this byboth answers are incorrectexplicitly computing the relevant expectations and probabilities.

2. NOTATION AND PRELIMINARIES

We use standard notation, where denotes the probability that event occurs. denotes theTÐEÑ E TÐElFÑprobability that event occurs, given that event has occurred. The mean, or expected value of a randomE Fvariable is denoted The conditional expectation, denoted , is the expected value of \ IÐ\ÑÞ IÐ\l] Ñ \given and is a function of We will need the following results, the proofs of which can be found in] ß ] Þalmost any introductory probability text. My personal favorite is [ ].1

© 2010 Polygon 1

Waiting for a patterná

PROPOSITION 1.1

If and are discrete random variables with finite expectation, then\ ]

IÐ\Ñ œ IÐ\l] Ñ T Ð] œ CÑÞ"C

See [ , p.335] for a proof.1

PROPOSITION 1.2

In a sequence of independent trials, each of which has probability of success, with the: ! : "ßexpected number of trials until a success is first observed is "Î:Þ

See [ , p.168] for a proof.1

The latter proposition gives the mean of the geometric distribution. In particular, when tossing a fair coin,the expected number of tosses required to observe heads is 2.

3. COMPUTING THE EXPECTED TIMES

Let denote the time (number of tosses) required to observe the first occurrence of in a sequence ofRE HHtosses of a fair coin. Conditioning on the outcomes of the first two tosses, we have

first two tosses2 first two tosses are , w.p.

first two tosses are w.p. first

IÐR l Ñ œ"Î%

# IÐR Ñ ß "Î%" IÐR Ñ

E E

E

ÚÛÜ

HHHT

toss is , w.p. 1/2 .

T

Unconditioning, that is, applying Proposition 1.1, we have

IÐR Ñ œ # † Ð"Î%Ñ Ò# IÐR ÑÓ † Ð"Î%Ñ Ò" IÐR ÑÓ † Ð"Î#ÑÞE E E

Solving for yields IÐR Ñ IÐR Ñ œ 'ÞE E

Now let denote the number of tosses required to observe . Calculation of the expected time is a bitRF THsimpler.

first toss .first toss is , w.p.

time to first ) first toss is , w.p. 1/2IÐR l Ñ œ

" IÐR Ñ "Î#" IÐF

Fœ HH T

Unconditioning, and recalling that time to first we haveIÐ Ñ œ #ßH

IÐR Ñ œ Ò" IÐR ÑÓ † Ð"Î#Ñ $Î#ßF F

and solving for yields IÐR Ñ IÐR Ñ œ %ÞF F

2

Andreoli

To summarize:

IÐ Ñ œ 'time to first occurrence of .HHÐ"Ñ

IÐ œ %Þtime to first occurrence of )TH

We must conclude then, that

time to first occurrence of time to first occurrence of ),IÐ Ñ Á IÐHH TH

a result many people find counterintuitive.

4. COMPUTING THE PROBABILITY THAT ONE PATTERN PRECEDES ANOTHER

Let and respectively denote the sequences and Define the following random variables.E F HHH THT.

R œ EE the number of tosses until appears.R œ FF the number of tosses until appears.R œ E FElF the additional number of tosses for to appear after has appeared.R œ F EFlE the additional number of tosses for to appear after has appeared.Q œ ÐR ßR ÑÞmin E F

Finally, let denote the probability that pattern occurs before pattern Our goal in this section is toT E FÞE

find As a bonus we will also find T Þ IÐQÑÞE

We begin by computing Note that for pattern to occur, the pattern must occurIÐR Ñ œ IÐR ÑÞ EE ElF HH first. Conditioning on the result of the toss immediately following the first occurrence of , we have, inHHview of (1),

IÐR l œ ' Þ" IÐR ÑE

Enext toss after

if next toss is , w.p. 1/21 if next toss is , w.p. 1/2

HHHT

Ñ œUnconditioning, and we conclude thatIÐR Ñ œ ( Ð"Î#ÑIÐR ÑßE E

IÐR Ñ œ IÐR Ñ œ "%ÞE ElF

In the same way we can compute and we find thatIÐR ÑßF

IÐR Ñ œ IÐR Ñ œ "!ÞF FlE

Moreover, following Ross [ p.232], we have2

IÐR Ñ œ IÐQÑ IÐR QÑE E

œ IÐQÑ IÒR QlF EÓÐ" T ÑE Ebefore

œ IÐQÑ Ð" T ÑIÐR ÑÞE ElF

3

Waiting for a patterná

Similarly,

IÐR Ñ œ IÐQÑ T IÐR ÑÞF E FlE

Solving these equations yields

T œ ßIÐR Ñ IÐR Ñ IÐR Ñ

IÐR Ñ IÐR ÑE

F ElF E

FlE ElF

and

IÐQÑ œ IÐR Ñ IÐR ÑTF FlE EÞ

For the particular case at hand,

T œ œ ß"! "% "% &

"! "% "#E

IÐQÑ œ "! "!Ð Ñ œ Þ& $&

"# '

In particular, we note that occurs before a result many people find counterintuitive.T œ TÐE FÑ "Î#ßE

5. INTUITION ADJUSTMENT

When faced with a counterintuitive result, most of us scrutinize what went wrong with our intuition, andtry to improve it. We offer the following scenario as an aid to "intuition adjustment".

Suppose we are to observe independent tosses of a fair coin and are to be awarded a large sum of moneywhen the pattern first occurs. When the first heads occurs, our pulse quickens. Suppose alas, that theHHnext toss is tails. We are discouraged, for now we must start from scratch. On the other hand, suppose weare to be awarded a large sum of money when the pattern first occurs. When the first tails appears, ourTHpulse quickens, but suppose, alas, that the next toss is tails. We are disappointed, of course, but things arenot so bad. We need not start from scratch, in fact we may win on the very next toss.

In view of these considerations, perhaps the results we have derived in this note do not seem so surprising.Yet, the heuristic argument above is of no help in actually computing the expected time for a pattern tooccur, or in computing the probability that one pattern precedes another.

6. GENERALIZATIONS

Many generalizations to the questions addressed in this note suggest themselves. In the first place, the coinmight be biased where the probability of getting heads on a single toss is and the probability of tails isß :ß; œ " :Þ Actually this does not present any substantial difficulty if the length of the patterns involved isrelatively small, say two or three as considered above. The reader is encouraged to work out the answersto Q1 and Q2 for a biased coin. A far more serious drawback to the methods presented here comes aboutwhen we consider longer patterns, such as computing the expected time required to observe the patternHHHTHTHHH. 4

Andreoli

The reason is obvious if one recalls that to compute the expected time to , we needed to first deriveHHHthe expected time to . The amount of calculation for long patterns grows daunting in a hurry.HH

Then there is the issue of generalizing the results to an experiment where a single trial may result in 8 #possible outcomes, where outcome occurs with probability Imagine tossing a "ten sided biased coin"3 : Þ3for example, and trying to compute the expected time until some pattern of length 30 appears.

Fortunately, the problem has been solved in complete generality. The interested reader may consult Ross[ , pp. 231-233] for one method of doing so. Ross uses the theory of Martingales in his analysis. While he2only works out two specific examples, these examples make it clear how to proceed to the general case,with only a modest amount of calculation. Ross uses a completely different method than the one used here,except as noted in section .3

ACKNOWLEDGMENT

I am indebted to Ross for bringing this type of problem to my attention in the first place.I took the liberty of using Ross' notation, where the symbols and are employed.R ß R TE EFlE

REFERENCES

1. Sheldon Ross, , 4th ed., Macmillan, New York, 1994.EJ3<=>G9?<=/ 38T<9,+,363>C2. Sheldon M. Ross, Wiley, New York, 1983.W>9-2+=>3- T <9-/==/=ß

5

6

Polygon

Spring 2010 Vol. 4, 6-10

COMMON MISTAKES MADE BY NATIVE SPANISH SPEAKERS

M. Orro

1

1

Department of ESL and Foreign Languages, Miami Dade College, North

Campus, Miami, FL 33167, USA. Email: morro1@mdc.edu

ABSTRACT

Language errors are quite common in any language, so it shouldn't come as a surprise

that native speakers of Spanish would make mistakes when speaking their language, and

although they generally aren't the same mistakes that are likely to arise in English, they

are probably as common. This paper presents a sample of some of the most common

errors made by native speakers of Spanish. Such mistakes are addressed in the courses

SPN2340 and SPN2341 [Spanish for Native Speakers I and II] at Miami Dade College.

Both courses also satisfy several of the Learning Outcomes of MDC, most notably #1

[Communicate effectively using listening, speaking, reading, and writing skills], and #5

[Demonstrate knowledge of diverse cultures, including global and historical

perspectives].

KEYWORDS

Spanish, lexical variations, common mistakes, spelling, grammar.

1. INTRODUCTION

Unless you're an incessant perfectionist for grammatical details, chances are you could

make dozens of errors each day in the way you speak. And you might not notice until

you're told that a sentence, or a word wrongly said, is enough to make some language

perfectionists grit their teeth.

Since language errors are so common in English, it shouldn't be surprising that

Spanish speakers often make their share of mistakes too when speaking their language.

Mistakes, particularly in grammar, are probably every bit as common in Spanish as they

are in English.

In many instances, there is no such thing as right or wrong when it comes to language,

only differences in how various word usages might be perceived. For example, there are

7

lexical variations noted in many standard Spanish words such as ‘piscina’ (swimming

pool), that in Mexico is referred to as ‘alberca’, but in Argentina is ‘pileta’, or ‘frijoles’

(beans) which in Venezuela are called ‘caraotas’, in Puerto Rico ‘habichuelas’, and in

Argentina ‘porotos’, and also ‘campesino’ (country person), which in Cuba is named

‘guajiro’, but in Chile is known as ‘huaso’, and in Puerto Rico ‘jíbaro’. There are also

cases in which one word may have different meanings, depending on the region where it

is used, as is the example of the slang word ‘guagua,’ which in the Caribbean is a bus,

but in the Andes region is a baby, or the verb ‘coger’ (to catch, to get), which in most

parts is used in its proper meaning, but in some other places carries a vulgar connotation.

I could go on and on citing many other similar examples, but that would be the topic for

another article. The point I wanted to bring across in presenting the few examples above

is that, although there is generally a standard lexicon used in all Spanish-speaking

countries, nonstandard varieties should not be dismissed as useless or undesirable

mistakes, but rather as different uses of the same word.

When it comes to grammar though, the situation is quite different because in this case,

it’s not a matter of simply dealing with lexical variety, but with mistakes regarded as

‘unacceptable’ by most educated people.

2. Most Common Errors Made by Spanish Speakers

Following is a list of some of the most common errors that Spanish speakers often

make; several of them are so common, they even have names to refer to them. Although

some speakers, especially in informal contexts, may find these mistakes acceptable, most

grammarians and language purists view them as uneducated or plain wrong. So then,

since there isn't unanimous agreement in all cases about what is to be considered correct

in language usage, some of the examples presented below will be referred to as

“improper” rather than as "incorrect".

Dequeísmo — In some areas, the use of de que in lieu of que has become so common,

that it is on the verge of being considered a regional variant, but in other areas it is

strongly looked down on as being the mark of an inadequate education.

Improper: No creo de que Pedro sea mentiroso.

Proper: No creo que Pedro sea mentiroso. (I don’t believe Pedro is a liar.)

8

Loísmo and laísmo — Le is the correct pronoun to use as the indirect object meaning

"to/for him" or " to/for her." However, lo is sometimes used for the male indirect object

pronoun, particularly in some parts of Latin America, and la for the female indirect object

pronoun, especially in certain parts of Spain.

Improper: La envié una carta. Lo escribí.

Proper: Le envié una carta (a ella). Le escribí (a él). (I sent her a letter. I wrote

to him.)

Leísmo — On the other hand, lo is the correct pronoun to use as the direct object

meaning “him.” However, le is sometimes used for the masculine direct object, although

mainly in Spain.

Improper: Le vi ayer.

Proper: Lo vi ayer. (I saw him yesterday)

Quesuismo — Cuyo is often the Spanish equivalent of the adjective "whose," but it is

used infrequently in speech. One quite popular alternative is the use of que su.

Improper: Conocí a una señora que su gato estaba muy enfermo.

Proper: Conocí a una señora cuyo gato estaba muy enfermo. (I met a lady

whose cat was very sick.)

Plural use of existential haber — In the present tense, there is practically no confusion

in the use of haber in a sentence such as "hay una silla" ("there is one chair") and "hay

tres sillas" ("there are three chairs"). In all other tenses, the rule is the same — the

singular conjugated form of haber is used for both singular and plural subjects. However,

in most of Latin America, and also in some parts of Spain, plural forms are often heard

and are sometimes simply considered as a regional variant.

Improper: Habían tres sillas.

Proper: Había tres sillas. (There were three chairs.)

9

Misuse of the gerund — The Spanish gerund (the verb form ending in -ando or -iendo,

generally the equivalent of the English verb form ending in "-ing") should generally be

used to refer to another verb, not to nouns as can be done in English. Yet, it appears to be

increasingly common to use gerunds to anchor adjectival phrases.

Improper: No conozco al hombre hablando con Teresa.

Proper: No conozco al hombre que habla con Teresa. (I don't know the man

speaking with Teresa.)

Errors in verb conjugation — There are numerous mistakes made when conjugating

verbs in different tenses. One of the most recurrent gaffes made in this category is the

addition of an the letter ‘s’ to the second person singular form (tú) of verbs in the preterit

tense, for example: hablastes instead of hablaste (you spoke); or the improper usage of

irregular verbs in either the preterit or the subjunctive, such as: conducí instead of

conduje (I drove), and indució instead of indujo (he/she induced), or haiga instead of

haya (there is/there are) and satisfazca instead of satisfaga (satisfy); last, but not least,

the common use nowadays of the non-standard past participle rompido instead of the

standard roto (broken).

Spelling mistakes — Since Spanish is a very phonetic language, it is normal to think that

mistakes in spelling should be unusual. However, while the pronunciation of most words

can almost always be deduced from their spelling (the main exceptions are words of

foreign origin), the reverse isn't always true. Native speakers frequently mix up the

identically pronounced b and v, or y and ll, for example, and occasionally add a silent h

where it doesn't belong or vice versa. It isn't unusual either for native speakers of Spanish

to be confused on the use of orthographic accents, that is, they may mistake aun (even)

with aún (still), el (the) with él (he), mas (but) with más (more), mi (my) with mí (me),

que (that) with qué (what), si (if) with sí (yes), solo (alone) with sólo (only), or tu (your)

with tú (you), which are pronounced identically.

10

3. CONCLUSION

SPN2340 and SPN2341, two courses offered at MDC specifically designed for native

speakers of Spanish, provide our considerably large population of bilingual students with

the opportunity, not only to learn about all the common mistakes presented above (and

many more), but to develop and improve their communicative skills [LO#1]. These

courses also expose students to the history, literature, films and current events of the

Hispanic world, thus expanding their cultural horizons and encouraging them to explore

other corners of the world in a different light [LO#5].

REFERENCES

Marqués, Sarah (2005). La lengua que heredamos. Curso de español para bilingües.

(5

th

Ed.) New Jersey: John Wiley & Sons, Inc.

Ortega, Wenceslao (1988). Redacción y composición. Técnicas y prácticas.

Mexico: McGraw-Hill.

Valdés, G., Dvorak, T., & Pagán-Hannum, T. (2008). Composición. Proceso y

síntesis. (5

th

Ed.) New York: McGraw-Hill Higher Education.

11

Polygon

Spring 2010 Vol. 4, 11-14

THE IMPORTANCE OF THE STUDY OF EVOLUTION IN THE COURSE

PSC1515 “ENERGY IN THE NATURAL ENVIROMENT”

A. Rodriguez

1

1

Department of of Chemistry/Physics/ Earth Sciences, Miami Dade College,

North Campus, Miami, FL 33167, USA. Email: arodri10@mdc.edu

ABSTRACT

This paper demonstrates the importance and relevance of the PSC 1515 course for the

students pursuing an Associate in Arts Degree at Miami Dade College (MDC). This

course not only provides a general overview of the scientific method but also of the

different physical, natural and earth sciences. Of particular relevance is the study of

evolution, which is a recurrent controversial topic in our society because of the apparent

conflict between the scientific and religious points of view. In this paper, it is

demonstrated that this controversy is mostly limited only to the United States, although to

some degree, it is also expanding to the United Kingdom and other parts of Europe due to

the American influence in that part of the world. This course, PSC1515 also satisfies

several of the Learning Outcomes (LO) received by MDC’s graduates, particularly LO

#3, #6 and #10.

KEYWORDS

Evolution, creationism, intelligent design, science, religion, and scientific method.

INTRODUCTION

One of the most popular courses taken by Miami Dade College (MDC) students, as

part of the General Education Requirements for the Associate in Arts Degree, is PSC

1515 “Energy in the Natural Environment”. This course is included in the Natural

Science section, Group B – Physical Sciences of the General Education Requirements. In

the College Catalog, it appears in the Physics section, as one of the Physical Sciences

with a Multidisciplinary approach. The course description in the Catalog portrays it as an

“Investigation of the physical Environment using energy as a theme to demonstrate the

impact of science and technology on the environment and on the lives of people”.

This course satisfies several of the General Education Learning Outcomes (LO) that

demonstrate the knowledge acquired by MDC’s students, regardless of their major,

particularly Learning Outcomes #3, #6 & #10. Learning Outcome #3 establishes the

following: “As graduates of MDC, students will be able to solve problems using critical

and creative thinking and scientific reasoning”. This LO is approached since the first

12

chapter, in which the Scientific Method is discussed, and it is pursued throughout the

entire course content.

LO #10 establishes “how natural systems function and recognize the impact of

humans in the environment”. The goal of this LO is achieved throughout multiple

chapters in the course that discuss energy and its interrelationship with natural systems,

as well as the impact of human activities in the environment; special emphasis is placed

on global warming and its countless negative impacts in the environment and society,

ranging from the impacts on the ecosystems, health, the economy and –even- national

security.

The importance of LO #6 cannot be highlighted enough. This outcome “creates

strategies that can be used to fulfill personal, civic and social responsibilities”. The

issues that are discussed in the course, like evolution, global warming, and others will

help our students make informed decisions, as members of our society in many personal,

civic and social aspects, like voting for the appropriate candidate elections at different

levels, and also choosing the correct organizations to be involved with; and these are

decisions that reflect what is important, useful and necessary for the well-being of our

nation.

To fully understand the great importance of the depth of the scientific knowledge that

the learning of evolution provides to our students, we must consider the results of the

public opinion poll released by the Pew Forum on Religion and Public Life on August 30,

2005, which reveals that “nearly two thirds of Americans want both creationism… to be

taught along with evolution in public schools. Fewer than half of Americans – 48% -

accept any form of evolution… and just 26% accept Darwin’s theory of evolution by

means of natural selection. Fully 42% say that all living beings, including humans have

existed in their present form since the beginning of time” (cited by Jacoby, 2008).

According to Jacoby, 2008, this level of scientific unawareness cannot be blamed

solely on the low level of science education in American elementary and secondary

schools, as well as in many community colleges. In her book The Age of American

Unreason, Jacoby clearly states: “Only 27% of college graduates believe that living

beings have always existed in their present form, but 42% of Americans with only a

partial college education and half of high school graduates adhere to the creationist

viewpoint that organic life has remained unchanged throughout the ages. A third of

Americans mistakenly believe that there is substantial disagreement about evolution

among scientists – a conviction reinforcing and reflecting… that evolution is “just a

theory” (Jacoby, 2008).

The graduates of Miami Dade College who take the PSC1515 course, will not be

caught in the “just a theory” argument, because the first chapter of this course is

dedicated to the study of science and the scientific method, as well as the relationship

between science and religion. In this chapter, the students learn the scientific definition of

theory. To our students, a theory is ‘a synthesis of a large body of information that

encompasses well-tested hypotheses about certain aspects of the natural world’. Thus,

13

after taking the PSC1515 course, students of Miami Dade College become part of a

considerable percentage of college-educated Americans who will be thoroughly informed

about this transcendental scientific theory.

1. CREATIONISM

Advocates of the opposition to the study of evolution have attempted to substitute the

study of this theory, with the study of the afore cited theory of creationism, which can be

briefly defined as the religious belief that human life, the Earth and the Universe were

created in some form by a supernatural being, a God. For the Christian religion,

creationism is usually based on a literal interpretation of the book of Genesis in the Bible.

2. INTELLIGENT DESIGN

The concept of intelligent design was developed by a group of American creationists

who reformulated their argument in the creation-evolution controversy to evade court

rulings that ban the teaching of creationism as science. Intelligent design is the allegation

that some features of the universe (and of living things) are best explained by an

intelligent cause, not an undirected process such as natural selection. It is a more

contemporary form of the conventional teleological argument for the existence of God,

but without specifying the nature or identity of the ‘designer’, or creator. The discussion

about intelligent design must start by indicating that most of the scientific community has

rejected this idea. The U.S. National Academy of Sciences, the U.S. National Science

Teachers Association, and the American Association for the Advancement of Sciences

have all denounced intelligent design as a pseudoscience, because it is not testable

according to the principles and methods of science.

In a statement adopted on July 2003 by the Board of Directors of the National Science

Teachers Association, we can read: “The National Science Teachers Association (NSTA)

strongly supports the position that evolution is a major unifying concept in science and

should be included in the K-12 science education frameworks and curricula.

Furthermore, if evolution is not taught, students will not achieve the level of scientific

literacy they need”.

3. EVOLUTION

In his book, Richard Dawkins states: “all except the woefully uninformed are forced

to accept the fact of evolution”, adding to his statement that “…no reputable scientist

disputes it [evolution]” (Dawkins, 2009).

The National Academy of Science (NAS) and the Institute of Medicine (IOM)

released Science, Evolution and Creationism in 2008, where the importance of the

teaching of evolution in the science classroom was emphasized, or as the President of the

National Academy of Science, Ralph Cicerone, states: “The study of evolution remains

one of the most active, robust, and useful fields in science” (Cicerone, NAS, 2008).

14

The President of the Institute of Medicine, Dr. Harvey Fineberg, says: “Understanding

evolution is essential to identifying and treating disease. For example, the SARS virus

evolved from an ancestor virus that was discovered by DNA sequencing. Learning about

SARS’ genetic similarities and mutations has helped scientists understand how the virus

evolved. This kind of knowledge can help us anticipate and contain infections that emerge

in the future” (Fineberg, NAS, 2008). The same could even be said today about the

H1N1 virus causing the swine flu.

CONCLUSIONS

The importance of the study of PSC 1515 [Energy in the Natural Environment] is

such, that this class is at the basis of the scientific literacy acquired by the graduates of

Miami Dade College, and encompasses many of the Learning Outcomes that form the

core of a college education.

In PSC1515 students learn about science and the scientific method, and the basic

elements of evolutionary biology, in contrast to creationism and intelligent design. The

most important aspect of the study of evolution in this course is that our students are not

mandated to accept it or believe in it. They are given the elements of the three

approaches, and then are allowed to draw their own conclusions based on what they have

learned about the scientific method. The study of the chapter on evolution is

complemented with the study of the Universe and the Solar System, which includes the

theory of the Big Bang, the Nebular Theory and the evolution of the Universe and our

Solar System.

This class should be recommended to all MDC students, and the chapter on evolution

in particular must be considered of high relevance in the teaching of the course.

REFERENCES

Dawkins, Richard (2009). The Greatest Show on Earth. The Evidence for Evolution.

New York: Free Press

Jacoby, Susan (2008). The Age of American Unreason. New York: Pantheon Books

National Academy of Sciences/Institute of Medicine [NSTA/IOM] (2008). Science,

Evolution and Creationism. Retrieved January 9, 2008 from

http://www.8.nationalacademies.org/onpineews/newsitem.aspx?RecordID=11876

National Science Teachers Association [NSTA] (2007). Teaching of Evolution. The

NSTA Position Statement. Retrieved February 23, 2007 from

www.nsta.org/positionstatement&psid=10.

15

Polygon

Spring 2010 Vol. 4, 15-26

ON AN ITERATIVE ALGORITHM IN MULTIOBJECTIVE OPTIMIZATION

J. A. Serpa

1

1

Department of Mathematics, Miami Dade College, Inter-American

Campus, Miami, FL 33135, USA. Email: jserpa@mdc.edu

ABSTRACT

Multiobjective optimization is commonly used in every field where decisions are

made to determine optimal values for a given object or process. It’s been particularly

expanded in management and business and a wide variety of methods has been

developed. In this paper an original iterative algorithm is presented which takes into

account the difficulties for decision-maker to mathematically formalize priorities on the

functions vector.

KEYWORDS

Multiobjective optimization, mathematical programming, decision-maker, Pareto-

optimal solutions, iterative algorithms, adaptability depth.

AMS Subject Classification: 90C11, 90C29, 90B50, 90C31, 90C80

1. INTRODUCTION

Multiobjective Optimization Problem (MOP) arises more often than we could think.

Optimization as it is understood in Mathematical Programming is reduced to the

maximization (minimization) of an Objective Function where the Domain of possible

solutions (alternatives) is given by a set of inequalities and equations. Defining one single

Objective Function is often too risky, since other parameters for the given system could

result with very undesirable values. The presence of multiple conflicting goals causes the

necessity of a new approach: Multiobjective Optimization. Different methods have been

developed: optimizing one single objective while on the other objectives constraints are

16

imposed; defining a global function as a combination of all objective functions; iterative

algorithms; and more recently evolutionary algorithms. Iterative algorithms are

particularly useful in situations where MOP regularly has to be solved and the task for

decision-maker to formalize the priorities on the functions vector becomes too hard and

eventually impossible. We show below some aspects of an original iterative algorithm

where optimization occurs after several runs of the mathematical model. On each step the

Domain is reduced to a subset within the set of Pareto-optimal solutions by following an

evaluation rule and eventually a single solution is obtained.

2. MULTIOBJECTIVE OPTIMIZATION

2.1 THE PROBLEM

Let’s define MOP as follows:

min,))(),...,(),((

21

xfxfxfF

m

(1)

x

where

m

is the number of Objective Functions, and the Domain

is given by

linear inequalities and equations defined on the variable

x

. A trivial solution is

obtained when the optimum occurs simultaneously for all functions. This rarely happens

in real-world problems.

2.2 THE SOLUTION

Basic Principles of the Algorithm

The algorithm is based on the following statements:

Let

III

pp

,

(

I

- the set of the Objective Functions) and let

ppb

i

IIIif \,

be given boundary values.

17

Let’s define preference relation

P

such that

xPy

if

,),()(

p

ii

Iiyfxf

(2)

and for at least one value

i

the inequality is strict and, in addition

pb

ii

Iifxf ,)(

(3)

Then the idea of narrowing the Pareto-Optimal Solutions set (

T

) can be executed

as follows. Let the point

y

is fixed and ‘’preferable’’ rather than any

z

according to decision-maker’s evaluation rule,

p

zTzz ,:

,

region

p

is defined by inequalities (2)-(3) .

In the region

p

T

is executed the optimization. This resembles the idea of

set of ‘’individuals’’ after selection process and prior to ‘’recombination’’ and

‘’mutation’’ in Evolutionary Algorithms [1],[5].

Given

p

I

and

y

, found after initial approximation, the optimization is carried out

according to the principle of minimum deviation from

p

i

Iiyf ),(

. As a rule

minimal deviation is not obtained simultaneously for all mentioned functions. Then

principle of best guaranteed value is applied, i.e. minmax principle.

Let functions

Iixf

i

),(

are transformed to dimensionless functions

))(( xfW

ii

keeping preference order of the original functions vector.

miWW

i

,...,1},{

are defined on

WW

d

region of transformed

functions,

d

W

.

Let

s

w

be an intermediate solution (at iteration s ),

ss

wf

.

18

At every iteration of the algorithm, the decision-maker redefines the preference

vector based on the obtained intermediate alternative.

s

I

is defined as the set of

functions to be submitted to ‘’improvement’’ on the given iteration.

Boundary values on the iteration (

2,, sIif

sbs

i

) are determined by

recurring relations:

)1()2(

)1()1(

,

,

ss

i

ssb

i

bs

i

Iif

Iif

f

On iteration )1(, ss the problem is reduced to:

)(

maxminarg

)1(

s

ii

s

s

d

s

ww

Ii

Ww

w

(4)

here

ss

iid

s

d

s

d

IiwwWwWwW

,,/:

)1(

and at least

for one value

i

the inequality is strict,

sbs

ii

Iiww ,

sssss

IIIIIII \,,:

Statement I : if

s

w

is unique solution to problem (4) in

d

W

, then it is Pareto-

Optimal.

Proof by contradiction:

Let

s

w

be unique solution but not Pareto-Optimal, then there exists

d

Ww

'

such that

Iiww

s

ii

,

'

(5)

19

and for one value of

i

the inequality is strict.

From

0

1

s

i

w

we have

Iiwwww

s

i

s

i

s

ii

,

)1()1('

)(

maxmin

)(

max

)(

max

)1()1()1('

s

ii

s

s

d

s

i

s

i

s

s

ii

s

ww

IiWw

ww

Ii

ww

Ii

(6)

from

s

d

s

Ww

and (5) follows

s

d

Ww

'

and either

s

w

is not unique

solution of (4) , what happens for strict inequality at (6), either

)(

max

min

arg

)1('

s

ii

s

s

d

ww

Ii

Ww

w

then

s

w

is not unique solution.

Statement (I) is proved.

In case of not uniqueness of solution in (4) the following problem is solved:

s

i

Ii

xW

min)(

(7)

s

s

i

s

i

s

i

Ii

ww

Ii

xW

,

)(

max)(

)1(

(8)

IiWxW

s

di

,)(

(9)

Initialization (iteration ‘’0’’):

20

From extreme values of Objective Functions in

is defined

}{

**

i

ff

and

Iif

b

i

,

1

),(

11** bb

wfwf

.

Weighing coefficients vector

}{

i

is defined [2] according to:

Iq

ij

Ij

i

ij

Ij

i

i

w

w

*

*

(10)

The problem at this step is reduced to

ii

d

w

Ii

Ww

w

maxminarg

0

0

The consistency of the problem at

0s

is given by

d

Ii

s

i

s

d

WwW ],0[

The parallelepiped is generated from

10 b

ii

ww

and for

:1s

sbs

i

ss

i

i

Iiw

Iiw

w

,

,

)1(

Inconsistency in the Domain of alternatives can be overcome by introducing

auxiliary variables

i

y

to weaken the constraints at step ‘’0’’:

Ii

ii

ych min

(11)

Iifffhxf

iiiii

,/)()(

minminmax

(12)

21

Iifyxf

b

iii

,)(

1

(13)

0

i

y

(14)

x

(15)

And

0

i

c

are such penalties that worsening of function as

i

y

increases is more

significant rather than its improvement at

h

worsening.

Solution to (11)-(12) allows correction of boundary values of Objective Functions

using

i

y

in case of inconsistency. On the other hand if the system is consistent

then the auxiliary variables are ‘’0’’ and no correction is needed.

At iteration ‘’s’’ the MOP (4) becomes:

minl (16)

ss

iiii

Iiffflxf

,)()(

)1(minmax

(17)

ss

iii

Iifkxf

,)(

)1(

(18)

sbs

ii

Iifxf ,)(

(19)

x

(20)

Here

s

i

Iik ,0

are set conveniently small and at least for one value

i

applies strict inequality. It serves the fast convergence of the algorithm.

maxmin

,

ii

ff

are minimum and maximum respectively of functions in

.

Suggested transformation of functions:

Ii

ff

fxf

xfW

ii

ii

ii

,

)(

))((

minmax

min

22

We need to prove the following statement.

Statement II:

rss

d

r

wwWw ,

there can be found

s

Ii

'

such that

r

i

s

i

ww

''

.

Proof:

For

}1{

s

I

it is obvious.

From

s

d

r

Ww

we have

)(

max

)(

max

)1()1(

s

i

r

i

s

s

i

s

i

s

ww

Ii

ww

Ii

(21)

In case of strict inequality in (21) then at least for

)(

max

)(

:

)1()1('

s

i

r

i

s

s

i

r

i

ww

Ii

wwi

applies

r

i

s

i

ww

''

In case of equation at (21), then

s

w

is solution to (7)-(9). Let’s prove this part of

the statement by contradiction:

Let

ss

i

s

i

s

i

r

i

Iiwwww

,

)1()1(

, then

)()(

)1()1(

s

i

s

i

s

s

i

r

i

s

ww

Ii

ww

Ii

(22)

Inequality (22) contradicts (7)-(9).

Statement II is proved.

23

Fast convergence of the algorithm demands carefully handling the set

s

I

. In this

regard the following statement is useful:

Statement III: If

ss

II

)1(

, then

d

Ii

s

i

Ww ],0[

and MOP

)(

maxmin

)1(

s

ii

ss

d

ww

IiWw

has no solution.

Proof by contradiction:

Let

)1( s

w

be such that

)1(

)1()1(

)1(

,

,

s

ss

i

ss

i

s

i

Ii

Iiw

Iiw

w

ss

i

s

i

Iiww

,

)1(

(23)

From

s

d

s

d

ww

)1(

follows

s

d

s

Ww

)1(

(24)

But (23)-(24) contradict ‘’Statement II’’ .

Statement III is proved.

Evaluation rule

Search for solution of MOP stops at iteration ‘’s’’ if one of the following conditions

applies:

1. The solution satisfies evaluation rule.

24

Ability to react changing conditions of preferences over the objective functions in

the search of solution to MOP can be measured with ‘’adaptability depth’’

H

, its

maximization serves as evaluation rule:

1

H

H

H

'

1

1

i

m

i

i

H

m

H

,

'

1

1

i

m

i

i

H

m

H

2

*

*

*

**

1

*

*

***

'

,

,

1

Ii

ff

ff

Ii

ff

ff

H

ii

ii

ii

ii

i

21

, II

are the sets of functions to maximize and minimize respectively.

mixff

ii

,...,1),(

***

xmixff

ii

,,...,1),(max

*

xmixff

ii

,,...,1),(min

*

The decision-maker reconsiders the functions to be improved at this iteration by

measuring

i

ii

ii

i

H

H

H

'

'

i

,

i

are boundary values of vector

}{

i

To determine

s

I

, it is solved:

25

),min/(

''

**

)1()1(**

IiHHii

s

ii

s

ii

(25)

2. Decision-maker attempts to continue the search, however

III

ss

''

,

it turns

out

'

s

d

W

. Hence

)1( s

w

is the solution to MOP.

Formal Algorithm

The algorithm is performed following the steps:

1. Single optimization problems are solved for all functions:

maxmin,

i

f

2. Decision-maker defines

Iif

b

i

,

1

and ‘’ideal’’ alternative

}{

**

i

ff

.

Functions are transformed into

))(( xfW

ii

, and vector

}{

i

is defined as

per (10).

Initialization

0s

.

3. The problem (11)-(15) is solved.

If the solution satisfies evaluation rule go to the end.

4.

1 ss

. By solving (25) state

s

I

5. Solve (16)-(20). In case of not uniqueness solve (7)-(9). If conditions 1 or 2 are

satisfied, go to end, otherwise go to 4.

6. End.

3. CONCLUSIONS

An algorithm for the solution of MOP has been presented. The algorithm consists of

an iterative process. At each iteration, according to an evaluation rule, the set of

26

alternatives is reduced to ‘’more preferable’’ points. Narrowing the searching Domain

serves the approximation to the ‘’ideal’’ alternative, a point that rarely in practice is

achieved. Some statements have been proved to show convergence of the algorithm and

Pareto-Optimal character of the solution. Decision-maker deals directly with objective

functions vector, which has considerably lower dimension rather than the Domain of

alternatives.

REFERENCES

Coello, C. A. (2004). Applications of Multiobjective Evolutionary Algorithms. Mexico-

USA.

Mikhalevich, V. S, and Volkovitch, V. L. (1982). Computational Methods of Researching

and Designing Complex Systems, Moscow (in Russian).

Petrenko, V. L., Mirzoakhmedov F., Nguyen, V. H., and Serpa, J. (1987). An Approach

to Solving Multiobjective Optimization Problems in Adaptable Planning Systems.

Operations Research and Automated Management Systems, Kiev, Ukraine (in

Russian).

Serpa, J. (1988). Modeling in Short-term Management of Seaports. Doctoral Thesis,

Donetsk, Ukraine (in Russian).

Zitzler, E. (1999). Evolutionary Algorithms for Multiobjective Optimization: Methods

and Applications. Doctoral Thesis, Zurich.

27

Polygon

Spring 2010 Vol. 4, 27-42

AFRICAN-AMERICANS IN MATHEMATICAL SCIENCES -

A CHRONOLOGICAL INTRODUCTION

M. Shakil

1

1

Department of Mathematics, Miami Dade College, Hialeah Campus,

Hialeah, FL 33012, USA. Email: mshakil@mdc.edu

ABSTRACT

In this paper, a chronological introduction of African-Americans in the field of

Mathematical Sciences is presented.

KEYWORDS

African-Americans, mathematical sciences.

AMS Subject Classification: 01A05; 01A07; 01A70; 01A85

1. INTRODUCTION

The accomplishments of the past and present can serve as pathfinders to present and

future mathematicians. African- American mathematicians have contributed in both large

and small ways that has been overlooked when chronicling the history of science. By

describing the scientific history of selected African-American men and women within

mathematical sciences we can see how the efforts of individuals have advanced human

understanding in the world around us. The abilities and accomplishments of these Afro-

American scholars of science and mathematics cannot be underrated. History bears

testimony to their achievements. The purpose of this paper is to highlight and exhibit the

accomplishments of African-Americans within the Mathematical Sciences. The materials

presented are based on the “Mathematicians of the African Diaspora”,

(www.math.buffalo.edu/mad/index.html).

The organization of this paper is as follows. Section 2 contains a Tree Diagram of

African-Americans in the mathematical sciences by dividing it into four different periods,

beginning from 18th century to present. These periods have been further classified

indexed by year. In Section 3, a chronology of African-Americans in mathematical

sciences is presented. The statistics on the numbers of African-Americans receiving

Ph.D.’s in mathematics, during the period 1925 – 2004, have been presented in Section 4.

The achievements of African-Americans in the mathematical sciences are highlighted in

section 5. The concluding remarks are presented in Section 6.

28

2. A TREE DIAGRAM

The following is a Tree Diagram depicting the different periods of African-Americans in

Mathematical Sciences.

3. A CHRONOLOGY OF AFRICAN-AMERICANS IN MATHEMATICAL

SCIENCES

The following is a chronology of African-Americans in mathematical sciences.

3.1 AFRICAN-AMERICAN MATHEMATICIANS OF 18TH CENTURY

The names of the following African-Americans of 18th century are available through

historical records, who have contributed in the field of mathematical sciences:

(i) Muhammad ibn Muhammad (16?? - 1741)

(ii) Thomas Fuller (1710 - 1790)

(iii) Benjamin Banneker (1731 - 1806)

Development of African-American influence in mathematical sciences began with the

work of Benjamin Banneker, who used the method of doubling sequences to generate an

estimate for the method of false position. Benjamin Banneker is often recognized as the

first African American mathematician. However, the names of ex-slave Thomas Fuller

and the Nigerian Muhammad ibn Muhammad also appear in history, whose mathematical

African-American

Mathematicians

18th Century

19th Century

20th Century

21st Century

2000 - 2004

1925 - 1999

1700 - 1799 1800 - 1899

29

activities predate Benjamin Banneker. It is interesting to note that none of these men had

formal degrees.

3.2 AFRICAN-AMERICAN MATHEMATICIANS OF 19TH CENTURY

Below is the list of three African-American mathematicians of 19th century, who are

prominent for their contribution to the knowledge and advancement of mathematical

sciences.

(i) Charles Reason (1814 - 1893) is considered to be the first African-American to

receive a faculty position in mathematics, in the year 1849, at a predominantly white

institution - Central College in Cortland County, New York.

(ii) Edward Alexander Bouchet was the first African-American to earn a Ph.D. in

Physics (Science), in the year 1878, from Yale University, and only the sixth American to

possess a Ph.D. in Physics. It should be noted that Yale University became the first

United States of America institution, in the year 1862, to award a Ph.D. in mathematics.

(iii) Kelly Miller was the first African American to study graduate mathematics, in the

year 1886, at Johns Hopkins University. It will be interesting to note that Johns Hopkins

University was the first American University to offer a program in graduate mathematics.

3.3 AFRICAN-AMERICAN MATHEMATICIANS OF 20TH CENTURY

The list of African-American mathematicians of 20th century is very exhaustive. In the

following paragraph, a chronology of African-Americans, who have excelled and

contributed to the knowledge and advancement of mathematical sciences, during the

period 1900 – 1999, is presented, (see, for example, the “Mathematicians of the African

Diaspora” website created and maintained by Professor Dr. Scott W. Williams, Professor

of Mathematics University at Buffalo, SUNY, among others).

(1) 1925: Elbert Frank Cox was the first African-American to earn a Ph.D. in

Mathematics in 1925 from Cornell University. There were 28 Ph.D.'s awarded in the

United States that year.

(2) 1928: Dudley Weldon Woodard was the second African-American to earn a Ph.D.

in Mathematics in 1928 from the University of Pennsylvania.

(4) 1933: William Schieffelin Claytor was the third African-American to earn a Ph.D.

in Mathematics (University of Pennsylvania). Dr. Claytor had an extraordinary promise

as a mathematician.

(5) 1934: Walter R. Talbot was the fourth African-American to earn a Ph.D. in

Mathematics (University of Pittsburgh).

30

(6) 1938: Ruben R. McDaniel (Cornell University), and Joesph Pierce (University of

Michigan) were the fifth and sixth African-Americans to earn a Ph.D. in Mathematics in

the year 1938.

(7) 1941: David Blackwell was the seventh African-American to earn a Ph.D. in

Mathematics, in the year 1941, from the University of Illinois. Dr. Blackwell earned his

Ph.D. at the age of 22. He is regarded as one of the greatest African-American

mathematician of the 20th century. Dr. Blackwell is famous and well-known in the world

of mathematics for his seminal “Rao-Blackwell Theorem” which gives a technique for

obtaining unbiased estimators with minimum variance with the help of sufficient

statistics (see, for example, Dudewicz and Mishra (1988), Kapur (1999), and Rohatgi and

Saleh (2001), among others). In 1954, Dr. David Blackwell became the first African-

American to hold a permanent position at one the major universities, University of

California at Berkley.

(8) 1942: J. Ernest Wilkins became the eighth African-American to earn a Ph.D. in

Mathematics, in the year 1942, from the University of Chicago. Dr. Wilkins earned his

Ph.D. at the age of 19. He is also regarded as one of the greatest and rarest African-

American mathematician of the 20th century

(9) 1943: Euphemia Lofton Haynes (Catholic University), the first African -American

woman, and Clarence F. Stephens (University of Michigan) were the ninth and tenth

African-Americans, respectively, to earn a Ph.D. in Mathematics (see, for example, the

websites “Black Women in Mathematics” and “Timeline of African American Ph.D.'s in

Mathematics,” among others). The Morgan-Potsdam Model is the name given to a

method of the teaching of mathematics developed by Dr. Clarence F. Stephens at Morgan

State University and refined at the State University of New York College at Potsdam. Dr.

Clarence F. Stephens also received the Mathematical Association of America Gung-Hu

Award for the Pottsdam Miracle. Under the direction of Dr. Clarence Stephens, Morgan

State University became the first institution to have three African-Americans of the same

graduating class (1964), who obtained a Ph.D. in Mathematics. These people were Dr.

Earl Barnes (University of Maryland, 1968), Dr. Arthur Grainger (University of

Maryland, 1972), and Dr. Scott Williams (Lehigh University, 1969). This is still a record

that stands among all U.S. universities and colleges.

(10) 1944: This is the year when the eleventh, twelfth and thirteenth African- Americans,

Joseph J. Dennis (from Northwestern University), Wade Ellis, Sr. and Warren Hill

Brothers (both from University of Michigan), respectively, earned a Ph.D. in

Mathematics.

(11) 1945: Jeremiah Certaine was the fourteenth African-American to earn a Ph.D. in

Mathematics, in the year 1945, from the University of Michigan.

31

(12) 1949: Evelyn Boyd Granville was the fifteenth African-American and the second

African-American Woman to earn a Ph.D. in Mathematics, in the year 1949, from Yale

University.

(13) 1950: Marjorie Lee Browne (University of Michigan), the third African-American

Woman, and George H. Butcher (University of Pennsylvania) were the sixteenth and

seventeenth African-Americans, respectively, to earn a Ph.D. in Mathematics, in the year

1950.

(14) 1953: Luna I. Mishoe was the eighteenth African-American to earn a Ph.D. in

Mathematics from New York University.

(15) 1954: Charles Bell was the nineteenth African-American to earn a Ph.D. in

Mathematics from the University of Notre Dame.

(16) 1955: Vincent McRea (Catholic University) and Lonnie Cross (Cornell University)

were the twentieth and twenty-first African-Americans to earn a Ph.D. in Mathematics.

(17) 1956: Lloyd K. Williams (University of California at Berkeley) and Henry M.

Elridge (University of Pittsburgh) were the twenty-second and twenty-third African-

Americans to earn a Ph.D. in Mathematics in the year 1956.

(18) 1957: Eugene A. Graham, Jr. (University of Turin in Italy) and Elgy S. Johnson

(Catholic University) were the twenty-fourth and twenty-fifth African-Americans to earn

a Ph.D. in Mathematics in the year 1957. Dr. Graham, probably, was the first African-

American earning a Mathematics Ph.D. outside the U.S.

(19) 1959: Laurence Harper, Jr. (University of Chicago) was the twenty-sixth African-

American Ph.D. in Mathematics.

(20) 1960 – 1999: Above, we have tried to enlist the African-Americans in the field of

mathematical sciences from 1900 to 1959. It is gratifying to note that a number of

African-Americans earned their Ph.D.’s in the field of Mathematical Sciences from 1960

to 1999, (see, for example, the website

“http://www.math.buffalo.edu/mad/yearindex.html,” for details). For the interest of the

readers, their names are presented below in chronological order.

(i) 1960: Charles G. Costley; Joshua Leslie; Argelia Velez-Rodriguez

(ii) 1961: Jesse P. Clay; Sadie Gasaway; John Gilmore; Rogers Newman

(iii) 1962: Robert O. Abernathy; Joseph Battle; John Henry Bennett; Gloria Conyers

Hewitt; Georgia Caldwell Smith; Louise Nixon Sutton; Theodore R. Sykes

32

(iv) 1963: Simmie S. Blakney; Earl O. Embree; William A. McWorter

(v) 1964: Louis C. Marshall; Alfred D. Stewart; Mary C. Wardrop-Embry

(vi) 1965: James A. Donaldson; Beryl E. Hunte; John H. McAlpin

(vii) 1966: John A. Ewell III; William T. Fletcher; Eleanor Dawley Jones; Eugene W.

Madison; Vivienne Malone Mayes; Shirley Mathis McBay; Charles E. Morris

(viii) 1967: Harvey T. Banks; Llayron L. Clarkson; Geraldine Darden; Samuel H.

Douglas; Annie M. Watkins Garraway; Melvin Heard; Percy A. Pierre; Thyrsa Anne

Frazier Svager; Ewart A. C. Thomas; Ralph B. Turner; Irving E. Vance

(ix) 1968: Earl R. Barnes; Dennis D. Clayton; Mary Deconge-Watson; Lloyd Demetrius;

Milton A. Gordon; Velmer Headley; Guy T. Hogan; Phillip E. McNeil; Ronald E.

Mickens; Wilbur L. Smith; Donald F. St.Mary; Donald Weddington; James H. White

(x) 1969: Boniface Eke; David M. Ellis; Etta Falconer; Fannie Ruth Gee; Raymond L.

Johnson; Wendell P. Jones; Benjamin J. Martin; Robert Smith; Scott W. Williams;

Vernon Williams

(xi) 1970: John C. Amazigo; Dean R. Brown; Japeth Hall, jr.; Lonnie W. Keith; Curtis S.

Means; Mutio Nguthu; G. Edward Njock; Sonde Nwankpa; Winston A. Richards; Nathan

F. Simms, Jr.; Eddie R. Williams

(xii) 1971: Roosevelt Calbert; Joella Hardeman Gipson; Orville Edward Kean; Hugh

G.R. Millington; Dolores Spikes

(xiii) 1972: Ethelbert Nwakuche Chukwu; Oscar H. Criner, III; Carlos Ford-Livene;

Christopher Olutunde Imoru; C. Dwight Lahr; John Nguthu Mutio; James A. White;

Floyd L. Williams

(xiii) 1973: Annas Aytch; Garth A. Baker; Robert Bozeman; Therese H. Braithwaite;

Lloyd Gavin; Seyoum Getu; James E. Ginn; Isom H. Herron; Frank A. James; Manuel

Keepler; Clement McCalla; Michael Payne; Evelyn Thornton; Hampton Wright

(xiv) 1974: Elayne Arrington; Della D. Bell; Roosevelt Gentry; Tepper L. Gill; Johnny L.

Houston; Arthur M. Jones; Nathaniel Knox; Rada Higgins McCreadie; Kevin Osondu;

Chester C. Seabury; Willie E. Taylor; Alton S. Wallace; Harriet R. Junior Walton

(xv) 1975: Bola Olujide Balogun; Arthur D. Grainger; Roy King; James Nelson, Jr;

Wandera Ogana; Osborne Parchment

33

(xvi) 1976: David I. Adu; James Howard Curry; David Green, Jr; Leon B. Hardy; Salah-

Eldin A Mohammed; Lawrence R. Williams

(xvii) 1977: Eddie Boyd Jr.; Gerald R. Chachere; Louis Dale; Ebenezer O. George;

Theodore R. Hatcher; David M. James; Carl L. Prather

(xviii) 1978: Reuben O. Ayeni; Clifton Edgar Ealy; Carroll J. Guillory; Fern Y. Hunt;

Karolyn Ann Morgan; Jonathan Chukwuemeka Nkwuo; Donald St. P. Richards; Wesley

Thompson; Henry N. Tisdale

(xix) 1979: Samuel Omoloye Ajala; Gary S. Anderson; Johnny E. Brown; Emma R.

Fenceroy; R. Charles Hagwood; Walker Eugene Hunt; Donald R.King; Keith Mitchell;

Claude Packer; George A. Roberts

(xx) 1980: Curtiss A. Barefoot; Robert M. Bell; Ronald Biggers; Sylvia T. Bozeman;

Suzanne Craig; Gaston M. N'guérékata; James E. Robinson; Daniel Arthur Williams

(xxi) 1981: Overtoun M. Jenda; Corlis P. Johnson; William A. Massey; David O.

Olagunju; Gabriel A. Oyibo

(xxii) 1982: William A. Hawkins jr.; Peter D. Nash; Janice B. Walker

(xxiii) 1983: Melvin R. Currie; Carolyn Mahoney; Bernard A. Mair; Bessie L. Tucker

(xiv) 1984: Abdulkeni Zekeria; Curtis Clark; Carl Graham; Kevin Oden; Alade Tokuda

(xv) 1985: Darry Andrews; Donald Ray Cole; Ibula Ntantu; Ronald Patterson; Bonita V.

Saunders; Daphne Letitia Smith

(xvi) 1986: Semere Arai; Stella R. Ashford; Busiso Chisala; Kevin Corlette; Arouna

Davies; Lorenzo O. Hilliard; Iris Marie Mack; Walter M. Miller; Denise M. Stephenson-

Hawk; James C. Turner

(xvii) 1987: Richard Lance Baker; Shiferaw Berhanu; Dennis Davenport; Nathaniel

Dean; George Edmunds; Dawit Getachew; Amos Olagunju; DeJuran Richardson; Hanson

Umoh; Nathaniel Whitaker

(xviii) 1988: Emery Neal Brown; Dominic P. Clemence; Vanere Goodwin; Abdulcadir

Issa; Amha Tume Lisan; Frank Albert Odoom; Kweku-Muata Agyei Osei (Noel Bryson);

Wanda Patterson; Lemuel Riggins; Elaine Smith; Gregory Smith; Vernise Steadman;

Leon Woodson; Roselyn Elaine Williams; Leon C. Woodson; Paul E. Wright

(xix) 1989: Tor A. Kwembe; Joan Sterling Langdon; Jean-Bernard Nestor; Abdul-Aziz

Yakubu

34

(xx) 1990: Gideon Abay Asmerom; Teresa Edwards; Rodney Kirby; Janis Oldham;

Michael M. Tom

(xxi) 1991: Harun Adongo; Adebisi Agboola; Patricia Beaulieu; Aniekan A. Ebiefung;

Jacqueline M. Hughes-Oliver; Sizwe G. Mabizela; Katherine Okikiolu; Yewande

Olubummo; Broderick O. Oluyede; Arlie O. Petters; Philippe Rukimbira (FIU)

(xxii) 1992: Evans Afenya; Gerald Yinkefe Agbegha; Donald Martin; Bi Roubolo Vona

(xxiii) 1993: Halima Ali; Danielle Carr; Duane Anthony Cooper; Koffi Fadimba; Stanley

Einstein-Matthews; Abba Gumel; Lancelot F. James; Camille A. McKayle; Christine

McMillan; Tonya M. Smoot

(xxiv) 1994: Kokou Y. Abalo; Patty Anthony; Ron Buckmire; Dawn Lott; Zephyrinus

Okonkwo; Gregory Smith; Frederick J. Semwogerere; Barama Toni

(xxv) 1995: Joseph Apaloo; Gregory Battle; Kossi Edo; Suzanne L. Weekes

(xxvi) 1996: Randolph G. Cooper III; Neil Flowers; Henry Gore; Errol Rowe; Temba

Shonhiwa; Aissa Wade

(xxvii) 1997: Afi Davis Harrington; Francis Y. Jackson; Michael Keeve; Tuwaner

Lamar; Alfred Noël; Richard F. Patterson; Sonya Stephens; Asamoah Nkwanta; Remi

Ombolo; Elaine Terry; Alain Togbe; Enoch Z. Xaba

(xxviii) 1998: Paulette Ceesay; Terrence Edwards; Neal Jeffries; Julie S. Ivy; Trachette

Jackson; Mark Lewis; Lemuel Riggins; Rhonda Sharpe; Monica Y. Stephens; Kim Y.

Ward; Pamela J. Williams

(xxix)1999: Garikai Campbell; Gelonia Dent; Berhane T. Ghaim; Edray H. Goins; Daniel

Lee Hunt; Anthony D. Jones; Alvina M. Johnson; Chawne Monique Kimber; Kathryn M.

Lewis; Cassandra McZeal; Desmond Stephens; Peter Stephens; Shree Whitaker

3.4 AFRICAN-AMERICAN MATHEMATICIANS OF 21ST CENTURY (2000 –

2004)

The names of African-American mathematicians, for the period 2000 - 2004, are

presented below in chronological order.

(i) 2000: Kim Woodson Barnette; Serge A. Bernard; Shea Burns; Illya V. Hicks; Keith E.

Howard; Tasha Inniss; Otis B. Jennings; Sean Paul; Selemon Getachew; Sherry Scott;

Talitha M. Washington; Kimberly Weems

(ii) 2001: Jamylle L. Carter; Naiomi T. Cameron; Shurron M. Farmer; Jeffery Fleming;

Russell Goward; Leona Harris; Rudy Horne, Jr.; Clifford Johnson; Daniel R.Krashen;

35

Lynnell Matthews; Jillian McLeod; Shona Davidson Morgan; Kimberly Flagg Sellers;

Idris Stoval; Craig Sutton; Talitha M. Washington

(iii) 2002: Gabriel Ayine; Martial Marie-Paul Agueh; Louis Beaugris; Nancy Glenn;

Jean-Michelet Jean-Michel; Djivede A. Kelome; Lynelle Matthews; Jillian McLeod; Iris

Gugu Moche; Tolu Okusanya; Jean M. Tchuenche; Howard Thompson; Gikiri Thuo;

Donald C. Williams

(iv) 2003: Sammani D. Abdullahi; Gerard M. Awanou; Sharon Clarke; Berhane T.

Ghaim; Jean-Michelet Jean-Michel; Llolsten Kaonga; Nolan MacMurray; Monica

Jackson; Kasso Okoudjou; Miranda I. Teboh-Ewungkem; Archie Wilmer III

(v) 2004: Milton H. Nash; Donald Outing; Rachel E. Vincent

4. STATISTICS OF AFRICAN-AMERICAN Ph.D.’s IN

MATHEMATICAL SCIENCES (1925 – 2004)

According to the list as presented in Section 3 above, it is interesting to note that a

total of 392 African-Americans had received a Ph.D. in mathematics during the period

1925 – 2004. For the sake of our statistical computations, we have divided this period

into four different sub-periods: 1925 – 1944, 1945 – 1964, 1965 – 1984, and 1985 –

2004. Out of 392 African-American Ph.D.’s in mathematics, 3.32 % received their

Ph.D.’s during the period 1925 – 1944, 8.42 % received their Ph.D.’s during the period

1945 – 1964, 40.05 % received their Ph.D.’s during the period 1965 – 1984, and 48.21 %

received their Ph.D.’s during the period 1985 – 2004. From the analysis presented here, it

is easily seen that the maximum number of African-Americans receiving Ph.D.’s in

mathematics was during the period 1985 – 2004. The statistics on the numbers of

African-Americans receiving Ph.D.’s in mathematics, during the period 1925 – 2004,

have been presented inthe Figure 4.1 below.

# African-Americans Ph.D.'s in the Mathematical Sciences

1925 - 2004

Total: 392

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

1925 - 1944 1945 - 1964 1965 - 1984 1985 - 2004

YEAR

Ph

.D

.'s

in

M

ath

em

atic

s (%

)

# African-Americans

Ph.D.'s in the

Mathematical Sciences

Figure 4.1: African-American Ph.D.’s in Mathematical Sciences (1925 – 2004)

36

5. HIGHLIGHTS ON THE ACHIEVEMENTS OF AFRICAN-AMERICANS IN

MATHEMATICAL SCIENCES

In the following paragraphs, achievements of some African-Americans in the field of

mathematical sciences are highlighted.

It is interesting to note that, during the period 1925 - 1947, 12 African-

Americans earned a Ph.D. in Mathematics.

Furthermore, half of all African-Americans who had earned their

Ph.D.'s in Mathematics, by the time of the year 1945, were students of

the University of Michigan.

During the period 1943 - 1969, thirteen African-American women

earned a Ph.D. in Mathematics.

It is also interesting to know that one of the most important landmarks

and rarest achievements in the field of mathematical sciences was when

three African-American Women, Drs. Tasha Innis, Kimberly Weems,

and Sherry Scott, received the Ph.D. in mathematics, in the same year

2000, from the same university, University of Maryland, College Park,

Maryland.

In 1929, Dr. Dudley Woodard was the first African-American to

publish a research paper in mathematical sciences in an accredited

mathematics journal, entitled, “On two dimensional analysis situs with

special reference to the Jordan Curve Theorem,” Fundamenta

Mathematicae, 13 (1929), 121-145.

The first African American publication in a top research journal was

Dr. William W. S. Claytor's Topological Immersian of Peanian

Continua in a Spherical Surface, Annals of Mathematics, 35 (1934),

809-835.

Dr. Gloria Ford Gilmer is considered to be the first African-American

woman to publish the first two (non-Ph.D.-thesis) mathematics

research papers, jointly with another African-American, Dr. Luna I.

Mishoe, in the year 1956, entitled:

(a) “On the limit of the coefficients of the eigenfunction series

associated with a certain non-self-adjoint differential system”, Proc.

Amer. Math. Soc. 7 (1956), 260-266.

(b) “On the uniform convergence of a certain eigenfunction series”,

Pacific J. Math. 6 (1956), 271-278.

37

The second joint research paper by two African-Americans, Charles

Bell and David Blackwell, in collaboration with Leo Breiman, was

published in the year 1960, entitled “On the completeness of order

statistics,” Ann. Math. Stat., 31, 1960, 794-797.

In 1961, Dr. Lonnie Cross shocked the African-American and

mathematics community by changing his name to Abdulalim

Shabbazz, and becoming the first African-American scientist to

embrace the followers of Elijah Mohammed, the leader of the African-

American Moslem community.

In 1963, Dr. Grace Lele Williams became the first Nigerian woman to

earn a Ph.D. in Mathematics from the University of Chicago.

In 1964, Dr. David Blackwell became the first African-American

mathematician to Chair a department, Department of Statistics, at one

of the major universities, University of California at Berkeley.

In 1965, Dr. David Blackwell became the first African-American

named to The National Academy of Sciences.

From 1968 to 1969, Dr. Percy A. Pierre was White House Fellow for

the Executive Office of the President of the United States.

In 1969, Clarence Ellis became the first African-American to earn a

Ph.D. in Computer Science from the University of Illinois.

Two mathematics graduate students, Johnny Houston and Scott

Williams, at the January 1969 Annual Meeting of The American

Mathematical Society, called together a group of African-American

mathematicians, and begat an adhoc organization, called “Black and

Third World Mathematicians,” which, in 1971, changed its name to

The National Association of Mathematicians (NAM).

In 1969, the book “Negroes in Science - Natural Science Doctorates”

by James M. Jay was published by the Balamp Company.

In 1972, Professor Morris Sika Alala became the first Kenyan

African Full Professor of Mathematics at the University of Nairobi.

In 1974, Dr. J. Ernest Wilkins, Jr., became the President of the

American Nuclear Society.

Alton Wallace became the first African-American to earn a Ph.D. in

mathematics, in the year 1974, under the direction of an African-

American thesis advisor, Dr. Raymond L. Johnson, at the University

38

of Maryland.

The African Mathematical Union (AMU) was founded in Africa In

1975. Its first president was a Cameroonian mathematician, Professor

Henri Hogbe Nlend.

The first AMU Pan-African Congress of Mathematicians was held in

Rabat, Morocco, in the year 1976.

In 1976, Dr. J. Ernest Wilkins, Jr., became a member of The

National Academy of Engineers.

Howard University established the first Ph.D. program in

Mathematics at a Historically Black University and College (HCBU),

in the year 1976, under the guidance of Dr. James Donaldson, the

Chair of its Mathematics Department, and Dr. J. Ernest Wilkins, Jr.,

then a member of its Physics Department.

In 1979, Dr. David Blackwell won the von Neumann Theory Prize

of the Operations Research Society of America.

The National Association of Mathematicians (NAM) inaugurated the

first Claytor Lecture, in 1980, with Professor James Josephs as the

speaker.

In 1980, the first book on African American Mathematicians, “Black

Mathematicians and their Works,” by V. K. Newell, J. H. Gipson, L.

W. Rich, and B. Stubblefield, was published by Dorrance & Company.

The Southern African Mathematical Sciences Association

(SAMSA) was founded among the 12 countries of Southern Africa in

1980.

In 1981, Dr. C. Dwight Lahr became the first African-American to get

tenure in a department of mathematics of an Ivy League School.

In 1984, Dr. C. Dwight Lahr became the first African-American to

become Full Professor in a department of mathematics of an Ivy

League School.

In 1986, the first issue of the African Mathematical Union's

Commission on the History of Mathematics in Africa (AMUCHA)

was presented.

In 1990, the African Mathematical Union Commission on Women

in Mathematics in Africa (AMUCWMA) was founded with Dr.

39

Grace Lele Williams as its Chairman.

In 1992, Dr. Gloria Gilmer became the first woman to deliver a major

the National Association of Mathematicians (NAM) lecture.

In 1995, the first Conference for African American Researchers in

the Mathematical Sciences (CAARMS1) was held at the

Mathematical Sciences Research Institute (MSRI), University of

California, Berkeley. The conference was organized by three prominent

African-American mathematicians, Drs. Raymond Johnson, William

Massey, and James Turner, in collaboration with Dr. William

Thurston. Since then CAARMS has been held each year.

In 1997, Dr. Katherine Okikiolu became the first African-American

to win Mathematics' most prestigious young person's award, the Sloan

Research Fellowship. She also was awarded the new $500,000

Presidential Early Career Awards for Scientists and Engineers.

In 1997, the organization Council for African American Researchers

in the Mathematical Sciences (CAARMS) was formed to oversee the

CAARMS conferences and to aid African Americans interested in

research in mathematics.

Also in 1997, Nathaniel Dean's book “African American

Mathematicians” was published by the American Mathematical

Society.

In 2001, Dr. William A. Massey became the first African-American

Full Professor (Edwin S. Wilsey Professor) of Operations Research and

Financial Engineering at Princeton University.

The following is the list of some articles published in best and reputed

mathematics journals of high quality by African-American

mathematicians:

Schiefelin Claytor, Topological Immersion of Peanian

Continua in a Spherical Surface, The Annals of

Mathematics, 2nd Ser. 35 (1934), 809-835.

Schieffelin Claytor, Peanian Continua Not Imbeddable in

a Spherical Surface, The Annals of Mathematics, 2nd Ser.

38 (1937), 631-646.

Blackwell, David, Idempotent Markoff chains, The

Annals of Mathematics, 2nd Ser. 43, (1942). 560--567.

40

Wilkins, J. Ernest, Jr. Multiple integral problems in

parametric form in the calculus of variations. The Annals

of Mathematics (2) 45, (1944). 312--334.

Blackwell, David, Finite non-homogeneous chains, The

Annals of Mathematics, 2nd Ser. 46, (1945). 594--599.

Wilkins, J. Ernest, Jr. A note on the general summability

of functions. The Annals of Mathematics (2) 49, (1948).

189--199.

Bellman, Richard; Blackwell, David On moment spaces.

The Annals of Mathematics, 2nd Ser. 54, (1951). 272--

274.

Kevin Corlette. Archimedean superrigidity and

hyperbolic geometry. Annals of Mathematics 2nd Series

135 (1992), no. 1, 165-182

Gangbo, Wilfrid. McCann, Robert J. The geometry of

optimal transportation. Acta Mathematica 177 (1996), no.

2, 113--161.

Okikiolu, Katherine. Critical metrics for the determinant

of the Laplacian in odd dimensions. The Annals of

Mathematics, 2nd Ser. 153 (2001), no. 2, 471--531.

E. A Carlen and W. Gangbo. Constrained steepest descent

in the 2-Wassertein metric, Annals of Math. 157, May

(2003).

The First Africans

1947: The earliest record of a Mathematics Ph. D. by an

African appears to be a Ghanaian African, Dr. A. M. Taylor

from Oxford University, U.K., in 1947.

Nigeria: Indigenous mathematics research activities in

Nigeria were pioneered by Drs. Chike Obi, Adegoke

Olubummo (1955), and James Ezeilo, who obtained their

Ph.D.’s in mathematics from British Universities in the 1950's

(see, for example, “Mathematics in Nigeria Today,” among

others). Dr. Grace Lele Williams became, in 1963, the first

Nigerian woman to earn a Ph.D. in mathematics from the

University of Chicago.

41

6. CONCLUDING REMARKS

The purpose of this paper was to present a chronological introduction of African-

Americans in the field of Mathematical Sciences. It is evident that these African-

American Mathematicians remain as a source of inspiration to us to excel in mathematics

and other fields of knowledge, and achieve our goals. The achievements of these African-

American Mathematicians, despite the difficulties they had to overcome, stand as a

beacon for us. It is hoped that the materials presented in this article will be useful to the

practitioners and researchers in various fields of theoretical and applied sciences who are

interested in the knowledge of diverse cultures, including global and historical

perspectives, with special reference to the field of mathematical sciences.

ACKNOWLEDGMENT

The author would like to express his sincere gratitude and acknowledge his

indebtedness to the various authors and, specially, to Dr. Scott W. Williams, Professor of

Mathematics, The State University of New York at Buffalo, whose works were liberally

consulted during the preparation of this article.

REFERENCES

Allen, J. E. (1971). Black History, Past and Present. Exposition Press Inc., Jericho, N. Y.

Carwell, H. (1977). Blacks in Science: Astrophysicist to Zoologist, Exposition Press,

Hicksville, N.Y.

Dudewicz, E. J., and Mishra, S. N. (1988). Modern Mathematical Statistics. John Wiley

& Sons, New York.

Kapur, J. N., and Saxena, H. C. (1999), Mathematical Statistics. S. Chand & Company

Ltd., New Delhi.

Kenshaft, P. C. (1987). Black Men and Women in Mathematical Research. Journal of

Black Studies, December, 19:2, 170 - 190.

Newell, V. K., Gipson, J. H., Rich, L. W., and Stubblefield, B. (1980). Black

Mathematicians and their Works, Dorrance & Company.

Rohatgi, V. K., and Saleh, A. K. M. E. (2001). An Introduction to Probability and

Statistics, John Wiley & Sons, Inc., New York.

Sammons, V. O. (1989). Blacks in Science and Education. Hemisphere Publishers,

Washington, D.C.

42

Sertima, I. V. (1983). Blacks in Science. Transactions Books.

Taylor, J., editor (1955). The Negro in Science. Morgan State College Press.

Williams, S. W. (1999). Black Research Mathematicians, African Americans in

Mathematics II. Contemporary Math. 252, 165 - 168.

Williams, S. W. A Modern History of Blacks in Mathematics.

www.math.buffalo.edu/mad/madhist.html.

Williams, S. W. Mathematicians of the African Diaspora.

www.math.buffalo.edu/mad/index.htm.l

Zaslavsky, C. (1973). Africa Counts: Number and Pattern in Africa Culture. Prindle,

Weber & Schmidt.

.

43

Polygon

Spring 2010 Vol. 4, 43-55

SURVEY OF STUDENTS’ FAMILIARITY WITH GRAMMAR AND

MECHANICS OF ENGLISH LANGUAGE – AN EXPLORATORY ANALYSIS

M. Shakil

1

, V. Calderin

2

and L. Pierre-Philippe

3

1

Department of Mathematics, Miami Dade College, Hialeah Campus,

Hialeah, FL 33012, USA. Email: mshakil@mdc.edu

2

Department of English, Miami Dade College, Hialeah Campus, Hialeah, FL

33012, USA. Email: vcalderin@mdc.edu

3

Department of ESL and Foreign Languages, Miami Dade College, Hialeah

Campus, Hialeah, FL 33012, USA. Email: lpierrep@mdc.edu

ABSTRACT

In recent years, there has been a great interest in the problems of grammar and

mechanics instruction to the freshman English. In this paper, the students’ familiarity

with grammar and mechanics of English language has been studied from an exploratory

point of view. By administering a survey on the grammar and mechanics in some classes,

the data have been analyzed statistically which shows some interesting results. It is hoped

that the findings of the paper will be useful for researchers in various disciplines.

KEYWORDS

ANOVA, grammar, hypothesis testing, mechanics, prescriptivist approach, Shannon’s

diversity index.

1. INTRODUCTION

As noted by Teorey (2003), although the usage of prescriptivist approach to grammar

instruction was rejected by the linguistic community nearly one hundred years ago, its

importance in the present day instruction of English language cannot be overlooked. It

appears from the literature that not much work has been done on the problem of students’

familiarity with grammar and mechanics of the English language. Certain guessing

experiments to measure the predictability (defined in terms of entropy) of ordinary

literary English were devised by Shannon (1951). A study to determine the predictability

of English whether it is dependent on the number of preceding letters known to the

subject was conducted by Burton and Licklider (1955). The variations in the predicting

capacities of students learning English as a foreign language were studied by Siromoney

(1964). Recently, Joyce (2002) has studied the use of metawriting to learn grammar and

mechanics. Using freshman composition, the problems of grammatical errors and skills

have been studied by Teorey (2003). In this paper, we propose to study the students’

familiarity with grammar and mechanics of English language from an exploratory point

of view. The data have been analyzed statistically. The organization of this paper is as

44

follows. Section 2 discusses the methodology. The results are given in section 3. The

discussion and conclusion are provided in Section 4.

2. METHODOLOGY

A survey consisting of 20 multiple choice questions (see Appendix I) was constructed

to test students’ familiarity with English grammar and mechanics in six different courses

in the spring semester of 2009. The courses selected were ENC 0021, ENC 1101, ENC

1102, EAP 1640, MGF 1107 and MAC 2233. The survey was administered by the

instructors in each of these courses. A total of 121 students participated in the survey the

details of which are provided in the following Tables 1 and 2 below.

Table 1: Surveyed Courses

Discipline Courses Respondents

ENC ENC 0021, ENC 1101,

ENC 1102, EAP 1640

71

MAT MGF 1107, MAC 2233 50

Total 6 121

Table 2: Survey Respondent Characteristics

Gender Native

English

Speakers

Non-native

English

Speakers

Total

Male 23 34 57

Female 29 35 64

Total 52 69 121

3. RESULTS

3.1 MASTERY REPORT

The total number of questions in the survey was 20. Each question was assigned 1

point. The possible points in the survey were 20. The score unit was assumed to be

percent. The minimum % to pass was 60. The mastery report of the survey participants is

provided in the Figure 1 below.

45

Figure 1: Mastery Report

3.2 ITEM ANALYSIS

For the standard item analysis report of the survey questions, the participants were

divided into three different groups, that is, Group I: (ENC 0021, EAP 1640); Group II:

(ENC 1101, ENC 1102); and Group III: (MGF 1107, MAC 2233). The descriptive

statistic of the performance of these groups in the survey is provided in Table 3 below.

Table 3: Descriptive Statistic of Group Performance

Group Respondent Mean

Score

Median

Score

S.

D.

Reliability

Coefficient

(KR20)

Highest

Score

(out of

20)

Lowest

Score

(out of

20)

I 32 13.88 13.90 2.75 0.63 20.00 5.00

II 39 14.03 14.64 2.13 0.44 17.00 9.00

III 50 14.22 14.27 2.18 0.41 19.00 6.00

Further, the standard item analysis report of the survey questions for the said three groups

is provided in the Figure 2 below.

Figure 2: Standard Item Analysis Report

3.3 HYPOTHESIS TESTING: INFERENCES ABOUT TWO MEAN SCORES

This section discusses the hypothesis testing and draws inferences about the mean

46

scores of two independent samples. Following the procedure on pages 474-475 in Triola

(2010) of not equal variances: no pool, the hypothesis testing was conducted for three

sets of two independent groups by using the statistical software package STATDISK. The

results of these tests of hypotheses are provided below.

(I) INFERENCES ABOUT MEAN SCORES OF ENC AND MAT PARTICIPANTS

For this analysis, we defined the two groups as follows:

ENC/EAP: ENC 0021, ENC 1101, ENC 1102, EAP 1640

MAT: MGF 1107, MAC 2233

The descriptive statistic of ENC/EAP and MAT participants is given in Table 4 below.

Table 4: Descriptive Statistic of ENC and MAT Participants

Group Respondent Mean

Score

S. D.

ENC/EAP 71 13.96 2.44

MAT 50 14.22 2.18

The results of the hypothesis test to draw the inferences about the mean scores of

ENC/EAP and MAT participants are provided in Table 5 and Figure 3 below.

Table 5: Hypothesis Testing about Mean Scores of ENC/EAP and MAT

Assumption: Not Equal Variances: No Pool

Let µ1 = Mean Score of ENC/EAP and µ2 = Mean Score of

MAT.

Claim: µ1 = µ2 (Null Hypothesis)

Test Statistic, t: -0.6147

Critical t: ±1.981298

P-Value: 0.5400

Degrees of freedom: 112.3724

95% Confidence interval:

-1.098025 < µ1-µ2 < 0.5780247

Fail to Reject the Null Hypothesis

Sample does not provide enough evidence to reject the claim

47

Figure 3: Hypothesis Testing about Mean Scores of ENC/EAP and MAT

(II) INFERENCES ABOUT MEAN SCORES OF NATIVE ENGLISH SPEAKING

AND NON-NATIVE ENGLISH SPEAKING PARTICIPANTS

For this analysis, we defined the two groups as follows:

ENG: Native English Speaking Participants

NON-Eng: Non-native English Speaking Participants

The descriptive statistic of ENG and NON-ENG participants is given in Table 6 below.

In order to compare the scores of ENG and NON-ENG participants, the respective

boxplots are drawn on the same scale in Figure 4 below.

Table 6: Descriptive Statistic of ENG and NON-ENG Participants

Group Respondent Mean

Score

Median S. D.

ENG 52 73.84615 75 10.36658

NON-ENG 69 67.68116 70 12.05318

Figure 4: Comparing Scores of ENG (Col. 1) and NON-ENG (Col. 2) Participants

48

The results of the hypothesis test inferences to draw about the mean scores of ENG and

NON-ENG participants are provided in Table 7 and Figure 5 below.

Table 7: Hypothesis Testing about Mean Scores of ENG and NON-ENG

Assumption: Not Equal Variances: No Pool

Let µ1 = Mean Score of ENG and µ2 = Mean Score of NO-ENG.

Claim: µ1 = µ2 (Null Hypothesis)

Test Statistic, t: 3.0182

Critical t: ±1.980468

P-Value: 0.0031

Degrees of freedom: 116.8722

95% Confidence interval:

2.119718 < µ1-µ2 < 10.21026

Reject the Null Hypothesis

Sample provides evidence to reject the claim

Figure 5: Hypothesis Testing about Mean Scores of ENG and NON-ENG

(III) INFERENCES ABOUT MEAN SCORES OF MALE AND FEMALE

PARTICIPANTS

For this analysis, we defined the two groups as follows:

M: Male Participants

F: Female Participants

The descriptive statistic of the Male and Female participants is given in Table 8 below.

In order to compare the scores of Male and Female participants, the respective boxplots

are drawn on the same scale in Figure 6 below.

49

Table 8: Descriptive Statistic of Male and Female Participants

Group Respondent Mean

Score

Median S. D.

M 57 69.91228 70 10.79398

F 64 70.70313

75 12.56308

Figure 6: Comparing Scores of Male (Col. 1) and Female (Col. 2) Participants

The results of the hypothesis test to draw the inferences about the mean scores of Male

and Female participants are provided in Table 9 and Figure 7 below.

Table 9: Hypothesis Testing about Mean Scores of Male and Female Participants

Assumption: Not Equal Variances: No Pool

Let µ1 = Mean Score of M and µ2 = Mean Score of F.

Claim: µ1 = µ2 (Null Hypothesis)

Test Statistic, t: -0.3724

Critical t: ±1.980123

P-Value: 0.7103

Degrees of freedom: 118.8560

95% Confidence interval:

-4.995995 < µ1-µ2 < 3.414395

Fail to Reject the Null Hypothesis

Sample does not provide enough evidence to reject the claim

Figure 7: Hypothesis Testing about Mean Scores of Male and Female Participants

50

3.4 ANALYSIS OF VARIANCE (ANOVA) AND DIVERSITY ANALYSIS

This section discusses the analysis of variance for testing the hypothesis of equality of

the mean scores and diversity analysis for testing the hypothesis of evenness ratio of

respondent performance based on gender-language spoken. All these analyses were

carried out by using the statistical software packages STATDISK and EXCEL.

(I) Respondent Performance Based on Gender-Language Spoken

The performance of respondent based on gender-language spoken is provided in Table 10

and Figure 8 below.

Table 10: Respondent Performance Based on Gender-Language Spoken

Group Gender – Language

Spoken

% of Students Scoring

60 or above

% of Students

Scoring Below 60

AA Male-English 18.18181818 0.826446281

AB Male-Spanish 24.79338843 3.305785124

BA Female-English 23.14049587 0.826446281

BB Female-Spanish 23.14049587 4.958677686

BC Female-Other 0.826446281 0

Figure 8: Respondent Performance Based on Gender-Language Spoken

(II) Analysis of Variance (ANOVA)

Following the procedure on pages 628-631 in Triola (2010), this section discusses the

ANOVA for testing the hypothesis of equality of the mean scores of four independent

groups based on gender-language spoken, that is, AA, AB, BA, and BB. The results of

ANOVA are provided in Table 11 and Figure 9 below. (Note: There was only one female

who spoke French and so was included in group BB for analysis purposes.)

51

Table 11: ANOVA: Hypothesis Testing About Equality of Mean Scores

ANOVA OF AA, AB, BA, BB (BC included in BB)

Alpha = 0.05

Source: DF: SS: MS: Test Stat, F: Critical F: P-Value:

Treatment: 3 1156.315368 385.438456 2.941614 2.682134 0.036012

Error: 117 15330.461492 131.029585

Total: 120 16486.77686

Reject the Null Hypothesis

Reject equality of means

Figure 9: ANOVA: Hypothesis Testing About Equality of Mean Scores

(III) Diversity Analysis

Applying the Shannon’s Measure of Diversity Index (in terms of entropy) (Shannon,

1948), this section discusses the diversity analysis for testing the hypothesis of evenness

ratio of respondent performance based on gender-language spoken, that is, AA, AB, BA,

BB, and BC. The results of Diversity Analysis are provided in Table 12 below.

Table 12: Diversity Analysis Based on Gender-Language Spoken

Group Gender – Language Spoken Proportion (p) of Students

Scoring 60 or above

AA Male-English 0.181818182

AB Male-Spanish 0.247933884

BA Female-English 0.231404959

BB Female-Spanish 0.231404959

BC Female-Other 0.008264463

52

Hypothesis: Does the respondent performance (that is, proportion of students scoring 60

or above based on gender-language spoken, that is, AA, AB, BA, BB, and BC, as

provided in Table 12 above) suggest more diversity in the groups’ familiarity with the

English grammar and mechanics?

The Shannon’s Measure of Diversity Index H and Evenness Ratio

H

E , where

10

H

E , for the above Table 12, are computed as follows. Note that if 1

H

E ,

there is complete evenness.

1.372718H

0.852918

H

E

Since 10.852918

H

E , there appears to be complete evenness in the respondent

performance (that is, proportion of students scoring 60 or above based on gender-

language spoken, that is, AA, AB, BA, BB, and BC, as provided in Table 12 above).

4. CONCLUSIONS

This paper discussed the students’ familiarity with grammar and mechanics of English

language from an exploratory point of view. A total of 121 students from six different

courses, that is, ENC 0021, ENC 1101, ENC 1102, EAP 1640, MGF 1107 and MAC

2233, participated in the survey. The minimum % to pass was 60. Out of 121 survey

participants, 90.10 % scored 60 or above. Based on the hypothesis testing, the following

inferences were drawn about the survey participants.

1. There was sufficient evidence to support the claim that the mean scores of Male

and Female participants were same.

2. There was sufficient evidence to support the claim that the mean scores of

ENC/EAP and MAT participants were same.

3. There was sufficient evidence to reject the claim that the mean scores of

Native English speaking and Non-native English speaking participants were

same.

4. There was sufficient evidence to reject the claim of the equality of mean scores of

four independent groups based on gender-language spoken, that is, AA, AB, BA,

and BB.

5. There appears to be complete evenness in the respondent performance (that is,

proportion of students scoring 60 or above based on gender-language spoken).

53

It is hoped that the findings of the paper will be useful for researchers in various

disciplines.

ACKNOWLEDGMENT

The authors would like to express their sincere gratitude and acknowledge their

indebtedness to the students of the courses, that is, ENC 0021, ENC 1101, ENC 1102,

EAP 1640, MGF 1107 and MAC 2233, in the spring semester of 2009, for their

cooperation in participating in the survey. Further, the authors are thankful to Professor

Francia Torres for allowing us to administer the survey in her ENC0021 course and to

Mr. Cesar Ruedas for assisting in test item analysis.

REFERENCES

Burton, N. G., and Licklider, J. C. R. (1955). Long-range constraints in the Statistical

Structure of Printed English. American Journal of Psychology, 68, pp. 650 – 653.

Joyce, J. (2002). On the Use of Metawriting to Learn Grammar and Mechanics. The

Quarterly, Vol. 24, No. 4, pp. 1 - 5.

Shannon, C.E. (1948). A Mathematical Theory of Communication. Bell System Technical

Journal, 27, pp. 379 - 423; 623 - 656.

Shannon, C.E. (1951). Prediction and Entropy of Printed English. Bell System Technical

Journal, 30, pp. 50 - 64.

Siromoney, G. (1964). An Information-theoretical Test for Familiarity with a Foreign

Language. Journal of Psychological Researches, viii, pp. 267 – 272.

Teorey, M. (2003). Using Freshman Composition to Analyze What Students Really

Know About Grammar. The Quarterly, Vol. 25, No. 4, pp. 1 - 5.

Triola, M. F. (2010). Elementary Statistics. Addison-Wesley, N. Y.

APPENDIX A

Grammar Research Project Spring 2009

Sentence Structure – Identify the type of sentence:

A. Simple B. Compound C. Complex

1. Pat and Rob both work in the industrial complex.

2. While Pat is in the accounting department, Rob is an engineer.

3. Rob works the late shift, so he rarely sees Pat.

54

4. Pat needs to leave work by 3PM in order to pick up his son from school.

Verb Tenses and Forms - Which Answer Corrects the Sentence

5. As I began to write my essay, my computer falled off the desk and broke.

A. begins B. fell C. breaked

6. Before the pitcher threw the ball, the player ran and stealed second base.

A. throw B. runs C. stole

7. When Kelly saw the dish, he will eat all the food and forget to save some for Saul.

A. sees B. will eats C. forgot

8. Whenever I study for an exam, I closed my door and turn on my desk lamp.

A. studying B. close C. turned

Commonly Confused Words - Which Answer Corrects the Sentence

9. Drinking too many sodas can effect your health.

A. to B. affect C. you’re

10. A lot of investors loose money through risky investments.

A. A lot B. lose C. though

11. The buyers should have tried to except their offer.

A. should of B. accept C. they’re

12. Mary would like to take the Design course, but it’s all ready full.

A. coarse B. its C. already

Punctuation – Identify the correct sentence

13. A. After watching the movie, Sally needed to return the DVD, so she borrowed her

father’s car.

B. After watching the movie Sally needed to return the DVD, so she borrowed her

father’s car.

C. After watching the movie, Sally needed to return the DVD so she borrowed her

father’s car.

14. A. Marco can go to the meeting, but not the party because somebody’s going to

his house for dinner.

55

B. Marco can go to the meeting but not the party because somebody’s going to his

house for dinner.

C. Marco can go to the meeting but not the party, because somebody’s going to his

house for dinner.

15. A. Samuel took a month’s leave of absence in order to be with his Aunt May,

who was very ill.

B. Samuel took a month’s leave of absence in order to be with his Aunt May who

was very ill.

C. Samuel took a month’s leave of absence, in order to be with his father, who was

very ill.

16. A. The new business plan is said to have many advantages, such as maintaining

facilities increasing profits and allowing for raises and new hires.

B. The new business plan is said to have many advantages, such as maintaining

facilities, increasing profits and, allowing for raises and new hires.

C. The new business plan is said to have many advantages, such as maintaining

facilities, increasing profits, and allowing for raises and new hires.

Spelling - Identify the misspelled word.

17. It was (a.) truley an (b.) honor to have (c.) known Dr. Livingstone.

18. My brother is (a.) pursuing a (b.) career as a (c.) licenced broker.

19. The (a.) committee was able to (b.) accomodate the new members without (c.)

noticeable difficulties.

20. Luis had an uneasy (a.) conscience for having (b.) embarassed Samantha with the (c.)

surprise party.

56

Polygon

Spring 2010 Vol. 4, 56-80

EFFECTS OF DEVELOPMENTAL COURSES ON STUDENTS’ USE OF

WRITING STRATEGIES ON THE FLORIDA COLLEGE BASIC SKILLS EXIT

TEST

M. L. Varela

1

1

Department of Communication, Arts & Philosophy, Miami Dade College,

InterAmerican Campus, Miami, FL 33135, USA. Email: mvarela@mdc.edu

ABSTRACT

The writing strategies students use most often in preparing for the subjective and

objective tests of writing for College Preparatory Writing 3 were examined. To address

this, data was collected using a comprehensive survey that asked students about the

strategies they used in four different domains: vocabulary strategies, comprehension

strategies, grammar strategies, and strategies to specifically improve writing skills. It was

hypothesized that students’ use of writing strategies on the exit exam resulted in a

substantial percentage of students retaking the course. The results indicated that the

percentage of students using different strategies varied dramatically. Some strategies

were used very frequently while others were not.

KEYWORDS

Developmental writing, exit tests, writing skills, writing readiness, community

college.

1. INTRODUCTION

In the 1970s and 1980s, a high school diploma guaranteed high-paying jobs, however,

given today's career markets and job competition, a college education has become

essential and necessary. Obtaining a college degree is valued and beneficial to the

potential college graduate (National Center for Education Statistics [NCES], 2003).

Students entering colleges or universities are expected to bring prior knowledge and

experiences learned at the high school level as a foundation for college study. Basic skills

in English, mathematics, reading, and writing are the underlying groundwork essentials

for a productive college experience and completion (NCES, 2003). These skills are then

57

further developed through a series of courses taken at the college or university level for

the purpose of obtaining a certificate or a degree. The harsh reality is that a majority of

students entering colleges and universities do not have the basic principles associated

with becoming a college student, and as a result require special interventions in the form

of developmental or remedial courses (Carter, Roth, Crans, Ariet, & Resnick, 2001).

In 1996, NCES revealed that 77% of higher education institutions in the nation with

an enrollment of freshmen offered at least one remedial reading, writing, or mathematics

course in fall of 1995. Similarly, the same research was conducted in 2000 and reported

in 2004. The research revealed that 76% of the higher education institutions still offered

at least one remedial reading, writing, or mathematics course in the fall of 2000. The

difference in the 1% drop in a four-year period is insignificant in relation to the number

of underprepared students currently entering colleges and universities nationwide (NCES,

2004).

Further, the Florida Department of Education (2007) reported in 1999 that 59% of

high school students entering the community college system require remediation in one

or more areas. The need for remediation is prevalent among community colleges and

while the exact percentages are not known, slightly 37% of entering college freshmen

needed at least one area of remediation. The presence of developmental programs in 94%

of public colleges and 82% of private colleges in Florida reflect the present continuing

need (Wyatt, 1992).

For one particular college in South Florida, 81% of students enrolled are

underprepared according to scores analyzed on the Computerized Placement Test (CPT)

(Bashford & Mannchen, 2005; Rodriguez, 2006). Since 1985, the State of Florida has

58

required entry-level testing for students seeking Associate in Arts and Associate in

Science degrees. In 2006 the College Academic Student Support Council stated “The

CPT is used for placement at all Florida community colleges for most programs” (p. 4).

Therefore, every degree-seeking student at the college must take the CPT. The College

Academic Student Support Council also stated the CPT is the test that determines how

college-ready the students are since it “assesses students' content knowledge in reading,

sentence skills, and mathematics” (p. 4). Since the CPT is an adaptive test, the computer

automatically determines which questions are presented to the students based on their

responses to prior questions. This technique zeroes-in on just the right questions to ask

without being too easy or too difficult. Consequently, Morris (2006) stated “The greater

the students demonstrate skill level, the more challenging will be the questions

presented” (p. 2).

Students who take any of the three levels of remedial writing should be prepared to

move to the next level, which is ENC1101 or regular freshman English Composition 1.

However, according to the subject college's records, the Research and Testing Committee

revealed that the progression of students from college preparatory writing to college level

English has declined for the past three years and is now 48% (Morris, 2006). Upon

learning this, the researcher set out to discover possible reasons why the decline was

consistent for three years. A set of 28 writing strategies where examined with the

sampled student population to identify a possible correlation between students’ frequent

use of strategies and their passing rate on the exit test.

59

2. RESEARCH QUESTIONS AND METHODOLOGY

RESEARCH QUESTIONS

Based on the concern that students may not be applying the proper strategies to

successfully pass the Florida College Basic Skills Exit Test, four research questions were

analyzed. Therefore, for the purpose of this study the researcher investigated strategies

used by the ENC0021 student population that could be predictors of the decline in

enrollment from ENC0021 to ENC1101. The purpose of this study was multifold and the

following research questions were addressed:

1. What are the most common writing strategies that students employ?

2. Is there a relationship between the use of different strategies? That is, do students who

frequently use one type of strategy (e.g., vocabulary) also use other strategies (e.g.,

grammar) with high frequency?

3. What are student’s perceptions of the Florida College Basic Skills Exit Test and the

content of its essay prompts?

4. Do writing professors think students feel writing has value in high school and college

courses, in overall academic performance, and in their future?

Research has indicated possible reasons as to why students enter college

underprepared. According to Hoyt and Sorensen (2001) the most popular trend in

education today is the “chain of blame” game. This “chain of blame” occurs when

“universities blame the high schools, the high schools blame the middle schools, and the

middle schools blame the elementary schools for poor student preparation” (p. 26). In

essence, the lack of preparation at the secondary level has become a hindrance for

students who wish to pursue a college education.

60

Furthermore, in a recent study of high school preparation and placement testing, Hoyt

and Sorensen found that as part of the standards movement, including their home state of

Utah, certain states are “implementing mandatory proficiency tests, releasing report cards

on schools,” and “differentiating high school diplomas, giving some students credit for

demonstrating competence in college preparatory courses based on proficiency exams”

(p. 32). A similar approach has also taken effect in Florida schools in regard to the

FCAT. Hoyt and Sorensen also discovered that teachers “may be awarding passing

grades to many students who have not adequately learned the material” (p. 32). This

scenario jeopardizes those students whose intentions are to attend college.

In addition, Hidi and Harackiewicz (2000) stated that another possible reason for the

underpreparedness of secondary students is the lack of motivation and effort. Hidi and

Harachiewicz affirmed that boring courses, demanding professors, and difficult

assignments all contributed to the college students’ lack of effort. However, the research

did not indicate as to when the underpreparedness occurred. There is clearly a need for

more structured readiness at the secondary level so that students will be well-prepared

prior to entering college, but research still indicates that a need for remediation at the

college level will continue to be prevalent today and in years to come (Hoyt & Sorensen,

2001; Wyatt, 1992).

Colleges and universities have a responsibility to maintain appropriate admission

standards. But the admissions process at open institutions, give underprepared students a

second chance at a college education, and should be structured to ensure that students are

prepared for college level course work (Hoyt & Sorensen, 2001).

61

The progression of students from College Preparatory Writing 3 to English

Composition 1 (ENC0021-ENC1101) respectively, has declined for the past three years

(Morris, 2005). In ENC0021 two state-mandated tests are to be taken and passed before

students are allowed to register for ENC1101. This study focused on tracking the number

of students who move from ENC0021 to ENC1101.

In another study of student preparation, Thot-Johnson and Vanniarajan (2002)

focused on students reading and writing strategies and high-stakes performance. Their

study indicated that students used writing strategies that they believed were useful

strategies. Thot-Johnson and Vanniarajan noted that students “would feel empowered and

would be further motivated to use them, which subsequently would result in increased

skill execution” (p. 5).

The study also specified that students who do not internalized writing strategies

experience difficulty in becoming independent thinkers and writers. However, research

showed that students of writing who are underprepared worked twice as hard and wrote

twice as many drafts as their “prepared” counterparts, and were conscientious about their

progress (Community College Survey of Student Engagement, 2005; Crouch, 2000).

Writing abilities vary by individuals. Each one has a set of unique life experiences

developed, different experiences with strategies, and different ways of communicating.

When the final exam writing prompt was given to students, no two writers used the same

prewriting techniques in order to develop a cohesive essay, nor did the student writers

expressed the same point of view. This was due in part because students were taught to

write in different ways.

62

According to Carter, Roth, Crans, Ariet, and Resnick (2001) the explanation most

commonly given by community college officials for the high failure rate on the CPT is

that “students’ course-taking choices in high school did not equip them with the skills

needed to do college-level work” (p. 73).

Thus, the possibility of these studies might have attributed to the causes of the

educational trends, but one can never be sure. Is the relationship between the chain of

blame game and students’ lack of success on the CPT so obvious and so closely related

that one influences the outcome of the other? If so, ultimately where does the chain of

blame game begin or end?

There is a need for a collaborative effort between the local high schools and the local

community colleges and universities. Hoyt and Sorensen (2001) suggested that college

and university faculty should assist high school instructors in the process of developing

English and mathematics curriculum to better prepare students for subsequent college

level course work. Perhaps pre college students would benefit from their suggestions

since the subject college is a diverse college.

And although only 19% of all entering students are college-ready, the college

promises to help produce individuals of great success and fortitude. Finally, the

implementation for newly designed placement exams at the college level are still

unknown at this time, but there is evidence that new proposals are in the work and will be

available in the near future (Sanchez, 2006).

63

METHODOLOGY

This study focused on a population made up of 74 college preparatory students. The

74 students were enrolled in five courses of ENC0021. Students and professors were

selected based on a volunteer basis and availability of time. A questionnaire (Appendix

B) surveying the 74 students was distributed to collect data addressing the research

questions. An additional questionnaire (Appendix C) was distributed to the professors

that taught writing for the spring term 2008 with the idea of gaining a greater perspective

of the students enrolled in ENC0021 as well as the professors' teaching philosophy. A

total of eight full- time professors volunteered for the study.

The participants, to include students and professors, were made aware of the

significance of the study via a Letter to Professors (Appendix D) and a Letter to Survey

Recipients (Appendix E). The data determined students' attitude about writing and about

the Florida College Basic Skills Exit test for the sole purpose of aiding the researcher in

reporting the findings.

In order to have conducted such an investigation, the researcher chose an

experimental design approach to determine if there was a correlation between the Florida

College Basic Skills Exit test and students’ non-passing status from the developmental

level of writing courses to regular level college courses.

3. CONCLUSIONS

This study will contribute to the literature as the existing literature has not studied the

correlation between students’ use of writing strategies and the Florida College Basic

Skills Exit Test. This chapter will highlight the summary of survey results, summarize

exit exam results, summarize qualitative teacher surveys, discuss implications for

64

practitioners, integrate findings with the current study with previous studies, discuss

limitations, and offer recommendations.

One of the primary research questions of this study addressed the use of different

writing strategies. To address this, data was collected using a comprehensive survey that

asked students about the strategies that they used in four different domains: vocabulary

strategies, comprehension strategies, grammar strategies, and strategies to specifically

improve writing skills. The subsequent analysis results summarize the use of these four

broad writing strategies, each of which was addressed using a series of questionnaire

items. For each strategy, students were first asked whether they used the strategy. If they

reported using a strategy, a follow-up question asked whether the student used the

strategy “Some of the time” or “Most of the time”.

The percentage of students using different strategies varied dramatically. Some

strategies were used very frequently while others were not. Considering all four

categories (vocabulary strategies, comprehension strategies, grammar strategies, and

strategies to specifically improve writing skills), the survey addressed 28 unique

strategies. Table 13 summarizes the overall results by rank ordering the 28 strategies

according to the percentage of students that use each approach. As seen in the table, only

6 of the 28 strategies (21.4%) were used by more than 90% of the students. Among these

top strategies, four were vocabulary-related.

A larger tier of 10 strategies were used by 80% to 90% of the students. As seen in the

table, this set of strategies included a mix from the four categories. Finally, nearly half of

the strategies were used by fewer than 70% of the students. Among this set of

approaches, two strategies were used with very low frequency: observing classmates’

65

essays (55.6%) and giving up on what to say (46.6%). Giving up is a poor strategy, so it

is not a surprise that this approach was ranked last. However, nearly half of the sample

reported using this strategy. Obviously, this has an important bearing on students’ ability

to improve their reading and writing skills.

Table 13

Overall Use of 28 Strategies

Survey Question Percent Category

Q24. Reread the paragraph 98.6 C

Q21. Use a different word with a similar meaning 95.9 V

Q13. Guess the meaning based on context 94.5 V

Q25. Distinguish the relevant details 93.2 C

Q19. Use the spell check function 93.2 V

Q16. Pay attention to how a word is used 90.5 V

Q30. Use the grammar check 89.2 G

Q31. Notice grammar mistakes when proofreading 89.2 G

Q39. Revise what you have written 87.7 W

Q28. Summarize the information after reading 86.5 C

Q33. Decide in advance what to write about 86.3 W

Q12. Use a dictionary 85.1 V

Q18. Remember the context in which it occurs 84.9 V

Q34. Decide in advance what content to put in 84.7 W

Q32. Make an outline 83.8 W

Q29. Pay attention to grammatical structure 82.4 G

66

Q27. Make predictions about the contents of essay 76.7 C

Q26. Make comparisons with your own experiences 76.4 C

Q35. Focus on learning grammar 75.3 W

Q14. Ask your instructor for examples 74.0 V

Q20. Write the word down 68.9 V

Q15. Look it up if it is important 65.8 V

Q38. Show your writing to others 65.8 W

Q22. Consult the thesaurus 62.2 V

Q36. Read a lot of books 60.8 W

Q17. Translate the word in your native language 60.3 V

Q37. Observe how essays are written by classmates 55.6 W

Q23. Give up what you want to say 46.6 V

Note. V = vocabulary, C = comprehension, G = grammar, and W = writing

A separate set of analyses examined the impact of the Florida State Writing Exit Test

on course performance. Specifically, students were categorized according to whether they

had satisfactory performance in the class prior to taking the exam. Among the students

who were performing satisfactorily, 88.5% passed the exit exam. This means that 11.5%

of the students who were otherwise performing well had to repeat the course because they

failed the exit exam. Looking at these results differently, 29 students failed the exit exam.

Among these students, 24% had satisfactory performance prior to taking the exit exam.

This suggests that the exit exam does result in a substantial proportion of students

retaking the course.

67

An analysis of research question 3 revealed that professors believe their students

employ the capabilities of being successful at writing. The overall consensus was that one

view looks at writing as a process of filling in the blanks of a 5-paragrah formula that

doesn’t have much meaning beyond preparation for standardized exams. Another view

looks at writing as a genuine process of exploration and creative reflection that is part of

living their lives. However, the overall opinion was that some students’ view are

somewhere in the middle of the two extremes. And while many students understand the

more creative model, they do not see it as one that is valued in school, even though they

may apply it on their own. Although at diametric extremes in years of experience, the

overall philosophies were similar. The instructors interests were on behalf of their

students’ successes and capabilities in learning how to writing at the college level and to

become life-long learners.

In accordance with the outcome of table 13, the top six strategies students used with

most frequency are considered weak strategies. These strategies are not consistent with

approaches that will improve student performance. With the exception of paying attention

to how a word is being used in context, the overall results of the top six strategies are

ineffective according to the writing curriculum at the college level. Cleary, practitioners

need to be made aware of the types of strategies being used by the writing student

population in the classroom, since these same strategies are most likely the same ones

being implemented when students take the Florida College Basic Skills Exit Test.

The strategies used by 80% to 90% of the students are strategies that could be

considered helpful depending on the goals of each individual writing instructor. And

although instructor goals may vary, generally the ultimate outcome is for students to feel

68

comfortable with writing in a college setting. Therefore, instructors need to emphasize on

the strategies that are used by the larger population of students and not necessarily the

ones they use most frequently in the classroom. This finding also has important

implications for high school educators, counselors, and parents. High school students

should be advised as early as the ninth grade of college preparedness. One study revealed

that the more students that take the more difficult courses in high school consequently

score higher on standardized test, thus eliminating the need for remediation at the college

level. (Carter, Roth, Crans, Ariet, & Resnick, 2001)

On the whole, the implications of the results on instruction indicate that students use

writing strategies with high frequency at least 80% of the time. Students will use what

instructors teach them. If that is the case, it is obvious then that effective strategies need

to be taught. One reason to teach students these strategies is due in part because writing is

process based as opposed to content based. Instructors can only teach students how to

learn to write (Thot-Johnson & Vanniarajan, 2001).

It is important to integrate the results of this study with previous research studies.

Several studies had similar outcomes in regards to students’ frequent use of writing

strategies and performance on standardized testing.

Thot-Johnson and Vanniarajan's (2002) study revealed that by the time students enter

undergraduate studies they realize that they must possess reading and writing abilities in

order to become “independent learners of academic material” (p. 4). Another similarity

between this study and the researcher’s study was that the majority of the writing student

population did not find the writing prompt interesting. Although the researcher’s

69

participants did not feel the topic was too American culture, it perhaps did not target the

participants’ schema and therefore the topic was found uninteresting.

Moreover, the sample size was also closely related (Thot-Johnson’s &

Vanniarajan=77, the researcher=74). However, when students were questioned on their

self-perceived level of writing ability in English in Thot-Johnson’s and Vanniarajan’s

study, “24 students (31.2%) felt that their writing ability was below average, 36 students

(46.8%) felt it was average, and 4 students (5.2%) perceived that their ability was good”

(p. 8). These results are for a total of 64 students. The study did not report on the writing

ability of 13 of the students sampled. And when students were asked the same question

on the researcher’s study, 3 students (4.5%) felt their writing ability in English was below

average, 23 students (31.08%) felt it was average, 8 students (10.81%) reported it was

very good, 2 students (2.70%) felt it was excellent, and 38 students (51.35%) felt their

writing ability in English was good. It was interesting to reveal that 79.9% of students

whose native language is Spanish felt that their writing ability in English was good. The

research suggested that although Spanish is the language most often used by students at

the college, it did not affect students writing ability in English.

As noted, the study most closely related to the researcher’s study was Thot-Johnson

and Vanniarajan (2002). And although the studies had many similarities, they differed in

geographical location. Thot-Johnson and Vanniarajan conducted their study in California

(West Coast), whereas the researcher conducted her study in Florida (East Coast).

Moreover, Hoyt and Sorenson’s (2001) study revealed the importance of validating

standardized testing and accurate placement of students. They stressed that standardized

tests that asses writing skills are problematic because of the “difficulty in accurately

70

measuring writing abilities” (p. 33). The same was true for this study in regards to the

Florida College Basic Skills Exit Test. The ENC0021 exit test cannot be taught in terms

of content. Again, what instructors need to focus on is teaching students how to learn to

write instead.

The researcher did notice however that at least one study had a difference outcome.

While Hidi and Harackiewicz’s (2000) study revealed that students’ underpreparedness

was a lack of motivation and effort, the researcher’s study indicated that 53.4% of the

participants did not give up on what they wanted to say in their final exam essay.

Students in this study as compared to Thot-Johnson and Vanniarajan's (2002) study used

16 of the 28 strategies questioned on the survey. They use strategies they felt comfortable

with and strategies they knew well.

After reading the research studies, the researcher was aware that students’ lack of

preparedness at the secondary level was affecting their ability to perform well on the CPT

as well as on the ENC0021 exit test. The researcher’s findings were consistent with the

literature except in terms of geographical area and age group.

The researcher’s study contributes to the literature by studying a sample size that

ranged in age from 18 to 54 and where the primary language of 79.7% of the participants

is Spanish.

A number of limitations should be noted about this study’s results. As a general

caveat, the use of a survey design warrants caution when interpreting the study results.

Specifically, the survey asked students to retrospectively recall which writing strategies

that they used. It is difficult to determine whether these retrospective accounts accurately

reflect what students actually use in practice. The accuracy of these survey questions

71

requires that students are cognitively aware of the strategies that they are employing as

they write. The level of awareness that allows students to accurately answer these survey

questions probably varies considerably across people.

Another limitation of this study is that it was not possible to link student reports of

strategy use to their actual test performance. Anonymity requirements did not allow the

surveys to contain identifying information, so it was not possible to link a survey record

to course performance or to test performance. Ideally, it would have been desirable to

determine whether the use of certain strategies is associated with better course

performance or better exam performance. Unfortunately, this was not possible.

Third, generalizability is always something that should be considered when

interpreting the results from a study. The student population from which this study’s

sample was drawn is quite different from the general college student population.

Specifically, the students ranged between 18 and 54, with a mean of M = 25.24 (SD =

8.84). This is a somewhat non-traditional age range for college students. Also, the vast

majority of students (79.7%) in the sample reported that Spanish was their native

language, and only 10.8% of students reported English as their native language. The high

rate of Spanish language speakers is not surprising, given that the study was conducted in

a large metropolitan city in South Florida, but it is not representative of the broader

college student population. Finally, many of the students reported relatively low levels of

reading and writing ability. This may or may not be representative of students at other

universities.

This investigation was also limited to the writing developmental students enrolled at

the college used in this study. An experimental group was selected to represent the entire

72

writing student population at the college. In doing so, it was believed that the outcome

would be representative of the effectiveness of the Florida College Basic Skills Exit Test

administered to developmental writing students at the community college level. This

study was limited to the faculty members teaching ENC0021 and ENC1101. Other

faculty teaching subsequent sections of writing were not included in the study.

Consequently, the faculty will not have access to the data and end results to possibly aid

their own developmental students. Furthermore, the shortcoming ingrained in the use of

questionnaires to collect the type of data needed for this study might have impacted the

validity or reliability of the data.

While this study adds to the literature, it is recommended that future researchers

should take these findings and conduct additional research on students’ use of effective

strategies in the classroom through observation. And, compare if the effective strategies

correspond with the ones that this study found were used most frequently.

The data also revealed that 44 (59.5%) students felt that there was not enough time to

complete the essay part of the exit test. And 38 (51.4%) students felt there was not

enough time to complete the grammar portion of the exit test. Given these data, more

time allotted on the Florida College Basic Skills Exit Test is recommendation. It is

inferred that if more time was given, more students would have done better on the test.

It is also recommended for instructors to assess their students’ proficiency in the

English language and use of writing strategies. They can do this by administrating a

diagnostic assessment in writing at the beginning of each ENC0021 course. Once they

have scored the diagnostic assessment, instructors need to examine and determine the

73

students’ level of learning and achieved practices. Instructors should also determine how

results will be disseminated.

Finally, with proper techniques on how to write effective essays, proper use of writing

strategies and cognitive skills in English, instructors can teach ENC0021 students on how

to successfully achieve a passing score on the Florida College Basic Skills Exit Test.

REFERENCES

Bashford, J. (2005). What happens to students with all-but-FCAT certificates of completion?

Retrieved October 1, 2006 from www.mdc.edu

Carter, R. L., Roth, J., Crans, G., Ariet, M., Resnick, M. B. (2001). Effect of High School Course-

taking and grades on passing a college placement test. The High School Journal, 84(2),

72-87.

Community College Survey of Student Engagement (CCSSE). (2005). Engaging students,

challenging the odds. Retrieved November 3, 2006 from http://www.ccsse.org

Crouch, M. (2000). Looking back, looking forward; California grapples with remediation. Journal

of basic writing, 19(2), 44-71.

Florida Department of Education. (2007). K-20 Articulation: Policies, Procedures and

Challenges. Retrieved November 5, 2007, from

http://www.fldoe.org/cc/chancellor/newsletters/clips/articulationchartsynthesis1.asp?style

=print

Hidi, S. & Harackiewicz, J. M. (2000). Motivating the academically unmotivated: A critical issue

for the 21st century. Review of Educational Research, 70(2), 151-179.

Hoyt, J. E. & Sorensen, C. T. (2001). High School preparation, placement testing, and college

remediation. Journal of Developmental Education, 25(2), 26-33.

Morris, C. (2006). Computerized placement test. Retrieved October 1, 2006, from www.mdc.edu

National Center for Education Statistics (NCES). (2003). Remedial Education at Higher

Education Institutions in Fall 1995, NCES 97-584, Washington, DC: 2006. Retrieved

October 1, 2006, from http://nces.ed.gov/pubs/97584.pdf

74

Rodriguez, S. (2006). Basic skills assessment results fall terms 2001 through 2005. Retrieved

October 8, 2006, from www.mdc.edu

Sanchez, C. (2006). Commission mulls standardized testing in colleges. National Public Radio.

Heard on

February 14, 2006.

Thot-Johnson, I. D. (2002). Students' reading and writing strategies and their WST performance.

The CATESOL journal, 14(1), 73-101.

Wyatt, M. (1992). The past, present, and future need for college reading courses in the U.S.

Journal of Reading, 36(1), 10-20.

Appendixes

Appendix B

A Survey on Students’ Writing Strategies and Their Florida State Exit Writing Exam

Performance

Directions: Please answer all the questions as accurately as possible. This information is

being requested for research purposes and will remain confidential. Thank you for your

participation.

Part A: Background Information

1. Gender: Male_______ Female ________

2. Age: ___________

3. Academic Level: ________________

4. What is your major? ____________________________________

5. What is your native language?

________________________________________

6. How would you describe your current reading ability in English?

a. Below average

b. Average

c. Good

d. Very good

e. Excellent

7. How would you describe your current reading ability in your native language?

a. Below average

b. Average

75

c. Very good

d. Excellent

8. How would you describe your current writing ability in English?

a. Below average

b. Average

c. Good

d. Very good

e. Excellent

9. How would you describe your current writing ability in your native language?

a. Below average

b. Average

c. Good

d. Very good

e. Excellent

10. Was your elementary school education in English?

Yes/No

If yes, from which grade? From grade: _______

11. Was your high school education in English?

Yes/NO

If yes, from which grade? From grade: _______

Part B: Writing Strategies Vocabulary

12. When you come across an unknown word while reading in English, do

you use a dictionary? (either English or bilingual)?

Yes/No If yes: a. Most of the time b. Some of the time

13. When you come across an unknown word while reading in English, do

you try to guess the meaning of the unknown word based on the

context?

Yes/No if yes: a. Most of the time b. Some of the time

14. When you come across an unknown word while reading in English, do

you ask your instructor for examples of how to use the word?

Yes/No if yes: a. Most of the time b. Some of the time

15. When you look up an unknown word in a dictionary while reading in

English, do you look it up only if it is important?

Yes/No if yes: a. Most of the time b. Some of the time

16. When reading in English, do you pay attention to how a word is used?

Yes/No if yes: a. Most of the time b. Some of the time

76

17. When you are trying to learn a new word in English, do you try to

remember its meaning by translating it in your native language?

Yes/No if yes: a. Most of the time b. Some of the time

18. When you are trying to learn a new word in English, do you try to

remember its meaning by remembering the context in which it occurs?

Yes/No if yes: a. Most of the time b. Some of the time

19. While writing essays on the computers, do you use the spell check

function?

Yes/No if yes: a. Most of the time b. Some of the time

20. When you are trying to learn the spelling of a new word in English, do

you try to remember it by writing it down one or more times?

Yes/No if yes: a. Most of the time b. Some of the time

21. When you do not know the exact word you want while writing in

English do you attempt to use a different word that has a somewhat

similar meaning?

Yes/No if yes: a. Most of the time b. Some of the time

22. When you do not know the exact word you want while writing in

English do you consult the thesaurus?

Yes/No if yes: a. Most of the time b. Some of the time

23. When you do not know the exact word you want while writing in English do

you give up what you want to say?

Yes/No if yes: a. Most of the time b. Some of the time

Comprehension

24. When you don’t understand a paragraph while reading in English, do

you reread it?

Yes/No if yes: a. Most of the time b. Some of the time

25. When you read in English, can you distinguish the relevant and

important details from the irrelevant and unimportant details?

Yes/No if yes: a. Most of the time b. Some of the time

26. When you read a paragraph, a story, or a news item in English, do you

make connection or comparisons between your own experiences and

those of your characters?

Yes/No if yes: a. Most of the time b. Some of the time

27. When you start to read an academic essay in English, can you make

predictions about what the essay will contain in the second half?

Yes/No if yes: a. Most of the time b. Some of the time

77

28. When you read a chapter in a textbook or a journal article, or an

academic essay in English, can you summarize the

information after you have read it in order to remember it?

Yes/No if yes: a. Most of the time b. Some of the time

Grammar

29. When you read in English, do you pay attention to how sentences are

grammatically constructed?

Yes/No if yes: a. Most of the time b. Some of the time

30. When writing essays on the computer, do you use the grammar check?

Yes/No if yes: a. Most of the time b. Some of the time

31. While proofreading your written essays, do you notice any grammar

mistakes?

Yes/No if yes: a. Most of the time b. Some of the time

Improving Writing Skills

32. Before you start writing an academic essay, do you make an outline?

Yes/No if yes: a. Most of the time b. Some of the time

33. In order to improve your writing skills, do you decide in advance what

to write about?

Yes/No if yes: a. Most of the time b. Some of the time

34. In order to improve your writing skills, do you decide in advance what

content to put in which paragraph?

Yes/No if yes: a. Most of the time b. Some of the time

35. In order to improve your writing skills, do you focus on learning

grammar (either by enrolling in grammar classes or on your own)?

Yes/No if yes: a. Most of the time b. Some of the time

36. In order to improve your writing skills, do you read a lot of books?

Yes/No if yes: a. Most of the time b. Some of the time

37. In order to improve your writing skills, do you observe how essays are

written by your classmates?

Yes/No if yes: a. Most of the time b. Some of the time

38. In order to improve your writing sills, do you show your writing to

another person aside from your teacher?

Yes/No if yes: a. Most of the time b. Some of the time

78

39. In order to improve your writing skills, do you revise what you have

written more than once?

Yes/No if yes: a. Most of the time b. Some of the time

Part C: The Florida State Writing Exit Exam

40. When are you planning to take the Florida State Writing Exit Exam?

(Please enter date) ___________________

41. What do you think of the exit exam as a writing test?

Excellent Good Poor

42. What do you think of the exit exam as a grammar test?

Excellent Good Poor

43. Do you think that there is enough time (60 min) to do the essay part of

the exit exam?

a. Yes, there is enough time to do the essay part of the exit exam.

b. No, there is not enough time to do the essay part of the exit

exam.

c. I’m not sure if there is enough time to do the essay part of the

exit exam.

44. Do you think there is enough time (45 min) to do the grammar part of

the exit exam?

a. Yes, there is enough time to do the grammar part of the exit

exam.

b. No, there is not enough time to do the grammar part of the exit

exam.

c. I’m not sure if there is enough time to do the grammar part of

the exit exam.

45. Does the essay prompt (content-wise) interest you?

a. Yes, the essay prompt interests me.

b. No, the essay prompt does not interest me.

c. I’m not sure if the essay prompt interests me.

46. Is the essay prompt (content-wise) too American –culture specific?

a. Yes, the essay prompt is too American-culture specific.

b. No, the essay prompt is not too American-culture specific.

c. I’m not sure if the essay prompt is too American-culture

specific.

47. Do you have a hard time writing with pen and/or pencil?

79

a. Yes, I have a hard time writing with pen and/or pencil.

b. No, I do not have a hard time writing with pen and/or pencil.

c. I’m not sure if I have a hard time writing with pen and/or

pencil.

Note. The Students’ Writing Strategies and their Florida State Exit Writing Exam

Performance questionnaire is from “Students’ Reading and Writing Strategies and Their

WST Performance,” by I. D., Thot-Johnson and S. Vanniarajan, 2002, The CATESOL

Journal, 14, pp. 73-101. Copyright 2002 by The CATESOL Journal. Adapted with

permission.

Appendix C

A Survey of Faculty Opinion on Student Writing

Directions: Please respond to all the questions as accurately as possible. This information

is being requested for research purposes and will remain confidential. Thank you for your

participation.

1. How long have you been teaching developmental writing?

2. What is your teaching philosophy?

3. In your professional opinion, do you think students see writing as valuable tool

for general college courses? Why or why not?

4. In your professional opinion, do you think students see writing as valuable tool

for overall academic performance? Why or why not?

5. In your professional opinion, do you think students see writing as valuable tool

in their future? Why or why not?

6. How often do you use the Holistic Scoring Guide for ENC0021 when grading

the Florida College Basic Skills Exit Essay Exam?

7.

a. All the time b. Most of the time

c. Some of the time d. Never

8. How are students’ writing evaluated in your writing class? (Circle all that

apply.)

a. Student/teacher conferences

b. Peer conferences

c. Self-evaluation

d. Holistic Scoring

e. Analytic Scoring

f. Teacher generated rubrics

g. Students generated rubrics

h. The college or district rubrics

9. How often would you say students seek your for help with their writing during

office hours?

80

a. All the time b. Most of the time

c. Some of the time d. Never

Appendix D

Letter to Professors

Dear ENC0021 Instructor:

My name is Marisol Varela and I am a doctoral student in the Fischler School of

Education and Human Services at Nova Southeastern University. As part of my applied

research dissertation, I am conducting a survey of students enrolled in remedial writing

courses. The students’ writing strategies, their subsequent performance and attitude

towards the Florida State Writing Exit Exam are the primary focus of this study. Clarence

Jones EdD is my dissertation advisor.

I will be contacting you during your office hours to schedule a time to visit your class(es)

and administer the survey. Please do not hesitate to contact me via electronic mail or

telephone with concerns or questions on this study.

Thank you in advance for your cooperation and extend my deepest appreciation.

Sincerely,

Marisol Varela

Appendix E

Letter to Survey Recipient

Dear ENC0021 Student:

You have been selected to participate in a study on the Florida State Writing Exit Exam.

The information will be kept confidential and the data will be analyzed anonymously.

Please answer all of the questions as truthfully as you can.

The result of this study, which is part of my applied research dissertation at NSU, will

enable the writing instructor to better understand how the Florida State Writing Exit

Exam impacts students as well as how your writing preferences help you in preparing for

the exam.

Your participation is greatly appreciated. Good Luck on your Florida State Writing Exit

Test!

Sincerely,

Marisol Varela

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Polygon

Spring 2010 Vol. 4, 81-82

COMMENTS ABOUT POLYGON

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Dr. Norma Martin Goonen

President, Hialeah Campus

Miami Dade College

Thank you, Dr. Shakil, for providing scholars a vehicle for sharing their research and

scholarly work. Without opportunities for sharing, so many advances in professional

endeavors may have been lost.

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N

M

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G

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Dr. Norma Martin Goonen

President, Hialeah Campus

Miami Dade College

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Dr. Ana María Bradley-Hess

Academic and Student Dean, Hialeah Campus

Miami Dade College

Welcome to the third edition of Polygon, a multi disciplinary peer-reviewed journal of

the Arts & Sciences! In support of the Miami Dade College Learning Outcomes, one of

the core values of Hialeah Campus is to provide “learning experiences to facilitate the

acquisition of fundamental knowledge.” Polygon aims to share the knowledge and

attitudes of the complete “scholar" in hopes of better understanding the culturally

complex world in which we live. Professors Shakil, Bestard and Calderin are to be

commended for their leadership, hard work and collegiality in producing such a valuable

resource for the MDC community.

Ana María Bradley-Hess, Ph.D.

Academic and Student Dean

Miami Dade College – Hialeah Campus

1800 West 49 Street, Hialeah, Florida 33012

Telephone: 305-237-8712

Fax: 305-237-8717

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Dr. Caridad Castro, Chairperson

English & Communications, Humanities, Mathematics, Philosophy,

Social & Natural Sciences

Hialeah Campus

Miami Dade College

POLYGON continues to grow and to feature our local MDC scholars.

Thanks to you and your staff for providing them this opportunity.

Cary

Caridad Castro, J.D., Chairperson

English & Communications, Humanities, Mathematics, Philosophy,

Social & Natural Sciences

Miami Dade College – Hialeah Campus

1776 W. 49 Street, Hialeah, FL 33012

Phone: 305-237-8804

Fax: 305-237-8820

E-mail: ccastro@mdc.edu

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Dr. Arturo Rodriguez

Associate Professor

Chemistry/Physics/Earth Sciences/Department

North Campus

Miami Dade College

I want to congratulate you and the rest of the colleagues who created the POLYGON that

is occupying an increasingly important place in the scholarly life of our College. Now,

the faculties from MDC have a place to publish their modest contributions.

arturo

Dr. Arturo Rodriguez

Associate Professor

Chemistry/Physics/Earth Sciences/Department

North Campus

Miami Dade College

11380 NW 27th Avenue

Miami, Florida 33167-3418

phone: 305 237 8095

fax: 305 237 1445

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