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  1. 1. 1 Chapter 1 Introduction Every culture on earth has developed some mathematics. In some cases, this mathematicshas spread from one culture to another. Now there is one predominant international mathematics,and this mathematics has quite a history. It has roots in ancient Egypt and Babylonia, then grewrapidly in ancient Greece. Mathematics written in ancient Greek was translated into Arabic.About the same time some mathematics of India was translated into Arabic. Later some of thismathematics was translated into Latin and became the mathematics of Western Europe. Over aperiod of several hundred years, it became the mathematics of the world. There are other places in the world that developed significant mathematics, such asChina, southern India, and Japan, and they are interesting to study, but the mathematics of theother regions have not had much influence on current international mathematics. There is, ofcourse, much mathematics being done these and other regions, but it is not the traditional math ofthe regions, but international mathematics. By the 20th century the edge of that unknown had receded to where only a few could see.One was David Hilbert, a leading mathematician of the turn of the century. In 1900 he addressedthe By far, the most significant development in mathematics was giving it firm logicalfoundations. This took place in ancient Greece in the centuries preceding Euclid. See Euclid‘s
  2. 2. 2Elements. Logical foundations give mathematics more than just certainty they are a tool toinvestigate the unknown.International Congress of Mathematicians in Paris, and described 23 important mathematicalproblems. Mathematics continues to grow at a phenomenal rate. There is no end in sight, and theapplication of mathematics to science becomes greater all the time. Arguably the most famous theorem in all of mathematics, the Pythagorean Theorem hasan interesting history. Known to the Chinese and the Babylonians more than a millennium beforePythagoras lived, it is a ―natural‖ result that has captivated mankind for 3000 years. More than300 proofs are known today. Exploring the concepts, ideas, and results of mathematics is a fascinating topic. On theone hand some breakthroughs in mathematical thought we will study came as accidents, and onthe other hand as consequences of attempts to solve some great open problem. For example,complex numbers arose in the study of the solution of cubic polynomials. At first distrusted andultimately rejected by their discoverers, Tartaglia and Cardano, complex numbers weresubsequently found to have monumental significance and applications
  3. 3. 3 In this course you will see firsthand many of the results that have made whatmathematics is today and meet the mathematicians that created them. One particularly interestingattribute of these ―builders‖ of mathematical structure is how clear they were about what toprove. Their results turn out to be just what is needed to establish other results sometimes in anunrelated area. What is difficult to understand for the ordinary mathematics students is just howbrilliant these people were and how tenaciously they attacked problems. The personality of thegreatest mathematicians span the gamut from personable and friendly to arrogant and rude.David E. Joyce (djoyce@clarku.edu) In December 2009, the district administration reported that 171 pupils or 13.9% of thedistrict‘s pupils received Special Education services. The District engages in identification procedures to ensure that eligible students receivean appropriate educational program consisting of special education and related services,individualized to meet student needs. At no cost to the parents, these services are provided incompliance with state and federal law; and are reasonably calculated to yield meaningfuleducational benefit and student progress. To identify students who may be eligible for specialeducation, various screening activities are conducted on an ongoing basis. These screeningactivities include: review of group-based data (cumulative records, enrollment records, healthrecords, report cards, ability and achievement test scores); hearing, vision, motor, andspeech/language screening; and review by the Instructional Support Team or Student Assistance
  4. 4. 4Team. When screening results suggest that the student may be eligible, the District seeks parentalconsent to conduct a multidisciplinary evaluation. Parents who suspect their child is eligible mayverbally request a multidisciplinary evaluation. In 2010, the state of Pennsylvania provided $1,026,815,000 for Special Educationservices. The funds were distributed to districts based on a state policy which estimates that 16%of the district‘s pupils are receiving special education services. This funding is in addition to thestate‘s basic education per pupil funding, as well as, all other state and federal funding. Line Mountain School District received a $723,333 supplement for special educationservices in 2010. The District Administration reported that 44 or 3.51% of its students were gifted in 2009.By law, the district must provide mentally gifted programs at all grade levels. The referralprocess for a gifted evaluation can be initiated by teachers or parents by contacting the student‘sbuilding principal and requesting an evaluation. All requests must be made in writing. To beeligible for mentally gifted programs in Pennsylvania, a student must have a cognitive ability ofa least 130 as measured on a standardized ability test by a certified school psychologist. Otherfactors that indicate giftedness will also be considered for eligibility.
  5. 5. 5 The mathematics of general relativity are very complex. In Newton‘s theories of motions,and object‘s mass and length remain constant as it changes speed, and the rate of passage of timealso remains unchanged. As a result, many problems in Newtonian mechanics can be solved withalgebra alone. In relativity, on the other hand, mass, length, and the passage of time all change asan object‘s speed approaches the speed of light. The additional variables greatly complicatescalculations of an object‘s motion. As a result, relativity requires the use of vectors, tensors,pseudotensors, curvilinear coordinates and many other complex mathematical concepts. In 2007, the district employed 91 teachers. The average teacher salary in the district was$47,418 for 180 days worked. The district‘s average teacher salary was the second highest of allthe Northumberland Country school districts in 2007. The district administrative costs per pupil were $723.52 in 2008. The lowestadministrative cost per pupil in Pennsylvania was $398 per pupil. In 2007 the board approved afive contract with David Campbell as superintendent. His initial salary was $88,000 plus anextensive benefits package including life and health insurance. The Pennsylvania School BoardAssociation tracks salaries for Pennsylvania public school employees. It reports that in 2008 theaverage superintendent salary in Pennsylvania was $122,165.
  6. 6. 6 The district administration reported that per pupil spending in 2008 was $13,243 whichranked 159th in the state 501 school districts. In January 2010, the Pennsylvania Auditor General conducted a performance audit of thedistrict. Findings were reported to the administration and the school board, including possibleconflicts of interests in the actions of board members. The district is funded by a combination of: a local occupation assessment tax 430%, a 1%earned income tax. A property tax, a real estate transfer tax – 0.50%, per capita tax (678) $5, percapita tax (Act 511) $5, coupled with substantial funding from the Commonwealth ofPennsylvania and the federal government. Grants can provide an opportunity to supplementschool funding without raising local taxes. In the Commonwealth of Pennsylvania, pension andSocial Security income are exempted from state personal income tax and local earned income taxregardless of the individuals wealth. Math, as seen by many school aged children and even some adults, is considered boringand useless. There are many areas in life where math can help you, I found out the hard way andfigured out that it was the simple stuff I had gotten stuck on and once that was in placee,everything else came into view. You can see examples of math in use daily with all aspects ofbuilding, finance industry, all areas of management, clerial and other customer facing jobs. Even
  7. 7. 7if all calculations are done for you wherever you go, you still have to balance a budget, savemoney, pay bills no one is exempt from these tasks. It‘s common to hear children say things like ―I‘m‖ going to be the ‗big boss‘ like myDad, I don‘t need math.| I‘d suggest showing that child every example of where math wasrequired to complete a task or project first at home and then if desired, in work decisions. Whenmom planted that garden, there was math involved or when dad submitted that bid for a contract,math again was heavily involved. Any way you look at it we use math daily. Those inimproverished situations can generally trace the causes back to choices they made. Choosing tolease the newest car every year despite your company‘s shaky situation in the current market andthen being shocked and dismayed when you got laid off, losing your car in the process. Math as seen by many school aged children and even some aduts, is considered boringand useless. There are many areas in life where math can help you, I found out the hard way andfigured out that it was the simple stuff I had gotten stuck on and once that was in place,everything else came into view. You can see examples of math in use daily with all aspects ofbuilding, finance industry, all areas of management, clerical and other customer facing jobs.Even if all calculations are done for you wherever you go, you still have to balance a budget,save money, pay bills, no one is exempt from these tasks.
  8. 8. 8 ‗Doing the math‘ consistently and effectively in regards to your finances is crucial toyour daily life. Those who know this go father, faster, Knowing math and how to use it in dailylife will by no means protect you from all possible pitfalls but it does go a long way inminimizing them. Different levels of mathematics are staught at different ages and in somewhat differentsequences in different countries. Sometimes a class may be taught at an earlier age than typicalas a special or ―honors‖ class. Elementary mathematics in most countries is taught in a similarfashion, though there are differences. In the United States fractions are typically taught startingfrom 1st grade, whereas in other countries they are usually taught later, since the metric systemdoes not require young children to be familiar with them. Most countries tend to cover fewertopics in grater depth that in the United States. In most of the US, algebra, geometry and analysis(pregreated depth than in the United States. In most of the US, algebra, geometry and analysis(precalculus and calculus) are taught as separate courses in different years of high school.Mathematics in most other countries (and in a few US states) is integrated, with topics from allbranches of mathematics studied every year. Students in many countries choose an options orpredefined course of study rather than choosing courses a la carte as in the United States.Students in science-oriented curricula typically study differential calculus and trigonometry atage 16-17 and integral calculus, complex numbers, analytic geometry, exponential andlogarithmic functions, and infinite series in their final year of secondary school. You need mathevery day.
  9. 9. 9 The Line Mountain School Board has provided the districts antibully policy online. AllPennsylvania schools are required to have an anti-bullying policy incorporated into their Code ofStudent Conduct. The policy must identify disciplinary actions for bullying and designate aschool staff person to receive complaints of bullying. The policy must be available on th schoolswebsite and posted in every classroom. All Pennsylvania public schools must provide a copy ofits anti-bullying policy to the Office for Safe Schools every year, and shall review their policyevery three years. Additionally, the district must conduct an annual review of that policy withstudents. The Center for Schools and Communities works in partnership with the PennsylvaniaCommission on Crime & Delinquency and the Pennsylvania Department of Education to assistschools and communities as they research, select and implement bullying prevention programsand initiatives. Education standards relating to student safety and antiharassment programs are describedin the 10.3. Safety and Injury prevention in the Pennsylvania Academic Standards for Health,Safety and Physical Education. Wikipedia, the free encyclopedia.
  10. 10. 10GENERAL OBJECTIVE:This study seeks to establish the comparative performance in math between BSMT and BSMAR-E of the VMA GLOBAL COLLEGE this first Semester of Academic Year 2011-2012.Specific Objective:Specifically the study aims to answer the following question. 1. What is the profile of the BSMT and BSMAR-E Students in MATH. 1.a. Age 1.b. High school attainment (private or public) 2. To know the capacity of BSMT and BSMAR-E Students in Math. 2.a. Fraction and Decimal 2.b. Algebra 2.c. Trigometry 3. Is there significant difference in the performance of BSMT and BSMAR-E in Math?
  11. 11. 11 Hypothesis The opinions of the correspondents do not differ significantly as regards to the factorsthat affect enrolment decline in Marine Engineering compared to Marine Transportation. Theeffects on these factors in the overall condition of maritime education and maritime industry inthe country are negligible.
  12. 12. 12Theoretical Framework Mathematics relies on both logic and creativity, and it is pursued both for a variety ofpractical purposes and for its intrinsic interest. For some people, and not only professionalmathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. Forothers, including many scientists and engineers, the chief value of mathematics is how it appliesto their own work. Because mathematics plays such a central role in modern culture, some basicunderstanding of the nature of mathematics is requisite for scientific literacy. To achieve this,students need to perceive mathematics as part of the scientific endeavor, comprehend the natureof mathematical thinking, and become familiar with key mathematical ideas and skills.This chapter focuses on mathematics as part of the scientific endeavor and then on mathematicsas a process, or way of thinking. Recommendations related to mathematical ideas are presentedin Chapter 9, The Mathematical World, and those on mathematical skills are included in Chapter12, Habits of Mind.Mathematics is the science of patterns and relationships. As a theoretical discipline, mathematicsexplores the possible relationships among abstractions without concern for whether thoseabstractions have counterparts in the real world. The abstractions can be anything from strings ofnumbers to geometric figures to sets of equations. In addressing, say, "Does the interval betweenprime numbers form a pattern?" as a theoretical question, mathematicians are interested only infinding a pattern or proving that there is none, but not in what use such knowledge might have.In deriving, for instance, an expression for the change in the surface area of any regular solid as
  13. 13. 13its volume approaches zero, mathematicians have no interest in any correspondence betweengeometric solids and physical objects in the real world.A central line of investigation in theoretical mathematics is identifying in each field of study asmall set of basic ideas and rules from which all other interesting ideas and rules in that field canbe logically deduced. Mathematicians, like other scientists, are particularly pleased whenpreviously unrelated parts of mathematics are found to be derivable from one another, or fromsome more general theory. Part of the sense of beauty that many people have perceived inmathematics lies not in finding the greatest elaborateness or complexity but on the contrary, infinding the greatest economy and simplicity of representation and proof. As mathematics hasprogressed, more and more relationships have been found between parts of it that have beendeveloped separately—for example, between the symbolic representations of algebra and thespatial representations of geometry. These cross-connections enable insights to be developed intothe various parts; together, they strengthen belief in the correctness and underlying unity of thewhole structure.Mathematics is also an applied science. Many mathematicians focus their attention on solvingproblems that originate in the world of experience. They too search for patterns andrelationships, and in the process they use techniques that are similar to those used in doing purelytheoretical mathematics. The difference is largely one of intent. In contrast to theoreticalmathematicians, applied mathematicians, in the examples given above, might study the intervalpattern of prime numbers to develop a new system for coding numerical information, rather thanas an abstract problem. Or they might tackle the area/volume problem as a step in producing amodel for the study of crystal behavior.
  14. 14. 14The results of theoretical and applied mathematics often influence each other. The discoveries oftheoretical mathematicians frequently turn out—sometimes decades later—to have unanticipatedpractical value. Studies on the mathematical properties of random events, for example, led toknowledge that later made it possible to improve the design of experiments in the social andnatural sciences. Conversely, in trying to solve the problem of billing long-distance telephoneusers fairly, mathematicians made fundamental discoveries about the mathematics of complexnetworks. Theoretical mathematics, unlike the other sciences, is not constrained by the realworld, but in the long run it contributes to a better understanding of thatworld.(http://www.project2061.org/publications/sfaa/online/chap2.htm)Conceptual Framework In order to accomplish the objective of this study is to set forth to identify the followingvariables. The ideas were established to give the direction or the research in the choices ofaccumulated data. This conceptual framework has to set guide to identify the comparativeperformance of BSMT and BS-Mar E Student‘s and each respondents. Students have widelyknowledge in using the different kinds of formula in every problems they encounter. Each ofthese variables was guide us to present the following choices that correspond the respondents. The research has identify in term of course, section, and year level is interrelated withtheir comparative performance in math, on board calculations, conversation and theoreticalknowledge and trainings. Through this, the researchers were set up a performance level programto identify how these undertaking works to the BSMT and BS Mar-E of the VMA GlobalCollege.
  15. 15. 15Figure 1. Schematic diagram of performance level of BSMT & BSMAR-E in Math. Students of the VMA Gloabal College BSMT BSMar-E PROFILE: PERFORMANCE: 1.Age 1.Fraction & Decimal 2.High School 2.Algebraic expression attainment 3.Trigometry Performance Level
  16. 16. 16Scope and Limitation The research study focuses on the comparative performance between the BSMT andBSMAR-E Students in Math. There are three years level in the BSMT and three year level in theBSMAR-E Students but the researcher focus on the BSMT 3 and BSMAR-E 3. Which the thirdyear of BSMT 3 and BSMAR-E 3 is divided in sections. There are four sections in BSMT andthree sections BSMAR-E the subjects understudied where the third year level which encountermany Math problem and navigational calculation which they use on board ship. But theresearcher focus in section Bravo only. The study was conduct on the first semester of theacademic year 2011-2012. The researcher select the third year level of BSMT and BSMAR-E Students of the VMAGLOBAL COLLEGE being the nearest and easiest school to address the problem, theresearchers encounter regarding time constrained, financial incapability and distance of thelocality. These have considerably improve the speedy conduct and development of the study. Selecting VMA GLOBAL COLLGE as the study ground help the researchers tominimize the expenses in money, time, and effort.
  17. 17. 17Definition of terms The following were defined for the clearer understanding of the study.Comparative. One that compares with another. (Webster third new international dictionary).Performance. The act or process carrying something, the execution of an action (Webster thirdnew international dictionary). In this study, it is refer to the comparative performance of the BSMT3 and BSMAR-E3.Math. The science of expressing and studying the relationship between quantities and magnitudeas represented by numbers and symbols (The new Webster dictionary of the English language). In this study, it refers to the academic performance in math.Profile. This terms is defined as the biographical sketch of the person(Webster universaldictionary and thesaurus. In this study refers to the biographical sketch of BSMT3 and BSMAR-E3 cadetswho are subject respondent of the study. It include there biographical sketch is therepersonal profile term of age, and high school attainment.Year Level . It is refers to the level of the students (Webster dictionary). In this study, year level refers to the BSMT3 and BSMAR-E3 cadets academic performance on the first semester of school year 2011-2012.
  18. 18. 18Course . It is refers to a prescribe number of lesson, and lecture in educational curriculum.(Wikipedia, the free encyclopedia).Fraction and Decimal . It refer to the separation or division of number and to a number expressin the scale of tens (Webster third international dictionary.Volume and Pressure . It is refer to the dealing with or involving large quantities in the burdenof physical or mental distress (The new Webster dictionary of the English language).Conversation . It refers to a converting or being convert In the study refer to the method of teaching and how to solve the problem, deliver and discuss to compare the performance of BSMT3 and BSMAR-E3 in Math.Significance of the studyThe finding of the study may provide significance information which may be value to the:School – that they had implemented further the basic math, conversation, and the navigationalproblem and was providing more undertaking to their students concerning the great importancein math.Students – That they were be aware on the importance in math especially those who are engagedin maritime field and would guide them to the practice in math not only in school but also intheir everyday life and be able to apply that knowledge in their future profession.
  19. 19. 19Researchers – That give information where there the BSMT3 and BSMAR-E3 have theessential knowledge pertaining to the basic math problem and calculation that are seeing requiredand were provide them a between understanding and supplement on how they can solve nauticalseamanship and navigational problem. Thought this study it had been promote in the Maritimeand Allied Industry.Faculty – That give and examine those student and grade their accordingly on theirperformance. Which they are rank the students and they well know what is capacity and theperformance of the student on some particular of the subject.Curriculum – Development that record and gather those information of what students can reachand they gather these percentage of those students that good in math and need more practice fortheir performance. VMA GLOBAL COLLEGE, that helps the student to build the future andhave a successful life someday, that give a better learning and trained the student and supportthose shipping companies a well trained student.Maritime Industry – That accept intelligent and well trained that has capacity to lead andbecome an officer on board the vessel.Parents – That give as everything we need and being supported in everything we do and beproud of what their son‘s know about what they learned.
  20. 20. 20 Chapter 2 Review related literatureForeign literatureCollege math courses are very different than the ones in high school. They usually meet lessoften and move faster, typically covering material at about twice as fast as a high school course.College professors expect students to keep up. They cannot wait for students that fall behind.In many cases, it is actually assumed that a few of the students will need to repeat the course.Remember, it isnt fair to hold back the rest of the class when some students have not kept up orsought out help when they need it. Students that have kept up have paid to be in the class.Most college math professors do not grade homework - students are expected to "practice" mathskills and come to class prepared to move on. When a student has questions or problems; theyare expected to get help, often, outside of class. Students are responsible for their learning, notthe college professor. The college math class has tests and quizzes spaced farther apart.Each "checkpoint" probably tests on a larger amount of material.Students can expect to spend more time doing homework in a college math class (even when thathomework is not graded). In general, it is expected that a student spend 2 hours of homework forevery hour spent in class - and that might not even be enough time for some. In most cases,college math classes are designed to prepare students for higher-level math, science, and avariety of other important courses.
  21. 21. 21We all need help at some point - especially in math classes. Because college math classes are sodifferent from high school classes, many students, especially freshman or return adults, will findthat they need help. PLEASE GET HELP JUST AS SOON AS YOU THINK YOU NEED IT!Dont wait until you fail a quiz or exam. Instructors appreciate it when students can recognizeproblems BEFORE they are behind - it make life easier for everybody. Asking questions isimportant - there is no such thing as a "dumb" question, but some questions are more helpfulthan others. When working with others, try to ask questions that will allow them to see whereyou need help."I dont understand this section," is better than no question at all, but it is hard to see where theproblem is. A more meaningful question might be, "I dont see why f(x+h) doesnt equal f(x) +f(h)." If you ask this question to someone that understands math, for example, they willimmediately see that the problem is a misunderstanding about function notation. When doinghomework, it can help to create a list of questions to ask the professor in class or during officehours, or to another person.Creating a study-group for a math class is a great way to meet people, get involved on campus,and make a math class more meaningful and fun. Classmates, friends, or students in othersections can often work together to the benefit of all.Most campuses have "Academic Support" to provide assistance to students that are ready to gethelp and take responsibility for doing so. Often, one-on-one tutoring or study groups areavailable - on some campuses, at no cost. Take advantage of all the resources available.
  22. 22. 22Today, many high-quality resources are online - virtually any math topic is supported online.Often, there are examples, tutorials, and alternative presentations. They represent a great way tohelp and build information and technology literacy skills.Math is learned by doing problems. Do the homework. The problems help you learn the formulasand techniques you do need to know, as well as improve your problem-solving prowess.A word of warning: Each class builds on the previous ones, all semester long. You must keep upwith the Instructor: attend class, read the text, and do homework every day. Falling a day behindputs you at a disadvantage. Falling a week behind puts you in deep trouble.A word of encouragement: Each class builds on the previous ones, all semester long. Yourealways reviewing previous material as you do new material. Many of the ideas hang together.Identifying and learning the key concepts means you dont have to memorize as much.Math is a skill. To develop that skill you must practice. Do your homework in a quiet place,similar to the classroom if possible. Do not spend "hours" on one problem. If you cannot solve aproblem, look for a similar problem in your notes or your text. If you still cannot solve theproblem, skip it and work on other problems. Try the problem later. Many times you will comeup with an idea after you have done something else for a while. If you still cannot solve theproblem, get some help.
  23. 23. 23Local literature The Institute of Mathematics is the leading institution for mathematics research andeducation in the Philippines. Since 1998, it has been recognized by the Philippine Commissionon Higher Education as a Center of Excellence. It is home to the countrys best and morepromising researchers in mathematics. Apart from offering an excellent BS Mathematics program, the Institute also grants thefollowing graduate degrees: MA Mathematics, Professional Masters in Applied Mathematics,MS Applied Mathematics, MS Mathematics and PhD Mathematics. Formerly known as the Department of Mathematics, the Institute is the largest institute inthe University of the Philippines System, with about 100 full-time faculty members supported by9 administrative and computer staff. It nurtures about 300 undergraduate and 200 graduatestudents, and handles all the mathematics courses of some 5000 undergraduate students in thewhole UP Diliman campus. The Mathematical Society of the Philippines held its 2011 annual convention on 20-21May 2011 (Fri-Sat). The 2011 Convention was hosted by the University of Santo Tomas, on theoccasion of its quadricentennial anniversary. On this occasion, the MSP celebrated its 38 th yearas the country‘s largest professional organization dedicated to the promotion of mathematics andmathematics education.
  24. 24. 24 Researchers and educators in all areas of pure and applied mathematics, mathematicseducation, computing, statistics and other related areas presented short papers for oral or posterpresentation during the convention. This convention was fully endorsed by the Commission onHigher Education (CHED). Plenary talks were given by Elvira de Lara-Tuprio (Ateneo de Manila University),Manuel Joseph Loquias (University of the Philippines), Frank Morgan (Williams College, MA,USA), Akihiro Munemasa (Tohoku University, Japan), and Edwin Tecaro (University ofHouston). April 10, 2008 marks a historic event for Malayan Colleges Laguna (MCL), a wholly-owned subsidiary of Mapua Institute of Technology; and Philippine Transmarine Carriers, Inc.,(PTC), one of the country‘s largest crew management companies, as they launch the MAPUA-PTC COLLEGE OF MARITIME EDUCATION AND TRAINING. The partnership between these two institutions, both leaders in their respective fields,represents an industry-academic linkage which aims to further develop globally competitive Filipino maritime professionals, equipped with a solid background in MarineTransportation and Marine Engineering and quality hands-on training and instruction to meetindustry standards of competence. With Mapua‘s long history of excellence in the fields ofMathematics, Science and Engineering and PTC‘s 29 years of experience in crew managementand training, the MAPUA-PTC College of Maritime Education and Training is envisioned toensure that the Philippines continues to maintain its position as the leading provider of qualitymaritime manpower worldwide. This is especially crucial in light of the worldwide shortage inmarine officers, projected to reach as many as 27,000 in 2015.
  25. 25. 25 The College aims to provide world-class instruction and training. Aside from a fullMarine Transportation and Marine Engineering curriculum which will be offered at the MalayanCollege campus in Cabuyao, Laguna, the students will undergo hands-on training at PTC‘s state-of the-art training facility, PHILCAMSAT, which provides a wide range of training coursesincluding exposure to bridge, engine and cargo handling simulators, international shippingenvironments, and technology-based instruction. At the formal launching of the Mapua-PTC College of Maritime Education and Training,MCL was represented by Dr. Reynaldo B. Vea, President of Malayan Colleges Laguna andMapua Institute of Technology, and PTC by Mr. Carlos C. Salinas, its Chairman and ChiefExecutive Officer. The ceremony took place at the PTC Office in First Maritime Place, MakatiCity. According to Dr. Reynaldo B. Vea, ―This linkage between PTC and Mapua, via oursubsidiary Malayan Colleges Laguna, is undoubtedly the most substantial linkage we haveforged with a private company in the country, in the whole history of our institution. This isgoing to help a lot of Filipinos attain a higher level of professionalism in their maritime careers,which translates to greater job opportunities.‖ Carlos C. Salinas also lauded the benefits of being allies with Mapua. ―We have finallyfound an institution that will provide the strong fundamentals in math, science and physicsrequired for the development of the global Filipino maritime professional. This partnershipallows our company to be associated with the finest engineering school in the country, andallows us to be a complete crew management and development company, involved with themolding of quality maritime manpower,‖ he said.
  26. 26. 26Foreign studyAvailable data on U.S. student performance in mathematics and science present a mixed picture.Although data show some overall gains in achievement, most students still perform below levelsconsidered proficient or advanced by a national panel of experts. Furthermore, sometimessubstantial achievement gaps persist between various U.S. student subpopulations, and U.S.students continue to do poorly in international comparisons, particularly in the higher grades.This section describes long-term trends based on curriculum frameworks developed in the late1960s, recent trends based on frameworks aligned more closely with current standards, and theperformance of U.S. students relative to their peers in other countries.The National Assessment of Educational Progress (NAEP), also known as "The Nations ReportCard," has charted U.S. student performance for the past 3 decades (Campbell, Hombo, andMazzeo 2000) and is the only nationally representative, continuing assessment of what studentsknow and can do in a variety of academic subjects, including reading, writing, history, civics,mathematics, and science. NAEP consists of three separate testing programs. The "long-termtrend" assessment of 9-, 13-, and 17-year-olds has remained substantially the same since it wasfirst given in mathematics in 1973 and in science in 1969, and it thereby provides a good basisfor analyzing achievement trends. [More detailed explanations of the NAEP long-term trendstudy are available in Science and Engineering Indicators — 2002 (National Science Board2002) and at http://www.nces.ed.gov/naep3/mathematics/trends.asp.] A second testing program,the "National" or main NAEP, is based on more contemporary standards of what students shouldknow and be able to do in a subject. It assesses students in grades 4, 8, and 12. A third program,"state" NAEP, is similar to national NAEP, but involves representative samples of students from
  27. 27. 27participating states. The NAEP data summarized here come from the long-term trend assessmentand the national NAEP. Chapter 8 covers the considerable variation by state.The most recent NAEP long-term trend assessment took place in 1999. Because the 1999 NAEPdata have already been reported widely (including in the 2002 version of this report), this chapteronly summarizes the main findings. The NAEP trend assessment shows that student performancein mathematics improved overall from 1973 to 1999 for 9-, 13-, and 17-year-olds, although not ata consistent rate across the 3 decades (Campbell, Hombo, and Mazzeo 2000) (figure 1-1). Ingeneral, declines occurred in the 1970s, followed by increases in the 1980s and early 1990s andrelative stability since that time. The average performance of 9-year-olds held steady in the1970s, increased from 1982 to 1990, and showed additional modest increases after that. For 13-year-olds, average scores improved from 1978 to 1982 with additional improvements in the1990s. The average performance of 17-year-olds dropped from 1973 to 1982, rose from 1982 to1992, and has since remained about the same, resulting in an overall gain from 1973 to 1999.Average student performance in science also improved from the early 1970s to 1999 for 9- and13-year-olds, although again, not consistently over the 3 decades. Achievement declined in the1970s and increased in the 1980s and early 1990s, holding relatively stable since that time. By1999, increases had overcome the declines of the 1970s. In 1999, 9-year-olds averageperformance was higher than in 1970. Among 13-year-olds, average performance in 1999 washigher than in 1973 and essentially the same as in 1970. By 1999, 17-year-olds had not recoupeddecreases in average scores that took place during the 1970s and early 1980s. This resulted inlower performance in 1999 than in 1969 when NAEP first assessed 17-year-olds in science.
  28. 28. 28The NCLB Act requires every student, regardless of poverty level, sex, race, ethnicity, disabilitystatus, or English proficiency, to meet challenging standards in mathematics and science.Patterns in the NAEP long-term trend data can show whether the nations school systems areproviding similar learning outcomes for all students and whether performance gaps betweendifferent groups of students have narrowed, remained steady, or grown. Thus far, this section has presented NAEP results based on the long-term trendassessments, which use the same items each time. The next analysis uses data from the nationalNAEP program, which updates instruments to measure the performance of students based onmore current standards. These assessments are based on frameworks developed through anational consensus process involving educators, policymakers, assessment and curriculumexperts, and representatives of the public, then approved by the National Assessment GoverningBoard (NAGB). NAEP first developed a mathematics framework in 1990, then refined it in 1996 (NCES2001c). It contains five broad content strands (number sense, properties, and operations;measurement; geometry and spatial sense; data analysis, statistics, and probability; and algebraand functions). The assessment also tests mathematics abilities (conceptual understanding,procedural knowledge, and problem solving) and mathematical power (reasoning, connections,and communication). Along with multiple-choice questions, assessments include constructed-response questions that require students to provide answers to computation problems or describesolutions in sentence form. NAEP developed the science framework in 1991 and used it in the 1996 and 2000assessments (NCES 2003c). It includes a content dimension divided into three major fields of
  29. 29. 29science (earth, life, and physical) and a cognitive dimension covering conceptual understanding,scientific investigation, and practical reasoning. The science assessment also relies on bothmultiple-choice and constructed-response test questions. A subsample of students in each schoolalso conducts a hands-on task and answer questions related to that task. Student performance on the national NAEP is classified according to three achievementlevels developed by NAGB that are based on judgments about what students should know and beable to do. The basic level represents partial mastery of the knowledge and skills needed toperform proficient work at each grade level. The proficient level represents solid academicperformance at grade level and the advanced level signifies superior performance. Disagreementexists as to whether NAEP has appropriately defined these levels, but they do provide a usefulbenchmark for examining recent changes in achievement.Local study Filipinos in general have never been noted for mathematical ability. Internationalsurveys (including the Trends in Mathematics and Science Study, TIMSS 2004) have placed thecountry near the bottom; and local studies similarly reflect such performance - by students andteachers alike. In 2004 the Department of Education (DepEd) launched a bridge program toaddress basic deficiencies in elementary math, among others (less than 10% of elementarygraduates scored 75%). Several years ago, the Mathematics Teachers Association of thePhilippines (MTAP) tested pre-service teachers in arithmetic, algebra, and geometry, anddiscovered that the overall mean for high school teachers was 16 out of 50 (questions), while thatfor their elementary school counterpart was only 10 (Lee, 1993).
  30. 30. 30 The Philippines is a country of paradox. We are vibrant part of Asia, yet our sensibilitieshave been heavily influenced by the West, especially the US. We pride ourselves on being theonly predominantly Catholic country in the continent, and on speaking English well enough togive us an edge in overseas professional employment (many teachers and nurses in the West areFilipino). Our pro-West stance is usually thought to be due to lengthy colonization by Spain andthe US, and archival documents reveal this to be quite likely in the case of education. At the of the 19th century, the revolutionary Filomeno Bautista noted that Filipinos wereconquered "not by American guns, but by American schools" and that "boxes of books were thereal peace makers" (Gates, 1973, p. 277). Certainly these boxes contained various math primers,and in 1906, the most prolific textbook writer in the US, George Wentworth, authored A FirstBook in Arithmetic for the Philippine Islands. When native-born authors started producing theirown books in the 1920s, they were hugely influenced by their US counterparts. In 1925, acommittee of educators headed by Prof. Paul Monroe of Columbia University tested 32, 000children, interviewed teachers, and observed classrooms. They reported that primary arithmeticteaching was done well, and that Filipino students performed at par with their US peers. (Onlywhen the English language became more difficult to understand in higher texts did Filipinos lagbehind.) Monroe also late reported that of the many countries he had visited, the advances he sawin the Philippines were the most impressive (Pecson & Racelis, 1959). However, even with a US-style education system still in place, at the start of thismillennium, Filipinos seem to have lost their edge. In the TIMSS, even though the US has mid-range scores, other Asian countries such as Singapore and Chinese Taipei occupy the top ranks.Much research has been conducted concerning the factors behind our poor performance, such as
  31. 31. 31society (Abasolo-Ababa, 2002), teacher education (Ibe, 1995), learning styles (Arellano, 1997),curriculum (Ulep, 2000), and ways of remediation. In recent decades, several groups in the Philippines have aimed to develop in the youth abalance between foundational understanding and higher-level creativity. Established in 1989 atthe Ateneo de Manila University under the leadership of Dr. Jose A. Marasigan, PEM primarilytrains gifted students for the most prestigious fest - the International Mathematical Olympiad(IMO). PEM invites to be co-trainers, and screens potential IMO participants from all over thecountry. Patterned after Germany, the two-pronged screening process divides participants fromthe National Capital Region (NCR) from those from the rest of the country. For the NCR, at the start of each school year in June, challenging questions areformulated and distributed through the DepEd network. Solutions are submitted by September,and PEM invites the top 30 scorers for each level to undergo a training program from - Octobertill July of the following year. Members of the Philippine team to the IMO are selected from theparticipants, who are rigorously exposed to number theory, combinatorics, functions, solidgeometry, advanced algebra - all beyond the scope of the average Filipino secondary mathcurriculum, which centers on elementary algebra, geometry, trigonometry, and statistics. Since1988, approximately 20 Filipino students have garnered silver/bronze medals, or honorablemention in various IMOs, and most of the winners have taken advantage of scholarship offers byuniversities abroad. For students in the 15 other regions of the country, the route to the IMO isjust as challenging. They have to be winners in the premier local math competition: the PMO. Under Prof.Josefina Fonacier of the University of the Philippines, Diliman, the first PMO was conducted in
  32. 32. 321984, and since then it is held every two years, with the Department of Science and Technologyas major sponsor. The PMO also promotes professional growth of teachers, with expert coaches from theNCR conducting free seminars of teachers, with expert coaches from the NCR conducting freeseminars for teachers in other areas. These sessions, which have become very popular, deal withspecific problem-solving skills and content. Advanced classes in problem solving for the tertiary level are not known, so in thesummer session of April to May 2001, we decided to teach high-level non-routine problemsolving to selected college science majors, with the help of Paul Zeitz The Art and Craft ofProblem Solving (1999). Encouraged by the positive response of the students (as shown by class participation andreflection papers), we decided to continue the course. We authored a case study, providingconcrete data regarding factors and effects surrounding structured problem solving (Nebres &Lee-Chua, 2001). Year level, gender, course major, and high school background do notsignificantly affect subsequent problem solving performance but beliefs and attitudes do.According to the students, the techniques and mind set acquired are perceived to be useful inother classes and in real life. They also feel a sense of satisfaction, especially after having solvedproblems they had grappled with for so long; and learn to appreciate the beauty of math,especially the elegance of proofs and the connectedness of seemingly disparate ideas. They alsofeel that learning under master teachers enables them to fully understand the abstract conceptsinvolved.
  33. 33. 33 After taking this course, some college volunteers train gifted grade school and highschool students themselves, in an attempt to develop the problem-solving culture early on. Theability and knowledge they acquire are showcased in the Ateneo Math Olympiad, now on itsthird year.
  34. 34. 34 Chapter 3 METHODOLOGY In this chapter, the researcher present the research method used, the respondents of thestudy, the date gathering instruments and statistical tools for date analysis.Research Design This study aimed to determined the performance level BSMT 3 and BSMAR-E 3students math of VMA Global College this 1st semester of A.Y. 2011-2012. To meet the objective of this study the descriptive research design will be used todescribe the nature of situation or a given state of affairs in terms of specified aspects or factorsor characteristic of individual or group or physical environment or conditions (David 2002).With this study the researcher want to know if there is a significant difference to the performancelevel between the BSMT 3 to BSMAR-E 3 students in math of the VMA Global College for thefirst semester of 2011-2012. Likewise the study would give an insights to the faculty in theadministration to deliver quality education.Subject /Respondents The respondents of the study are the third year students of the VMA Global College thatwill be given self-administered questionnaires.
  35. 35. 35 The surveyed total population is 400. However, the respondents are selected in terms ofsection. The total number of section of which is 7 (as the present School Year 2011-2012) therespondent for section are selected randomly to present their section as a group; the researcherwill have to survey the respondents.Total Population - 400Total number of section -7No. of Male = 400 Using the Lynch formula, the researcher got the number of sample subject to present topopulation on which is based on any statement about the population from which it is drawn.n=NZ2 p(1-p)Ne2 +Z2p(1-p)Where:n = Of sample subjectN = Total number of sectione = Margin Error (5% or 0.05%)z = Confidence level valueP = Largest possible portion, usually 50% or 0.5
  36. 36. 36Validity of Research Instrument To test the validity of the instruments, content validity will be used. The instrument willbe shown to 3 jurors for them to go over the items to job the appropriateness and to makeaccommodation in order to improve the research instrument. Each jurors was requested toanalyze and rate the questionnaire based on criteria presented by Carter V. Good and Douglas B.Scates. Validation for questionnaire rated 3.7 which interpreted ―Very Good‖.Reliability of Research Instrument To test the reliability of the questionnaire, the Z – test method will be used. Theprocedure involves two values (odd items and even items) scoring of the 1st half and then the 2ndhalf in the instrument separately each person and then calculating a correlation coefficient for thetwo sets of score. The questionnaire will be given to 20 respondents with similar characteristicsto the actual respondents of the study.After calculating the test on desired date, the retest will soon be conducted after the week.Data Gathering Procedure The researcher conducted an interview schedule where the interviewer prepared two setsoff questionnaire, and carefully prepared information from the respondents of the study.
  37. 37. 37Statistical Tools and Analytical Scheme In accordance with the objectives of the study and the statement of the problem, the datathat the researcher will gather will be subjected to tabulation, statistical analysis andinterpretation. The data that will be obtain will be computed and analyze using the statisticaltools to answer the problem of the study.For problem no. 1 we use percentage to determine the level of performance of the BSMT andBSMAR-E in basic math of the VMA GLOBAL COLLGE in terms of their age, and last highschool attainment (public school or private school). For problem no. 2 we use the main to knowthe capacity of BSMT and BSMAR-E in basic math.For problem no. 3 is to determine if there is significant deference between the academicperformance of BSMT and BSMAR-E in basic math we used. = meanr = roman rx = scorey = statistic score
  38. 38. 38 BIBLIOGRAPHY A. BOOKSArdales, Venacio B. ( 2001 ). Basic Concepts and Methods VMA Global College LibraryDavid, Fely (2002) Understanding and Doing Research Work: a handbook for beginners. VMA Global College Library.Oxford Popular School Dictionary. Oxford University Press.Angeles , Ma. Felisa D. (2005) Simplified Approach to Statistics VMA Global College Library.William L. Hart (1964) College algebra 4th Edition
  39. 39. 39 B. Webliographywww.yahoo.comwww.google.comwww. Teaching college math.comwww.clubtnt.org/my_collegian/college_math.htmwww.math society phil.orgwww.ptc .com.phwww.nsf .gov/statisticswww.fuse.org.phhttp://www.math.upd.edu.ph/http://www.ptc.com.ph/news_display2.php?articleid=27http://www.nsf.gov/statistics/seind04/c1/c1s1.htmhttp://www.mathsocietyphil.org/
  40. 40. 40 Appendix A Data Gathering Instrument QUESTIONNAIRE ON COMPARATIVE PERFORMACE OF BSMT AND BSmar-E IN BASIC MATHWe, the Graduation students of the VMA Global College are currently conducting aresearch on “COMPARATIVE PERFORMANCE OF BSMT AND BSMAR-E MATH” asa part of our requirements in the research subject rest assured that your opinions andresponse on this questionnaire will be treated with almost confidentially.Part 1 (Respondents Profile)Course: ________ BSMT ________ BSMar-EAge: ________Part 2 (Fraction to Decimal)Instruction: Convert the following fraction into decimal form. Encircle the latter of the correct answer.1.)a) 0.667 b) 1.541 c) 1.00 d) 1.112) 1a) 1.411 b) 1.040 c) 1.380 d.) 1.0375
  41. 41. 413)a) 0.4 b) 0.333 c) 0.34 d) 0.4134)a) 7.35 b) 5.37 c) 5 d) 3.755) 1 +2a) 3.333 b) 3.88 c) 4 d) 3.8336) +a) 1.167 b) 1.611 c) 1.600 d) 1.5667) +a) 0.578 b) 0.785 c) 0.758 d) 0.8758)a) 23 b) 0.23 c) 2.3 d) 0.0239a) 13 b) 15 c) 14 d) 1610.a) 8 b) 9 c) 6 d) 10
  42. 42. 42PART 3 (Algebraic Expression)Instruction: Find the value of X. Encircle the letter of the correct answer. 1) 8x – 24 = 0 a. 3 b. 4 c. 2 d. 5 2)24x – 8x = 4 a. b. c. d. 5 3)2x-25= -8x a. b. c. d. 4) (-2x) – 38 (-5x) = 11 a. b. c. d. 5)40 + 10 = 5x a. 8 b. 9 c. 10 d. 5 6) -30 -6x = 60 a. -3 b. -15 c. -12 d. -5 7) (3x) (10) = 70
  43. 43. 43 a. b. 4 c. 2 d. 5 8) 10x + y = 40 + y a. 3 b. 4 c. 2 d. 5 9) X + 10 = 13 a. 3 b 4 c. 2 d 5 10) x + 20 = 50 a. 60 b 40 c 2 d. 5PART 4 (TRIGOMETRY)Instruction: Identify the following. Encircle the letter of the correct answer.1.________is a form by rotating a ray around its end point?a. sides c. vertexb. angle d. line2. An angle measuring more than 90 degrees but less than 180 degrees?a. acute angle c. right angleb. scalene d. obtuse angle3. An angle exactly 180 degrees?a. vertex c. right angle
  44. 44. 44b. straight line d. scalene4. 1 degrees is equal to?a. 60mins. c. 90mins.b. 30mins. d. 180mins.5. what is the unit use in measuring angle?a. minutes c. secondb. degree d. hour6. a complete rotation of a ray result in an angle measuring?a. 180 degrees c. 90 degreesb. 360 degrees d. 45 degrees7. what is a formula of a circle?a. 4s c. r2b. 2Lx2w d. Lxw8. does vertical angle have equal measure?a. true c. sometimesb. false d. never9. does parallel line intersect with each other?a. true c. sometimesb. false d. never10. what is the measure of right angle?a. 90 degrees c. 360 degreesb. 180 degrees d. 30
  45. 45. 45 Appendix B VALIDATION OF INDEPENDENT OBSERVER’S QUESTIONNAIRE COMPARATIVE PERFORMANCE OF BSMT AND BSMAR-E IN BASIC MATHJuror:________________________ Using the criteria developed for evaluating survey questionnaire by Carter V. Good and DouglasB. Scates, a jury of experts evaluated the self-made questionnaire instruments specifically for this study. Rating: 5-Excellent 4-Very Good 3-Good 2-Fair 1-PoorArea Criteria Jury 1 Jury 2 Jury3 1 The questionnaire is short enough that the respondents 4 4 4 respect it and it would not drain much precious time. 2 . The questionnaire is interesting and has a fair appeal 4 3 4 such the respondents will be induced to respond to it and accomplish it fully. 3 The questionnaire can obtain some depth to the 3 3 4 responses and avoid superficial answer. 4 The items/questions and their alternative responses 4 2 5 are neither too suggestive nor unstimulating. 5 The questionnaire can elicit responses, which are 4 3 5 definite but not mechanically forced. 6 Questions/items are stated in such a way that the 4 3 5 responses will not be embarrassing to the person/persons concerned. 7 Question/items are formed in a manner to avoid 4 4 4 suspicion on the part of the respondents concerning hidden responses in the questionnaire. 8 The questionnaire is not too narrow nor restricted or 3 3 4 limited in philosophy. 9 The responses to the questionnaire when taken as a 3 4 4 whole could answer the basic purpose for which the questionnaire is designed and therefore considered valid. Total 3.6 3.2 4.3 Rating 3.7 Interpretation Very GoodSource: Good, Carter V and Scates, Douglas B, Methods of Research, Philippines Copyright, Appleton-Century-Grofts, Inc. 1972.Pp 615-616
  46. 46. 46 Appendix C Vertical Interpretation for ValidityRating Scale Verbal Interpretation 4.21-5.00 Excellent 3.41-4.20 Very Good 2.61-3.40 Good 1.81-2.60 Fair 1.00-1.80 Poor
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  50. 50. 50 CURRICULUM VITAEName: Jerome Marianito J. GuillermoHome address: Brgy. Miranda, PontevedraTelephone/Mobile No.: 09466208500Email address: Jerome_blackspder@yahoo.comPersonal BackgroundDate of Birth: December 2, 1991Place of birth: Bacolod CityAge: 19Citizenship: FilipinoGender: MaleStatus: SingleEducational backgroundElementary: Calvary Learning CenterHigh School: Calvary Learning CenterCollege: VMA Global CollegeCourse: Bachelor of Science in Marine Transportation
  51. 51. 51 CURRICULUM VITAEName: Rone Ryan R. DesiertoHome address: Brgy. Mandalagan Bacolod CityTelephone/Mobile No. 09094656360Email address: roneryandesierto@rocketmail.comPersonal BackgroundDate of Birth: December 5, 1992Place of birth: Bacolod CityAge: 19Citizenship: FilipinoGender: MaleStatus: SingleEducational backgroundElementary: Abkasa Elementary schoolHigh School: Maranatha Christian CollegeCollege: VMA Global CollegeCourse: Bachelor of Science in Marine Transportation
  52. 52. 52 CURRICULUM VITAEName: Crister S. HuervaHome address: Brgy. Malingin Bago City Negros Occ.Telephone/Mobile No. 09052941755Email address: cristerhuerva@yahoo.comPersonal BackgroundDate of Birth: February 17, 1993Place of birth: Bago CityAge: 18Citizenship: FilipinoGender: MaleStatus: SingleEducational backgroundElementary: Jalsis Elementary SchoolHigh School: Ramon Torres Malingin National High SchoolCollege: VMA Global CollegeCourse: Bachelor of Science in Marine Transportation
  53. 53. 53 CURRICULUM VITAEName: Matt Ryan J. AguirreHome address: Balangigay Pontevedra Neg. Occ.Telephone/Mobile No. 09102108898Email address: ryan_aguire@yahoo.comPersonal BackgroundDate of Birth: August 18,1988Place of birth: PontevedraAge: 20Citizenship: FilipinoGender: MaleStatus: SingleEducational backgroundElementary: Miranda Elementary SchoolHigh School: Pontevedra National High SchoolCollege: VMA Global CollegeCourse: Bachelor of Science in Marine Transportation
  54. 54. 54 CURRICULUM VITAEName: Richard D. LumanogHome address: Brgy. Look, Calatrava Neg. Occ.Telephone/Mobile No. 09494898145Email address: Richard_123@yahoo.comPersonal BackgroundDate of Birth: August 15,1990Place of birth: Calatrava Neg. Occ.Age: 21Citizenship: FilipinoGender: MaleStatus: SingleEducational backgroundElementary: Calatrava 2 Central SchoolHigh School: Calatrava National High SchoolCollege: VMA Global CollegeCourse: Bachelor of Science in Marine Transportation
  55. 55. 55 CURRICULUM VITAEName: Jerrybelle G. Bunsay Jr.Home address: 18th Aguinaldo Street Bacolod CityTelephone/Mobile No. 09306531552Email address: jerrybellebunsay@yahoo.comPersonal BackgroundDate of Birth: February 20,1992Place of birth: Bacolod cityAge: 19Citizenship: FilipinoGender: MaleStatus: SingleEducational backgroundElementary: Andress Bonifacio Elementary SchoolHigh School: Bata National High SchoolCollege: VMA Global CollegeCourse: Bachelor of Science in Marine Transportation
  56. 56. 56 CURRICULUM VITAEName: Eduardo P. Jallorina Jr.Home address: Brgy.Tuburan E.B. Magalona Neg. Occ.Telephone/Mobile No. 09282397361Email address: edards@yahoo.comPersonal BackgroundDate of Birth: August 7,1992Place of birth: Brgy. TuburanAge: 19Citizenship: FilipinoGender: MaleStatus: SingleEducational backgroundElementary: St.Joseph Academy of Savaria IncHigh School: St.Joseph Academy of Savaria Inc.College: VMA Global CollegeCourse: Bachelor of Science in Marine Transportation

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