Readiness in college algebra

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Published on March 12, 2014

Author: feljrhone

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i READINESS OF STUDENTS IN COLLEGE ALGEBRA An Institutional Research Presented to the Research Management Office Saint Louis College City of San Fernando, La Union by: Ragma, Feljone G. Manalang, Edwina M. Rodriguez, Mary Joy J. Hoggang, Gerardo Fernandez, Mark Edison Oredina, Nora A. Parayno, Dionisio Jr. Hailes, Imelda Lyn R. Coloma, Roghene A. February 26, 2014

ii TABLE OF CONTENTS Page TITLE PAGE………………………………………………………………… i TABLE OF CONTENTS………………………………………………….. ii LIST OF TABLES…………………………………………………………. v LIST OF FIGURES……………………………………………………….. vi CHAPTER I INTRODUCTION……………………………………………… 1 Background of the Study.……......………….......... 1 Theoretical Framework……………………………..... 4 Conceptual Framework……………………………….. 6 Statement of the Problem…………........................ 9 Hypotheses……………………………………........... 9 Importance of the Study……………...................... 9 Definition of Terms…………………………………..... 11 II METHOD AND PROCEDURES…………………………… 14 Research Design……………………………………… 14 Sources of Data………………………………………. 14 Locale and Population of the Study……………... 14 Instrumentation and Data Collection ..……….... 16 Validity and Reliability of the Questionnaire…………………………………….. 16

iii Page Data Analysis …………………………………………. Data Categorization………………………………..... 16 19 Parts of the Learning Activity Sheets..….………………………………………………. 21 Ethical Considerations…………………………...... 22 III RESULTS AND DISCUSSION…………………………….. 23 Profile of the College Students…………………….. Level of Readiness of Students in College Algebra…………………………………………….. 23 25 Correlation between Profile and Level of Readiness………………………………………….. 27 Comparison on the Level of Readiness of the three respondent groups……………………….. 29 Strengths and Weaknesses of Students in College Algebra………………………………….. 31 Learning Activity Sheets………..…………………… 33 IV SUMMARY, CONCLUSIONS AND RECOMMEN- DATIONS……………………………………………….. 96 Summary………………………………………………. 96 Findings………………………………………………… 96 Conclusions…………………………………………… 98 Recommendations…………………………………… 99 BIBLIOGRAPHY……………………………………………… 101

iv APPENDICES………………………………………………… 95

v LIST OF TABLES Table Page 1 Distribution of Respondents…………………………. 2 Profile of Respondents ………………………………. 24 3 Level of Readiness of Students in College Algebra …………………………………………………. 26 4 Correlation between Profile and Level of Readiness………………………………………………. 28 5 Difference in the Level of Readiness among the respondent groups………………………………. 30 6 Strengths and Weaknesses of Students in College Algebra …………………………………… 32 7 Level of Validity of the Learning Activity Sheets…………………………………………………

vi LIST OF FIGURES Figure Page 1 The Research Paradigm ……………………………………….. 8

1 CHAPTER I INTRODUCTION Background of the Study Quantitative Literacy, as defined by the Mathematical Association of America (MAA), is the ability to apply the minimum computational competency or fluency to solve problems in the real world (http://www.maa.org/college-algebra). It is implicit that when a person is quantitatively literate, he is able to use his mathematical skills in dealing with situations in his life, whether it is in the complex line of business, economics, and politics or in the simple context of time reading, scheduling, and many others. Indeed, Mathematics is necessary. One mathematics subject that is necessary to person’s life is College Algebra. Packer (2004) explains that College Algebra is the introductory mathematics subject to any university or community college. He added that College Algebra is the starting course for students to be trained logically as they would deal with algebraic expressions, axioms of equations, functions and the like. Furher, Leeyn (2009) exemplifies that College Algebra is a critical element to 21st century jobs and citizenship. Gateschools staff (2013) also asserts that it is the gatekeeper subject. It is so because it is used by professionals ranging from electricians to architects to computer scientists. Robert Moses

2 (2009), founder of the Algebra Project, says that learning College Algebra is no less than a civil right. As such, College Algebra is really very important. However, no matter how important College Algebra is, it is still considered by most students as a non-helpful subject. According to a paper presented in the Mathematics Association of America (MAA) conference in the year 2009 which revealed that College Algebra is the last mathematics course many students take. A majority entered the classroom having already decided that it would be their final mathematics course. Data, contained in the same conference report, indicated that only one in ten College Algebra students go on to take other higher math subjects. Many would skip College Algebra if they did not have to pass it to get the degree they need to enter their chosen career field. In addition, enrollment in this subject tends to fall dramatically when colleges make quantitative reasoning or intermediate algebra the requirement. It was also reported that, a few years after finishing the course, the students cannot recall anything they learned. All of these pinpoint to the fact that college algebra seemed hard for most students (http://www.maa.org/college-algebra). As a result, readiness, evident in their performances, declines. According to the New York Times, in the last fall of 2013, results from national math exams stirred

3 up a tempest in a standardized test. It turned out that math scores declined more quickly. It was also mentioned that math scores haven’t improved since 2007 (http://www.nytimes.com/). In addition, Shepherd (2005) revealed that most students do not excel in their Algebra course. Most of them cannot perform indicated operations, especially when fronted with word problems. Students find it hard to solve problems in Algebra. Some just do not answer at all. These situations reflect poor understanding of and performance in the course (The Journal of Language, Technology & Entrepreneurship in Africa, Vol. 2, No.1, 2010).Moreover, Kuiyuan (2009) also mentioned that in University of Florida, the student’s success rate in College Algebra is more than the desired level. Kuiyan (2009) stressed that with this trend in dismal performance, the readiness of students in such subject is very low. In the Philippines, College Algebra is a pre-requisite subject in all course curricula. CHED Memorandum Order 59 series of 1996 mandates the inclusion of College Algebra as a basic subject in all courses. The country is not exempted from the predicaments on College Algebra performance. A recent study of on the readiness graduating high school students of Marian Schools in College Algebra revealed that their readiness is only at the moderate level. This means that the students did

4 not yet fully attain the desired competence to be able to hurdle the demands of College Algebra. In the provincial scene, the recent study of Ragma (2014) revealed that the students have only poor performance in College Algebra. In Saint Louis College, the study of Oredina (2009) revealed that the students had only moderate performances. Additionally, the mathematics instructors, the researchers of the study, observed that most students enrolled in College Algebra are not yet ready for the subject. This is shown in their quizzes, exams and grades. In fact, in a class of 50, more than 40% have failing grades in their prelim grades. The state of dismal performances in this subject point out to the fact that the students are not ready to take up College Algebra. The foregoing situations encouraged the math instructors to embark on assessing the level of readiness of SLC students in College Algebra for school year 2013-2014 as basis for formulating learning activity sheets. Theoretical Framework E. Thorndike (1978) proposed the law of readiness. The readiness theory states that a learner’s satisfaction is determined by the extent of

5 his preparatory set. It implies the need of acquisition of necessary pre- requisite skills so that learners will be ready to tackle the succeeding lessons and at the same time, they can anchor the new lessons to the previous ones. This theory serves as the main foundation of the proposed study since it looked into the level of readiness of students in College Algebra. Central to the theory of readiness are the concepts where the theory is founded. According to the theory, there are several factors affecting readiness. These include maturation, experience, relevance of materials and methods of instruction, emotional attitude and personal adjustment. In addition, the same theory proposes several strategies in building readiness skills. These strategies include the analysis of skills using diagnosis or pre-assessment and the design of an instructional intervention programmed to match the individual’s level of readiness. This central concept of the readiness theory provided the justification of formulating a College Algebra readiness test as a form of diagnostic assessment among students. Moreover, Jeane Piaget (1964), a Swiss psychologist and biologist formulated one of the most widely used theories of cognitive development. Piaget’s theory stresses that the potentials of formal operational thought develop during the middle school years. These

6 potentials can be actualized by ages 14, 15, or 16 years. Apparently, learning mathematics involves formal operational thought. The research of Piaget shows that individuals are formal operational thinkers by ages 15 or 16, the usual ages of college freshmen in the Philippines. In this connection, this study utilizes this Piaget’s theory to investigate whether a group of college freshmen performs at the expected level of formal thought, in other words, if they are ready to take up collegiate courses in Mathematics. The law of readiness and its central concept laid the concepts in structuring the research. The cognitive development theory, on the other hand, gave additional foundations in formulating the learning activity sheets. The learning activity sheets are worksheets that contain the topic, its objectives, activities with the teacher and activities for group and independent learning. Conceptual Framework Teaching and learning mathematics becomes more meaningful and directed when the teachers know the level of the learners’ preparation and when the learners are ready to grasp concepts presented in the teaching-learning process. In this manner, the teachers know where to

7 start, how to start and what concepts need to be more emphasized; students, on the other hand, know when to study more and where to focus on. As part and parcel of improving performance, instructional materials such as worktext, activity books and activity sheets are inevitable. The learning activity sheets are instructional support materials that provide supplements to classroom instruction and give opportunities for students to study on their own and deal with some more additional exercises. These materials provide avenue for the students to enhance more their competencies required in each topic by providing relevant activities pertinent to the full understanding of the topic. Students can even have advanced studies and make study work using the learning activity sheets. It is in this light that this study is formulated and thought of. The research paradigm in figure 1 highlights the relationship of the indicated variables. The input incorporates the profile of the respondents along sex, high school graduated from and the mathematics high school final grade. It also includes the level of readiness of the students along elementary topics, special products, factoring, rational expressions, linear equations, systems of linear eqautions and radicals and exponents.

8 The process includes the interpretation and analysis of the profile, the level of readiness of the students, the strengths and weaknesses based on the level of readiness, the correlation between the profile variables and the level of readiness, and the difference among the level of readiness among the three colleges: ASTE-IT-CRIM, CCSA, CEA. The output, therefore, are validated learning activity sheets in College Agebra.

9 Process OutputInput Validated Learning Activity Sheets in College Algebra for Saint Louis College I. Analysis and Interpretation of: a. Profile b. Level of Readiness II. Correlational Analysis of Profile and Level of Readiness III. Difference on the level of readiness among ASTE-IT- CRIM, CCSA, CEA IV. Analysis and Interpretation of the Strengths and Weaknesses of the Students in College Algebra III. I. Profile of the Students in College Algebra along: a. gender b. type of high school graduated from c. HS Math IV grade II. Level of Readiness of the students in College Algebra along: a. Elementary Topics b. Special Products and Patterns c. Factoring d. Rational Expressions e. Linear Equations in One Variable f. Systems of Linear Equations in Two Variables g. Exponents and Radicals Figure 1. The Research Paradigm

10 Statement of the Problem This study aimed primarily to determine the level of readiness of frsehmen in College Algebra in Saint Louis College for the first semester, school year 2013-2014. Specifically, it aimed to answer the following questions: 1. What is the profile of the students in College Algebra along: a. Gender; b. High School Math IV Final Grade; and c. Type of High School Graduated from? 2. What is the level of readiness of the students along the following topics in College Algebra: a. Elementary Topics; b. Special Products and Patterns; c. Factoring; d. Rational Expressions; e. Linera Equations in One Variable; f. Systems of Linear Equations in Two Variables; and g. Exponents and Radicals? 3. Is there a significant relationship between profile and the level of readiness of the students?

11 4. Is there a significant difference between the level of readiness of a. ASTE-IT-CRIM and CCSA; b. ASTE-IT-CRIM and CEA; and c. CCSA and CEA? 5. What are the major strengths and weakness of the students along the specified topics in College Algebra? 6. Based on the results, what learning activity sheets can be proposed? Hypotheses The researchers were guided with the following hypothesis: 1. There is no significant relaionship between profile and the level of readiness of the students in College Algebra 2. There is no significant difference among the level of readiness among ASTE-IT-CRIM, CCSA, CEA. Importance of the Study The researchers considered this endeavor vital not only to them as mathematics instructors, but also to the school community specifically the administrators, students as well as future researchers. The SLC Administrators. The results of this study can serve as one of the bases for curricular evaluation and planning. It will also guide

12 the administrators in their conscious effort to undergo planned changes in drawing up systematic scheme of evaluating students’ performance. The Mathematics Instructors. The knowledge of the level of readiness including the specific areas of deficiencies of their students will lead them to a conscientious and periodic evaluation of the courses of study. They will be led in formulating instructional strategies and interventions that suit their students’ level of readiness. The students. The output of this study can enhance the students’ readiness level; thus, increasing their competence level in College Algebra. The future researchers. The future researchers can make use of this study in formulating researches in other disciplines. Definition of Terms The following terms are operationally defined to further understand this study: College Algebra. This is a requisite subject in college. The topics in this subject include elementary topics, special product patterns, factoring patterns, rational expressions, linear equations in one unknown, systems of linear equations in two unknowns and exponents and radicals.

13 Elementary Topics. These topics include concepts on sets, real number system and operations, and polynomials. Factoring patterns. These include the topics in factoring given a polynomial. These include common monomial factor, perfect square trinomial, general trinomial, factoring by grouping and factoring completely. Linear Equations in One Unkown. This includes topics on equations with one variable such as 2x- 4 = 10 and 5x - 2x=36. The main thrust of this topic is for an unkown variable to be solved in an equation. Rational Expressions. These are expressions involving two algebraic expressions, whose denominator must not be equal to zero. This includes topics on simplifying and operating on rational expressions. Special Product Patterns. These topics include the patterns in multiplying polynomials easily. These patterns include sum and difference of two identical terms, square of a binomial, product of two binomials, cube of a binomial and square of a trinomial. Systems of Linear Equations in Two Unknowns. This topic discusses how the solution set of a given system is solved. The methods that are used in this certain topics include graphical, substitution and elimination methods.

14 Readiness Level. This is the degree of preparation of the students along the specified topics in College Algebra. This is categorized into: highly ready, ready, slightly ready and not ready. Strengths. An area under readiness level is considered strength when it has a decriptive equivalent of highly ready and above. Validated Learning Activity Sheets. This is the output of the study. It consists of the rationale, the learning objectives and the varied activities that address the needs of the students based on the identified level of readiness. Weaknesses. An area under readiness level is considered a weakness when it has a decriptive equivalent of ready and below.

15 CHAPTER II METHOD AND PROCEDURES This chapter presents the research design, the sources of data, data analysis and ethical considerations. Research Design The descriptive method of investigation was used in the study. Calmorin (2005) describes descriptive design as a method that involves the collection of data to test hypothesis or to answer questions regarding the present status of a certain study. This design is apt for the study since the study is aimed at describing the level of readiness of students in College Algebra. Further, since the comparisons on the level of readiness among the three departments and the relationship of profile and the level of readiness were established, the descriptive-comparative and the descriptive-correlational methods were employed, respectively. Sources of Data Locale and Population of the Study

16 The total population of 1,349 students enrolled in College Algebra for the first semester, school year 2013-2014 was surveyed. Since the population reached 500, random sampling was conducted. The sample population of the study was computed using the Slovin’s Formula. The formula is: n = where: n = the sample population N = the population 1 = constant e = level of significance @ 0.05 Thus, the sample population is 309 students distributed according to the three departments: 72 for CASTE-IT-CRIM, 155 for CCSA and 82 for CEA. Table 1 shows the distribution of the number of specified respondents. Table 1. Distribution of Respondents Department N n CASTE-IT-CRIM 316 72 CCSA 675 155

17 CEA 358 82 Total 1349 309 Instrumentation Documentary analysis was used to get the needed data for profile, specifically for gender, high school Math IV final grade and type of high school graduated from. To gather the data pertinent to the level of readiness, a researcher- made test was made. The researcher-made test is 50-point item test covering all the topics in College Algebra. (Please see appended table of specifications) The readiness test was administered by all the Mathematics instructors during the 2nd week of June in their respective classes. A one-hour period was allotted to each student. The instructors guaranteed that calculators were not utilized in taking the readiness test. Data Analysis

18 The data which were gathered, collated and tabulated were subjected for analysis and interpretation using the appropriate statistical tools. The raw data were tallied and presented in tables for easier understanding. For problem 1, frequency counts and rates were used to determine the status of the profile of the respondents along gender, high school Math IV final grade and the type of high school graduated from. The rates were obtained by using the formula below: R = n x 100 N where: R - rate n - number of frequencies gathered in each item N - the total number of cases 100 – constant For problem 2, mean and rates were utilized to determine the level of readiness in College Algebra. The formula for mean is as follows (Ybanez, 2002): M = ∑x N Where: M – mean x – sum of all the score of the students

19 N – number of students For problem 3, the Pearson-r moment of correlation was used to determine the significance of relationship between profile and the level of readiness in College Algebra. The formula according to Ybanez (2002) is: where: X – observed data for the independent variable Y – observed data for the dependent variable N – size of sample r – degree of relationship between X and Y The computed correlation coefficients were subjected to significance; thus the formula used (http://faculty.vassar.edu/lowry/ch4apx.html) was: where: r – computed correlation coefficient n-2 – degree of freedom t – degree of significance for r For problem 4, t-test independent (t-test between means), taken two at a time was used to determine the difference in the perceptions of

20 the respondents. The formula for t-test for means (http://en.wikipedia.org/wiki/Student%27s_t-test) is: where: = estimator of the common standard deviation of the two samples n = number of participants, 1 = group one, 2 = group two. n – 1 = number of degrees of freedom for either group n1 + n2 – 2 = the total number of degrees of freedom, which is used in significance testing. t = degree of difference For problem 5, the major strengths and weaknesses were deduced based on the findings, particularly on the level of readiness in College Algebra through statistical ranking. An area was considered strength when it received a descriptive rating of highly ready; otherwise, the area was considered a weakness.

21 The MS Excel Data Analysis Tool was employed in treating the data. Data Categorization For the profile of the students along high school grade in Math IV, the scale system was used: Grade range Descriptive Equivalent 92.6-97.00 Outstanding Performance 88.2-91.59 Very Satisfactory Performance 83.8-88.19 Satisfactory Performance 79.4-83.79 Fair Performance 75-79.39 Poor Performance For the level of readiness in each topic in College Algebra, the Scale System was utilized. Elementary Topics/ Factoring Score Range Level of Readiness/ DER 7.20-9.00 very highly ready 5.40-7.19 highly ready 3.60-5.39 fairly ready 1.8-3.59 slightly ready 0.00-1.79 not ready

22 Special Products and Patterns/ Systems of Linear Equations Score Range Level of Readiness/ DER 5.60-7.00 very highly ready 4.20-5.59 highly ready 2.80-4.19 fairly ready 1.40-2.79 slightly ready 0.00-1.39 not ready Rational Expressions/ Linear Equations in One Variable Score Range Level of Readiness/ DER 6.40-8.00 very highly ready 4.80-6.39 highly ready 3.20-4.79 fairly ready 1.60-3.19 slightly ready 0.00-1.59 not ready Exponents and Radicals Score Range Level of Readiness/ DER 1.60-2.00 very highly ready 1.20-1.59 highly ready 0.80-1.19 ready 0.40-0.79 slightly ready 0.00-0.39 not ready

23 For the general level of readiness, the scale below was used: 40.00-50.00 80%-100% very highly ready 30.00-39.99 60%-79.99% highly ready 20.00-29.99 40-59.99% fairly ready 10.00-19.99 20-39.99% slightly ready 0.00-9.99 0-19.99% not ready For the strengths and weaknesses, an area was considered strength if it got descriptive equivalent rating of highly ready and above; otherwise, it was considered a weakness. Parts of the Learning Activity Sheets The learning activity sheets comprise of the rationale, the learning objectives, the subject matter, the learning activities and sheets. The learning activities are either with the help of the teacher or are designed for independent learning. Ethical Considerations To establish and safeguard ethics in conducting this research, the researchers strictly followed and obeyed the following: The respondents’ names were not mentioned in any part of this research. The respondents were not coerced just to answer the test.

24 Proper document sourcing or referencing of materials was done to ensure copyright. A communication letter was presented to the registrar’s office to ask authority to get the needed data on profile.

25 CHAPTER III RESULTS AND DISCUSSION This chapter presents the data analysis and interpretation of the gathered data. Profile of the Students The first problem of the study is on the profile of the students in College Algebra. Table 2 presents the profile of the students along sex, type of high school graduated from and their high school final math grade. It shows that out of 309 students, 161 or 52.10% are males while 148 or 47.90% are females. This means that there are more male respondents than the females. This is easy to understand since the courses which include college algebra in their curriculum for the first semester are along engineering, architecture, business administration and criminology. Massey (2011) highlights that male students are more inclined to enrolling to a course aligned to mathematics, engineering, architecture, business management and criminal education. Registrar records as of July 2013 also indicated that there were really more males than females.

26 Further, out of 309 students, 125 or 40.45% graduated from public schools while 184 or 59.55% graduated from private schools. This means that majority of the students came from private schools in and Table 2. Profile of Students Profile variables Frequency Rate A. Sex Male Female 161 148 52.10% 47.90% B. Type of High School Graduated from 309 100% Public Private 125 184 40.45% 59.55% C. HS Final Math Grade 309 100% 75-78 79-84 39 106 12.62% 34.30%

27 85-88 89-93 94-97 92 64 8 309 29.77% 20.71 2.59% 100% outside of La Union. This is because majority of the students came from families that can afford education offered in the private schools. A testament to this is their enrolment in SLC, a private HEI. Lastly, it also shows the grade range of the students in their high school mathematics subject. It reveals that 39 or 12.62% have grades ranging from 75-78%, interpreted as poor performance, 106 or 34.30% have grades ranging from 79-84%, interpreted as fair performance, 92 or 29.77% have grades ranging from 85-88%, interpreted as satisfactory performance, 64 or 20.71% have grades ranging from 89-93%, interpreted as very satisfactory performance and only 8 or 2. 59% have grades ranging from 94-97, interpreted as outstanding performance. It means that majority of the students had fair-satisfactory performance in their high school mathematics. This points out to the fact that the students had not fully mastered the desired learning competencies of

28 Mathematics IV. The finding of the study jibes with Oredina (2011) stating that students in College Algebra had not fully mastered the competencies. Level of Readiness in College Algebra The second problem of the study is on the level of readiness of the students in College Algebra. Table 3 shows the level of readiness of students in College Algebra. It is shown that the students have a mean score of 2.87 or 31.88% in elementary topics, 3.70 or 52. 86% in special product patterns, 3.6 or 40% in factoring, 3.84 or 48% in rational expressions, 3.36 or 42% in linear equations in one variable, 2.8 or 40% in systems of linear Table 3. Readiness in College Algebra TOPIC Mean Score Rate Descriptive Equivalent Elementary Concepts 2.87 31.88% Slightly ready Special Product Patterns 3.70 52.86% Fairly Ready Factoring 3.6 40% Fairly Ready

29 Rational Expressions 3.84 48% Fairly Ready Linear Equation in One Variable 3.36 42% Fairly Ready Systems of Linear Equations in Two Variables 2.8 40% Fairly Ready Exponents and Radicals 1.13 56.50% Fairly Ready TOTAL 21.3 42.60% Fairly Ready equations and 1.13 or 56.50% in exponents and radicals. Thus, the students were slightly ready in elementary concepts while ready in the other remaining topics which include special products and factoring, rational expressions, linear equations, systems of linear equations and exponents and radicals. This means that the students were not so much prepared to hurdle topics on sets, number line, operations on integers, algebraic expressions and polynomials. Further, this means that the students were prepared to apply special product and factoring patterns, manipulate rational expressions, solve linear equations and systems and deal with expressions involving exponents and radicals. However, since

30 the rates of the mean scores are only between 30-57%, the students still lack the necessary mastery to be able to hurdle the challenges of the specified topics in College Algebra. Generally, the students’ mean score is 21.3, equivalent to 42.60%, interpreted as ready. Thus, students are generally ready for the course content of College Algebra. They are familiar with the course contents since majority of the contents of the course are just a review of high school mathematics. However, it can be construed that students have not really mastered well the competencies required in each topic. Testament to this is the fair-poor performance of the students based on their high school math grades. This finding of the study corroborate with Kuiyuan (2009) stating that the level of readiness of the students in College Algebra is at the moderate level only. It was mentioned that students did not possess the needed pre-requisite skills. Correlation between Profile and Level of Readiness The third problem of the study is on the significant relationship between the profile and the level of readiness of the students. Table 4 shows the relationship between profile and the level of readiness of the students. It shows that the correlation coefficient between sex and the level of readiness is 0.18, interpreted as negligible

31 Table 4. Correlation between profile and level of readiness Profile Variables Level of Readiness t- critical @ 0.05 Interpretation Sex 0.18 Negligible 0.112 Significant Type of HS graduated from 0.12 Negligible 0.112 Significant HS math final grade 0.63 marked 0.112 Significant correlation. This negligible correlation is significant at 0.05 level of significance. This signifies that sex does not significantly affect the level of readiness and vice versa. Thus, sex does not determine the level of readiness in college algebra. Further, it also shows that the correlation coefficient between type of high school graduated from and the level of readiness is 0.05. This negligible correlation is significant at 0.05 level of significance. This denotes that the type of high school graduated from does not significantly affect the level of readiness and vice versa. Thus, the type of

32 high school graduated from does not necessarily determine the level of readiness. This is true since schools, regardless of type, offer the same curriculum provided by the Department of Education, hence, the students still learned the same content in their secondary schools. Moreover, it also divulges that the correlation coefficient between high school math grade and level of readiness in College Algebra is 0.63. This marked correlation is significant at 0.05 level of significance. This means that high school math grades significantly affect the level of readiness. This means that the high school mathematics performance of students affect their level of readiness in College. This is easy to understand since the high school mathematics subjects provide solid foundation for students to hurdle the course contents of College Algebra, especially so that the contents of the course are review of the high school topics. This finding of the study corroborates with the study of Kuiyuan (2009) stating that high school GPA strongly correlates to college readiness. This finding run parallel to the study of Kuiyuan (2009) revealing that high school and college GPA had strong correlation with the students’ level of readiness in College Algebra, while the other factors such as national exam scores, type of school graduated from had weak correlations.

33 Comparison on the Level of Readiness of the Students in the Three Colleges The fourth problem of the study is the significant difference between the level of readiness of the students in the three colleges, CASTE-IT-CRIM, CCSA, and CEA. Table 5. Comparison on the Level of Readiness Departments Mean Difference Computed t- value p-value Interpretation ASTE-IT- CRIM and CCSA 2.173 1.80 0.0729 Not Significant ASTE-IT- CRIM and CEA 3.82 3.09 0.0023 Significant CCSA and CEA 1.64 1.43 0.1531 Not Significant Table 5 reveals the comparison of the level of readiness of students in the three (3) departments of SLC, the CASTE-IT-CRIM, the CCSA, and

34 the CEA. It shows that the comparison on the level of readiness of students from CASTE-IT-CRIM and CCSA has a computed t-value of 1.80. This is not significant at 0.05 level of significance since the p-value is larger than 0.05. Thus, it can be inferred that the mean difference of 2.173 is not significant. This denotes that there is no significant difference in the performance of the students in the CASTE-IT-CRIM and the CCSA. Thus, it is safe to construe that students in CASTE-IT-CRIM are not better than CCSA students, and vice versa. This finding runs parallel to the hypothesis of the study that there is no significant difference in the performance of the students in the two identified departments. Further, it shows that the comparison on the level of readiness of students from CASTE-IT-CRIM and CEA has a computed t-value of 3.09. This is significant at 0.05 level of significance since the p-value is smaller than 0.05. Thus, it can be inferred that the mean difference of 3.82 is significant. This denotes that there is a significant difference in the performance of the students in the CASTE-IT-CRIM and the CEA. This finding does not run parallel to the hypothesis of the study that there is no significant difference in the performance of the students in the two identified departments. Thus, students in CEA are better in College Algebra than the students in CASTE-IT-CRIM. This is easy to understand

35 since students enrolled in engineering and architecture courses are inclined to mathematics. It also shows that the comparison on the level of readiness of students from CCSA and CEA has a computed t-value of 1.43. This is not significant at 0.05 level of significance since the p-value is larger than 0.05. Thus, it can be inferred that the mean difference of 1.64 is not significant. This denotes that there is no significant difference in the performance of the students in the CCSA and the CEA. This means that students CSA are not better in College Algebra than students in the CEA, and vice versa. This finding runs parallel to the hypothesis of the study that there is no significant difference in the performance of the students in the two identified departments. Strengths and Weaknesses in the Level of Readiness in College Algebra The fifth problem of the study is the strengths and weaknesses in the level of readiness of the college students. Table 6 shows the strengths and weaknesses of the students in College Algebra as culled out from their level of readiness. It can be seen from the table that all the content areas under College Algebra are considered as weaknesses of the students. This means that the students are not that prepared in taking the subject. This implies that they did not

36 possess yet the needed skills needed to hurdle the demands of the course. This finding of the study harmonizes with the study of Leongson (2001) that students’ performance in College Algebra is alarming. It was mentioned that the students were at the poor-fair levels only. This finding also corroborates with the study of Ragma (2014) revealing that all content areas in College Algebra are found to be constraints. He explained that the students were not able to successfully imbibe the skills in algebraic concepts and manipulations. Table 6. Strengths and Weaknesses in College Algebra TOPIC Mean Score Rate Classification Elementary Concepts 2.87 31.88% Weakness Special Product Patterns 3.70 52.86% Weakness Factoring 3.6 40% Weakness Rational Expressions 3.84 48% Weakness Linear Equation in One Variable 3.36 42% Weakness Systems of Linear Equations in Two Variables 2.8 40% Weakness Exponents and Radicals 1.13 56.50% Weakness

37 CHAPTER IV SUMMARY, CONCLUSIONS AND RECOMMENDATIONS This chapter incorporates the summary, findings, conclusions and recommendations of the study. Summary The study aimed to determine the level of readiness of frsehmen in College Algebra in Saint Louis College for the first semester, school year 2013-2014. It specifically looked into the profile of the students, their level of readiness along the specified topics, the significant relationship between profile and the level of readiness, the significant difference betweeen the level of readiness of the students in the three departments of the college, the strengths and weaknesses based on the level of readiness and the proposed learning activity package. The study is descriptive with a validated researcher-made readiness test as the main data-gathering tool. Findings The findings of the study are: 1. a. There were 161 males and 148 females; b. Out of 309 students, 125 came from public schools while 184 came from private schools.

38 c. 237 students had a high school math grade ranging from 75-88%; while 72 had grades ranging from 89-97%. 2. The students were slightly ready in elementary topics while fairly ready in the remaining topics which include special product and factoring patterns, rational expressions, linear equations, systems of linear equations and exponents and radicals. Generally, they were failry ready in College Algebra. 3. a. There was a negligible correlation between sex and level of readiness. b. There was a negligible correlation coefficient between type of high school graduated from and level of readiness. c. There was a marked correlation between high school final math grade and level of readiness. 4. a. There was no significant difference between the level of readiness of students from the CASTE-IT-CRIM and CCSA. b. There was a significant difference between the level of readiness of students from the CASTE-IT-CRIM and CEA. c. There was no significant difference between the level of readiness of students from the CCSA and CEA. 5. All the topics were found to be weaknesses.

39 Conclusions In the light of the above-cited findings, the following conclusions are drawn: 1. a. Majority of the students were males. b. Majority of the students were graduates of private high schools. c. Majority of the students had fair-poor performance in their high school mathematics. 2. The students were not able to acquire sufficient pre-requisite skills to be able to hurdle the demands of College Algebra. 3. a. Sex did not significantly affect level of readiness and vice versa. b. Type of high school graduated from did not significantly affect the level of readiness. c. High school final math grades significantly affected the level of readiness. 4. a. The level of readiness of students from the CASTE-IT-CRIM and CCSA was the same. CASTE-IT- CRIM students were not better than CCSA students and vice versa. b. The level of readiness of students from the CASTE-IT-CRIM and CEA was not the same. CEA students were better than CASTE-IT-CRIM students.

40 c. The level of readiness of students from the CCSA and CEA was the same. CCSA students were not better than CEA students and vice versa. 5. Students were really not that ready to take College Algebra course. Recommendations Based on the conclusions of the study, the researcher recommends the following: 1. The learning activity sheets should be adopted by mathematics instructors. 2. The readiness test used in this research should be utilized as a diagnostic tool by all College Algebra instructors before starting the formal lessons every start of the school year. 3. Students who wish to enroll in mathematically-inclined subjects should be really good in mathematics. 4. A future study looking into the effectiveness of the learning activity should should be conducted.

41 BIBLIOGRAPHY A. Books Becker, Jon (2004). Flash review for college algebra. U.S.A.: Pearson Education, Inc. Barnett, Raymond (2008). College algebra with trigonometry. Boston: McGraw Hill. Bautista, Leodegario, et al. (2007). College algebra. Quezon City: C & E Publishing, Inc. Calmorin, L. (2005). Methods of research and thesis writing. Manila: Rex Bookstore, Inc. Cayabyab, Sheila P., et al. (2009). College algebra for filipino students. Quezon City: C & E Publishing, Inc. Covar, Melanie M., and Rita May L. Fetalvero (2010). Real world mathematics, intermediate algebra. Quezon City: C & E Publishing Inc. Ee, Teck. (2011). Maths gym. Singapore: SAP Group Pte Ltd. Huettenmueller, Rhonda (2003), Algebra demystified. New York: McGraw-Hill Companies Inc. Lial, Margaret (2001). College algebra. Boston: Addison-Weley, Inc. Oredina, Nora (2011). College algebra. Manila: Mindshapers Co., Inc. Parreno, Elizabeth (2001). College Algebra. Mandaluyong City: Books atbp. Petilos, Gabion (2004). Simplified college algebra. Quezon City: Trinitas Publishing, Inc. Rider, Paul (2009). College algebra. New York: Macmillan Co. Inc.

42 Sta. Maria, Antonia C. et al, (2008). College mathematics: modern approach. Mandaluyong City: National Bookstore. B. E-journals and Online Sources http://www.emergo.ca/RecentCourses-Disorder_201111- Celebrating_Women,_Understanding_Men_Introduction.htm (retrieved July 23, 2013) http://www.maa.org/college-algebra (retrieved February 21, 2014) Leeyn, Shiela http://www.enablemathcollege.com/enablemath/algebra.jsp (retrieved February 21, 2014) http://www.greatschools.org/students/academic-skills/354-why- algebra.gs (retrieved January 20, 2013) Moses, Robert (2009). The Algebra Project; http://answers. ask. com/ science/ mathematics/ why_is_algebra_important (retrieved February 20, 2014) http://www.nytimes.com/ (retrieved February 10, 2014) The Journal of Language, Technology & Entrepreneurship in Africa, Vol. 2, No.1, 2010 Kuiyuan, L. P. (2007). “A study of college readiness in college algebra.” The e-Journal of Mathematical Sciences and Mathematics Education Retrieved July 29, 2013 from http://www.uwf. edu/mathstat/Technical%20Reports/Assestment2%202010-1- 6.pdf Leongson, J. A. (2001). Assessing the mathematics achievement of college freshmen using Piaget’s logical operations. Bataan, Philippines. Retrived August 11, 2013 from www.cimt. plymouth.ac.uk/ journal/limjap.pdf

43 http://www.mariancatholichs.org/download.axd?file=ba3db97c-eee0- 475b-a77b-7182c50b7ad9&dnldType=Resource (retrieved February 21, 2014) http://www.google.com.ph/url?sa=t&rct=j&q=worskheets%20in%20sign ed%20numbers%20.doc&source=web&cd=1&cad=rja&ved=0CCcQ FjAA&url=http%3A%2F%2Fwww.yti.edu%2Flrc%2Fimages%2FMat h_Integers.doc&ei=kqkJU8qRLaidiAfEmYHYBw&usg=AFQjCNFJPdi Bq4UQGqn-1fLtkbypEI9_gQ (retrieved February 21, 2014) http://www.google.com.ph/url?sa=t&rct=j&q=activities%20in%20polyno mials.doc&source=web&cd=2&cad=rja&ved=0CCwQFjAB&url=http %3A%2F%2Fwww.wsfcs.k12.nc.us%2Fcms%2Flib%2FNC0100139 5%2FCentricity%2FDomain%2F822%2FPolynomials%2520Handou t.doc&ei=TawJU730IISZiQevhoCYBw&usg=AFQjCNE0gj5KIHWOqs oUHmeEQAqWGJfN0A (retrieved January 15, 2014) http://www.google.com.ph/url?sa=t&rct=j&q=worksheets%20in%20facto ring%20patterns.doc&source=web&cd=10&cad=rja&ved=0CFYQFj AJ&url=https%3A%2F%2Fwww.santarosa.k12.fl.us%2Flessonplan s%2FHigh%2FPreviousYear%2FWorrell%2520Lesson%2520Plan.do c&ei=2LQJU6WcJunkiAf6jYHwBw&usg=AFQjCNFp4nwVpTc9VIyfR 5L7fkSPuF0W_g&bvm=bv.61725948,d.aGc (retrieved February 21, 2014) C. Unpublished Researches Oredina, Nora A. (2010). “A validated worktext in college algebra.” Institutional Research. Saint Louis College, City of San Fernando, La Union. Ragma, Feljone G. (2014). “Error Analysis in College Algebra in the Higher Education Institutions of La Union.” Unpublished Dissertation. Saint Louis College, City of San Fernando, La Union.

44 APPENDIX Saint Louis College City of San Fernando, La Union READINESS TEST IN COLLEGE ALGEBRA Name:_________________________________Yr & Course:________________Score:______ I. MULTIPLE-CHOICE TYPE: Write the letter of the correct/best answer on the answer matrix given. WRITE CAPITAL LETTERS ONLY. (50 pts.) 1. If U is the set of integers and set A is the set of counting numbers, what is A’? a. 0 c. the union of whole and negative numbers b. whole numbers d. 0 and the negative numbers 2. In a survey of a group of college freshmen, it was found out that 800 love Mathematics, 750 love English and 450 love both subjects. How many students were surveyed? a. 1,100 b. 1,250 c. 1,550 d. 2,000 3. Which of the following statements is always true? a. Decimals are rational numbers. c. Integers are fractions. b. Zero is counting. D. Zero is whole. 4. Which property is being illustrated by (2x+y) + 4 = 4 + (2x + y)? a. distributive b. associative c. commutative d. identity 5. What is the answer in 22+3•4-12+8-(2-4)3+8÷(-2+4)? a. 0 b. 12 c. 24 d. -1 6. Which has a degree of 15? a. 2x9y5z b. 12x13y2 c. 15x15 d. all of the options 7. What is the result when –{-[-4(-x)-(3x-(x+2))]} is simplified? a. 7x-2 b. -2x +2 c. -2 d. 2x+2 8. What is the simplified form of [(4x3y5)/ (2x4y3)]2 ? a. 4x2y4 b. (4y4)/x2 c. 2y2/x4 d. 22x4y2 9. Which is equal to {12,500 x3]0 – (5x/5)? a. 1-x b. -1 c. 5-x d. 1+x 10. What is the product of (2x-y)(x-y+z)? a. 2x +y-z b. 2x2-3xy+2xz+y2-yz c. 2x2-y2-yz d. 2x2+x-y+2z 11. The volume of a rectangular solid is expressed as 4x3+6x2+4x+2. If its base area is expressed as 4x2+2x+2, what is the solid’s height? a. 4x + 4 b. 4x2 + 4 c. x+1 d. x-1 12. Which is the product of (2x-4)(2x+4)? a. (2x-4)2 b. 4x2-16 c.4x2+8 d. 4x2+16 13. Which is the square of the binomial (2x+3y)? a. 4x+9y b. 4x2+9y2 c. 4x2+6xy+9y2 d. 4x2+12xy+9y2 14. Which is the expanded form of (x+2)3? a. x3+23 b. x3+6x2+12x+8 c. x3-6x2-12x+8 d. x3+6x2+12x+6

45 15. Which is the expanded form of (x+y+3)2? a. x2+y2+9+2xy+6x+6y c. x2-y2+6+2xy+6x+6y b. x2-y2+9+2xy-6x+6y d. x2+y2+6+2xy+6x+6y 16. What is the area of a square if its side measures (2x-12) cm? a. 4x- 48 cm2 b. 4x2-24x+144 cm2 c. 4x2-48x+144 cm2 d. 4x2 +144 cm2 17. Which is the common monomial factor of the expression 2x5y + 10x3y7 – 6x4y3? a. 2xy b. 2x5y7 c. x3y d. 2x3y 18. Which is the factored form of x2n + x n+2? a. xn (xn+x2) b. x2 (xn+x2) c. x2 (xn+x) d. cannot be factored 19. Which is the factored form of 16x2-36y4? a. (4x+6y2) (4x-6y2) c. (4x-6y2) (4x-6y2) b. (8x+18y2) (8x-18y2) d. (4x+6y) (4x-6y) 20. Which of the following is a perfect square trinomial? a. 4x2-20xy+25y2 b. x2+2xy + y2 c. x2-10x+25 d. all options 21. Which is the factored form of x2-6x+8? a. (x-8)(x+1) b. (x-4)(x+2) c. (x-8)(x-1) d. (x-4)(x-2) 22. Which is not factorable? a. x2+1 b. x2-1 c. 2x+4xy d. 100-x2 23. Which is the factored form of x2-2xy+y2-x+y? a. (x+y)(x-y-1) b. (x-y)(2y) c. (x-y)(y-1) d. unfactorable 24. Which must be placed on the blank (m8-n8) = (m4+n4)(m2+n2) (____) (m-n) to make a correct factoring process? a. m-n b. m2-n2 c. m+n d. n2 25. The area of a square is expressed as 16x2+24xy+9y2, what is the measure of a side of the square? a. 4x-3y b. 4x +3y c. 16x + 9y d. 16x- 9y 26. Which is the simplified form of 6x8/8x6? a. ¾ b. 3x/4 c. 3x2/4 d. 3/4x 27. Which is the answer when (5t/8) is multiplied to (4/3t2)? a. 5/6t b. 5/6 c. 5/t d. 6t 28. Which is the quotient of (2x/3) and (x/9)? a. 2 b. 3x c. 6x d. 6 29. Which is the sum of (5/4x2) and (7/6x)? a. 19x/12x2 b. 19/12x2 c. (15+14x)/12x2 d. (15+4x)/12 30. Which is not a rational expression? a. 5x/x b. (2x-1)/(x-1) c. 2x/ x d. none 31.Which is the simplest form of (2x-4)/ (x2-4)? a. ½ b. 2/(x+2) c. 2/(x-2) d. 2x-4 32. Which is the sum of 1/3 and 1/5? a. 2/8 b. ¼ c.8/15 d. cannot be added

46 33. Which is the simplified form of the complex fraction, ? a. ½ b. 7/10 c. ¼ d. 1/5 34. Which is the value of x in 2x+5x+3 = -11? a. 2 b. 14 c. -2 d. -14 35. One number is greater than the other by 13. If their sum is 41, what are the 2 numbers? a. 12, 29 b. 40, 1 c. 27, 14 d. 16, 25 36. If a rectangle has a length of 3 cm less than four times its width and its perimeter is 19 cm, what are the dimensions of the rectangle? a. 3 and 7 b. 5.25 and 10 c. 2.5 and 7 d. 8 and 11 37. Lorna is 20 years older than her daughter, Rudylyn. In ten years, she will be twice as old as her daughter, how old are they now? a. 25, 35 b. 10, 20 c. 15, 25 d. 20,30 38. Two buses leave the station at the same time but in different directions. Bus A drives at a distance of 24 km while Bus B at a distance of 28 km. If they arrive at their destinations at the same time, what are their average rates if Bus A’s average rate is 12 km/hr less than Bus B’s? a.72 kph, 84 kph b. 7 kph, 12 kph c. 2 kph, 8 kph d. 70 kph, 80 kph 39. An encoder can finish a file of documents in 4 hours. Another encode can do the same job in 3 hours. How long will it take for the job to be done if the 2 encoders help each other? a. 1 hr 13 mins and 13.21 secs c. 1hr 42 mins and 51.43 secs b. 2 hr 12mins and 12.23 secs d. 2 hr 2mins and 12.23 secs 40. Feljone has 56 bills consisting of 10-peso and 5-peso bills, If he has a total of 440 pesos, how many 10- peso bills does he have? a. 32 b. 18 c. 24 d. 48 41. Three consecutive even integers have a sum of 138. What is the largest among the three numbers? a. 40 b. 42 c. 44 d. 48 42. In what quadrant can (-2, 4) be located? a. QI b. QII c. QIII d. QIV 43. What is the slope of 2x- 3y = 4? a. 2/3 b. -4/3 c. -2/3 d. 4/3 44. Which has an undefined slope? a. diagonal line b. horizontal line c. vertical line d. all lines 45. Which equation has an x- intercept of 8 and y-intercept of -16? a. y = 2x-16 b. y = -2x -16 c. y = -2x +16 d. y = 2x +16 46. Which is the solution of the system x- y =5 ? X+2y=2 a. (0,-5) b. (4,-1) c. (3,1) d. (1,1) 47. Which of the following have infinitely many solutions? a. parallel lines b. skew lines c. intersecting lines d. perpendicular lines

47 48. The sum of two numbers is 315. Their difference is 119. What are the two numbers? a. 115, 200 b. 15, 300 c. 150, 165 d. 98, 217 49. Which is equal to (81)-3/4? a. ½ b. 1/36 c. 1/27 d. 2/5 50. Which will make the equation correct? a. 12 b. 16 c. 18 d. 24

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