Simplifying Complexities: a Proposed Syllabus for Rational Functions in General Mathematics

The study’s main cause was to improve the performance of the students of Luray II National High School with regards to Rational Function of General Mathematics. To give remedy to such problem, the researcher focused on two major inquiries. First, measure the difficulty level encountered by grade 11 students in the sub-topics of Rational functions. Second, assess the factors that contribute to their difficulties. The study had its input on the Curriculum Guide for SHS Core Subject-General Mathematics, Bloom’s Taxonomy and Constructivist Approach. This study used a descriptive-analytic method. A researcher-made achievement test and a revised-adopted survey questionnaire were used as research instrument. The result of the study showed that students found this topic very difficult.

Therefore, the learners need proper facilitation and student-engaging activities to change students’ perception towards the subject. It also revealed that the factor which greatly contributed to the difficulty they encountered was student-related, specifically neglect of homework, doubts about fundamentals, distaste for subject, mental causes and lack of practice. However, the aspect Apathy towards Methods under teacher-related factor was found to be moderately serious which means that the students encountered difficulty of the stated indicators in many cases. The result of the study was the basis of the researcher in formulating the proposed syllabus for Rational Functions in General Mathematics. This syllabus will help teachers facilitate the class; consequently, improving students’ performance in said topic of General Mathematics.

KEYWORDS General Mathematics, Rational Functions, Difficulty Level1

Mathematics involves the development of all types of deductive reasoning. It is a science which involves numbers and calculation. It is a tool to train a learner’s logical and critical thinking, reasoning and analysis. However, some people believe that mathematics is nothing but a boring and difficult subject. With this negative attitude towards Mathematics, many learners perform poorly in Mathematics and shows little or no interest at all. Nevertheless, Ganal (2014), stated that this has been proven in details from the International Mathematics Olympiad, which showed that the Philippines ranked 79th out of 82 countries in 2003 and 80th out of 85 countries in 2004. With a highest possible score of 225, 220 was the score of China being the highest, 126 for Vietnam, Thailand got 9 and the Philippines got 16. Moreover, the data of the Department of Education showed that the Math achievement rate of fourth year students decreased from 50. 70% in SY 2005-2006 to 47. 82% in SY 2006-2007. (Carballo, 2009) On the average, the fourth-year students obtained an MPS of 48. 90 in the 2012 NAT, an improved performance when compared with the previous years. But still, the goal of 75% is too difficult to attain. (Philippines Basic Education, 2013)

The problem worsened when students entered senior high school. These students were mentally tortured due to plunging into more complicated math subject, General Mathematics. The researcher experienced on hand the difficulty encountered by last year’s grade 11 specifically in the topic, Rational Functions. Aware of this problem, the researcher conducted this study with the goal of assessing the students’ problem on the said topic among the Grade 11 Students of Luray II National High School. The results served as bases on the formulation of a proposed syllabus for Rational Functions. The output of the study, intended to satisfy the present needs and concerns of the learners. This further aimed to improve the teaching-learning process to help the students cultivate a positive attitude towards Rational Functions of General Mathematics, appreciate the beauty of numbers and recognize the importance of mathematics in their daily lives.

Simplifying Complexities: Comprehensive and Detailed SyllabusThe output is entitled, “Simplifying Complexities. ” It contains a syllabus and lesson plans attached with learning activities and worksheets. A syllabus is an instructional program which consists of objectives, teaching-learning activities and summary of topics to be covered in Rational Functions. This syllabus has the following components: (a) objectives/learning competencies; (b) Code; (c) Learning Outcome; (d) Teaching-Learning Activities; (e) Materials/ Resources and (f) Evaluative Measure. The teaching and learning of mathematics, like any other subject, requires that both the teacher and learners should communicate and interact effectively. This researcher-made output contains a section called Learning Package. This is a collection of written activities developed with the main purpose of teaching a concept/skill to a learner. The package’s components are the following: (a) pre-test paper to test students’ prior knowledge upon the discussion of the said topics; (b) lesson plan to guide the teacher on what to do; (c) Learning Activities which are ready-to-print to help teachers manage their time in preparing such lesson; and (d) post-test paper.

This Learning Package is self-instructional. It is aligned with the Curriculum Guide provided by the Department of Education. It requires lesser time for the teacher to prepare and little direct supervision by the teacher. It serves as a guide for the teachers handling the subject. The Lesson plans prepared by the researcher followed the DLL format. It contained complete parts of a lesson plan. The Learning Activities adopted by the researcher was in three categories: Individual, by pair and Group. This is because some activities are needed to be done individually by the students while some needs more heads to work out. This also caters the individual differences of the students. These learning activities also cater the assumed diverse learners a teacher usually has in his/her class. Instructions in these learning activities are explained in the simplest and most understandable manner. The learning activities and worksheets are attached as annexes to the lesson plans made. The last part is the post test at the end the discussion of Rational functions. The teacher has to compare the pre-test and the post test results to see if there were improvements.

The primary purpose of this research was to determine the difficulties in Rational Functions, a topic in General Mathematics, among Grade 11 students of Luray II National High School. Specifically, it sought to answer the following queries:

What is the level of difficulties encountered by grade 11 students of Luray II National High School in the following learning competencies of Rational functions:

1. Representing Rational Real-Life Situations Using Rational Functions
2. Rational Function, Rational Equation, and Rational Inequality
3. Solving Rational Equations and Inequalities
4. Representations of Rational Functions1. 5) Domain and Range of a Rational Function
5. Intercepts, Zeros and Asymptotes of Rational Functions
6. Graphing Rational Functions
7. Solves Problems Involving Rational Functions, Equations, And Inequalities

What are the factors that contribute to the difficulties encountered by the students in specific topic of General Mathematics? 3. Based on the findings of the study, what Instructional Program in Rational Functions of General Mathematics can be designed?

The respondents of the study were the 310-bona fide grade 11 students of Luray II National High School of school year 2017-2018 who took up General Mathematics during the first semester. Since the population was quite numerous, the researcher made use of Taro Yamane Formulae which suggested 175 respondents. These samples were taken as research respondents to arrive at a more realistic, reliable and scientific result of the study. These respondents answered questions pertaining to learning competencies in Rational Functions. They also answered questions on the problems they commonly encounter towards this topic.

The study used two kinds of questionnaire: a researcher-made achievement test and survey questionnaire. These were the main instruments of the data collection in the study. The achievement test was based on the content and performance standards as well as the learning competencies written in the Curriculum Guide provided by the Department of Education. It was composed of 40 items that covered the learning competencies to be accomplished by the students in Rational functions. It was designed to measure the grade 11 students’ difficulty level upon dealing with those eight sub-topics in rational functions. The survey questionnaire on the other hand consisted of three (3) factors namely: student-related, teacher-related and learning environment. Student-related factors had seven aspects, teacher-related factors had four aspects and Learning Environment has only one aspect. Each sub-items had three questions which was designed to seek information regarding the factors that contribute to the difficulties of specific topic in General Mathematics.

It is always a pleasure to acknowledge individuals who played a role in the development of this research. The writing of such has been a painstaking effort that would have been impossible without the stimulus of many truthful counsellors and collaborators. The researcher sincerely wishes to express her heartfelt thanks and gratitude to all those who rendered their assistance which made this study a success; especially to the following: First and foremost, to God Almighty for His constant guidance and enlightenment all throughout the conduct of the study; without Him, my effort will all be in vain;Dr. Juliet A. Jeruta, OIC-Regional Director of DepEd Region VII, for approving the travel order of the researcher. Dr. Leo B. Acibar, Region 7 Research Coordinator of Policy Planning and Research Division (PPRD), for his brilliant ideas and technical assistance during the signing of MOA;Dr. Joseph Irwin A. Lagura, Toledo City Schools Division Superintendent, whose sincerity and encouragement will never be forgotten, for the suggestion during the presentation of proposals and for the acceptance of this research title. Dr. Irene Abalde, the SEPS-PRU of Toledo City Division, for the professional advice, invaluable ideas, suggestions, sincere support and encouragement;Mrs. Trinidad P. Evangelista, principal of Luray II National High School, for the administrative support and cooperation in allowing the researcher to conduct the study inside the school premises; for giving desktop computer set with printer for the researcher’s convenience in doing the research;Mrs. Herisa Bahena, Mr. Baldomero Jumawan, Mr. Jefferson Largo, and Mrs.

Melna Mae Camoro, the teachers of the grade 11 students, who spared a portion of their time and accommodated the researcher during the data gathering;Grade 11 students of section Cherry, Jeff, Nhap, Sherwin, Jaypee, and Glicerio, for sincerely answering the test and questionnaires;Grade 12 students namely Regin Mari Sinoy, Marivic Oberes, Mary Joy Atamosa, Axell Tapanan, Genevieve Rubin, Loreine Kyra Lebumfacil, Phoebe Marie Baratbate, Harry Gabisan, Jaro Gerald Barcenas, Reggie Ruiz, for their support during the preparation and distribution of snacks and instrument;Researcher’s colleague, Mrs. Ji-An M. Catibig, for her valuable suggestions and support towards the conduct of this research;Lastly, the family, friends and loved ones of the researcher, the researcher’s inspirations, for giving the researcher their undying moral and financial support. And to all the people who in one way or another have given their full support when it was most needed.