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Guided Approach (GA) In Teaching Rational Functions Relationships to Graphs

Armando A. Camaña Jr. and Gretchen Mae G. Gementiza

· Volume I Issue I


Significance of the Study / Rationale

One of the goals of the K to 12 program of Philippine education system is to develop and transform learners equipped with 21st century skills encompassing not only skills in communication, collaboration, creativity, but also in critical thinking, otherwise known as the 4Cs. In its paper titled, “Preparing 21st Century Students for A Global Society,” the National Education Association cites the American Management Association’s 2010 Critical Skills Survey that says the 4 Cs would become even more important to organizations in the future. Three out of four (75.7 percent) executives said they believe these skills and competencies will become more important to their organizations in the next three to five years, particularly as the US economy improves and organizations look to grow in a global marketplace.

Barrier to the goal mentioned above is the low academic performance of learners in the academic subject areas, most specifically Mathematics, based on the data revealed by several standardized tests, including the National Achievement Test (NAT). The Department of Education reported that the NAT percentage score in Mathematics for high school in S.Y. 2012-2013 was 46.83%, which is very far from the 75.00% target score. Furthermore, Dela Cruz (2017) pointed out that one of the main reasons of this deflation of academic performance in Mathematics is the lack of critical thinking skills integration in the teaching and learning process.

Though the results were based on the data several years ago, there has still been a continuing line on the low academic performance of students in Mathematics until this date. In fact, in the Senior High School curriculum, one of the core subjects taken by Grade 11 students is General Mathematics which fully requires critical thinking skills, not sole memorization. However, in Valenzuela National High School, it was found out through the consolidated mastery level in the first quarterly examination in General Mathematics that some of the Grade 11 students are not performing well in the subject. With the frequency of 41 who got the correct answer out of 174 students who took the examination, it was revealed that the learning competency which has the lowest mean percentage score of 23.56% interpreted as least mastered is the rational functions relationships to graphs.

The data mentioned is the compelling reason why the researchers would like to increase student’s academic performance and to develop students’ critical thinking skills at the same time (since these two variables are in consonance with each other) through Guided Approach in teaching the subject. This approach shows the transition of the instruction from the teacher-facilitator to the learners who should be ready to do on their own. By doing so, the learners are guided with the things that they already know and those which they do not know yet. With the aim to develop their critical thinking skills, this approach in teaching will engage them in the wide array of learning experiences focused on rational functions relationships to graphs.

Tumilty (2018) emphasized that guided approach is a constructivism approach that regards learning as an active experience. She believed that students learn best from their interactions. With guided instructional teaching practices, the students take an active role in the learning process and the teacher acts as a facilitator or guide. With guided instruction, students learn from their experiences, making it an inquiry-based or discovery-based model of teaching which can be mostly applied in Sciences and Mathematics.

Relative to the principle, the researchers believe that Guided Approach will help best the Grade 11 students to fully understand rational functions. The students will be provided with a module containing content and guided examples. It is imperative that they should read the first column on what and how to answer a given example before proceeding to the next step. Through one example in a step by step manner, the students will be fully guided in accomplishing the module. The module will be checked and evaluated first according to content, language, and form to ensure that the main objective of conducting the study will be met. Likewise, a pilot experimentation using the module will be done to selected students to validate the understandability of content, and reliability of learning outcomes, and to gather feedback geared towards the improvement of the module.

Research Questions

This study aims to find out the effectiveness of Guided Approach in teaching rational functions relationships to graphs to Grade 11 students of Valenzuela National High School.

Specifically, this seeks to answer the following questions:

  1. What is the academic performance of the two groups in rational functions as shown in the pre-test and post-test?
  2. Is there a significant difference between the mean scores in the post-test of the controlled (non-experimental) group and the experimental group?
  3. What are the attitudes of the experimental groups toward learning Rational Function Relationships to Graph using the module?


To counter the background and the specific research problem, these null hypotheses are formulated and to be tested.

Ho: There is no significant difference between the mean scores in the post-test of the controlled group and the non-experimental group.

Ho: There is no significant relationship between the weighted mean scores on the attitudes toward learning Rational Function Relationships to Graph using the module and the post-test score of the experimental groups.


The findings on the basis of statistical treatment used in this study are the following:

  • The pre-test of the controlled group has a mean score of 5.45 and an standard deviation of 2.06 while the experimental group has a mean score of 4.12 and has a standard deviation of 3.20;
  • Using the module for the experimental group as part of the guided approach strategy, the post-test result has a mean score of 14.17 and has a standard deviation of 2.70 while the controlled group has a mean score of 12.63 and standard deviation of 2.83 after taking up the post-test;
  • There is a significant difference in the mathematics performance (in the pre – test and post – test) of the participants before and after the execution of the guided approach and using the module.
  • There is a significant relationship between the attitudes of the participants toward learning the Rational Functions Relationship to Graphs.
  • In particular, the researchers’ finding indicate that learners must be engaged to learning in order to promote interaction between class discussion, moreover learners must be guided accordingly when some of the lessons taught inside the classroom is very technical in terms of its learning competencies.


After recording and analyzing the outcome of the study, herewith are the conclusion drawn.

Guided Approach can help to have a positive outcome if the learners were properly motivated. Guided Approach was great help in Mathematics subject. Using validated researchers-made module was the key ingredient for them to realize that they could enjoy mathematics subjects and at the same time they learn.

The use of guided approach can help teachers encourage their students to interact and participate in the class.

Same way, modules or any learning paraphernalia was also a big help for learners learning because it was an outside factor that gives reason for the learners to learn.


Based on the findings and conclusions of the study, the following recommendations were drawn:

Teachers in Mathematics should employ and improve teaching strategies that will maximize instruction and motivate learning. Ample time should be given in the discussion of the topics where learners are having difficulties and should be encouraged to bring out their ideas for clearing doubts and relieve their mathematics difficulties. Effort and proper conducting of remedial class will be given to the students.

Moreover, schools administrators should provide seminars workshops and in-service training on the content of strategies for teacher to enhance their capabilities that will help them to be more aware what are the reasons why students are not performing well. It is also suggested that teachers must pursue a higher and continuing education that they will be more equipped in other teaching strategies in Mathematics particularly the guided approach strategy. In addition, school should use important mathematics technology which teacher can use in their teaching and keep them with the trends both in content and methods of teaching.