Abstract

This study investigated the effect of using modified guided practice model employing the I Do, You Do with Key Answers Support, and You Do with Parallel Problem Support to improve students’ academic achievement in Differential Equations. It was conducted for one semester with participants composed of 74 1^st year students enrolled in BSEd Science program in the University of Science and Technology of Southern Philippines, Cagayan de Oro campus. The participants belonged to intact classes assigned as the experimental and control groups. The research design used was quasi-experimental pretest posttest control group. Both groups were given pretest on a 32-item researcher made achievement test in Differential Calculus in which went through item analysis, content validity and reliability. The same test was administered after the experiment. The data gathered were statistically analyzed using mean, standard deviation and Analysis of Covariance (ANCOVA) with unequal (n). Results of the analysis revealed that before the start of the experiment, both experimental and control group showed relatively similar prior knowledge. After the intervention, the students in both groups have shown gradual improvement. This connotes that the students from both groups have learned the expected competencies and skills. The modified guided practice model used in the experimental group was found effective to improve students’ academic achievement in Differential Calculus. Thus, the increase between the posttest scores implies that the improvement in the experimental group was not due to chance. In addition, the result in the analysis of covariance (ANCOVA), revealed that there is a significant difference in students’ academic achievement in differential calculus between the experimental and control group. Furthermore, different teaching methods or curriculum approaches including the teaching quality, and student engagement may affect student achievement in general. The researcher recommended that mathematics teachers may use modified guided practice model employing the I Do, You Do with Key Answers Support, and You Do with Parallel Problems Support in teaching content subjects in mathematics to improve the students’ academic achievement which requires the students’ active engagement and will boost their mathematical skills. Similarly, for some teachers, that they may utilized modified guided practice model to other fields such Physics, Engineering to test if it is also effective.

1. Introduction

Calculus is the beginning of a whole new branch of mathematics and a “right passage” into many areas of the physical sciences, engineering and social sciences, making Calculus a very important course for those who specialized physics, engineering, and mathematics ¹.

Calculus as a course in general, must be learned in a manner that is comprehensive and with much depth as it provides necessary concepts needed by the learners towards the attainment of its twin goals – critical thinking and problem-solving skills. However, due to the course's abstraction and complexity, it is considered to be the primary cause of undergraduate students' failure ². As a result, the majority of students have always regarded calculus as one of the challenging tertiary-level subjects that they are attempting to avoid.

Students' struggles with learning calculus concepts, particularly derivatives, were brought on by their inadequate mathematical backgrounds and their difficulties identifying the kinds of functions that needed to be derived. The tricky part of succeeding in calculus is knowing when you don’t understand something.

An initial survey done by the researcher to the selected students enrolled in science education who finished differential calculus course last semester SY 2021-2022, as to “What difficulties they encounter in learning calculus”? Most of the reasons students have difficulty learning calculus are as follows: (S1) they don’t understand the lessons taught, (S2) they can’t follow the class discussion, (S3) they lack of prior knowledge, (S4) they think that it is a tiresome, (S5) they are not under the STEM strand during their senior high school, and (S6) they can’t work/study independently.

Undeniably, teachers’ instructional method contributes to mathematics academic performance. This is supported by ¹ who contend that teachers’ instructions have the great influence on students’ academic performance. But to determine which approach is the most effective to improve mathematical performance, there is no precise answer. Nevertheless, mathematics educators worldwide continue to research on new teaching method or innovation to achieve high performance.

The goal of any teaching innovation is to improve students learning towards calculus. NCTM further urges to raise the standards of teaching by advocating to redesign methods of teaching.

In view of the above reasons stated during the initial interview, the present study would like to investigate the effect of modified guided practice model on students’ academic achievement in differential calculus.

This study focuses on determining the effect of using modified guided practice model to the achievement of BSED Science students. Since learning usually takes place every after the delivery of instruction given by teacher, the following theories are deemed to be relevant to the study.

The term "scaffolding" describes a teaching method in which instructors provide students with a specific form of assistance while they acquire and master a brand-new idea or ability. A teacher could give fresh information or show students how to address an issue while using the instructional scaffolding methodology.

A general framework for instruction based on the study of cognition is Bruner's constructivist theory. The hypothesis is heavily influenced by studies on child development. The concepts presented in ³ were inspired by a conference on science and mathematics education. Programs for young children in mathematics and social science were used by Bruner to exemplify his thesis ³. The social constructivist theory known as Bruner's scaffolding theory first came into existence around the year 1976. Bruner believed that in order for children to understand new concepts, teachers and other adults must actively encourage them. They initially rely on their adult help, but as they develop greater mental independence and pick up new abilities and information, the support may gradually diminish. This type of planned interaction between the child and the adult is comparable to the scaffolding used during building construction. As the project is finished, it is gradually disassembled.

Bruner's also emphasized on the student discovering the subject material for themselves initially appears to relieve the teacher of a lot of effort. However, in order for his methodology to be effective, teachers must actively participate in lessons and provide cognitive scaffolding that will help students learn.

The term "cognitive scaffolding" refers to instructor actions that support students in carrying out tasks, reaching goals, or solving problems that are beyond their capacity to do so on their own ⁴.

Meanwhile, ³ also held the opinion that the educational process gives priority to engaging activities in the classroom. He argued that, in contrast to other teaching methodologies, the learning by doing method enables pupils to innovate on what they are learning. He also argued that the learning process should be applicable to students' daily lives because doing so improves their conceptual understanding, which is essential for the development of concepts. The Confucian idea that "I hear and I forget, I see and I remember, I do and I understand" is supported by this theory.

Moreover, Lev Vygotsky, a psychologist best known for his numerous significant contributions to educational theory, is associated with instructional scaffolding. He coined the term "zone of proximal development," which is based on a student's present developmental level and potential developmental level. The teacher focuses on the student's zone of proximal development and offers support that progressively decreases as the learner gains knowledge and independence to help them master a new task or topic ⁵.

Although a teacher may scaffold instruction in a number of ways, it is nevertheless important to note that there are two critical elements to keep in mind when using instructional scaffolding (1) Modeling: Students should have the opportunity to see their teacher repeatedly model or explain each phase of the assignment or method throughout the learning process. Students can learn how to do each step and why it is necessary through such modeling and repetition. Knowing how and why leads to students’ successful performance of the task. (2) Practice: Students must have the chance to work cooperatively with the teacher to put the assignment or approach into practice, either individually or in groups.

Summarily, it is common to refer to the instructional scaffolding approach as modified guided practice employing the "I do. You do. You Do” model. Applying support leads to more profound student understanding as the new information is actually integrated into the students’ existing knowledge schemes ⁶. By applying the support provided, students are better able to continue working constructively and extend and deepen their understanding ⁶. In a very precise sense, scaffolding is a means to narrow down the options available to a youngster so they may concentrate solely on learning the necessary skill or knowledge ⁷. Because of the theory's simplicity and beauty, scaffolding can be used in any industry, with every age group, and for any subject matter. The thrust of this study is schematically shown in the figure below.

The present study would like to examine the effect of modified guided practice model “I do, You Do with Key Answers, You Do with Parallel Questions” for the Experimental Group and the Conventional guided practice model for the control group on students’ academic performance in Differential Calculus which can be measured in terms of their pretest and posttest results.

Consequently, the researcher aimed to investigate the effect of modified guided practice model to improve students’ academic achievement in differential calculus; primarily, it seeks to answer the following questions: what is the academic achievement of the participants before and after instruction? Is there a significant difference in students’ academic achievement in differential calculus between the experimental and control group?

2. Methodology

This study utilized a quasi-experimental pretest-posttest control group research design. This design of the study examined the effect of integrating modified guided practice model in Differential Calculus. The extent of the significance difference of the academic achievement of both experimental and control group was tested using the Pretest-Posttest Control Group Design as illustrated below:

The treatment represents the treatment accorded to the experimental groups of this study which integrated the modified guided practice model employing the I Do, You Do with key answers support, and You Do with parallel problem support in the context of Differential Calculus, and the treatment represents the treatment applied to the control group where they were taught using the conventional guided practice model employing the I do, We do, and You Do model in the context of Differential Calculus. The academic achievement of the students was measured using their test scores in the achievement test in Differential Calculus. The purpose for this approach is that the result of the quantitative data provides a general understanding of the research problem.

The study was conducted at University of Science and Technology of Southern Philippines (USTP) formerly known as Mindanao University of Science and Technology (MUST), Cagayan de Oro City campus, one of the top state universities in the Philippines especially in the field of science, mathematics and engineering. USTP offers a strategic location advantage for the institution to train and develop students from all other regions of Mindanao. Its mission is to bring the world of work into actual higher education and training of students, offer entrepreneurial opportunities, and contribute significantly to the National Development Goals of food security and energy sufficiency through technology solutions. The university envisioned to become a nationally – recognized Science and Technology university providing the vital link between education and the economy. The USTP-CDO campus has five colleges (College of Engineering and Architecture, College of Science and Mathematics, College of Technology, College of Information and Technology Computing, and College of Science and Technology Education) offering courses which are aligned to the university mission or mandate.

The participants of this study were the first (1^st) year Bachelor of Secondary Education major Science students who were enrolled in Differential Calculus for the second (2^nd) semester of the school year 2023-2024 at the University of Science and Technology of Southern Philippines (USTP) -Cagayan de Oro City Campus. There were two groups used in the study. One group was taught using Conventional Guided Practice Model employing the “I do, We Do, You Do” model, composed of 36 students, while the other group was taught using the Modified Guided Practice Model employing the “I Do, You Do with Key Answers Support, You Do with Parallel Problems Support” model, composed of 38 students. These students came from different parts of the city and in some parts of Misamis Oriental province, and neighboring provinces such as Bukidnon, Camiguin, Lanao del Norte, Lanao del Sur, and many more.

The main instrument used in this study was the researcher-made pretest-posttest to assess the participants academic achievement in differential calculus. The instrument composed of 32 items two-tiered multiple-choice tests with moderate difficulty. Prior to the questions construction, the researcher made a 50-item two-tiered multiple-choice test, a table of specification (TOS) was done. A panel of experts in Mathematics Education examined each item of this test for face and content validity. The experts made some corrections and suggestions, after which the researcher modified the instrument, and tried it out to the 3^rd year and 4^th year college students who already took up Differential Calculus of this same school for pilot testing. The students’ test papers were corrected and item analyzed. After the item analysis was done, the reliability coefficient was determined and found to be 0.78 which is highly acceptable.

The researcher secured permission from the Vice -Chancellor for Academic Affairs (VCAA) thru the dean of the College of Science and Technology Education (CSTE) to allow her to use the 1^st year Bachelor of Secondary Education major in Sciences students of University of Science and Technology of Southern Philippines (USTP) as the research participants in the study. Upon approval, arrangements will be made, as to how and when the conduct of the study is going to happen. The researcher conducted the study in a full face-face learning modality ensuring that proper class orientation was done first.

In the control group, the teacher will employ the I Do, We Do, You Do Method. In the “I Do” stage the teacher models the appropriate way of solving problems through examples which are included in the new concept being taught. This step helps the students to process and understand the concept. No one is moving ahead. All students are listening and watching the process being modeled to them ⁸. In the “We Do” stage the teacher will let the students work together with a partner (teacher or classmates) to develop a deeper level of learning and understanding towards the concept taught. This stage helps build confidence especially for the timid students. ⁸. In the “You Do” stage the teacher allows the student to demonstrate their initial level of understanding through independent practice.

In the experimental group, the teacher will employ the modified guided practice model: “I Do, You Do with Key Answers Support, You Do with Parallel Problems Support” Model. In the “I Do” stage, the teacher models the appropriate way of solving derivatives through examples which are included in the new concept being taught. This step helps the students to process and understand the concept. All students are listening and watching the process being modeled to them ⁸. In the “You Do with Key Answers Support” the student will practice solving the problem with the answer key given independently while in the “You Do with Parallel Problems Support” stage, the student will solve the given problem similar to the problems given by the teacher. This stage will help the teacher to assess whether the students learned or not.

The researcher will employ both descriptive and inferential statistics. For the descriptive statistics, the researcher will use the mean and standard deviation to describe the participants’ academic achievement in differential calculus. These descriptive statistics are appropriate since academic achievement will be measured quantitatively using a continuous scale of measurement. Furthermore, the researcher will also employ Analysis of Covariance (ANCOVA) at significance level of 0.05 using the pretest score as covariate to determine which method is better in improving the students’ academic achievement in differential calculus provided that the assumptions on homogeneity of regression slopes, normality, and independence were met ⁹.

Before the implementation of the study, permission and informed consent from the relevant authorities will be obtained. This is in accordance with Republic Act 10173, also known as the Data Privacy Act, which safeguards people from the unauthorized processing of personal data that is private, or not accessible to the general public; and identifiable, or where the identity of the person is obvious either through direct attribution or when combined with other information available.

3. Results and Discussions

This study presented the analysis and interpretation of the data gathered to determine the effect on students’ academic achievement in Differential Calculus for both the experimental and the control groups using Modified Guided Practice Model and Conventional Guided Practice Model as shown below.

It is shown that the experimental and control group of the BSED Science students obtained a pretest mean score difference of 0.86 which indicates that the experimental group has a slightly higher prior knowledge as compared with the control group. This result indicates that before the start of the experiment, both groups showed relatively similar prior knowledge of the topics covered in Differential Calculus.

Meanwhile, in the unadjusted posttest, the students in experimental group shows a mean score of 17.45 and control group shows a mean score of 13.97. It can be noted that both groups have increased their posttest mean scores by 6.9 and 4.28 respectively. This confirms that, even without covariate adjustments, the experimental group outperformed the control group, reinforcing the effectiveness of the intervention. Also, in the adjusted posttest scores for both experimental and control group, it can be seen that the mean scores were 17.12 and 14.31 respectively. This tells us that after adjusting for covariates, the experimental group achieved a significantly higher adjusted posttest mean score compared to the control group. This suggests that the intervention applied to the experimental group had a positive effect on students’ mathematics achievement.

Moreover, the increase in posttest scores both adjusted and unadjusted indicates that the interventions was effective in improving students’ achievement in Differential Calculus. The difference between the adjusted posttest means implies that the improvement in the experimental group was not due to chance. This aligns with the previous research showing that innovative teaching methods, such as active learning, problem-based learning, and technology-enhanced instruction, can improve mathematics achievement. ^{10, 11}.

The standard deviation of the pretest mean scores of the experimental group is lower than the control group. This means that some variability in achievement with a slightly more dispersion in the control group. While in the unadjusted posttest, the standard deviation of experimental group is 5.14 which is higher than that of the control group. This shows that result in experimental group is slightly greater variability in the student achievement compared to the control group. On the other hand, the standard deviation of the adjusted posttest scores of the experimental group were relatively similar. This indicates that the variability in the students’ achievement remained similar in both groups after the adjustment.

Summarily this finding indicates that after the treatment, both experimental and control group became more homogeneous. Thus, the treatment of the two groups have varied effects on students’ achievement scores. To determine if there is a significant difference of their posttest mean scores, further examination was done using Analysis of Covariance (ANCOVA) unequal n’s at alpha=0.05

The Table 2 showed the analysis in the pretest yielded a computed F-ratio of 18.02 with a probability value of 0.0001 which is less than 0.05 level of significance thus led to the rejection of the null hypothesis that there is no significant difference in the students’ achievement test scores in differential calculus. The effect size Partial Eta Squared, indicates that 20% of the variance in the posttest scores is explained by pretest scores. This suggests that students’ prior knowledge (pretest achievement) has a substantial impact on their posttest achievement. This means that the mean score of the BSED Science students in the experimental group of 10.55 differ significantly from the 9.69 achievement score of the control group.

The analysis of covariance also yielded an F-ratio of 7.22 and a probability value of 0.01 which is less than the critical value of 0.05 level of significance which led to the rejection of the null hypothesis. This implies that there is a significant difference in the posttest scores across groups, even after adjusting the pretest scores. Also, the effect size (Partial Eta Squared, ) indicates that the group membership explains 9% of the variance in posttest scores. While the effect size is moderate ¹², it suggests that the intervention in group differences had an impact on students’ achievement. This result implies that, since the pretest has a strong predictive power, future studies should consider controlling for prior knowledge when evaluating interventions. The significant group effect suggests that the intervention or treatment applied to different groups has an impact, meaning different teaching methods or curriculum approaches including the teaching quality, and student engagement may influence student achievement to the posttest scores.

This study investigated the effect of utilizing modified guided practice model employing the I Do, You Do with key answers support, You Do with parallel problem support to improve students’ academic achievement in Differential calculus. This study was conducted for one semester with participants composed of 74 1^st year students enrolled in BSEd Science program in the University of Science and Technology of Southern Philippines, Cagayan de Oro campus. The participants belonged to intact classes hence the experimental and control groups were not randomly assigned.

This study employed quasi-experimental pretest posttest control group design. The instrument used in this study was a 32-item researcher made achievement test in Differential Calculus in which went through item analysis, content validity and reliability. Before the conduct of the experiment, a pretest was given to all groups. The researcher handled both the experimental and control groups in one semester. The experimental group was taught using the modified guided practice model employing the I Do, You Do with key answers support, You Do with parallel problem support while the control group was taught using conventional guided practice model employing the I Do, We Do, You Do. After the conduct of the experiment, posttest was administered to both groups and observation was employed to avoid bias. The data gathered were statistically analyzed using mean, standard deviation and Analysis of Covariance (ANCOVA) with unequal (n). The ANCOVA was used because the participants were not randomly selected.

Based on the analysis, the researcher found out that before the start of the experiment, both experimental and control group showed relatively similar prior knowledge. After the intervention, the students in both groups have shown gradual improvement. This connotes that the students from both groups have learned the expected competencies and skills.

The modified guided practice model used in the experimental group was found effective to improve students’ academic achievement in Differential Calculus. Thus, the increase between the posttest scores implies that the improvement in the experimental group was not due to chance.

In terms of the result in the analysis of covariance (ANCOVA), the researcher found out that there is a significant difference in students’ academic achievement in differential calculus between the experimental and control group.

Based on the aforementioned findings, the researcher come up with the conclusions that modified guided practice employing the I Do, You Do with Key Answers Support, and You Do with Parallel Problems Support are effective in improving students’ academic achievement in Differential Calculus. Furthermore, different teaching methods or curriculum approaches including the teaching quality, and student engagement may affect student achievement in general.

Based on the findings and conclusions of the study, the researcher recommends that mathematics teachers may use modified guided practice model employing the I Do, You Do with Key Answers Support, and You Do with Parallel Problems Support in teaching content subjects in mathematics to improve the students’ academic achievement which requires the students’ active engagement and will boost their mathematical skills. Also, teacher training should focus more on the evidence-based instructional methods that promote student engagement in order to bridge the gap of the students’ level of understanding. Similarly, for some teachers, that they may use this modified guided practice model to other fields such Physics, Engineering to test if it is also effective. In addition, future researchers may conduct similar studies implementing qualitative data analysis to explore on the students’ perceptions on the modified guided practice model.

ACKNOWLEDGEMENTS

The researcher would like to express her heartfelt gratitude to all significant people who supported and guided me in completing this study. These people are no other Dr. Rosie G. Tan, the researcher adviser who patiently guided and encouraged the researcher by giving her expertise in making this research complete. To my family who extended their utmost support despite the circumstances came along the way whether it is financially, emotionally or mentally. The researchers friends and USTP colleagues, who showed continuous support in writing the paper. The participants of this study, and above all to the Almighty God for His protection, wisdom, enlightenment and divine intervention, this work would not be possible.

References