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The Competency of Grade 7 Students in Solving Problems involving Polynomial

Functions and Equations GRACE D. SOSO

https://orcid.org/0000-0001-8660-6510xang_fire87@yahoo.com

San Vicente National High SchoolButuan City, Philippines

Gunning Fog Index: 15.00 • Originality 99% • Grammar Check: 99%Flesch Reading Ease: 31.51 • Plagiarism: 1%

ABSTRACT

Mathematics is an interesting but challenging subject where students manifest a negative attitude on the subject. The study aimed to determine the competency of Grade 7 in solving problems involving polynomial functions and equations. A descriptive research design was used in the study. The respondents of the study were the 190 Grade 7 students of San Vicente National High School who were selected after determining the sample size. The findings reveal that the high level of utilization of different teaching strategies indicates students’ ability to solve problems. The continuation and sustaining of the use of different teaching strategies in problem solving are indicated to improve the students’ mastery level. The level of utilization of the teaching strategies of the teachers determines the problem-solving performance in mathematics. Also, capability building activities are essential to develop a mathematics teacher’s teaching capabilities and strengthen their academic and professional orientation and competencies on instruction. It was recommended that school administrators should assess the current competencies level of teachers and provide them pieces of training to enhance their skills in teaching strategies to improve the level performance of the students..

SMCC Teacher Education JournalISSN Print: 2008- 0598 • ISSN Online: 2008-0601

Volume 2 • June 2020DOI:

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KEYWORDS

Competency on Polynomial Functions and Equations, descriptive, Philippines

INTRODUCTION

.Mathematics is a fascinating yet challenging subject where students show negative attitudes to the subject. Once they cannot develop the skills in math problem solving, they immediately give up. They think they are just not born for mathematics, or the subject is not for them. According to Renard (2017), some students are slow in learning the subject and solving exercises, but it does not mean that they cannot learn.

.Silver (2012) cited that each student must have a strong foundation in Algebra. Algebra gives them the knowledge and skills for making better decisions in everyday life, and for students going into college, it will set the tone for the rest of their math education. The complex math courses that students have in college are useful as Algebra as the base. If Algebra foundation is not that strong, students are required to take a remedial math class before they can be allowed to take math classes in line with their degree, costing extra time and money.

.According to Deziel (2018), a polynomial is not as complicated as it sounds, because it is just an algebraic expression with several terms. Polynomials have more than one term, and each term can be a variable, a number, or a combination of variables and numbers. Some use polynomials in their heads every day without realizing it, while others do it more unconsciously. For the professionals, the ones most likely to use polynomials daily are those who need to make complex calculations. An engineer designing a roller coaster would use Polynomials to model the curves, while a civil engineer uses it to design roads, buildings and other structures. Polynomials are essential tools for predicting traffic patterns to appropriate traffic control measures such as traffic lights. Economics uses it to model economic growth patterns, and medical researchers use them to describe the behavior of bacterial colonies.

Algebra is commonly referred to as the “gatekeeper subject.” This is true when the challenges of adolescence begin to rise, and when falling off track with school performance can affect future success. A student who proceeds successfully through Algebra has more opportunities for reaching a higher level of mathematics in high school, and the completion of higher-level mathematics is related to a higher likelihood of entering a 4-year college or university (Jacobson, 2015).

.Basic Algebra is used by electricians, engineers, and nearly everyone. From everyday life decision-making to advanced training in science and technology, the ability to understand and apply Algebra is a stepping stone to a successful life journey with great opportunities and discoveries.

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.Elementary Algebra encompasses Algebra’s basic concepts as one of the branches of mathematics that taught to secondary students important in building their understanding of arithmetic. Arithmetic deals with specified numbers, while Algebra introduces quantities without fixed values known as variables. The use of variables entails the use of algebraic notation and an understanding of the general rules of the operators introduced in arithmetic.

Marsh (2014) stated that equations are useful in solving daily life problems. Today’s computer chips used in all machines use in daily routine like washers, dryers, cars, backs, etc. All chips used in these machines are based on mathematical equations and algorithms. It is also used in traffic control, aircraft, space program, and medicine.

.It has been observed that Filipino students excel in knowledge acquisition in mathematics but considerably low in lessons requiring higher-order thinking skills. According to Paten & Dinglasan (2013), how students learn and how to measure student performance in the areas of mathematics is a priority concern of policymakers and educators worldwide. Benito (2010) said that mathematics skills are needed to cope with the demands of life, such as being numerically literate, gaining tools for future employment, developing the prerequisites for further education, and appreciating the relationship between mathematics and technology. Mathematics as the language of the sciences, and many disciplines depend on the subject as a symbolic means of communication. This is where mathematics education plays an important role in developing students’ general decision making and problem-solving skills.

Learners have to be active in learning to take place. It has to be meaningful but not stressful and meaningless. Unfortunately, most students consider learning mathematics to be stressful and meaningless. For some, it is both emotionally and cognitively dreary when attending to mathematics teaching and learning. These students are affected by the phenomenon called mathematics anxiety, which greatly affects their success throughout their school life. Shore (2010) found mathematics anxiety a severe phenomenon of mathematics learning and suggested considering this anxiety factor during teaching and learning. Mathematics teachers can help children overcome their mathematics anxiety by helping them approach mathematics with confidence while concurrently assisting them in developing their basic mathematical understanding of the basics.

.According to Arem (2010), students have difficulty connecting symbols with the proper referent; in other words, students have a hard time comprehending the exact meaning of variables, especially viewing expressions as objects. Most students feel anxious and tense when manipulating numbers and solving mathematical problems. Mathematics anxiety is a psychological state when a student experiences or expects to lose self-esteem in confronting mathematical situations. Such anxiety prevents students from learning even the simplest mathematical task. It has been found that negative feelings and attitudes toward mathematics intrude on the development of formal reasoning abilities.

.The basic comprehension of mathematics skills among low achievers in school

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was seldom recognized. Hence, these low achievers continue to develop a negative attitude towards mathematics. This was shown in the 2017 National Achievement Test (NAT) result, where the mean percentage score (MPS) in mathematics was only 43.71% that indicated a low performance. In San Vicente National High School, most of the students consider mathematics a hard subject, and as a result, many of them failed during the examination period. In an interview with the low achievers in mathematics, they expressed that they have difficulty in the lessons because they do not have enough knowledge in Algebra, polynomial functions, and equations. In light of the aforementioned scenario, the researcher was motivated to study the competencies of polynomial function and equations of Grade 7 students of San Vicente National High School, Butuan City.

FRAMEWORK

The study was anchored on the constructivism learning theory. It explains that humans generate knowledge and meaning from their experiences. Over the years, mathematics has been taught as a fact that was transmitted, and those who did not succeed were left behind. In contrast, constructivism focuses on how people can learn and suggests that mathematical knowledge results in people forming models in response to the questions and challenges that come from activities involving mathematical problems and environment, not simply taking information, nor as merely the blossoming of an innate gift. The teacher’s role is not only to observe and assess students’ learning but also to involve them in completing activities and posing questions for the promotion of reasoning.

According to Crawford & Witte (2010), the best word to describe a constructivist classroom is energy. The active engagement of students in the learning process is essential. Obtaining this type of engagement requires a much different class from the authoritative and teacher-centered traditional classrooms in which the teacher stands at the front of the room, directing the content that is delivered to the students. And the notion that students will learn on demand the same material at the same pace.

Constructivism is based on observation to judge how students learn. According to Khalid (2012), constructivism hypothesizes learning as an active, contextualized, or constructive process. It is a reaction to teaching approaches such as behaviorism and programmed instruction. The learner acts as an information constructor and constructs knowledge based on their personal experiences and hypotheses of the environment. Learners actively construct or create their own subjective or objective reality. Through social negotiation, learners continuously test their hypotheses and create new knowledge, correct previous knowledge, or confirm present knowledge. And learner links new knowledge to prior knowledge.

However, constructivists argued that the learner is not a blank slate (tabula rasa) but brings past experiences and cultural factors to construct new knowledge in a given

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situation. Constructivism activates the student’s inborn curiosity about the real world to observe how things work. A common misunderstanding regarding constructivism assumes that all knowledge is constructed from the learner’s previous knowledge, regardless of how one is taught.

The study of Bernero (2011) revealed that cooperative learning has a positive impact on developing student’s social skills, academic performance achievement, self-esteem, and self-confidence. When efforts are structured cooperatively, there is considerable evidence that students achieve more, build more positive and supportive relationships, and develop in healthier ways.

According to Tolimson (2015), differentiated instruction is one of the promising approaches to maximizing each student’s learning potential. This teaching posits that students are provided with various learning opportunities. The teacher differentiates the content of their lesson, teaching process and support to their students, and students’ outputs and supports. Landry, Jacobs, & Newton (2014) stressed that there is a significant improvement in students’ performance after doing peer assessment on a cumulative basis. The results showed the importance of using peer assessment as a tool for student-based learning. More than 90% of the students either agreed or strongly agreed that peer assessment was a valuable learning experience.

A study by Qualters (2011) suggested that students do not favor active learning methods because of the class time taken by the activities, fear of not covering all of the materials in the course, and anxiety about changing from traditional classroom expectations to the active structure. Casado (2010) examined students’ perceptions across six teaching methods: lecture/discussion, lab work, in-class exercises, guest speakers, applied projects, and oral presentations and showed that students most preferred the lecture/discussion method. A study conducted by Bates & Poole (2003) provided evidence that students place greater emphasis on lecture. They rated it as the best teaching method. They reasoned out that in this method, the teacher provided all knowledge related to the topics, it is a time-saving method, and students listened to the lecture attentively.

On the other hand, the teachers’ use of games affects the children’s perspectives towards school and mathematics. The game has an important place in children’s thinking on numbers and initiating and maintaining mathematical communication (TrawickSmith, Swaminathan, & Liu, 2016). The game improves oral communication, top-level social interaction skills, creative thinking skills, imaginary and divergent thinking skills, and problem-solving skills of the children.

Compounding the theories and concepts considered in the study, the researcher developed and drafted the framework for the competency in problem-solving on polynomial functions and Grade 7 students’ equations. Figure 1 shows the research paradigm. The dependent variable is the level of skill in problem-solving on polynomial functions and equations in algebra. In contrast, the independent variable is the level of utilization of teaching strategies on problems involving polynomial functions and

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equations in terms of cooperative learning, differentiated instruction, peer-assisted learning, lecture method, and math games.

OBJECTIVE OF THE STUDY

.The study determined the level of utilization of the teaching strategies on the competency of the Grade 7 students of San Vicente National High School on problem-solving involving polynomial functions and equations.

METHODOLOGY

Research Design.A descriptive research design was used in the study. It is descriptive since the

information was obtained on the level of competency on problem-solving involving polynomial functions and equations and the level of utilization of the teaching strategies in terms of cooperative learning, differentiated instruction, peer-assisted learning, lecture method, and math games. It is correlational because it determined the significant relationship between the level of competency on problem-solving involving polynomial functions and equations and the level of utilization of the following teaching strategies in problem-solving involving polynomial functions and equations.

Research Locale.The study was conducted at San Vicente National High School, San Vicente,

Butuan City, the fourth largest school and one of the empowered high schools in Butuan City Division. It is located in the southwest of Butuan and 6 kilometers away from the city proper. San Vicente NHS has 66 teaching and non-teaching staff with a total student population of 1,067 from Grade 7 to Grade. Grade 7 comprises 8 sections with a regular class and a population of 363 students.

Respondents. The study respondents were the Grade 7 students of San Vicente National High

School for the school year 2018-2019. There were eight sections with 363 students, and with the use of the Slovin formula, 190 students became the sample size. Table 1 shows the distribution of the population and respondents.

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Table 1. Distribution of the Population and Respondents Section N n

Almeda 45 24

Banzon 44 23

Nazarea 47 24

Padolina 46 24

Quizumbing 47 24

Rizal 45 24

Sylianco 43 23

Zara 46 24

Total 363 190

Research Instrument.A researcher-made questionnaire was the instrument used in the study. It consists

of two ( 2 ) parts. Part 1 contained items on the level of competency in problem-solving involving polynomial functions and equations in a summative form. The competencies included were operations on polynomials, laws of exponents, solving problems involving algebraic equations, and solving problems involving functions. Part 2 consisted of items on the level of utilization of the teaching strategies in terms of cooperative learning, differentiated instruction, peer-assisted learning, lecture method, and math games. It was then submitted to the senior Mathematics teacher and Education Program Supervisor in Mathematics for content validation. It was tried out to 20 students who were excluded as respondents of the study for reliability testing. The result of the try-out was tested with run and re-run tests. The result showed a rating of 0.899 for the students’ competency in problem-solving involving polynomial functions and equations and 0.978 for the level of utilization of teaching strategies. This means that the instruments were valid and reliable.

Ethical Considerations.The researcher observed the ethical requirements in the conduct of the research

study and assured the respondents ethical guidelines were followed for their protection. The dignity and respect of the respondents were observed and protected at all times. The researcher assured the respondents of the confidentiality of their identity and responses.

Data Gathering ProceduresA letter of permission was sent to the Public Schools District Supervisor of Southwest

District and the school principal of San Vicente National High School to undertake a study. As soon as the permission was approved, the researcher asked permission to all Grade 7 advisers and subject teachers to used their first and last period for the students to answer the summative test in an hour. The researcher scheduled the distribution

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of the students in order not to disrupt the classes. The questionnaire was given to the students personally and was given one hour to answer the questionnaire. After an hour, they were retrieved, and the responses were tallied and encoded in Microsoft Excel for the analysis and interpretation of the gathered data..

Statistical Treatment.The mean was the statistical tool used for the analysis and interpretation of data

RESULT S AND DISCUSSION.

Table 2. The Summary Table on the Level of Utilization of Teaching Strategies in Problem Solving Involving Polynomial Functions and Equations.

Teaching Strategy Mean Interpretation

Cooperative Learning 3.21 High

Differentiated Instruction 3.26 Very High

Peer- Assisted Learning 3.30 Very High

Lecture Method 3.04 Very High

Math Games 2.85 High

Overall 3.13 High

Legend:3.26- 4.00 Very High (VH), 2.51-3.25 High (H), 1.76-2.50 Moderate Low(ML), 1.00-1.75 Very low (VL).

Table 2 reveals that among the teaching strategies, peer-assisted learning has the highest mean of 3.30, which has a very high level of utilization, while the lowest mean is 2.85, which is on Math Games. The data show that the teacher always uses peer-assisted learning in teaching mathematics as perceived by the students. The students learn and perform well when they are working with their peers. Students learned a great deal by explaining their ideas to others and participating in activities they can learn from their peers. They develop skills in organizing and planning learning activities, working collaboratively with others, giving and receiving feedback, and evaluating their learning.

On the other hand, though, the teacher uses math games for the students to understand better, but the teacher often uses it. The teacher often uses games in teaching because it requires a lot of time to prepare. According to Adams (2017), games can affect students mentally. For instance, students may want to play until they win or advance in the game.

The overall mean is 3.13, which reveals a high level of utilization. This means that the teacher uses a variety of teaching strategies to cater to students’ different needs. The study of Pascual (2014) showed that teachers’ competency in using a variety of instructional techniques/strategies in teaching is the key factor in coming up with a

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successful implementation of a special mathematics curriculum. Since the development of order higher thinking skills is one of the objectives of the curriculum, he added that in attaining the goals of educational experience, more considerable attention must be given to higher-level knowledge outcomes such as understanding of concepts and principles, problem-solving, interpreting data and the ability to use tools of inquiry.

Table 3. Level of competency of students in problem solving involving polynomial functions and equation Competency f % Interpretation

Operations on Polynomials(Addition, Subtraction, Multiplication and Division) 144 76 Moving Toward Mastery

Laws of Exponents 127 67 Moving Toward Mastery

Solving problems involving algebraic equation 111 58 Average Mastery

Solving problems involving functions 134 70 Moving Toward Mastery

Overall 129 68 Moving Toward Mastery.Table 8 reveals that polynomial operations have the highest percentage of 76%among

the competencies of students in solving problems involving polynomial functions and equations and the level of competency is moving toward mastery. It means that the students know how to solve and answer the competency. The lowest percentage of 58% is on problems involving algebraic equations. It means that the students have difficulty in solving problems involving algebraic equations. According to Arem (2010), students have difficulty in connecting symbols with the exact meaning of variable, especially with viewing expressions as objects. The overall percentage is 68, which implies that the level of competency of the students on solving problems involving polynomial functions and equation is moving towards mastery.

CONCLUSIONS

Based on the findings of the study, the following conclusions were drawn.1. The high level of utilization of different teaching strategies indicates the ability

of the students to solve problems. 2. The continuation and sustaining of the use of different teaching strategies in

problem-solving as indicated to improve the mastery level of the students.3. The level of utilization of the teaching strategies of the teachers determines the

students’ performance in mathematics.4. Capability building activities are important to develop the teaching capabilities

of a mathematics teacher and strengthening their academic and professional orientation and competencies on instruction.

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Generally, the study concludes that the level of utilization of teaching strategies such as cooperative learning, differentiated instruction, peer-assisted learning, lecture method, and math game influence the level of competency of the students on polynomial functions and equations.

RECOMMENDATIONS

Based on the conclusions drawn from the study, the following recommendations are offered for consideration.

1. School administrators should assess the current competencies level of teachers and provide them pieces of training to enhance their skills in teaching strategies to improve the level performance of the students.

2. Mathematics teachers should innovate and adapt learning strategies aligned with the 21st-century skills to ensure the quality education set by the Department of Education and improve the level of performance of the students in Grade 7 mathematics. They should make extra efforts and willingness to design, innovate, and continue updating their competencies to become technologically skilled in adapting the new trends in education for the 21st century.

3. Teachers may use varied strategies in teaching to improve the performance of students.

4. Teachers should undergo pieces of training, seminars, and capability building activities to improve their teaching competencies and strategies in teaching mathematics.

5. Future researchers are encouraged to further studies on the topic to validate the findings of the present study and consider other variables not included in the present study.

LITERATURE CITED

Arem, C. (2010). Conquering mathematics anxiety (2nd edition). Canada: Brooks Cole Publishing.

Bates, T., & Poole, G. (2003). Effective teaching with technology in higher education: Foundations for success. Retrieved on January 12, 2019 from https://bit.ly/334cbnF

Bernero, J. (2000). Motivating Students in Math Using Cooperative Learning. Retrieved from June 10, 2019 from https://bit.ly/3g7Yrfe

Casado, M. (2000). Teaching methods in higher education: A student perspective. Journal of Hospitality & Tourism Education, 12(2), 65-70. Retrieved on June 20, 2019 from https://bit.ly/3hRe1MZ

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Crawford, M., & Witte, M. (1999). Strategies for Mathematics: Teaching in Context. Educational Leadership, 57(3), 34-38. Retrieved on June 13, 2019 from https://bit.ly/30TIAe4

Deziel, C. (2018). Everyday Use of Polynomials. Retrieved on February 25,2019 from https://bit.ly/2X7tmRn

Landry, A., Jacobs, S., & Newton, G. (2014). Effective Use of Peer Assessment in Graduate level Writing Assignment: A case study. International Journal of Higher Education, 4(1), 38-51. Retrieved on January 10, 2019 from https://bit.ly/3gaOpKe

Marsh, J. (2014). Why Equations are Important in Our Life. Retrieved on February 25, 2019 from https://bit.ly/2BEN27H

Paten, E. R., and Dinglasan T. D. (2013). Students’ mathematics Performance and Self Efficacy Beliefs in a Rich Assessment Tasks Environment.

Pascual E. R., 2014. Teachers’ Competency in using Variety of Instructional Techniques/Strategies in Teaching.

Renard, L. (2017). What is Mastery Learning? A different approach to Learning. Retrieved on November 29, 2018 from https://bit.ly/3gb64l4

Shore,K. (2010). Dr.Ken Shore’s classroom solver math anxiety. Retrieved on November 28, 2018, from https://bit.ly/3gcIB2U

Silver, H.(2012). Conceptual and Procedural Understanding of Algebra Concepts in the Middle Grade. Retrieved on November 28, 2018 from https://bit.ly/3f8A53P

Trawick-Smith, J., Swaminathan S., & Liu, X. (2016) The relationship of teacher-child play interactions to mathematics learning in preschool. Early Child Development and Care, 186(5), 716-733. Retrieved on January 12, 2019 from https://bit.ly/3g4WyQu