Comprehensive Analysis on Least Learned Competencies in Mathematics for Grade 5: Basis for Learning Activities
This paper assessed the mathematics performance of grade five learners as basis for activity sheets. The competence gain in the study of Mathematics is widely used in all spheres of human life. Mathematics plays a key role in shaping how individuals deal with the various spheres of private, social, and civil life。 This justifies the compulsion of the study of the subject by all students who go through basic and secondary education in most countries. Mathematics is therefore a core subject at all levels of education in the Philippines. The findings of the study are that learners have a limited knowledge and understanding of visualizes division of decimal numbers using pictorial models, hence their performance in items on the topic is poor. A great proportion of the learners have serious misconceptions of the inclusion of decimals and division added on students’ understanding of the operation of division and decimal numbers. The study recommends a structured focus on visualizing division of decimal numbers using pictorial models. It recommends clarity for teacher trainers, textbook writers and teachers on what learners need to learn division. It recommends serious exploration of errors and misconceptions on inclusion of decimals on activities and a teaching approach that considers errors and misconceptions as opportunities for learning.
Keywords: Mathematics, education, least learned competencies, performance
Education is a process of human enlightenment and empowerment for the achievement of a better quality of life that leads to develop harmonious personality and involves all aspects of intellectual, religious, moral and physical of the personality of the Person. Schools are always transitional institutions. They prepare pupils for education or for occupation or for family life. Mathematics in the real sense is a science of space and quantity that helps in solving the problems of life needing numeration and calculation.
The competence gain in the study of Mathematics is widely used in all spheres of human life. Mathematics plays a key role in shaping how individuals deal with the various spheres of private, social, and civil life (Anthony & Walshaw, 2009). This justifies the compulsion of the study of the subject by all students who go through basic and secondary education in most countries. Mathematics is therefore a core subject at all levels of education in the Philippines.
Academic achievement has become an index of child’s future in this highly competitive world. Academic achievement has been one of the most important goals of the educational process. Achievement encompasses student ability and performance. It is multidimensional and intricately related to human growth and cognitive, emotional, social, and physical development also, reflects the whole child and not related to a single instance, but occurs across time and levels, through a student’s life. Mathematics is not enough to impart theoretical learning; that learning must be put into practice. True learning is that which affects behaviour and whereby the learner makes practical use of his knowledge.
In addition, Mathematics according to Maliki, Ngban, and Ibu (2009) is described as a subject that affects all aspects of human life at different degrees. According to The National Mathematics Advisory Panel (2008), mathematics is used throughout our daily lives. The importance of mathematics in day-to-day activities is no longer news. However, what remains news is the fact that students performance in mathematics has not improved significantly despite its importance, not even with the introduction and use of technology in mathematics, as confirmed by Chang and colleagues (2006) when they stated that, nowadays, students make use of computer-assisted problem-solving systems to better learn and understand mathematics.
Moreover, the topic on which the study will focus is expressing ratio in simplest form. It focuses on ratio because this is one of the topics included in Grade Five curriculum. The Department of Education for Mathematics curriculum expects Grade Five learners to be able to express ratio in simplest form. One of the reasons for the inclusion of this topic in the curriculum is that ratio is central to the development of proportional reasoning (Chick & Harris, 2007); and “proportional reasoning is the cornerstone of algebra and a wide variety of topics in mathematics” (Van de Walle, 2007, p. 353).
As division with decimals is introduced, conceptual understanding may be developed by asking students to draw upon their understanding of operations, decimals, and place value, to name a few. Conceptual understanding may be contrasted to procedural understanding which is, “composed of the formal language, or symbol representation system or rules for completing mathematical tasks” (Hiebert & Lefevre, 1986). The inclusion of decimals and division added additional foundational studies on students’ understanding of the operation of division and decimal numbers, including misconceptions on these two topics. Grade five learners of Mayor A.S. Fortuna Memorial Elementary School encounter the same problem. Thus, the purpose of this material is to find out the least learned competency the of the Grade Five learners during second quarter of school year 2018 -2019 as basis for the proposed mathematical activities to fill this gap.
Table 1 . Percentage of Correct Response of the Second Quarter Grade 5 Least - Learned Learning Competencies in Mathematics 5
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Percentage of Correct Responses Level of Performance
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All competencies have a dual nature, as they have an analytical and a productive aspect. The analytical aspect of a competency focuses on understanding, interpreting, examining, and assessing mathematical phenomena and processes, such as, for instance, following an controlling a chain of mathematical arguments or understanding the nature and use of some mathematical representation, whereas the productive aspect focuses on the active construction or carrying out of processes, such as inventing a chain of arguments or activating and employing some mathematical representation in a given situation. What follows is a summary of the least-learned competencies in mathematics for grade five during the second quarter that are an essential part of the knowledge base and skill base for all students. Students are best served by deep mathematical experiences in these areas. This is intended as a brief compilation of the truly essential topics, as opposed to topics to which students should have been introduced but need not have mastered. The skills and content knowledge that are prerequisite to grade six mathematics are of course still necessary for success in elementary.
As seen from Table 1, competency on visualizes division of decimal numbers using pictorial models has 17.39% correct responses interpreted in the parameter as low mastery. This is followed by the competency on expresses ratios in their simplest forms which has 23.91% with mastery while competency on recognizes when two quantities are in direct proportion has a 31.88% correct responses with low mastery and 31.61% correct responses on estimates the products of decimal numbers with reasonable results competency.
The findings implied that the corresponding competency manifests itself when dealing with the corresponding topic at the educational level at issue. So, in order for assessment to provide a fair and comprehensive coverage of the entire set of mathematical competencies, a board spectrum of activities are needed. Moreover, often a given activity gives rise to only some of the competencies, and different activities will involve different sets of competencies.