Importance of Basic Mathematics
Mathematics is the study of numbers, and counting, and measuring, but that is only the beginning. Mathematics involves the study of number patterns and relationships, too. It is also a way to communicate ideas, and perhaps more than anything, it is a way of reasoning that is unique to human beings. Mathematics is divided into pure or theoretical mathematics, and applied mathematics. Applied mathematicians focus on how to apply mathematical principles to questions people have about the world around them and other practical problems (The New Book of Knowledge, 2006). It is the study of relationships between numbers, between spatial configurations, and abstract structures. Traditionally the subject is divided into ARITHMETIC, which studies numbers, GEOMETRY, which studies space, ALGEBRA, which studies structures, ANALYSIS, which studies infinite processes (in particular, CALCULUS),and PROBABILITY THEORY AND STATISTICS, which study random processes (Universal Encyclopedia, 1996).
One of the very useful branches of mathematics is Algebra. Originally, it was no more than generalized arithmetic. Arithmetic deals with numbers, which may be divided into real numbers and complex numbers. Real number includes integers, fractions and irrational numbers (numbers that cannot be expressed as a ratio of two integers), such as √ 2 and √ 5 (Encyclopedia Americana, 2006). Algebra has been identified as a societal gatekeeper for further development of mathematical and scientific instruction, and for wide-ranging economic opportunities (Encyclopedia of Education, 2003).
Mathematics plays a vital role in the modernization of this civilization. It is every where and affects the everyday lives of people. Although it is abstract and theoretical knowledge, it emerges from the real world. Mathematics is one of the essential and basic areas of the college curriculum which has a wide field of subject matter. In education, mathematics plays an important role. It is the study of numbers the relationship between these number and various operations performed on them. It is the science of quantity, size and shape. It is also a way to communicate and analyze ideas, a tool for organizing and interpreting data and above all, perhaps a method of logical reasoning unique to man. Mathematics is a necessary part of other sciences. In the words of Physicist Richard Feynan “Nature talks to us in the language of mathematics, that is numbers, mathematical rules and equations help us to make sense of the world around us (The Book of Popular Science, 2002).
Different segments of society possess different views about
what constitutes mathematics. Some think of mathematics as a collection of rules and procedures to be learned and applied for basic living. From this perspective, the teaching of mathematics relies on those methods best suited to promote the acquisition of skills. Others see mathematics as a basis for developing critical thinking and problem solving skills. From this second perspective which is closely aligned to the NCTM (National Council of Teachers of Mathematics) standards, teacher education encourages reflection and promotes attention to critical thinking. How a community defines mathematics affects what, and how mathematics gets taught in the local schools. It can also have an impact on how teachers are trained to teach in those schools (Encyclopedia of Education, 2003). It is therefore important to note that the referred best methods suited to promote the acquisition of mathematical skills are the method that are simplified and don’t give much doubt in the young mind of the students. Teachers also must be resourceful and creative enough to present concept in a very organized and comprehensible way.
Modern View of Mathematics
This type of instruction is based on detailed knowledge of student’s construction of mathematical knowledge and reasoning. That is this teaching is based on a deep understanding of:
(a.) the general stages that students pass through in acquiring the concepts and procedures for particular mathematical topics;
(b.) the strategies that students use to solve different problems at each stage; and
(c.) the mental processes and the nature of the knowledge that underlies these strategies (Almonia et. al.,2006)
Solutions in mathematical problems doesn’t limit on a single pattern or method. Students has to choose their preference as to which they find easier to express their answers.
According to the National Research Council, much of the failure in school mathematics is due to a tradition of teaching that is inappropriate to the way most students learn. Yet, despite the fact that numerous scientific studies have shown that traditional methods of teaching mathematics are ineffective, and despite professional recommendations for fundamental changes in mathematics curricula and teaching, traditional methods of teaching continue (Encyclopedia of Education, 2003). As time evolves, knowledge evolves. In order for the students to grow knowledgeably, teachers also has to grow first. Learning don’t limit in the four walls of the classroom. Being resourceful is a big help to update what you have previously learned.
Mathematics has been regarded as essential to a liberal education at least since Plato maintained that proficiency in Mathematics was a prerequisite for the study of philosophy. Today, a good education in mathematics is important because of its usefulness in careers such as environmental studies, business, engineering, medicine, and psychology, as well as in the biological, mathematical, and physical sciences. Knowledge of mathematics also helps students understand CALCULATORS and COMPUTERS (Grolier Encyclopedia of Knowledge, 2002). Last statement stresses that in order to understand how to operate and perform mathematical operations in the technologies mentioned, a person must acquire first the basic knowledge.
Leinhart as cited by Abne, et. el. (2007) noted the use of particular teaching strategies that will enable students to learn and develop the conceptual understanding of the central content of the unit. The ability to deal with mathematical problem can easily be performed through mastery of the basic concepts of mathematics. This is then supported by Romberg who believed that learning of Mathematics is hereby dependent upon the acquisition of specific concepts and skills is a must and the learning of concept is the foundation of mathematical literacy as well as of further study of mathematics.
According to Abraham Maslow’s Hierarchy of Needs, the lower need in the hierarchy must be satisfied first before trying to satisfy higher level needs (Muchinsky, 2007). In learning mathematics, it implies that everything should start from the basic before going the most complex problems.
According to Sheperd and Rogan as cited by Almonia et. al (2006), in learning a mathematical concept, students should be actively involved in doing mathematics, for it is through such participation that clear and functioning conceptual understanding are created upon which increasingly abstract constructs maybe derived and supported.
This supports to John Dewey’s experiential learning which states that experience is the best source of learning. The best way to learn is by experience. Therefore in order for the students to learn mathematics, they should actually do the operations in mathematics (Lomarda et. al., 2006).
Section 1, Article XIV of the 1987 Philippine Constitution stated that;
The state shall protect and promote the right of all citizens to quality education at all levels and shall take appropriate steps to make such education accessible to all.
The teachers are the instrument in providing good education to the students and mold them into competent individuals. One of the primary factors of man that has to be developed is the mental faculty. Therefore the teacher must utilize the most effective instruction which could promote maximum learning.
According to the New Philippine Constitution, Article XIV, Section 10;
Science and Technology are essential for national development and progress. The state shall give priority to research and development, invention, innovation, and their utilization and to science and technology, education, training and services. It shall support indigenous appropriate and self-reliant scientific and technological capabilities and their application to the country’s productive systems and national life.
Science and Technology cannot stand without mathematics. Thus mathematics should be utilized correctly in the realization of national benefits for science and technology and the people in general. It is an accepted fact that mathematics is the queen of all sciences. As noted by Eric Bell, a Scottish American mathematician, mathematics is the “Queen and servant of the sciences” (Talictic et.al., 2008).
Stepelman as cited by Almonia et. al. (2006), among the sciences cultivated by mankind, none has been more useful than mathematics. It is also an accepted fact that mathematics is the queen of all sciences. Mathematics is always involved in every move of science, without it, science cannot stand alone. Inventions have been discovered and innovations developed through mathematics. The constitution directs the state to promote scientific research and technology, it is therefore important that mathematics will be fully utilized in exact and accurate way. It is in mathematics where science and technology complete the advancement essential for national development and progress.
Christian Wolff’s mind theory as cited by Almonia et. al, (2006), states that mind has the mental powers or faculties, such as memory, reason, judgment, attention, will, observation, and the like, each of which functions as a separate entity that can be improved through exercise or use. Hence, mental power can be further developed when it is used and applied in every situation specially in solving problems.
Albert Bandura’s cognitive learning theory is a king of learning that involves mental processes, such as attention and
memory; maybe learned through observation or imitation; and may not involve any external rewards or require the person to perform any observable behaviors (Plotnik, 2002). Thus, the student can learn to love mathematics simply by observing the behaviors of some one who shows great interest and passion in the subject. It is evident in a classroom setting through the behavior of the teacher. A knowledgeable teacher can explain it well with clarity and emphasis. In responds, student will also develop interest towards the subject. Then, he will imitate and absorb what was presented by the teacher.
Definition Theory says that you form a concept of an object, event, animal, or person by making a mental list of the actual or essential characteristics of that particular thing (Plotnik, 2002). Through an organized, concise and comprehensible presentation of the Mathematics lessons, the student can make the mental list of what will be the series of steps that he/she will undergo applying the concepts that has been introduced.
Talictic et. al. (2008) stated that being efficient cannot replace being effective. Hence, a strong foundation in basic mathematical skills should be strengthened. Since algebra is the foundation of higher mathematics, students should know how the fundamental laws and properties of integers, properties of exponents, special product of binomials and properties of radicals. Since mathematics is a commutative subject, previously learned mathematics principles and skills become the building blocks on which new skills are built. If a student happens not to understand some mathematics principles and skills today, this will hinder him from understanding the new mathematics principles and skills of tomorrow.
One of the multiple intelligences of human enumerated by Howard Gardner is the mathematical-logical intelligence. Every human has this type of intelligences only that in some people, this type of intelligence is less developed.