1Godwin Gemma Apav
2Benjamin Tarvershima Ako
1Department of Mathematics,
College of Education, Katsina-Ala
2Department of Integrated Science,
College of Education, Katsina-Ala
This article points out the divergent views of mathematicians on the concept of mathematics. Nevertheless, the fact remains that mathematics is vital to the existence of individuals as well as the society at large. In order to enhance effective teaching, learning and application of mathematics in our daily activities, the article advocates the use of recently developed methods of teaching the subject such as laboratory method, project method, problem solving method which emphasize the development and utilization of techniques of teaching and assessment based on individualized observation of pupils in concepts understanding and application. The article therefore considers laboratory method of teaching mathematics at 0’level to enhance its application to technology. The case of basket weaving is considered. Four stages of weaving a basket which teach the application of concepts such as “right angle”, “ratio”, “pattern”, “circularity” and “shape” (a hemisphere) to the pupils at 0’level of education have been explained. The article finally emphasizes the use of laboratory method since it encourages the application of mathematics in real life and enhances conceptual understanding and reduction of abstract nature of mathematics.
The term mathematics is said to have been coined by the Pythagoreans from the ancient Greek word “mathema”, meaning subject of instruction (Wikipedia, 2009). It is broadly divided into pure and applied mathematics. Whereas pure mathematics is developed on an abstract, self contained basis without any regard to any practical applications, applied mathematics is the application of pure mathematics in service of a given purpose (Kwen, 2012). Principles of applied mathematics have been useful in investigation in many areas of science which have led to the development of science and technology.
The discovery of mathematics on a general note was and still is motivated by the need to solve our social problems. It is therefore not out of place to say that, the need to solve man’s everyday problems has actually led to the discovery and development of mathematics.
It is however not easy to give one simple straight forward definition of what constitutes mathematics. This is because the term is an embodiment of many concepts, phrases, symbols and notations that are employed to make its language simple, clear and understandable. Therefore people have divergent views as to what mathematics is. Whereas others consider it as the science of numbers, their computation and relations and the language of symbol notations (Sidhu, 2006; Aminu, 2005; Kwen, 2012), others view it as the study of the knowledge of logical reasoning, principles, processes and relationships which manifests itself into aesthetic values of the term as is seen in manufacturing, building and construction, printing, footballing etc. (Herbor Peters, 2000; Odili, 2006). Yet others consider mathematics as the language of science which makes it the gate and key of all sciences without which it is practically impossible to make an inroad into science and technology advancement.
Sidhu (2006) notes that, mathematics is so invaluable to humanity and the existence of society so much so that the learning of the subject is very important for human existence because mathematics is all about finding solutions to human problems.
Despite the picture of importance and vital role mathematics plays in the life of individuals and the society, which have been portrayed by many authors, there is very low interest and therefore very poor performance in the subject at ordinary level of education in Nigeria (Obodo, 2004; Olaleye, 2004). One may therefore wonder what might be the problems confronting effective teaching and learning of the subject which have also culminated into students’ lack of interest in it as well as poor performance. Great anxiety has been expressed by government, employers of labour, parents and teachers about the fact that large numbers of students after secondary school courses are unable to perform many of the simple arithmetical and mathematical operations needed in their everyday life and work.
Several reasons have been proffered by researchers as the causes of the widespread low-level performance in mathematics in Nigerian secondary schools by students which are largely ascribed to mechanical and uninteresting teaching devoid of understanding of the meaning of mathematical concepts (Odili, 2006; Clements 2005; Omoifo and Oloruntegbe, 2000). Omoifo & Oloruntegbe (2000) point out that, the methods of teaching and assessment adopted by mathematics teachers are strong determinants of achievement in learning mathematics. According to them, the quality of explanation, adequacy of concept representation and appropriateness of solution strategies and frequency and flexibility of student monitoring for concept understanding and applications are strong indicators of effective learning by students. They are of the opinion that traditional methods of teaching mathematics such as lecture method and dogmatic method which encourage rote learning and do not develop the power of thinking, understanding and retention in the students should be discouraged in our ordinary level institutions of learning. The reason been that, these methods go with the traditional paper and pencil form of assessment which is not appropriate for assessing students on the use of concepts taught.
They thus advocate the use of new methods and techniques of teaching the subject such as laboratory method, project method and problem solving method. According to Omoifo and Oloruntegbe (2000), these methods encourage the development and utilization of techniques of teaching and assessment based on individualized observation of students in concepts understanding and their application to practical solution of problems. Improvement of students in concepts understanding and their application to solving problems is what is collectively termed “functional mathematics development” that facilitates technological development.
This article therefore considers laboratory method of teaching mathematics which enhances effective understanding of mathematical concepts and application to daily life activities.
Enhancing Effective Teaching and Learning of Mathematics through Laboratory Activities
Mathematics is a subject which has to be learnt by doing rather than by reading alone. Therefore the doing of mathematics gives rise to the need of a suitable method and place. Laboratory method and mathematical laboratory are the proper answers to it (Sidhu, 2006). This is due to the fact that many aspect of mathematics especially in geometry involve the use of some equipment in drawing and calculations. Therefore, their nature is that of practical or laboratory work.
Oko (2010) defines laboratory as a facility where controlled conditions are provided to enhance scientific research, experiments and measurement in nature. He is of the view that, a laboratory should not necessarily be a room or building where scientific activities can take place, but they can be done outside a building.
In essence, applying process skills of observation, measurement, data collection, data analysis and interpretation is what is actually required in a laboratory. This means that, a laboratory is a facility that provides enabling conditions that facilitate scientific activity through the application of process skills to the solution of problems. Hence laboratory method of teaching is an activity based method of learning where pupils are engaged in an activity to discover facts. The method is based on “learning by doing”, “learning by observation” and proceeding from concrete to the abstract. In this method, of teaching, pupils do not only listen to information and copy examples, but do something practically to discover principles, generalize them and establish facts.
Sidhu (2006) further notes that, for every mathematics teacher to be successful in whatever method of teaching, he needs to understand both educational and practical values of the mathematical concepts involved in the topic to be taught to be able to convince students of the values of the concepts to them. He states that, the teacher has to clear a set of questions about the topic to the students. These are:
- Why should everybody learn this topic?
- What is the place of this topic in any scheme of education
- What is the importance of this topic in an individual’s life?
- How does it make any contributions in the development of an individual and the society?
Therefore, a mathematics teacher who can provide convincing answers to these questions will develop in students the idea of the utility of mathematics and keep their interest in the subject burning. Hence in using laboratory method to engage students in craftwork activity to weave a basket, this will help the teacher to demonstrate practically concepts like “right angle”, “rectangle”,” equality”, “ratio”, “pattern”, “circularity”, “sphere” and “volume”.
The teacher could make this plan of activity with the pupils:
Stage I: Preparation
(i) Cut palm fronds
(ii) Remove the backs and shape them properly in long rectangular shape.
(iii) Provide strings or ropes.
The mathematical concepts involved in this preparation so far are accuracy in cutting fronds of equal lengths. The backs removed are rectangular in shape.
Stage II: Construction of the bottom of the basket
(i) Two of the removed backs of the plam fronds are crossed at right angles and tied together with a string or rope.
(ii) Subsequent backs are crossed in this order and tied together until the spaces in between the crossed backs become smaller such that they cannot contain any frond back any longer.
At the second stage, the students are exposed to the concepts of “right angle” and “ratio”. The teacher explains that, a good basket is woven in this order by crossing two frond backs at right angles at a time. Each time this is done, the ratio of the number of frond backs crossed to the spaces created are the same (i.e. 1:2). That is, 2 frond backs create 4 spaces giving the ratio of 1:2, 4 frond backs create 8 spaces, giving the same ratio of 1:2 and so on.
Stage III: Weaving the bottom of the basket.
The bottom of the basket is woven using a rectangular frond back at a time in a regular pattern of in-and-out rhythm as shown below.
Stage IV: Final weaving stage
At this stage, the unwoven remaining parts of the crossed frond backs are carefully folded upwards. They are held in this position with a string or rope to maintain the desired shape thus;
The regular weaving pattern of the frond backs using in-and-out rhythm continues at regular interval until a basket is completely woven. The mathematical concepts learnt at the last two stages are:
(i) Regular pattern
(ii) Circularity (circular mouth) of the basket
The product which is now called a basket is spherical in shape. However, in this case, it is a hemisphere (semi-sphere). The concept of shape is learnt at this stage and a particular shape (a hemisphere) is explained to the students.
The teacher may point out the concept of volume of the basket (hemisphere). That is, how much of a quantity it can contain.
The teacher may liken the basket to a globe which has lines of longitude and latitude. In this case, the basket will be taken as half of the globe, so that when two baskets of the same size are joined mouth to mouth, you then have a globe.
Despite the great positive impact laboratory method has on students, its major setback is that, it is very expensive and time consuming. Not every school can afford to spend large amounts of money on laboratory equipment. Moreover, it needs thorough planning and supervision in order to stop students from mere play with instruments.
However, since laboratory work is not typical mathematical work, and does not give any training to the learner in true mathematical reasoning, it should not be used exclusively from other methods such as oral work, written work, drill work, and homework. It should be used alongside other methods to demonstrate the reality or practical values of the concepts taught in the class.
On the other hand, cost can be reduced if equipment is improvised in the school itself. The young O’level pupils will be fascinated by this method if properly handled by the teacher. It should therefore be a ‘must’ where circumstances favour its application.
Mathematics is a subject that is best learnt by doing rather by reading and memorizing principles, formulae and theories. The doing of mathematics gives rise to the need of a suitable method and place of doing it. Laboratory method and mathematical laboratory are suitable for this at O’level of education. This is due to the fact that, the activity method carried out in the laboratory leads the pupils to discover mathematical facts through “learning by doing” and proceeding from concrete to abstract. This is a more elaborated and practical form of inductive method of teaching the subject. If properly used, it helps in the removal of the abstract nature of mathematics, thereby, making the utilitarian and aesthetic values of mathematics clear to the pupils. Finally this method inculcates the spirit of cooperation and exchange of ideas when pupils are used to perform laboratory work in group. The application of mathematics becomes increasingly evident to the learner. Thus the subject becomes functional and meaningful to the learners
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