Helping Students in Mathematics: Chapter Two



This chapter comprises the findings of other researchers in relation to the research question.

Meaning of Mathematics

When we begin to think about mathematics as a subject, we would find it very difficult to give a straight forward definition. However, some people think it is only about calculation including the four mathematical operations, such as addition (+), subtraction (-), division ( or /) and multiplication ( or *).

Nevertheless, the meaning of “mathematics” is as many as that of the authorities in the field.
According to Robert (1998), mathematics is a subject which allows us to predict future events and determine past trends. It also allows us to summarize complicated relationship and discover solution for solving difficult and interrelated problems.

According to Collins Cobuild Dictionary (2003), Mathematics is a subject which involves the study of numbers, questions, shapes etc. The Microsoft Encarta Encyclopedia (2005) explains Mathematics as the study of the relationships among quantities, magnitudes and properties of logical operations.

According to the Cambridge Dictionary (1996), mathematics is the study of our use of numbers and shapes to calculate, represent or describe things such as triangles, polygons and their properties. Example “the interior angles of a triangle add up to 180°).

Importance of Mathematics

From the definitions above, it can be found that the Mathematics is in all aspects of life across the globe. That is, it is a subject that one cannot do away with.

Palling (1991), said that, Mathematics is needed in finding answers to questions and problems which arises in everyday life in trade and other professions. This is because the value of Mathematics depends so much upon our experience.
According to Robert (1998), Mathematics allows us summarize complicated relationships.

According to Donkor et al (2005), the importance of Mathematics cannot be a single statement because of the diverse views of people towards the subject.
According to him, Mathematics helps us to use our knowledge in dealing with specific problems. It can also help us to recognize shapes and know some of the properties. An example is adding the interior angles of triangle it must give you 180°. In modern world, Mathematics is increasingly used in science, technology, industry, government, economics and education.

Mathematics assists us to design and play games such as draft, ludo, snake and ladder. Mathematics is necessary for further studies and many more.

The concept of the sum of interior angles of a triangle adds up to 180°.
A concept simply means an idea about something. Concept can also be viewed as an idea of something.
According to Cathemize (2005), of Oxford English Dictionary, angle is a space between two intersecting lines or surface at as close to the point where they meet.
Allotey (2010) views circle as a measure of 360°. One degree is equal to 60 minutes. Because 60 minutes on a clock is a full rotation by the minute hand and a full rotation is 360°. Angles are named according to their sizes. Angles are formed when two or more lines meet or intersect. Angles at a point are concepts which refer to the meeting of three or more lines at a particular point, the angle at a point add up to 360°, which is a complete revolution. Angle on a straight line, that is half turn also add up to 180° that is a straight angle.

According to Catherine et al (2005), Oxford Dictionary of Current English, triangle is a plane figure with three straight lines and three angles. The classifications of triangles are based on the angles as well as sides. For example scalene triangle, right-angle triangle, equilateral triangle and others.
Kuss-Appan (2003) stated that a polygon is a plane figure bounded by straight lines. Triangle is the smallest polygon with three sides.

The Gatsby Charitable foundation (2004), Mathematics enhancement programme, pupils’ textbooks (1- 6) also put it that the angle at a point always sum up to 360°. It does not matter when two or more angles are formed at the point of intersection. Their total will always be 360°. Angle at a point sum up to 360°.

Importance of Teaching and Learning Materials

Teaching and Learning Materials is important in teaching of the concept “the sum of interior angles of a triangle adds up to 180°” for the following reasons;
According to Farrant (1980), learning is the process by which we acquire and retain knowledge, understanding skills and capabilities that cannot be attributed to inherited behavior pattern. Learning depends on both inherited and environmental factors. Farrant goes on to say that increasing attention is being paid to research that is aimed at discovering ways of reducing educational problems which has to do with everyday life. Students use cans, tins, to make models of cars, fun and toys. Other genetic skills such as prediction, comparing and observation as well as investigation acquired by pupils eventually encourage them to have interest in studying Mathematics to the highest level.

Key (1971) says that teaching aids are the things (materials) which are intended to help teachers to teach more effectively and also enable pupils to learn more easily. One best methods of teaching is to guide pupils to realize and generalize how Mathematics concept came into existence. There should be a change in the behaviour when effective teaching has taken place. Mathematics taught using abstract methodology confuses pupils since their ability to think in abstract is influenced by many environmental and social factors.

Therefore, when pupils manipulate materials they feel secured and have assurance that Mathematics is not only theoretically oriented but practical and useful in everyday activities. Daniel, et al (2001) lay more emphasis on aims that are focused on planning of activities to make Mathematics not only appealing to the pupils, but also related to Mathematics in their daily life activities. Practical application of things taught in abstract seems to be difficult as compared to practical work.

The focus here is advance preparation on the side of the teacher to make available Teaching and Learning Materials (TLMs) for effective teaching and learning. Instrumental and theoretical teaching and learning of Mathematics can never make Mathematics interesting in any way.

However, concrete materials are needed in teaching of Mathematics. When concrete materials are used effectively, pupils will be fully involved in the lesson thereby making the lesson enjoyable. As a remedy advanced preparation of materials before lessons will eventually eradicate the misconception that Mathematics is difficult subject, hence their interest will be developed in the subject.

Ainley (1998) explains that games as learning aids assist us to teach Mathematics effectively and efficiently. They help in acquisition and development of skills provides enough motivation and develops problem solving strategies. Pupils learn unconsciously through games. They are motivated and also acquire skills like critical observations, accurate comparison and strategies for solving problem when using Mathematical games. Pupils will overwhelmingly choose games over regular classroom learning and when it is necessary to teach using games, it should be done.

Fianu (2000), also said that teaching aids help pupils to distinguish differences in what they see like pictures, objects and figures. He described them basically as aids to learning than to teaching because they go a long way to be clearer and easier the learning process.

Furthermore, Le admitted that when these objects are used to teach pupils, they begin to reason at a faster rate to identify the various differences between objects which are registered in their minds.

Amoakohene, et al (1998), enumerate some importance of Teaching and Learning Materials (TLMs).
They serve as effective substitution for real objects.
They make teaching very interesting to the learner and ensure

maximum participation of the learners. The advantages of Teaching and Learning Materials (TLMs) stated above are just confirming the value of attached to effective teaching and learning situations.
With this, mathematical concepts which are difficult for pupils to understand become easier and simpler. The learning situation is made interesting when these are used; therefore learning situation should be made to involve Teaching and Learning Materials (TLMs).
Kpabi (2003) says, instructional materials are important for the reasons below;
It helps avoid boredom if properly used.
The instructional materials save the teacher the trouble of lengthy verbal explanation and therefore save time and energy. It is clear that when one is tired, there is no motivation, proper work is never done. Therefore Kpabi (2003) brings to light that, Teaching and Learning Materials (TLMs) help to avoid boredom there by encouraging their uses.

Adjei (2001) explained that when Teaching and Learning Materials (TLMs) are used appropriately, it makes lessons practically oriented and real. He continues to say that, another importance of Teaching and Learning Materials (TLMs) is that, they make pupils have confidence in the teacher because as they interact with the materials, with the teacher and friends, they are made to express and share ideas freely. This also establishes the fact that good teacher-pupil relationship should be encouraged. Though this activities pupils learn very well.

Summary of the Review of Related Literature

From the various authors who wrote on the “sum of interior angles in a triangle add up to 180°” suggested that for the concept to go down well with pupils. It should be practically oriented and child-centered so as to enhance their understanding.

Also teaching and learning materials are very important and activities pupils perform during the lesson. However, for teachers to achieve their objectives they must use appropriate Teaching and Learning Materials (TLMs). Because it arouses and sustain whatever is taught. When lessons are taught in abstract, pupils find it very difficult to understand it.



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