The mathematics curriculum was designed to provide the knowledge and mathematical skills from various backgrounds and levels of ability. These skills will help them to build their own career in the future.
The primary school mathematics education aims to build pupil’s understanding of number concepts and their basic skills in computation that they can apply in their daily routines effectively and responsible in keeping with the inspirations of a developed society and nation. At he same time, they can use this knowledge to further their studies in whatever field they want.
v The teaching and learning processes emphasizes concepts building, skill acquisition as well as inculcation of positive values. There are others element that needed to be taken into account and learnt through the teaching and learning processes in the classrooms. There are five pillars in teaching and learning mathematics in school. The pillars are;
- Problem Solving in Mathematics
- Communication in Mathematics
- Mathematical Reasoning
- Mathematical Connections
- Applications of Technology
PROBLEM SOLVING IN MATHEMATICS
Problem solving is the main focus in the teaching and learning of mathematics. Understanding mathematical procedures and solving problems are two skills that emerge naturally when relational understanding is focused upon. As a result, problem solving approaches should be used to investigate and understand mathematical content. The teaching learning process must include exercises on problem solving skills which are comprehensive and cover the whole curriculum. The development of these skills must to be emphasized so that pupils are able to solve various problems effectively. The skills involved are: Various strategies and steps are used to solve problems and these can be applied to other learning areas. In solving these problems, pupils learn to apply mathematics and gradually become confident in facing new challenging situations. Among the problem solving strategies to consider are;
• Interpreting problems;
• Planning the strategy;
• Carrying out the strategy; and
• Looking back at the solutions.
There are many steps and strategies that can be used to solve the problems and these can be applied in other learning areas. In every problems that a student facing, they will learn new skills that can make them become confident to face any new problems that come to them. Pupil learns to apply mathematics and gradually become used to any problem that they are facing. Many strategies we can use in facing any problem solving question. Among the problem solving strategies are
Ø Working backwards
Ø Trying a simple cases
Ø Trial and improvement
Ø Draw a diagram
Ø Identifying patterns and sequences
Ø Make a table
Ø Make analogy
Using these problem solving strategies, student will be able to solve any problem easily. They will find that solving any problems in mathematic is a fun thing. They will try to do more problems solving after that.
Teachers should engage students in mathematical discourse about problem solving. This includes discussing different solutions and solution strategies for a given problem, how solutions can be extended and generalized, and different kind of problems that can be created for a given situations. All students should be made to feel that they have something to contribute to the discussion of a problem. Assessments should focus on the notion of whether mathematics is being taught in such a way as to promote these aspects of problem solving.
- COMMUNICATIONS IN MATHEMATICS
To help us to be more understand the content of mathematics, communications is one way that we can use to help us. Using good communication, we can share and clarify the understanding of mathematics. The mathematical ideas could be discussed and modified by talking and questioning. Through effective communications pupils will become efficient in problem solving and be able to explain concepts and mathematical skills to their friends and teachers.
Mathematical communication can occur when students work in cooperative groups. By working on problems with classmates, students also have opportunities to see the perspectives and methods of others. They can learn to understand and evaluate the thinking of others and to build on those ideas. They may benefit from the insights of students who solve the problem using a visual representation. Students need to learn to weigh the strengths and limitations of different approaches, thus becoming critical thinkers about mathematics. A teacher should monitor the student’s use of mathematical language to help develop their ability to communicate mathematics. This could be done by asking students if they agree with another student’s explanations or having students provide various representations of mathematical ideas and problems.
The communications skills in mathematics are;
1. listening process – occurs when individual respond to what
2. reading process – individuals collect information, they
rearrange the relationship through ideas and concepts.
3. Visualisation process – an individual makes an observation, analyses and synthesises into graphic form.
4. oral communication – involves the activities like listening, speaking,
reading and observing.
- two way interaction between teacher-pupil,
pupil-pupil and pupil-object.
5. Written communication – mathematical ideas shared through writing
- exercises, scrap books, folios and written test
The following methods can create and effective communication environment
Ø Identifying teaching materials
Ø Active learning
Ø Stimulating meta-cognitive skills
Ø Identifying the interest of pupils
Ø Creating the conducive learning environment
- MATHEMATICAL REASONING
Logical reasoning or thinking is the basis for understanding and solving mathematical problems. The development of mathematical reasoning is closely related to the intellectual and communicative development of the pupils. Emphasis on logical thinking during mathematical activities opens up pupils’ minds to accept mathematics as a powerful tool in the world today. Pupils are encouraged to predict and do guess work in the process of seeking solutions. Pupils at all levels have to be trained to investigate their predictions or guesses by using concrete materials, calculators, computers, mathematical representation and others. Logical reasoning has to be infused in the teaching of mathematics so that pupils can recognize, construct and evaluate predictions and mathematical arguments.
Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts and from the earliest grades. At all levels, students reason inductively from patterns and specific cases.
Teaching mathematics as an exercise in reasoning should also be commonplace in the classroom. Students should have frequent opportunities to engage in mathematical discussions in which reasoning is valued. Students should be encourage to explained their reasoning process for reaching a given conclusion or to justify why their particular approach to a problem is appropriate. The goal of emphasizing reasoning in the teaching of mathematics is to empower students to reach conclusions and justify statements on their own rather than to rely solely on the authority of a teacher or a textbook.
- MATHEMATICAL CONNECTIONS
In the mathematics curriculum, there are many topics that need to be learnt by a student. There are many cases that student failed to identify the connection between topics in the curriculum. The failure of identifying and doing the connection caused the student failed to master mathematics’ topic. In the mathematics curriculum, the opportunities for making connections must be created so that the pupils can link conceptual to procedural knowledge and relate topics in mathematics with the other subjects that related to what they learnt I mathematics. By making connections pupils are able to see mathematics as an integrated whole rather than a jumble of unconnected ideas. Teachers can foster connections in a problem-oriented classrooms by having pupils to communicate, reason
and present their thinking.
When these mathematical ideas are connected with real life situations and the curriculum, pupils will become more conscious in the application of mathematics. They will also be able to use mathematics contextually in different learning areas in real life. The mathematics curriculum consists of several areas such as arithmetic, geometry, measures and problem solving. Without connections between these areas, pupils will have to learn and memorize too many concepts and skills separately.
An emphasis on mathematical connections helps students recognize how ideas in different areas are related. Students should come both to expect and to exploit connections, using insights gained in one context to verify conjectures in another. The opportunity to experience mathematics in context is important. Students should connect mathematical concepts to their daily lives, as well as to situations from science, the social sciences, medicine, and commerce.
- APPLICATION OF TECHNOLOGY
The methods of teaching and learning have changed with the society and the rapid development of information technology. Teachers' role changes from a transmitter of knowledge to a facilitator of learning. Therefore, they should make appropriate use of information technology such as calculators, computers and ETV to design diversified learning activities that are related to pupils' daily life. It should facilitate the learning of pupils and hence enhance their level of mathematics.
The use of teaching resources is very important in mathematics. This will ensure that pupils absorb abstract ideas, be creative, feel confident and be able to work independently or in groups. Most of these resources are designed for self-access learning. Through self-access learning, pupils will be able to access knowledge or skills and information independently according to their pace. This will serve to stimulate pupils’ interests and responsibility in learning mathematics.
The application of technology in the teaching and learning give many advantages to us. In terms of students, the use of technology may
- Engage their attention and motivate them
- Stimulate their curiosity
- Encourage them to develop their problem-solving strategies
In terms of teacher
· Improve their efficiency
· Remove their administrative burden
· Provide better records
· Release more time to address students individually
In terms of schools, the technology may,
· Improve efficiency and reduce teaching costs
· Improve provision to students who are not learning in their native tongue
The application of technology helps pupils to understand mathematical concepts in depth, meaningfully and precisely enabling them to explore mathematical concepts. The use of calculators, computers, educational software, websites in the internet and available learning packages can help to upgrade the pedagogical skills in the teaching and learning of mathematics.