- understanding weather reports.
- reading a map to find directions.
- understanding loan repayments
- understanding economic indicators.
- calculating whether a cheap article is a good buy or not.
When a problem is presented and the skills required to solve that problem are developed, it motivates the student to learn mathematics and become more deeply involved in the learning process. Teaching through problem solving enhances logical reasoning. Problem solving also allows the person to develop as a whole.
There are three types of problems to which students should be exposed.
Preparing students for the challenges of life.
Word problems where the concept is embedded in real-life situations. The student is required here to recognize the problem and apply the necessary rule. The following examples will show how values such as sharing, caring and conserving energy may be used while preparing the problems
- 5 children went out one afternoon to pluck apples. They decided to share the total fruit amongst themselves. At the end of the day they had plucked 245 apples. How many apples did each child get
- Every evening from Monday to Friday, Shreya helps her mother in household chores for 1/4 hour. On Saturday and Sunday evenings she helps her for 1/2 hour. What is the total time spent by Shreya in a week to help in the housework ?
- An aeroplane used 4500 litres of fuel on a flight from Chennai to Mumbai. At Mumbai, the engine was cleaned and the flight returned to Chennai. It was discovered that on its return flight, the plane had used only 4000 litres of fuel. If fuel costs Rs 30/- per litre, how much more economical is a plane with a clean engine ?
Problems which contain too much of information so that the child can select what is relevant and important. Here the child must use his common sense and general knowledge rather than just bookish knowledge.Example : Last week Shekhar travelled by train from Lucknow to Bangalore covering a distance of 1093 kms. The train left at 8 am and travelled at a speed of 86 km/hr for the first four hours of the journey. At Jhansi station, the train was detained for one and half hours. It resumed its journey and travelled for another three hours at 78 km/hr. What was the distance travelled so far ?
Problems which encourage students to be resourceful. These problems are often known as Fermi problems after the mathematician who made them popular. When students first see a Fermi problem, they think they need more information to solve it. Actually, just common sense and experience can lead them to the solution. These problems can be solved in a cooperative environment.These problems can be related to social issues. Example :
- How many litres of petrol are used by people in your neighbourhood every day ?
- How much food is wasted by an average family in your locality in a week ?
- If a person walks to work everyday instead of driving or using a public transport, how much money would he save in a month ?
In order to enhance students' understanding, they can be asked to make up their own problems. This will encourage them to be flexible and to look at a problem in more than one way. The teacher can help by giving a theme so that it will help them to focus on the underlying values as well as the mathematics.
